biomechanics of the total ankle arthroplasty: stress ... · biomechanics of the total ankle...

Biomechanics of the Total Ankle Arthroplasty: Stress Analysis and Bone Remodeling

Daniela Sofia de Oliveira Salgado Rodrigues

Thesis to obtain the Master of Science Degree in

Biomedical Engineering

Examination Committee

Chairperson: Professor João Pedro Estrela Rodrigues Conde

Supervisors: Professor Paulo Rui Alves Fernandes

Professor João Orlando Marques Gameiro Folgado

Members of the Committee: Professor Jacinto Manuel de Melo Oliveira Monteiro

Professor Luís Alberto Gonçalves de Sousa

June 2013

I

Acknowledgements

First of all, I would like to thank my supervisors, Prof. Paulo Fernandes and Prof. João Folgado.

Prof. Paulo Fernandes has helped me since the beginning of my journey in IST. I have already

asked him millions of questions and he has always had an answer to give me. He is an enthusiastic

Professor and after attended his courses I thought that I could not have chosen a field of study other

than Biomechanics.

Prof. João Folgado is the most patient Professor in the world. I want to thank him for the countless

hours he spent teaching me, for the suggestions and support during this work. He showed me how

Biomechanics can be fascinating.

I want to thank Prof. Dr. Jacinto Monteiro and Dr. Nuno Ramiro for the clinical guidance during this

work.

I want to express my sincere gratitude to Prof. Alberto Leardini from Bologna, Italy. Since the first

e-mail, he always answered me with the same kindness and sometimes almost as fast as light. I want

to thank him for the availability in the clarifications of doubts.

I am eternally grateful to the entire IDMEC research group, Miguel Machado, Lina Espinha, Diogo

Almeida, Ângela Chan, Paula Fernandes, Marta Dias, Nelson Ribeiro, and specially Carlos Quental,

who was like my third supervisor, for sharing their time and knowledge with me.

I am especially grateful to my parents, for their unconditional support, patience and

encouragement in all the moments of my life.

I also want to thank my grandparents, my aunts, uncles and cousins for all their support and happy

moments.

I am thankful to all my friends, especially Nina, with whom I lived the last 5 amazing years, Joana,

Dé, Mariana and “the boys”, for all the unforgettable adventures that every day gave me motivation to

continue.

And now I would like to give a special thanks to Zé, for his help, encouragement and humour that

gave me enthusiasm to overcome the obstacles throughout this work.

Finally, I also want to thank FCT for the financial support through the funding of the Software

Development for Arthroplasty Preparation project (PTDC/SAU-BEB/103408/2008), in which this thesis

is integrated.

III

Abstract

The total ankle arthroplasty (TAA) is an alternative procedure to the arthrodesis in the treatment of

advanced arthritis in the ankle joint. However, the total ankle prostheses are not yet widely accepted

and do not have the same success rate of the hip, knee or even shoulder prostheses. Thus, the aim of

this work is the development of a finite element (FE) model of the ankle joint complex (AJC) in order to

study the influence of two different prostheses, Agility™ (considering two different designs) and

S.T.A.R.™, on the stress distribution and bone remodeling.

This work involved the geometric and FE modeling of the AJC and the prostheses, Agility™ and

S.T.A.R.™. Subsequently, the models simulating the TAA were created. Then, stress analysis was

performed, and the bone remodeling model developed in IDMEC/IST was used to determine the bone

density distribution in the talus and tibia.

The results indicated that the new design of Agility™ prosthesis has better performance than the

old design. However, both prostheses (especially Agility™) exceeded the contact stress

recommended for the intermediate/polyethylene component (10 MPa). Moreover, after the insertion of

both prostheses, the stresses increased near the resected surface in the talus, which may contribute

to early loosening and subsidence of the talar component. Regarding the bone remodeling analysis,

both prostheses showed evidences that may lead to stress shielding effect.

In conclusion, these prostheses still have some untested features and the optimal configuration is

currently not known.

Keywords: Biomechanics, Ankle joint complex, Total ankle arthroplasty, Finite element method, Bone

remodeling

V

Resumo

A artroplastia total do tornozelo (ATT) surge como alternativa à artrodese no tratamento da artrite

em estadio avançado no tornozelo. No entanto, as próteses do tornozelo ainda não são amplamente

aceites e não apresentam o mesmo sucesso registado nas próteses da anca, do joelho ou até do

ombro. Desta forma, o objectivo deste trabalho é a criação de um modelo de elementos finitos do

tornozelo, de forma a estudar a influência de duas próteses, Agility™ (considerando dois modelos

diferentes) e S.T.A.R.™, na distribuição de tensões e na remodelação óssea.

O trabalho envolveu a modelação geométrica e de elementos finitos do tornozelo e das próteses,

Agility™ e S.T.A.R.™. De seguida, os modelos que simulam a ATT foram criados. Posteriormente foi

feita a análise de tensões e o modelo de remodelação óssea desenvolvido no IDMEC/IST foi usado

para determinar a distribuição de densidade óssea no tálus e na tibia.

Os resultados indicaram que o novo modelo da prótese Agility™ apresenta um melhor

desempenho que o antigo modelo. No entanto, ambas as próteses (especialmente a Agility™)

excederam a tensão de contacto recomendada para o componente intermédio/polietileno (10 MPa).

Além disso, após a inserção das próteses, as tensões aumentaram perto da superfície ressecada no

tálus, contribuindo para o loosening e subsidência do componente talar. Relativamente à análise de

remodelação óssea, ambas as próteses mostraram evidências de que podem originar o efeito de

stress shielding.

Concluindo, estas próteses apresentam algumas características que ainda não foram analisadas,

sendo que a configuração óptima não é actualmente conhecida.

Palavras-Chave: Biomecânica, Tornozelo, Artroplastia total do tornozelo, Método dos elementos

finitos, Remodelação óssea

VII

Contents

Acknowledgements .................................................................................................................................. I

Abstract................................................................................................................................................... III

Resumo ................................................................................................................................................... V

Contents ................................................................................................................................................ VII

List of Figures ......................................................................................................................................... XI

List of Tables .......................................................................................................................................XVII

List of Symbols .....................................................................................................................................XIX

Abbreviations ........................................................................................................................................XXI

Chapter 1 – Introduction .......................................................................................................................... 1

1.1 Motivation ...................................................................................................................................... 1

1.2 Proposed Approach and Objectives .............................................................................................. 4

1.3 Contributions ................................................................................................................................. 6

1.4 Organization .................................................................................................................................. 6

Chapter 2 – Background .......................................................................................................................... 7

2.1 Anatomy ........................................................................................................................................ 7

2.1.1 Joints of the Human Foot ....................................................................................................... 7

2.1.2 Human AJC ............................................................................................................................ 8

2.1.2.1 Bony Configuration .......................................................................................................... 8

2.1.2.2 Ligamentous Configuration ............................................................................................. 9

2.2 Biomechanics .............................................................................................................................. 10

2.2.1 Standard Reference Terminology ........................................................................................ 10

2.2.1.1 Anatomical Reference Position ..................................................................................... 10

2.2.1.2 Anatomical Reference Planes and Axes ....................................................................... 10

2.2.1.3 Joint Motion Terminology .............................................................................................. 11

2.2.2 Axis of Rotation .................................................................................................................... 12

2.2.3 Range of Motion ................................................................................................................... 15

2.2.4 Restraint of Motion/Stability .................................................................................................. 16

2.2.5 Gait Cycle ............................................................................................................................. 17

2.2.6 Force Generation .................................................................................................................. 18

2.3 Total Ankle Prostheses................................................................................................................ 20

2.3.1 First Generation .................................................................................................................... 21

2.3.2 Second Generation ............................................................................................................... 22

2.3.2.1 Agility™ ......................................................................................................................... 23

2.3.2.2 S.T.A.R.™ ..................................................................................................................... 25

VIII

2.3.3 New Designs ........................................................................................................................ 26

2.4 Bone Remodeling ........................................................................................................................ 26

2.4.1 Bone Tissue .......................................................................................................................... 26

2.4.2 Bone Remodeling Process ................................................................................................... 29

2.4.3 Bone Remodeling Model ...................................................................................................... 30

2.4.3.1 Material Model ............................................................................................................... 31

2.4.3.2 Mathematical Formulation ............................................................................................. 32

2.4.3.3 Computational Implementation ...................................................................................... 33

Chapter 3 – Computational Modeling .................................................................................................... 35

3.1 Geometric Modeling .................................................................................................................... 35

3.1.1 Geometric Modeling of the Bones ........................................................................................ 35

3.1.2 Geometric Modeling of the Prostheses ................................................................................ 38

3.1.2.1 Agility™ ......................................................................................................................... 38

3.1.2.2 S.T.A.R.™ ..................................................................................................................... 40

3.1.3 Assembly of the Models – Virtual Surgical Procedure ......................................................... 41

3.1.3.1 Agility™ ......................................................................................................................... 42

3.1.3.2 S.T.A.R.™ ..................................................................................................................... 44

3.2 FE Modeling ................................................................................................................................ 46

3.2.1 Importation of the Models and Insertion of the Ligaments ................................................... 46

3.2.2 Material Properties ............................................................................................................... 47

3.2.3 Interaction between the Parts ............................................................................................... 49

3.2.4 Loading and Boundary Conditions ....................................................................................... 49

3.2.5 Mesh Generation .................................................................................................................. 53

Chapter 4 – Results and Discussion ..................................................................................................... 55

4.1 Stress Analysis ............................................................................................................................ 55

4.1.1 Contact Stress Distribution in the Intact Ankle Joint ............................................................ 55

4.1.1.1 Results ........................................................................................................................... 55

4.1.1.2 Discussion ..................................................................................................................... 57

4.1.2 Contact Stress Distribution in the Polyethylene Component ................................................ 60

4.1.2.1 Preliminary Test ............................................................................................................. 60

4.1.2.2 Results ........................................................................................................................... 61

4.1.2.3 Discussion ..................................................................................................................... 66

4.1.3 Internal Stress Distribution in the Talus ................................................................................ 69

4.1.3.1 Results ........................................................................................................................... 69

4.1.3.2 Discussion ..................................................................................................................... 70

4.2 Bone Remodeling Analysis ......................................................................................................... 71

4.2.1 Intact Model .......................................................................................................................... 71

4.2.1.1 Results ........................................................................................................................... 71

IX

4.2.1.2 Discussion ..................................................................................................................... 76

4.2.2 TAA+Agility™ and TAA+S.T.A.R.™ Models ........................................................................ 76

4.2.2.1 Preliminary Results ........................................................................................................ 77

4.2.2.2 Discussion ..................................................................................................................... 78

Chapter 5 – Conclusions and Future Directions.................................................................................... 79

5.1 Conclusions ................................................................................................................................. 79

5.2 Limitations of the Work and Future Directions ............................................................................ 82

Bibliography ........................................................................................................................................... 85

Appendix A ............................................................................................................................................ 97

Appendix B .......................................................................................................................................... 102

Appendix C .......................................................................................................................................... 105

Appendix D .......................................................................................................................................... 110

XI

List of Figures

Figure 2.1 The three main joints of the foot and its associated bones (adapted from [81]). ................... 8

Figure 2.2 At left, the anatomical reference position of the foot and the three anatomical reference

planes – sagittal, transverse and frontal. At right, the three anatomical reference axes applied to the

ankle joint (adapted from [80, 101]). ...................................................................................................... 11

Figure 2.3 All possible motions of the foot: A – Dorsi/Plantarflexion; B – Abduction/Adduction; C –

Pronation/Supination; D – Eversion/Inversion (adapted from [103]). .................................................... 12

Figure 2.4 Directions of the ankle joint axis: inclined posterolaterally in the transverse plane (at left)

and downward and laterally in the frontal plane (at right) (adapted from [117]).................................... 13

Figure 2.5 The different subphases of the stance and swing phases (adapted from [80]). .................. 17

Figure 2.6 The ankle and subtalar rotations in sagittal and frontal planes, respectively, during walking

in a complete normal gait cycle (adapted from [80]). ............................................................................ 18

Figure 2.7 The components of reaction forces at the ankle joint during stance phase of gait determined

by Seireg and Arkvikar [156]. ................................................................................................................ 19

Figure 2.8 The Agility™ prosthesis: the old version (at left) and the new version (at right) [180, 181]. 24

Figure 2.9 The S.T.A.R.™ prosthesis [184]. ......................................................................................... 25

Figure 2.10 Sections through the diaphysis of a long bone. From left to right: medullary cavity,

trabecular bone, cortical bone and periosteum. The repetitive structural unit of cortical bone is the

osteon while of trabecular bone is the trabecula (adapted from [192]). ................................................ 28

Figure 2.11 Material model for bone (adapted from [73, 218]). ............................................................. 31

Figure 2.12 Computational model flow diagram (adapted from [221]). ................................................. 34

Figure 3.1 Process of surface mesh adjustments for the talus: 1 – Talar surface mesh obtained from

VAKHUM project; 2 – Talar surface mesh after applying the smooth filter (300 iterations); 3 – Previous

modified talar surface mesh after applying decimate filter (80% reduction percentage); 4 – Previous

modified talar surface mesh after applying the smooth filter (300 iterations). Software used: ParaView.

............................................................................................................................................................... 36

Figure 3.2 At left, individual solid models of the fibula, calcaneus, talus, tibia. At right, the assembly of

all the bones. Software used: SolidWorks®. .......................................................................................... 36

Figure 3.3 The model of the AJC is constituted by the inferior extremities of tibia and fibula, the entire

bones, talus and calcaneus, the interosseous membrane and the cartilage of each bony

segment/bone. Software used: SolidWorks®. ........................................................................................ 37

Figure 3.4 The 5 hole, 1/3 semi-tubular Ti plate (at left) and the same plate with the two Ti screws of

2.9 mm diameter (at right). Software used: SolidWorks®. ..................................................................... 38

Figure 3.5 The old talar component design (at left) and the new talar component design (at right).

Software used: SolidWorks®. ................................................................................................................. 39

Figure 3.6 Assembly of all the prosthetic components of Agility™ prosthesis. Software used:

SolidWorks®. .......................................................................................................................................... 39

XII

Figure 3.7 Congruency in the sagittal plane between the talar component and fixed-bearing of Agility™

prosthesis. Software used: SolidWorks®. .............................................................................................. 40

Figure 3.8 Assembly of all the prosthetic components of S.T.A.R.™ prosthesis. Software used:

SolidWorks®. .......................................................................................................................................... 41

Figure 3.9 Congruency in the sagittal plane between the talar component and mobile-bearing of

S.T.A.R.™ prosthesis. Software used: SolidWorks®. ............................................................................ 41

Figure 3.10 The most important steps during virtual surgical procedure using Agility™ prosthesis: A –

The model after the bone resection; B – The model after the insertion of the tibial component and

fixed-bearing; C – The model after the insertion of the three components of the Agility™ prosthesis.


Figure 3.11 The most important steps during virtual surgical procedure using Agility™ prosthesis: A –

The model after the removal of part of the interosseous membrane and the insertion of the bone graft;

B – The final model with the bones, cartilages, interosseous membrane, Agility™ prosthesis, bone

graft, two screws and fibular plate; C – Magnification of the area of interest. Software used:

SolidWorks®. .......................................................................................................................................... 44

Figure 3.12 The most important steps during virtual surgical procedure using S.T.A.R.™ prosthesis: A

– The model after the bone resection; B – The model after the insertion of the talar component; C –

The model after the insertion of the talar and tibial components. Software used: SolidWorks®. .......... 45

Figure 3.13 The most important steps during virtual surgical procedure using S.T.A.R.™ prosthesis: A

– The model after the insertion of the three components of the S.T.A.R.™ prosthesis, which

corresponds to the final model with the bones, cartilages, interosseous membrane and S.T.A.R.™

prosthesis; B – Magnification of the area of interest. Software used: SolidWorks®. ............................. 45

Figure 3.14 Representation of the eight ligaments included in the model: 1 – DATiTa; 2 – TiCa; 3 –

DPTiTa; 4 – CaFi; 5 – PTaFi; 6 – PTiFi; 7 – ATaFi; 8 – ATiFi. Software used: ABAQUS®. ................. 46

Figure 3.15 At left, model used for determination of the loading conditions for the three models under

study (intact, TAA+Agility™ and TAA+S.T.A.R.™) at the neutral, dorsiflexion and plantarflexion

positions. At right, for exemplification purposes, the intact model of the AJC at the neutral position with

the applied loading and boundary conditions. Software used: ABAQUS®. ........................................... 51

Figure 3.16 A simplified free-body diagram of the forces acting on calcaneus at 70% of the stance

phase during walking. Vectors are shown slightly offset from the location of the force application,

which in turn is indicated by a dot. The red ellipses represent the surfaces assigned with the

“encastre” boundary condition (adapter from [154]). ............................................................................. 52

Figure 3.17 Ankle joint axes (yellow) before and after TAA using S.T.A.R.™ and Agility™ prostheses.

Software used: ABAQUS®. .................................................................................................................... 54

Figure 4.1 Inferior and superior views of the tibia and talus’s cartilages, respectively, overlaid with FE-

computed contact stresses (MPa) for the dorsiflexion, neutral and plantarflexion positions, considering

only an axial force of 600 N to the three positions. Legend: A – Anterior; P – Posterior; L – Lateral; M –

Medial. Software used: ABAQUS®. ....................................................................................................... 55



XIII

only an axial force of 1600 N, 600 N and 400 N to each position, respectively. Legend: A – Anterior; P

– Posterior; L – Lateral; M – Medial. Software used: ABAQUS®. ......................................................... 56



all the components of the concentrated force and the internal-external torque. Legend: A – Anterior; P

– Posterior; L – Lateral; M – Medial. Software used: ABAQUS®. ......................................................... 56

Figure 4.4 Comparison of the spatial distributions of the contact stresses (MPa) in the tibial surface

determined in the study of Anderson et al. [55] (at left) and in the present study (at right) for neutral

position and using an axial force of 600 N. Only for the present study, it was also included the result

when all components of the concentrated force and the internal-external torque were used as loading

condition (adapted from [55]). ............................................................................................................... 59

Figure 4.5 A typical contact pattern of the tibial surface with the ankle in neutral position and using an

axial load of 667 N – provided in study of Kura et al. [65]. Black regions correspond to articular contact

while white regions represent no contact between the tibia and talus. ................................................. 60

Figure 4.6 Inferior view of the polyethylene component’s lower surfaces that articulate with the talar

component of the Agility™ and S.T.A.R.™ prostheses and also the superior view of the polyethylene

component’s upper surface that articulates with the tibial component of the S.T.A.R.™ prosthesis,

overlaid with FE-computed contact stresses (MPa) for the dorsiflexion, neutral and plantarflexion

positions, considering only an axial force of 600 N to the three positions. Legend: A – Anterior; P –

Posterior; L – Lateral; M – Medial. Software used: ABAQUS®. ............................................................ 62





positions, considering only an axial force of 1600 N, 600 N and 400 N to each position, respectively.

Legend: A – Anterior; P – Posterior; L – Lateral; M – Medial. Software used: ABAQUS®. ................... 63





positions, considering all the components of the concentrated force and the internal-external torque.

Legend: A – Anterior; P – Posterior; L – Lateral; M – Medial. Software used: ABAQUS®. ................... 64

Figure 4.9 The Von Mises stress distribution (MPa) in the talus for the intact, TAA+Agility™ (including

the old and new talar component designs) and TAA+S.T.A.R.™ models, considering only an axial

force of 600 N with respect to the neutral position. Three cuts in the transverse plane at the talus for

each model are shown (superior view). From left to right: the cut is further from the surface where the

talar component is placed. Legend: A – Anterior; P – Posterior; L – Lateral; M – Medial. Software

used: ABAQUS®. ................................................................................................................................... 69

Figure 4.10 Comparison of the bone density distributions resulting from the bone remodeling computer

simulations (after 30 iterations) and the CT scan images. Software used: ABAQUS®. ........................ 72

XIV

Figure 4.11 Evolution of the bone mass throughout the iterative process of bone remodeling (30

iterations), dimensionless by its initial mass, for different values of parameters k and m. Software

used: MATLAB®. .................................................................................................................................... 74

Figure 4.12 The bone density distribution resulting from the bone remodeling computer simulation with

k = 0,007 N/mm2 and m = 2, after 100 iterations. Software used: ABAQUS

®. ...................................... 75

Figure 4.13 Evolution of the bone mass throughout the iterative process of bone remodeling (100

iterations), dimensionless by its initial mass, for k = 0,007 and m = 2. Software used: MATLAB®. ...... 75

Figure 4.14 Bone density distributions in the tibia and talus before and after the insertion of Agility™

prosthesis (frontal plane view). Software used: ABAQUS®. .................................................................. 77

Figure 4.15 Bone density distributions in the tibia and talus before and after the insertion of S.T.A.R.™

prosthesis (frontal plane view). Software used: ABAQUS®. ................................................................. 77

Figure A.1 Different views of the geometric model of the Agility™ prosthesis, considering the new talar

component design (for exemplification purposes). Software used: SolidWorks®. ................................ 97

Figure A.2 Different views of the geometric model of the tibial component of the Agility™ prosthesis.


Figure A.3 Different views of the geometric model of the polyethylene component/fixed-bearing of the

Agility™ prosthesis. Software used: SolidWorks®. ................................................................................ 98

Figure A.4 Different views of the geometric model of the new talar component design of the Agility™


Figure A.5 Different views of the geometric model of the old talar component design of the Agility™


Figure A.6 Different views of the geometric model of the S.T.A.R.™ prosthesis. Software used:

SolidWorks®. ........................................................................................................................................ 100

Figure A.7 Different views of the geometric model of the tibial component of the S.T.A.R.™ prosthesis.

Software used: SolidWorks®. ............................................................................................................... 100

Figure A.8 Different views of the geometric model of the polyethylene component/mobile-bearing of

the S.T.A.R.™ prosthesis. Software used: SolidWorks®. .................................................................... 101

Figure A.9 Different views of the geometric model of the talar component of the S.T.A.R.™ prosthesis.

Software used: SolidWorks®. ............................................................................................................... 101

Figure B.1 Illustration of the bone resection technique for implantation of Agility™ prosthesis (adapted

from [182]). .......................................................................................................................................... 102

Figure B.2 Illustration of the insertion of the prosthetic components of Agility™ prosthesis (3 – Tibial

component and fixed-bearing; 4 – Talar component) and of the arthrodesis performed at the end of

procedure (5) (adapted from [182]). .................................................................................................... 102

Figure B.3 Illustration of the bone resection technique for implantation of the tibial component of the

S.T.A.R.™ prosthesis (adapted from [229]). ....................................................................................... 103

Figure B.4 Illustration of the bone resection technique for implantation of the talar component of the

S.T.A.R.™ prosthesis (adapted from [229]). ....................................................................................... 103

Figure B.5 Illustration of the insertion of the prosthetic components of S.T.A.R.™ prosthesis: 1 – Talar

component; 2 – Tibial component; 3 – Mobile-bearing; 4 – TAA completed (adapted from [229]). .... 104

XV

Figure C.1 FE meshes of the intact model: A – Tibia (green) and the corresponding cartilage (blue); B

– Interosseous membrane (yellow); C – Fibula (green) and the corresponding cartilage (blue); D –

Talus (green) and the corresponding cartilages (blue); E – Calcaneus (green) and the corresponding

cartilage (blue); F – Intact model. Software used: ABAQUS®. ............................................................ 105

Figure C.2 The three positions under study for the intact model: A – Plantarflexion position; B –

Neutral position; C – Dorsiflexion position. Software used: ABAQUS®. .............................................. 106

Figure C.3 FE meshes of the TAA+Agility™ model: A – The two screws and the plate (purple); B –

Agility™ prosthesis; C – Tibial component (blue); D – Polyethylene component (orange); E – New talar

component design (yellow); F – Cut tibia and fibula (green), the interosseous membrane (yellow) and

bone graft (orange); G – Cut talus (green) and the corresponding inferior cartilage (blue); H –

TAA+Agility™ model. Software used: ABAQUS®. .............................................................................. 106

Figure C.4 The three positions under study for the TAA +Agility™ model: A – Plantarflexion position; B

– Neutral position; C – Dorsiflexion position. Software used: ABAQUS®............................................ 107

Figure C.5 FE meshes of the TAA+S.T.A.R.™ model: A – S.T.A.R.™ prosthesis; B – Tibial component

(blue); C – Polyethylene component (orange); D – Talar component (yellow); E – Cut tibia (green); F –

Cut talus (green); G – TAA+S.T.A.R.™ model. Software used: ABAQUS®. ....................................... 108

Figure C.6 The three positions under study for the TAA+S.T.A.R.™ model: A – Plantarflexion position;

B – Neutral position; C – Dorsiflexion position. Software used: ABAQUS®. ....................................... 109

Figure D.1 Algorithm flow diagram. ..................................................................................................... 110

XVII

List of Tables

Table 2.1 Summary of the maximum compressive forces at the ankle joint found in the literature. ..... 20

Table 3.1 Material properties defined in the three models under study (intact, TAA+Agility™ and

TAA+S.T.A.R™). ................................................................................................................................... 48

Table 3.2 Material properties of the ligaments used in the present work. ............................................. 49

Table 3.3 The concentrated forces proportionally scaled and the moment/internal-external torque used

as loading conditions in the present work – Reference: coordinate system used in the study of Seireg

and Arvikar [156]. .................................................................................................................................. 50

Table 3.4 Forces applied to the fibula in the three models under study (intact, TAA+Agility™ and

TAA+S.T.A.R.™) at the neutral, dorsiflexion and plantarflexion positions – Reference: global

coordinate system of ABAQUS®............................................................................................................ 51

Table 3.5 Forces applied to the tibia in the three models under study (intact, TAA+Agility™ and

TAA+S.T.A.R.™) at the neutral, dorsiflexion and plantarflexion positions – Reference: global

coordinate system of ABAQUS®............................................................................................................ 52

Table 4.1 The maximum and mean FE-computed contact stresses in the tibial surface for the three

loading conditions under study. Legend: D – Dorsiflexion; N – Neutral; PF – Plantarflexion. .............. 57

Table 4.2 Comparison of the contact stresses reported in the study of Anderson et al. [55] and the

FE-computed results of the present study............................................................................................. 58

Table 4.3 The maximum and mean FE-computed contact stresses in the polyethylene component’s

surfaces that contact with the old and new talar component designs of Agility™ prosthesis and with

the tibial and talar components of the S.T.A.R.™ prosthesis, considering only an axial force of 600 N

with respect to the neutral position. ....................................................................................................... 60


lower surface of the Agility™ prosthesis for the three loading conditions under study. Legend: D –

Dorsiflexion; N – Neutral; PF – Plantarflexion. ...................................................................................... 65


lower surface of the S.T.A.R.™ prosthesis for the three loading conditions under study. Legend: D –

Dorsiflexion; N – Neutral. PF – Plantarflexion. ...................................................................................... 65


upper surface of the S.T.A.R.™ prosthesis for the three loading conditions under study. Legend: D –

Dorsiflexion; N – Neutral; PF – Plantarflexion. ...................................................................................... 65

Table 4.7 Contact stress data from the literature for total ankle prostheses. Legend: D – Dorsiflexion;

N – Neutral; PF – Plantarflexion; AF – Axial force; APF – Anterior-posterior force; T – Interior-exterior

torque; PC – Polyethylene component; US – Upper surface; LS – Lower surface; TC – Talar

component. ............................................................................................................................................ 68

Table C.1 Number of elements and nodes of the FE meshes of the intact model. ............................. 105

Table C.2 Number of elements and nodes of the FE meshes of the TAA+Agility™ model. ............... 107

XVIII

Table C.3 Number of elements and nodes of the FE meshes of the TAA+S.T.A.R.™ model. ........... 108

XIX

List of Symbols

a, ai Microstructure parameters Microstructure parameters of the finite node e

( ) Microstructure parameters of the finite node e at the kth iteration

d Step length of the optimization process Component of the descent direction vector with respect to the parameters of the

microstructure

(

) Component of the descent direction vector with respect to the parameters of the

microstructure at the kth iteration

, Strain field

E Young’s modulus

Homogenized material properties tensor

Surface loads (applied in Γf)

Set of forces for load case P

Gap between the two bodies Biologic parameter, metabolic cost of maintaining bone tissue K Iteration number m Biologic parameter, corrective factor for the preservation of the intermediate densities

n Normal direction NC Number of load cases

P Index of load case

t Tangential direction

, Displacement for load case P

Relative normal displacement

Relative tangential displacement

XX

, Virtual displacement for load case P

Relative normal virtual displacement

Relative tangential virtual displacement

Weight factor of the load P

ν Poisson’ ratio

Γ Surface of the body

Γc Contact surface, candidate region to the interface between bodies

Γf Surface where the loads are applied

Γu Surface where the body is fixed

µ Relative density

θ, θ i Euler angles

Friction coefficient

Normal contact stress for load P

Tangential contact stress for load P

Ω Volume of the body (domain)

Ωb Volume of the body b

Ωp Volume of the body p

Stabilization parameter of the optimization process

XXI

Abbreviations

AJC Ankle Joint Complex ATaFi Anterior Talofibular ATiFi Anterior or Anteroinferior Tibiofibular BMU Basic Multicellular Unit BW Body Weight CaFi Calcaneofibular Co-Cr Cobalt-Chromium Co-Cr-Mo Cobalt-Chromium-Molybdenum DATiTa Deep Anterior Tibiotalar DPTiTa Deep Posterior Tibiotalar DOF Degrees of freedom FE Finite Element FEA Finite Element Analysis FEM Finite Element Method FDA Food and Drug Administration GRF Ground Reaction Forces ITiFi Interosseous Tibiofibular LCL Lateral Collateral Ligaments MCL Medial Collateral Ligaments OA Osteoarthritis PTaFi Posterior Talofibular PTiFi Posterior or Posteroinferior Tibiofibular PTA Post-Traumatic Arthritis RP Reference Point RA Rheumatoid Arthritis SS Stainless Steel SPTiTa Superficial Posterior Tibiotalar

XXII

SLC Syndesmotic Ligament Complex 3-D Three-Dimensional TiCa Tibiocalcaneal TiNa Tibionavicular TiS Tibiospring Ti Titanium TAA Total Ankle Arthroplasty 2-D Two-Dimensional UHMWPE Ultra-High-Molecular-Weight Polyethylene

1

Chapter 1

Introduction

This is an introductory chapter, in which the motivation of this work is explained as well as the

objectives, contributions and organization of the thesis.

1.1 Motivation

The ankle joint acts as a link between the leg and the foot, playing an important role in transferring

load from the leg to the foot, and vice-versa. The ankle and the foot constitute a complex mechanism.

The foot is extremely essential for maintain the body’s balance and providing the base for the body to

stand, lift, walk, run, jump and other activities. Thus, it is one of the most important parts of the body.

However, the ankle joint has a primary role during all those activities by absorbing the impact at each

step. In fact, the ankle joint has unique anatomical, biomechanical and cartilaginous structural

characteristics that allow the joint to withstand the very high mechanical stresses and strains during

walking, running and other activities [1].

The most common pathology that can disrupt ankle’s function is arthritis, which involves the

destruction of the articular cartilage. In a healthy condition, the articular cartilage cushions the articular

surfaces of bones, thus protecting the joint and allowing bones to move smoothly upon each other

without the friction that would come with bone-on-bone contact [2]. There are many forms of arthritis,

all of which have different causes [3]. The two more common types of arthritis include: osteoarthritis

(OA) and rheumatoid arthritis (RA) [2]. The OA, also called primary OA, is a progressive degenerative

joint disorder characterized by the “wear and tear” on cartilage through either the natural aging

process, constant use or after trauma. When it occurs after trauma, such as a fracture, severe sprain

or ligament injury, it is called post-traumatic arthritis (PTA) or secondary OA [2]. The RA is a systemic

disorder in which the body’s immune system mistakenly attacks healthy tissue, giving rise to the

inflammation of the membranes lining the joint, and eventually of all cartilage and bone [2, 4].

Arthritis is a serious form of joint disease that affects millions of people worldwide. According to the

Arthritis Foundation® [5], arthritis is the leading cause of disability in the USA and is actually a more

frequent cause of activity limitations than heart disease, cancer or diabetes. It can affect people of all

ages, races and genders and the number of people affected is growing fast. Although arthritis

predominantly affects the joints of the hip and knee and the exact prevalence of ankle arthritis is

difficult to quantify, in 2005 there were about 538000 people affected by OA in the foot/ankle only in

the USA [6]. However, while primary OA is the dominant type of arthritis in the hip and knee, clinical

experience and published reports of the treatment of ankle arthritis have indicated that primary ankle

OA is rare and that secondary OA/ PTA is the most common type of ankle arthritis [7-9]. Although the

actual number of people affected by ankle arthritis is smaller than that affected by hip or knee arthritis,

the number of ankle arthritis cases may increase in the following years. Orthopaedic surgeons have

2

noted an increase in the number and severity of ankle injuries, largely due to a more physically active

population, which may cause serious long-term problems. For instance, up to 15% of sport injuries

affect the ankle joint complex (AJC) [10]. Despite adequate treatment, 10-30% of lateral ligament

injuries progress to chronic instability [11], which in turn may lead to secondary OA/PTA later on. At

present, most types of arthritis cannot be cured but orthopaedic surgeons, working with other

physicians and scientists, have developed some treatments for arthritis [12]. Those treatments

encompass both non- and surgical measures. However, non-surgical measures have been shown to

have only small effects on pain relief, and when those treatments fail, surgical measures are required.

The most effective surgical measures are ankle arthrodesis and total ankle arthroplasty (TAA).

Arthrodesis is the artificial induction of joint ossification between bones. It has been the so-called

“gold standard” for the treatment of end-stage ankle arthritis, providing pain relief to the patients [13].

However, this procedure is far from the ideal one since the joint and thus the mobility provided by the

joint are eliminated. The restricted motion, besides the obvious discomfort, may increase the stresses

on the surrounding joints leading to the development of arthritis in the neighbouring joints [14], which

in turn may be a severe handicap to gait, leading to difficult ambulation [15]. Also, arthrodesis could

cause several complications, such as non-union, malalignment and infection [16], and there is no

satisfactory “salvage procedure” for a painful fused ankle. On the other hand, arthroplasty is the

replacement of an arthritic or injured joint with an artificial joint (prosthesis). This procedure is not only

aimed at relieving pain but also restoring mobility, stability and integrity of the joint, which challenges

the idea that arthrodesis is the best treatment for ankle arthritis [14]. Inspired by the success of the

total hip and knee arthroplasties, there was an interest in TAA and the first generation prostheses

were introduced in the 1970s. The short and intermediate term results of the TAAs were satisfactory,

but the long-term results were disappointing, and TAA was largely abandoned due to poor

survivorship [17]. Then, in the late 1980s and early 1990s there was a renewed interest in TAA with

the introduction of the second generation of total ankle prostheses which more closely replicated the

natural anatomy and mobility of the ankle, giving rise to improved clinical outcomes with mid-term

follow-up [18-24]. Since then, a more profound understanding of ankle biomechanics has led to the

development of new modern total ankle prostheses [13].

As short-, mid- and long-term results continue to be published, TAA has become a viable, even

superior option to ankle arthrodesis according to [18, 24-29]. Currently, the exact number of TAA

performed worldwide is not known but, for instance, in 2009, at least 800 TAA were being performed

per year in the UK [30], and in 2005 about 7000 TAA were performed in the USA, and at the time of

the study, it was estimated that by 2012 the number of TAA would increase to 11000 per year [31].

There are no studies in the literature with information regarding the number of TAA performed in 2012

but nowadays it is still expected that the number of TAA would increase substantially in the future [30].

Nevertheless, TAA is still seen as an inferior procedure to arthrodesis by many in the orthopaedic

community according to [15, 32-34]. In fact, the total ankle prostheses are not yet widely accepted and

do not have the same or even similar success rate of the total hip, knee or even shoulder prostheses

[35]. This is mainly because of the large forces acting across the ankle joint [36-38], the limited soft

tissue envelope (wound problems are common) [21], the small surface area for prosthetic support

3

(fixation is difficult) [21], and disregard for anatomical component shape and physiological ankle

biomechanics [39]. Also, another common problem of total hip and knee arthroplasties but largely

related to TAA is the thickness of polyethylene component that typically constitute the prosthesis. This

component needs to be sufficiently thick to maintain its integrity (avoiding wear and failure) but that

requires a larger resection, which weakens bone support [21]. Also, the magnitude and distribution of

the contact stresses can affect the wear rate and in some cases can lead to the fracture of the

polyethylene component. For instance, conformal geometries present lower contact stresses and also

lower wear rates than non-conformal geometries, but on the other hand, conformal surfaces create

small size particles that are believed to trigger more pronounced adverse bone reaction [40] such as

osteolysis, resorption at the bone-prosthesis interface and subsequent aseptic loosening of

prostheses [41-43], than large size particles. However, probably the main reason for TAA has taken

longer to develop than total hip and knee arthroplasties is the lack of research in TAA. The ankle is the

last joint in the lower limb in which total arthroplasty was attempted and therefore the amount of

research and development time dedicated to it has lagged behind that of the hip and knee [34].

Previously the prostheses were improved intuitively, based on clinical reports. Little or no

experimental, analytical or numerical stress analysis was carried out using bone-prosthesis models

[44]. Faced with the task of understanding a complex system, it is usually useful to extract its most

essential features and use them to create a simplified representation/”model” of the system [45]. In

fact, modeling is widely used in biomechanics: there are physical models that use real constructions

and mathematical models that use conceptual representations [45]. In particular, the need for

numerical methods arises from the fact that for most practical engineering problems analytical

solutions do not exist. The most widely used numerical model has been the finite element method

(FEM), which has given a great contribution in the field of orthopaedics, mainly for design and pre-

clinical analysis of prostheses; to obtain fundamental biomechanical knowledge like the stress and

strain state of musculoskeletal structures, such as bones, cartilage and ligaments; and to investigate

adaptive biological processes, such as bone remodeling, fracture healing and osteoporosis [45].

In fact, after an exhaustive literature review it was possible to confirm that many finite element (FE)

models were created for hip, knee and some for shoulder simulating total or partial replacement

surgeries, but very few can be found for TAA [46-54] or even to the intact ankle joint [55-62]. In

particular, some of the FE models created for the intact ankle joint are used in other areas of research

such as car crashes and ankle-foot orthosis. Furthermore, at the present state of knowledge, it was

only in 2002 that for the first time a three-dimensional (3-D) FE model, containing a prosthesis

(Agility™) and three bones (fibula, tibia and talus) was created [44, 52]. With the exception of that

study, there is no any 3-D FE model that includes more than one bone [44]. For instance, in 2001

McIff et al. [51] determined the contact and internal stress distributions for two different types of

prostheses but without considering the bones in the models. Also, in 2006 Reggiani et al. [54]

analysed the contact stresses in the polyethylene component of the BOX® prosthesis, but again the

bones were not included in the model.

Besides mathematical models, many studies included real models; some of them [63-65] analysed

the contact stress in the ankle joint, whereas others [66, 67] assessed the contact stress in the

4

polyethylene component of the prostheses. However, real models are difficult to obtain. They require

much time in preparation and are limited by the invasive measuring devices. Moreover, it is only

possible to use them once. Therefore, real models are not versatile as mathematical models. In some

cases, the predictions from FEM have been compared with those from real models in order to validate

them, but unfortunately in many cases the FE models cannot be confirmed directly by experiment.

Instead, indirect validation is achieved if the FE models produce the same conclusions as the

experimental or clinical results reported in literature [45].

Furthermore, FEM has been widely used in hip, knee and shoulder to investigate time-dependent

biological processes in tissues, such as bone remodeling process. The FEM coupled with specific

algorithms can provide computer simulations of tissue adaptation in response to biomechanical

factors. This way, it is possible to evaluate the changes in the bone adaptation before and after the

insertion of the prosthesis in the bone, and for instance, to estimate the amount of bone resorption

related to a specific prosthesis design. This is very important since the amount of bone resorption is

directly related to loosening, subsidence and at the end to the failure of the prosthesis. Thus,

computational models of bone adaptation are also useful for testing and optimizing the performance of

the orthopaedic devices. Therefore, a better understanding of the biological and mechanical changes

induced in bone tissue by prostheses will allow both orthopaedic surgeons to adopt the most

appropriate solution for each patient and implant manufactures to optimize the geometry of the

prosthesis. Nevertheless, regarding the bone remodeling process in the ankle joint only one study can

be found in literature. In 2011, Bouguecha et al. [68] evaluate the strain-adaptive bone remodeling

process separately for the tibia and the talus after the insertion of the S.T.A.R.™ prosthesis.

To conclude, for all that was mentioned before, there is clearly a need for further research in TAA.

1.2 Proposed Approach and Objectives

This thesis is integrated in the Software Development for Arthroplasty Preparation project

(PTDC/SAU-BEB/103408/2008), funded by FCT, which is being developed in IDMEC/IST. The aim of

this work is the development of a FE model of the AJC in order to study the influence of two different

prostheses, Agility™ and S.T.A.R.™, on the stress distribution and bone remodeling after a TAA. This

is done using the FEM provided by the commercial software ABAQUS® v6.10 (Hibbitt, Karlsson and

Sorensen, Inc., Pawtucket, Rhode Island, USA) together with the model of bone remodeling

developed in IDMEC/IST [69-74].

The FEM is a numerical analysis technique aiming to obtain approximate solutions to differential

equations that describe or approximately describe a wide variety of physical (and non-physical)

problems. The main idea behind the FEM is that a domain can be sub-divided into a series of smaller

regions, FEs, which constitute the FE mesh. The FEs are connected to each other at discrete node

points. Following the FE discretization, over each FE, an approximation to the solution is developed.

Finally, the assembly of all FEs enables to obtain the solution – the set of nodal displacements – of the

whole domain [45]. Then, the stress and strain can be calculated from the nodal displacements.

Regarding the model of bone remodeling used in the present work, it is based on a topology

optimization criterion. It all started when Wolff [75] proposed that bone morphology and structure

5

depend on applied loads and that the adaptation of trabecular bone to the mechanical environment

could be described by mathematical rules. This has encouraged many authors to propose different

mathematical models for bone remodeling. The computational model used in this work is an extension

of the model developed in Fernandes et al. [72], with the equilibrium equation expressed for the

contact problem being introduced by Folgado et al. [73, 74]. In essence, the model considers a porous

material and the aim is to obtain the stiffest structure for different load conditions. Thus, the application

of the topology optimization problem to the bone remodeling process is justified because it is generally

accepted that bone is a cellular/porous material that adapts itself to the applied loads, stiffening its

structure [69, 74]. This means that an increased applied load corresponds to an increased stress at

the bone, which in turn implies an increased bone mass/density (bone formation) in order to increase

stiffness. On the other hand, a decreased applied load originates bone resorption, and consequently

leads to weakening of the bone structure. For a full description of the model see [69, 71-74].

To summarize, the development of the 3-D solid models of the intact AJC, including the bones

(calcaneus, talus, fibula and talus), cartilages, interosseous membrane and some of most important

ligaments, and the Agility™ and S.T.A.R.™ prostheses is performed by using SolidWorks® v2012

(SolidWorks Corporation, Massachusetts, USA). Also, the assembly of the AJC with each prosthesis,

which allows the simulation of a TAA, is executed using the same software. These 3-D solid models

are suitable to generate FE meshes, and thus to perform a finite element analysis (FEA). Then, the

definition of materials properties, interaction between the models, loading and boundary conditions,

and mesh generation are defined using ABAQUS®. Afterwards, by integrating the FEM with the model

of bone remodeling it is possible to obtain the distribution of the bone density that is the solution of the

bone remodeling process.

In conclusion, this thesis has the following objectives:

Create a 3-D FE model for intact AJC and for TAA using Agility™ and S.T.A.R.™ prostheses.

These three models include the bones (calcaneus, talus, fibula and talus), cartilages,

interosseous membrane and some of most important ligaments of the AJC.

Analyse the contact stress distribution in the intact ankle joint for dorsiflexion, neutral and

plantarflexion positions under different loading conditions.

Analyse the contact stress distribution in the intermediate/polyethylene component of the

Agility™ and S.T.A.R.™ prostheses.

Evaluate the load transfer behaviour in the talus and the effect of the geometry of three

different talar component designs – two for Agility™ prosthesis and one for S.T.A.R.™

prosthesis – on host bone.

Investigate the bone remodeling process in two bones, tibia and talus, which are the bones

where the prosthetic components are inserted.

Evaluate the changes in the bone remodeling process that occurs in the tibia and talus after a

TAA using Agility™ and S.T.A.R.™ prostheses.

6

1.3 Contributions

This thesis has the following contributions:

At the present state of knowledge, these are the most detailed FE models of a TAA for two

different types of prosthesis, Agility™ and S.T.A.R.™, found in the literature. Future studies

can be performed using these FE models.

This work helps in understanding of the biological and mechanical changes induced in bone

tissue by total ankle prostheses, which in turn will allow orthopaedic surgeons to adopt the

most appropriate solution for each patient and implant manufactures to optimize the geometry

of the total ankle prosthesis.

Some of the work developed in this thesis was published and presented in the 5th Portuguese

Congress on Biomechanics [76].

1.4 Organization

This thesis is divided into five chapters.

The first, named Introduction, is an introductory chapter, in which the motivation of this work is

explained as well as the objectives, contributions and organization of the thesis.

The second chapter, named Background, reviews the anatomical and biomechanical

characteristics of the AJC. Then, the history of TAA is described and the first, second and new-

generation of total ankle prostheses are presented. Also, the main differences between the prostheses

under study, Agility™ and S.T.A.R.™, are discussed. Finally, both the histology of bone and the

biological basis of bone remodeling process are explained. Lastly, the bone remodeling model used in

the present work is briefly described.

The third chapter, named Computational Modeling, describes the steps involved in the

development of the 3-D FE models of the AJC before and after the simulation of a TAA using Agility™

and S.T.A.R.™ prostheses. In particular, the steps followed to create the 3-D solid models of the intact

AJC, including the bones (calcaneus, talus, fibula and talus), cartilages and interosseous membrane

are explained, as well as the fundamental steps on geometric modeling of the Agility™ and S.T.A.R.™

prostheses. Then, it is explained how was performed the assembly of the AJC with each prosthesis.

Afterwards, the set of steps involved in FEA, which includes the definition of materials properties,

interaction between the parts, loading and boundary conditions, and mesh generation, is explained.

Lastly, as explained before, FEM is integrated with the model of bone remodeling.

In the fourth chapter, named Results and Discussion, the results of both stress and bone

remodeling analyses are presented and discussed to each model under study (intact, TAA+Agility™

and TAA+S.T.A.R.™). Then, these results are compared with clinical and experimental results

obtained by other authors.

The fifth chapter, named Conclusions and Future Directions, presents the conclusions of the

present study. Then, the limitations of the study are analysed and some future directions are

proposed.

7

Chapter 2

Background

This chapter reviews the anatomical and biomechanical characteristics of the AJC. Then, the

history of TAA is described and the first, second and new-generation of total ankle prostheses are

presented. Also, the main differences between the prostheses under study, Agility™ and S.T.A.R.™,

are discussed. Finally, both the histology of bone and the biological basis of bone remodeling process

are explained. Lastly, the bone remodeling model used in the present work is briefly described.

2.1 Anatomy

The skeletal system, composed of bones, cartilage, joints and ligaments, is responsible for about

20% of the body weight (BW). The bones comprise most of the skeleton. The cartilages exist only in

specific areas such as the nose, ribs and parts of joints. Ligaments are responsible for the connection

between bones and also support the joints, allowing movement in some directions and at the same

time, restricting motion in other directions. The joints, which are regions of union between two or more

bones, provide high mobility and keep the bones together, playing a protective role in these

processes. In fact, the joints are the most fragile regions of the skeleton but still its structure resists

compression, tension, torsion or/and shear forces that threaten its perfect alignment [77].

2.1.1 Joints of the Human Foot

The human foot has three main joints namely the talocrural joint (well-known as the ankle joint),

the talocalcaneal joint (well-known as the subtalar joint) and the midtarsal joints (Figure 2.1) [78]. The

ankle joint is formed by the inferior extremity of the fibula and tibia, and the dorsum of the talus [35].

The subtalar joint consists of the talus and calcaneus whereas the midtarsal joints are formed by the

calcaneocuboid and talonavicular articulations [78]. These three main joints allow most of the motion

of the foot and the remaining ones only allow small motions, and do not involve frequent medical

consideration [44].

In general several authors [79, 80] describe the AJC as being constituted by the ankle and

subtalar joints. However, sometimes another joint is also described as part of the AJC namely the

distal/inferior tibiofibular joint, which is formed by the inferior extremities of the fibula and tibia. In the

present work it was considered the AJC as being constituted by the ankle, subtalar and distal

tibiofibular joints. However, it is important to mention that the main object of study in this work is the

ankle joint.

8

Figure 2.1 The three main joints of the foot and its associated bones (adapted from [81]).

2.1.2 Human AJC

As it was stated before, the human AJC consists of the ankle, subtalar and distal tibiofibular joints

[79, 80]. While the ankle joint is composed of three bones (fibula, tibia and talus), the subtalar joint is

only constituted by two (talus and calcaneus), as well as the distal tibiofibular joint (fibula and tibia).

Nevertheless, all of them are surrounded by collateral and syndesmotic ligaments, tendons, muscles,

nerves, veins and arteries [82].

2.1.2.1 Bony Configuration

The lower limb is divided in three different anatomic segments: thigh, leg and foot. The tibia and

fibula correspond to the bones present in the leg and the talus and calcaneus belong to the foot. The

main difference between these four bones is that the tibia and fibula belong to the group of long bones

whereas the talus and calcaneus are classified as short bones.

The fibula is located on the lateral side of the tibia, with which it is connected by the interosseous

membrane [44], and it is the most slender of all the long bones [83]. Like other long bones, fibula has

a body and two extremities. In particular, its inferior extremity inclines slightly forward, being on a

plane anterior to that of the superior extremity, and projects below the tibia, resulting in the

prominence on the lateral side of the ankle called the lateral malleolus [83]. It articulates with the talus

and tibia [83].

The tibia is situated at the medial side of the leg, and, apart from femur, is the longest bone of the

skeleton [83]. It is in a direct line between the femur and talus, and carries most of the load in the leg

[44, 78]. Like other long bones, tibia has a body and two extremities [83]. A particular aspect of the

tibia is that the inferior extremity is much smaller than the superior and it is prolonged downward on its

medial side as a prominence called the medial malleolus [83], which causes the tibial plafond (tibia’s

9

articular surface) to be asymmetric and provides a larger surface area to the ankle joint [44]. The arch

formed by the lateral and medial malleoli and the tibial plafond is named the ankle mortise [82].

The calcaneus is the largest and the strongest bone of the foot. It is located at the lower and back

part of the foot, being the main responsible for the transmission of the weight of the body to the

ground. It forms a strong lever for the muscles, and it articulates with the talus and cuboid [83].

The talus is the second largest bone of the foot [83] and consists of a cuboidal body, a neck and a

rounded head [44]. The body features several prominent articular surfaces; in particular, its superior

surface, constituted by two domes adjacent to each other in the frontal plane [84] presents a smooth

trochlear surface, the trochlea, for articulation with the tibia [83]. The trochlea is wider anteriorly than

posteriorly and due to that talus is commonly described as wedge-shaped [85, 86]. In front, trochlea is

continuous with the superior surface of the neck [83], which has a smaller cross section than the head

and therefore is the most prone part of the talus to fracture [44, 78]. Up to 60% of the talus is covered

by a comparatively thin articular cartilage [78, 82]. The articular cartilage of the ankle has an average

thickness of approximately 1.6 mm, whereas, for example, the articular cartilage of the knee has of 6-8

mm [87]. To conclude, the talus articulates with four bones: tibia, fibula, calcaneus and navicular [83].

2.1.2.2 Ligamentous Configuration

In reviewing the anatomy of the AJC, it is impressive the number of groups of ligaments and the

large number of smaller ligaments which make up each of these groups. Nevertheless, in general the

ligaments around the AJC can be divided, depending on their anatomic position, into three groups: the

lateral collateral ligaments (LCL), the medial collateral ligaments (MCL), also known as the deltoid

ligament, and the syndesmotic ligament complex (SLC) at the distal tibiofibular joint [88-90].

The LCL consists of the anterior talofibular (ATaFi), the calcaneofibular (CaFi), and the posterior

talofibular (PTaFi) ligaments [88, 91]. In particular, the ATaFi ligament is the most commonly injured

ligament of the ankle, typically following an ankle sprain, which is, in turn, the most common

mechanism of injury to the ankle ligaments [88, 92-94], and the CaFi is the only ligament of the LCL

bridging both the ankle and subtalar joints. Regarding the anatomical description of the MCL, it varies

widely in the literature, but in general most agree that is a multifascicular group of ligaments,

originating from the medial malleolus and inserted in the talus, calcaneus, and navicular, that is

composed of two layers: the superficial and the deep [95-98]. It belongs to Milner and Soames [96] the

most commonly accepted description of the MCL. They stated that the MCL consist of six

bands/components namely the tibiospring (TiS), tibionavicular (TiNa), deep posterior tibiotalar

(DPTiTa), superficial posterior tibiotalar (SPTiTa), deep anterior tibiotalar (DATiTa), and tibiocalcaneal

(TiCa) ligaments. The TiCa, TiS and TiNa ligaments comprise the superficial layer whereas the deep

layer consists of the DPTiTa, SPTiTa and DATiTa ligaments. Lastly, the SLC consists of the anterior

or anteroinferior tibiofibular (ATiFi), the posterior or posteroinferior tibiofibular (PTiFi) and the

interosseous tibiofibular (ITiFi) ligaments. Regarding the PTiFi ligament, numerous terminologies have

been postulated [99]; however, in general most agree that the PTiFi ligament is essentially formed by

two independent components: the superficial (also called the PTiFi ligament) and the deep (also called

the transverse ligament).

10

2.2 Biomechanics

2.2.1 Standard Reference Terminology

In describing the AJC or other joint motion, it is essential to have specialized terminology to

precisely identify the position and direction of the biomechanical system under study. The following

sections are aimed to describe the standard reference terminology of the human body applied to AJC.

2.2.1.1 Anatomical Reference Position

By convention, the body is in the anatomical reference position when it is in an erect standing

position with the arms hanging relaxed at the body sides, the palms of the hands facing forwards and

the feet slightly apart [100]. In describing the relative position of the AJC’s segments it is necessary to

use directional terms [100], which will be presented in the following, as well as some examples.

Superior: closer to the head. Example: the top of the foot (dorsal).

Inferior: farther away from the head. Example: the bottom of the foot, the sole (plantar).

Anterior: toward the front of the body. Example: the metatarsal bones are anterior to the

calcaneus.

Posterior: toward the back of the body. Example: the calcaneus is posterior to the metatarsal

bones.

Medial: closer to the midline of the body.

Lateral: further from the midline of the body.

Proximal: closer to the trunk.

Distal: further from the trunk.

Superficial: closer to the surface of the body.

Deep: the opposite of superficial; further into the body.

2.2.1.2 Anatomical Reference Planes and Axes

There are three imaginary anatomical reference planes that divide the body into two halves of

equal mass, namely the sagittal plane (also known as the anteroposterior plane), the transverse plane

(also called the horizontal or axial plane), and the frontal plane (also referred to as the coronal plane)

[100]. The sagittal plane is a vertical plane that divides the body into right and left halves, the

transverse plane is an horizontal plane that divides the body into superior and inferior parts, and the

frontal plane is a vertical plane mutually perpendicular to both transverse and sagittal planes, that

divides the body into anterior and posterior sections [100, 101]. These three anatomical reference

planes can be also applied to the foot, as shown in Figure 2.2 (at left). When the body is in the

anatomical reference position, all the anatomical reference planes intersect at a single point, which is

called the body’s center of mass or center of gravity [100]. In the case of the foot, the midline axis runs

from its anterior to posterior sections [102].

11

Figure 2.2 At left, the anatomical reference position of the foot and the three anatomical reference planes –

sagittal, transverse and frontal. At right, the three anatomical reference axes applied to the ankle joint (adapted

from [80, 101]).

The entire body may move along or parallel to an anatomical reference plane whereas the

movements of individual body segments may be described as sagittal plane movements, transverse

plane movements and frontal plane movements, which can occur at or in a plane parallel to the

sagittal, transverse and frontal planes, respectively. In particular, when a segment of the body moves,

it rotates around an imaginary axis of rotation that passes through a joint to which it is attached. In

fact, such as the three anatomical reference planes, there are three anatomical reference axes, each

of them perpendicular to one of the three planes. While the mediolateral axis is perpendicular to the

sagittal plane, the longitudinal axis is perpendicular to transverse plane and the anteroposterior axis is

perpendicular to the frontal plane. Therefore the rotation in the sagittal, transverse and frontal planes

occurs around the mediolateral, longitudinal and anteroposterior axes, respectively. Thus,

dorsi/plantarflexion motions occur around the mediolateral axis, abduction/adduction motions occur

around the longitudinal axis, and eversion/inversion motions occur around the anteroposterior axis

[100]. All these features are summarized above in Figure 2.2.

2.2.1.3 Joint Motion Terminology

Most of the human movements are “general motions”, combining linear (translation) and angular

(rotational) movements. When the human body is in anatomical reference position, all body segments

are considered to be positioned at zero degrees. Given this, the rotation of a body segment away from

anatomical reference position is named according to the direction of motion and is quantitatively

defined by measuring the angle between the position of the body segment and anatomical reference

plane [100].

Regarding the motion of the foot, and in particular the ankle joint, it occurs in the three anatomical

planes [80]. Dorsi/plantarflexion motions occur in the sagittal plane, abduction/adduction motions

occur in the transverse plane and eversion/inversion motions occur in the frontal plane [80] – see

Figure 2.2. There are two more possible motions of the foot, pronation and supination, which include

12

simultaneous motion in the three planes (sagittal, frontal and transverse), and due to that each of them

is termed “tri-plane motion”. All possible motions of the foot are summarized in Figure 2.3. The

description of each motion is presented below.

Figure 2.3 All possible motions of the foot: A – Dorsi/Plantarflexion; B – Abduction/Adduction; C –

Pronation/Supination; D – Eversion/Inversion (adapted from [103]).

Dorsiflexion is the movement of the foot when the toes are lifted off the ground, whereas

plantarflexion is when the toes are pushed down towards the ground. On the other hand,

adduction describes the motion of bringing something towards the midline of the body (medial

rotation), whereas abduction is the opposite that is when something is brought away from the midline

of the body (lateral rotation). Regarding inversion and eversion, the former is an internal rotation of the

foot while it is rolling over towards the medial side of the body, whereas the last is while it is rolling

over towards the lateral side (external rotation). Finally, pronation is a combination of abduction,

eversion, and dorsiflexion, and consists of the movement of the foot up and away from the center of

the body (the plantar surface faces laterally), whereas supination is a combination of adduction,

inversion, and plantarflexion, and involves the movement of the foot down and towards the center of

the body (the plantar surface faces medially) [78, 100, 101].

2.2.2 Axis of Rotation

Nowadays there are still some doubts regarding the axis of rotation of the ankle joint due to its

complex dynamic nature.

It all started with Hippocrates (B. C.), Bromfield [104] in 1773 and Fick [105] in 1911 when they

considered the ankle joint to be a hinge joint, allowing only rotation in sagittal plane. In contrast,

Lazarus [106] stated in 1896 that it was a screw joint, permitting not only rotation but also shifting

along the axis (lateral motion). In 1952 Barnett and Napier [85] demonstrated that the ankle had not a

horizontal fixed axis of rotation as Cunningham [107] suggested in 1943, but instead a changing axis.

During their study they examined the lateral and medial profiles of the trochlear surface of the talus

and they found out different medial and lateral radii of curvature, which along with the wedge shape of

13

the talus implied that tibiotalar congruency could not be preserved through sagittal plane motion

unless the talus presented coupled axial rotation. Besides this, they also reported that while the lateral

profile was an arc of a perfect circle and the axis of rotation passed through the center of this circle

every time and at any position of the talus, the medial profile was composed of arcs of two circles of

different radii, which would result in a changing axis of rotation. In dorsiflexion, the axis of rotation was

inclined downwards and laterally while in plantar flexion, it was inclined downwards and medially.

Moreover, the changing between these axes appeared to occur abruptly near the neutral position, and

in neutral position the axis was almost horizontal. In conclusion, Barnett and Napier [85] proved that

axial rotation must occur and that the ankle joint was not a simple hinge joint. This hypothesis seemed

to be consistent since in the following year (1953) Hicks [108] reported the existence of two main

ankle joint axes at dorsiflexion and plantarflexion positions, almost exactly in the same positions as

reported by Barnett and Napier [85]. In fact, this hypothesis has been confirmed by many other

studies, not only in vitro [36, 109-113] but also in vivo [114].

Nevertheless, in 1974 Kapandji [115] and later in 1976 Inman [116] stated that the ankle joint was

uni-axial. According to Inman [116] the trochlea can be represented as a section of a frustum of a

cone with its tip pointing medially, since he observed that it had a smaller medial and larger lateral

radii. In particular, during the experiments Inman discovered that the lateral surface was perpendicular

to the axis of rotation whereas the medial surface was inclined at 6 degree. As result, the lateral

surface was postulated as circular in shape whereas the medial surface as elliptoid. During this study

Inman also observed that in the frontal plane the ankle joint axis passed just below the tips of the

malleoli, tending to incline downward and laterally, whereas in the transverse plane the axis passed

through its centers, being inclined posterolaterally, as shown in Figure 2.4.

Figure 2.4 Directions of the ankle joint axis: inclined posterolaterally in the transverse plane (at left) and

downward and laterally in the frontal plane (at right) (adapted from [117]).

According to the "single" axis assumption for the ankle joint, Mann [102] reported in 1985 that in

frontal plane there was an angle of 80º formed by the ankle joint axis, a line passing through the tips of

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the malleoli, and the center of the tibial longitudinal axis, while in transverse plane the axis was

defined according to an angle of 84º from the midline axis of the foot. Later, in 1990, Morrissy [118]

defined the ankle joint axis in the transverse plane as the one that passed through the centers of the

malleoli. Despite the difference found in the frontal plane (8º observed by Inman [116] as shown in

Figure 2.4 comparing with 10º obtained by Mann [102]), these findings supported the previous

assumptions of Inman [116]. These values bring the ankle joint axis to within 84º of the mediolateral

axis in the sagittal plane, within 8º/10º in the transverse plane and within 6º in the frontal plane, as

shown in Figure 2.4. According to these studies, the ankle joint axis is an inclined axis of rotation,

which means that exist coupling/interaction (although being small) among the three axes, and for that

reason ankle motion occurs simultaneously in the three anatomical planes. More recently, Hintermann

[82] explained that it is due to this oblique orientation of the ankle joint axis that dorsiflexion results in

eversion and plantarflexion in inversion.

However, before the studies of Mann [102] and Morrissy [118], another idea was developed in

1977 by Sammarco [119]. He observed that the sagittal plane motion between the tibia and talus took

place about multiple centers of rotation, suggesting the existence of a changing axis of rotation and

considering the ankle joint as a multi-axial joint [82].

A few years later, in 1989, Lundberg et al. [120] analysed in three dimensions the ankle joint axis

using roentgen stereophotogrammetry in eight healthy individuals. The results of this investigation

were consistent with the idea that the ankle joint uses different axes for plantarflexion and dorsiflexion.

However, the changing between these axes appeared to occur gradually instead of abruptly. In

particular, in the frontal plane the plantarflexion axes were more horizontal, and inclined downward

and medially compared with those of dorsiflexion, which were inclined downward and laterally, as also

observed by Barnett & Napier [85] and Hicks [108]. On the other hand, in the frontal plane between

10º and 30º of dorsiflexion the axis tended to pass close to the tips of the malleoli, supporting the

findings of Inman [116] and later Mann [102]. Moreover, in all cases of motion it was observed that

when projected onto a transverse plane the ankle joint axis always ran close to the centers of the

malleoli, as reported by Inman [116] and after by Morrissy [118]. Furthermore, the overlapping of ankle

joint axes for one subject taking into account all motions performed showed that they cross at, or near,

one central point in the talus, which, in turn, seemed to constitute a “hub”, around which the ankle joint

had more degrees of freedom (DOF) than what was expected. This central point was described to be

at, or slightly lateral to, the midpoint of a line drawn between the tips of the malleoli. It would be

important to take this center of movement into account in designing the talar components of

prostheses.

Other studies using more accurate techniques for tracking small motions in three dimensions [79,

109, 111, 120-123] also showed that the ankle joint axis changed continuously during the motion.

More recently, Leardini et al. [79] formulated a mathematical model aiming to describe sagittal plane

motion (plantarflexion and dorsiflexion) in the AJC during passive motion. Early studies by these

authors [124-127] have demonstrated that in passive motion from plantarflexion to dorsiflexion

positions, the AJC works as a single-degree-of-freedom system, in which the ankle joint presents the

single-degree-of-freedom mechanism while the subtalar joint behaves as a flexible structure. They

15

confirmed the single-degree-of-freedom behaviour of the human AJC during passive motion, with a

changing axis placed about mulitple centers of rotation; in particular, the instant center of rotation

translates from a posteroinferior to an anterosuperior positions when the AJC moves from

plantarflexion to dorsiflexion positions, which, in turn, supports studies that reported that ankle is an

incongruent joint rotating about mulitple centers of rotation [111, 112, 120, 128-130]. Moreover, the

model developed in [79] predicted the shape of the trochlea as being polycentric and polyradial,

supporting the early findings of Barnett and Napier [85]. These authors pointed out that the articular

contact point shifted from the posterior part of the mortise in maximal plantarflexion to the anterior part

in maximal dorsiflexion, and that the articular surfaces could slide and roll upon each other. It is due to

the different centers of rotation that the talus glides and slides within the ankle mortise during sagittal

plane motion [120, 131].

As it has been described, there are several studies regarding the ankle joint axis which do not

support each other and so there are still some uncertainties about which assumption is better to

follow. Anatomy books refer to this axis as the empirical axis of the ankle joint [44], and during this

time, this empirical axis has been used for the design of total ankle prostheses (except the recent

BOX® prosthesis) and during the ankle replacement surgery for the positioning of the prosthesis in the

ankle joint. The empirical axis of the ankle joint follows the directions postulated by Inman [116], Mann

[102] and Morrissy [118]. For instance, clinicians can determined this empirical axis by placing fingers

on the tips of the malleoli. However, there are many critical points that still need to be clarified. In

general, everybody agrees that the dynamic nature of the ankle joint axis could be one of the reasons

for poor results in TAA [82]. Therefore, it would be important to determine the dynamic position of the

ankle joint axis and take that information into account in the design of new total ankle prostheses, in

order to restore the natural behaviour of the ankle joint axis, and consequently, restore the natural

behaviour of the ankle joint.

2.2.3 Range of Motion

For practical purposes, foot motion can be divided into two distinct types: non-weight-bearing

(passive condition) and weight-bearing (active condition). The difference is that in weight-bearing

motion there are forces produced by BW and muscle contraction acting to stabilize the joints while the

patient is standing, whereas in non-weight-bearing the patient is seated and lets the foot and ankle to

move freely with the help of the clinician [80].

Furthermore, as it was already stated, the ankle joint does not move as a pure hinge mechanism

[78, 85, 108, 120, 132]. In fact, the fit between the distal fibula and tibia with the talus allows the

movements of dorsiflexion and plantarflexion in the sagittal plane, which is the main plane of motion in

the ankle joint [82], but the ankle joint also rotates in the transverse plane, about 5/6º according to

[133] around the longitudinal axis, allowing the movements of abduction and adduction [78] and also in

the frontal plane (despite the smaller degree of rotation), allowing the movements of inversion and

eversion [82].

In general, the ankle joint motion varies between 20º to 60º with approximately 30º required for

walking, 37º for ascending stairs and 56º for descending stairs [38, 102, 120, 134]. In particular, the

values found in the literature for normal range of motion in the sagittal plane range from 23º to 56º of

16

plantarflexion and from 13º to 33º of dorsiflexion [38, 108, 114, 121, 135-141]. However, during the

stance phase of gait (the gait cycle is discussed further in Section 2.2.5) the range of motion is limited

on average to a maximum of 15º for plantarflexion and 10º for dorsiflexion [38, 114], as shown below

in Figure 2.6. On the other hand, there are several factors that influence sagittal plane motion of the

ankle joint. For instance, healthy older individuals have demonstrated a decreased plantarflexion [114,

137, 142], whereas individuals with a diseased ankle have exhibited a decreased dorsiflexion [82].

The range of motion needed for daily activities can be quantified as 10º-15º of dorsiflexion [120]. In the

case of a TAA, the goal is to provide a minimum range of motion for an appropriate “push-off” (period

when the heel is off the ground but the toes are in strong contact with the ground) that corresponds to

10º of dorsiflexion and 20º of plantarflexion [82].

Furthermore, Siegler et al. [111] postulated the existence of some coupling between the ankle and

subtalar joints during passive sagittal plane motion. It was observed that during dorsiflexion occurred

not only lateral rotation at ankle joint but also inversion at the subtalar joint. In particular, regarding the

subtalar motion, it is described as a complex motion that also occurs in three anatomical planes. The

subtalar joint is responsible along with the midtarsal joints for transforming tibial rotation into forefoot

supination and pronation [80]. For instance, Mann [143] described the coordination between the ankle

and subtalar motions, explaining that as the tibia internally rotates, the subtalar joint everts, which in

turn will cause pronation of the foot; in contrast, as the tibia externally rotates, the subtalar joint

inverts, which in turn will cause supination of the foot [80]. The subtalar joint motion varies between

20º to 30º for inversion and 5º to 10º for eversion. Moreover, during the gait cycle the subtalar joint

motion ranges from 10º to 15º [80, 144, 145]. The overall motion of the AJC is usually taken to be a

combination of the motion at the ankle and the subtalar joints [146].

2.2.4 Restraint of Motion/Stability

The stability of the AJC depends on both the geometry of the articular surfaces and ligaments [36,

82]. As far as the ankle joint mobility is concerned, the CaFi and TiCa ligaments and the articular

surfaces guide passive motion, while other ligaments limit but do not guide motion [127].

There is no consensus on this topic but in general most agree that loading the ankle results in

decreased range of motion and increased stability, due to the congruency caused by the articular

surfaces, especially during dorsiflexion. During most activities, the soft tissues are the major torsional

and anteroposterior stabilizers of the ankle [147, 148], while the articular surfaces are the major

inversion/eversion stabilizers with the LCL and MCL playing a secondary role [149, 150]. If a total

ankle prosthesis does not provide sufficient intrinsic inversion and eversion stability, the ligaments will

be exposed to abnormal inversion and eversion forces, and the result will be an unstable AJC [134,

139]. For instance, Burge and Evans [134] stated that the anteroposterior restraint provided by the

normal tibial articular surface – which is concave in the sagittal plane – may be lost when the surface

is replaced by a flat tibial component, such as the case of the tibial component of the S.T.A.R.™

prosthesis. They concluded that the more the geometry of the articular surfaces is changed from its

physiological condition, the more the prosthesis depends upon the soft tissues for stability. Therefore,

the prosthesis should be as anatomic as possible.

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2.2.5 Gait Cycle

The gait cycle is usually described as the time interval between the exact same repetitive events of

walking. Usually it is chosen the instant at which one foot contacts the ground to be the initial event of

the gait cycle, despite not being mandatory. According to that, the gait cycle starts at the moment at

which one foot contacts the ground and continues until the same foot contacts the ground again [151].

The gait cycle can be divided into two distinct periods: the stance phase and the swing phase [38, 80].

The stance phase occurs when the foot is in contact with the ground and comprises about 60% of the

cycle, whereas the swing phase occurs when the foot is in the air and constitutes the remaining

fraction (about 40%) [80, 151, 152]. Unfortunately there is no standard nomenclature to describe the

gait cycle, and therefore the following terms are not the unique terms used to describe the stance and

swing phases. According to [80] the stance phase can be divided into five subphases, such as “heel

strike”, “foot flat”, “heel rise”, “push-off” and “toe-off”, whereas in the swing phase it is possible to

distinguish three subphases, such as “acceleration”, “toe clearance”, and “deceleration” [80]. These

designations are based on the movement of the foot. All the different subphases are represented in

Figure 2.5.

Figure 2.5 The different subphases of the stance and swing phases (adapted from [80]).

The contact point of the heel with the ground is not in the center of ankle joint but rather offset

laterally from it, and it is in part because of that reason that the subtalar joint everts from “heel strike”

to “foot flat” – maximal eversion occurs at “foot flat” [78, 80]. Also during this period occurs internal

rotation of the tibia and pronation of the foot [78, 80], which all together give the foot the flexibility

needed to absorb shock and adapt to irregularities in the ground floor surface. Then, the subtalar joint

begins to invert – maximal inversion occurs at “toe-off” – and at “heel rise” and “push-off” occurs

external rotation of the tibia [78, 80]. The inversion of the subtalar joint and supination of the foot gives

the foot the rigidity needed to propel the body forward [78, 153]. The ankle and subtalar rotations in

sagittal and frontal planes, respectively, are represented in Figure 2.6, during walking in a complete

normal gait cycle.

18

Figure 2.6 The ankle and subtalar rotations in sagittal and frontal planes, respectively, during walking in a

complete normal gait cycle (adapted from [80]).

As can be confirmed by Figure 2.6, two movements of dorsiflexion and another two of

plantarflexion occur during walking in a complete normal gait cycle. In particular, both movements of

plantarflexion and one of dorsiflexion occur during stance phase and the other of dorsiflexion occurs

during swing phase. Furthermore, in the beginning of the gait cycle, when the heel first make contact

with the ground (“heel strike”) the ankle joint slightly and quickly dorsiflexes (not significant) due to the

load response. Promptly the first plantarflexion occurs. Then, it begins the first dorsiflexion, but it is

important to state that the foot is immobile, only the tibia moves. Around “foot flat” the neutral position

is reached, and dorsiflexion continues until about 48% of the cycle, which corresponds to the

maximum dorsiflexion (about 10º). Subsequently, there is a fast plantarflexion that reaches 15º at the

end of stance phase. After the “toe-off”, it starts the swing phase and it is initiated the last dorsiflexion

of the gait cycle. From “toe clearance” to the end of the gait cycle the ankle is maintained in neutral

position, however, sometimes during the end of swing phase occurs a small plantarflexion ranging

from 3º to 5º [152].

2.2.6 Force Generation

Forces transmitted across the AJC are a combination of external and internal forces. The external

forces are the forces produced by the body contacting the ground, namely ground reaction forces

(GRF), which can be measured experimentally during gait using a force platform. On the other hand,

the internal forces are produced by muscles and ligaments and so the determination in vivo of these

forces is difficult and the only way to do it is using computational methods [44]. Some biomechanical

models have been developed to calculate internal forces in the joints of the foot [37, 38, 154-156], but

these internal forces are not completely understood. Once again, this is in part due to the lack of

investigation in the AJC. The biomechanics of the major joints of the lower extremity, namely the hip

19

and knee joints have been extensively studied. For instance, there is a great amount of kinematic data

that was provided by inverse dynamic models, computer optimization models including muscle forces,

fluoroscopic studies of gait and even instrumented, telemeterized prosthesis for in vivo measurement

of forces [156-159]. However, as far as the AJC is concerned, the investigation has not had the same

extent, besides the renewed interest in this joint in the recent years. The following paragraphs are

aimed at describing some studies whose purpose was to calculate internal forces in the ankle joint.

In 1975, Seireg and Arkvikar [156] using a simplified GRF as the input for their 3-D model of the

lower extremity determined the joint reactions at the hip, knee and ankle joints. They used an

optimization technique to minimize the sum of the muscle forces. The maximum compressive (z

direction) force developed during stance phase of gait was 5.2xBW, while the maximum anterior-

posterior (x direction) and medial-lateral (y direction) tangential forces were 2xBW and 1xBW,

respectively [31, 44], as shown in Figure 2.7.

Figure 2.7 The components of reaction forces at the ankle joint during stance phase of gait determined by Seireg

and Arkvikar [156].

In 1977, Stauffer et al. [38] developed a two-dimensional (2-D) model of an ankle joint in the

sagittal plane. They studied the reaction forces in the ankle joint in a group of healthy subjects,

patients with disabling joint disease and some of the same diseased patients retested after undergoing

TAA. They used a 2-D inverse dynamics model to determine the reaction forces at the ankle joint. The

results showed that for healthy subjects the maximum compressive forces developed during the

stance phase of gait were in the range of 4.5-5.5xBW. In patients with disabling joint disease, the joint

load decreased to approximately 3xBW and did not increase significantly at one year postoperatively,

even among patients with good clinical results [31, 44, 82].

In 1982, Procter and Paul [37] conducted a 3-D analysis of the ankle joint during the stance phase

of gait by using a force platform. They determined an average maximum compressive force of 3.9xBW

(2.9-4.7xBW in range) and a maximum torque of 40 N.m due to in/external rotation of the foot [31, 44].

In 2006, Reggiani et al. [54] developed a 2-D FEM in order to study the kinematics, contact

pressures and ligament forces of the ankle joint. They used the forces predicted by Seireg and

20

Arkvikar [156] and Procter and Paul [37]. In particular, they used the compressive and anterior-

posterior tangential forces from the former work, and the internal-external torque and plantar-

dorsiflexion rotation from the later. However, Reggiani et al. [54] found that the data provided by

Seireg and Arkvikar [156] may be overestimated. In fact, comparison of the hip joint contact forces

predicted by Seireg and Arkvikar [156] with in vivo measurement of forces conducted by Bergmann et

al. [160] showed that the aforementioned forces were overestimated by a factor of 2.25. Based on this,

the force predictions reported by Seireg and Arkvikar [156] were proportionally scaled and for

instance, the maximum compressive force was reduced to 2.3xBW.

The maximum compressive forces at the ankle joint determined by the studies described above

are summarized in Table 2.1.

Table 2.1 Summary of the maximum compressive forces at the ankle joint found in the literature.

Source Maximum compressive force (xBW)

Seireg and Arkvikar [156] 5.2

Stauffer et al. [38] 4.5-5.5 (different subjects)

Procter and Paul [37] 2.9-4.7 (different subjects)

Reggiani et al. [54] 2.3 (proportionally scaled)

Regarding the weight-bearing capacity of the fibula, until the 1970s it was generally believed that

all loads were transferred through the tibia and talus and that fibula was only responsible for the

stabilization of the ankle joint [44]. However, this assumption was later confirmed not to be true. In

fact, three reports on the weight-bearing capacity of the fibula found in literature [161-163] described

that fibula carried a percentage of the total load acting across the ankle joint. In particular, Lambert

[161] determined that fibula carried 17% of the total load using strain gages. On the other hand,

Takebe et al. [162] reported that the percentage determined by Lambert [161] was overestimated. He

measured the weight-bearing capacity of the fibula by a direct method of inserting force transducers

into the resected portions of the two bones. This experiment showed that the percentage of load

carried by the fibula was only 6.4% and that the fibula carries more load in dorsiflexion and eversion

and less load in plantarflexion and inversion than in the neutral position. Furthermore, Wang et al.

[163] reported that a higher percentage of the load is carried by the fibula when higher loads are

transmitted through the leg.

2.3 Total Ankle Prostheses

The search for a workable total ankle prosthesis design has taken many different approaches.

However, despite the number of designs developed, early results with TAA were disappointing [164].

The variety of total ankle prosthesis can be classified according to: fixation type (cemented or

uncemented); number of components (two or three components); constraint type (constrained,

semiconstrained or unconstrained); congruency/conformity type (incongruent, partially conforming or

fully conforming/congruent); component shape (non- or anatomic); bearing type (fixed or mobile) [164].

21

Before going further, it is important to make clear the difference between “constraint” and

“congruency/conformity”. Constraint is the resistance of prosthesis to a particular degree of freedom.

Excessive constraint leads to high shear forces at the bone-prosthesis interface, which may lead to

loosening, subsidence and at the end to failure of the prosthesis [34, 165-167]. In order to mimic

normal joint range of motion and thus reduce the shear forces at bone-prosthesis interface a minimally

constrained prosthesis is required. On the other hand, congruency/conformity is a geometric measure

of closeness of fit between the articular surfaces of a joint/prosthesis. Fully conforming/congruent

prostheses have articular surfaces with the same sagittal radii of curvature, which results in full

articular contact. These prostheses typically show great stability and low wear rates due to the larger

contacting surfaces and lower local stresses, respectively. In contrast, incongruent or partially

conforming prostheses have reduced stability – relying on the ligaments to provide the stability – and

higher wear rates due to, respectively, the smaller contacting surfaces and higher local stresses [164].

The following sections are aimed at describing the first and second generations of total ankle

prostheses, and in particular the prostheses under study namely Agility™ (DePuy Orthopaedics, Inc.,

Warsaw, Indiana, USA) and S.T.A.R.™ (Waldemar-Link, Hamburg, Germany; acquired by Small Bone

Innovations, Inc., Morrisville, Pennsylvania, USA), as well as the explanation for that choice.

2.3.1 First Generation

The first generation prostheses consisted of two components: a polyethylene and a metal. In most

cases the tibial component was constituted of polyethylene and the talar component was made of

metal [34]. The first generation prostheses used cement as the method of fixation, reflecting the

tendency of joint arthroplasty in those days [34, 164], and they could be divided into two distinct

categories: constrained and unconstrained [34]. Typically, constrained prostheses are of the

congruent type, whereas unconstrained prostheses are of the incongruent type, with the exception of

spherical prosthesis, which is a congruent and simultaneously unconstrained prosthesis. The spherical

prosthesis, contrary to what was expected, is not suitable for TAA because although it is congruent

over the complete range of motion (unconstrained type), the stability is not guaranteed by the

prosthesis, as it was expected. Instead, it relies totally on the ligaments to limit the motion of the

prosthesis and thus to provide stability [168], which may be catastrophic, depending on the amount of

extra strain placed on the ligaments. This shows that unconstrained prostheses are not the ideal ones.

Instead, the ideal prosthesis should mimic just the normal/necessary ankle joint range of motion in

order to recreate the normal kinematics of the ankle joint.

The early reports of TAA were actually very good, however, long-term follow-up revealed high

failure rates and complications [164], such as: inappropriate surgical instruments, which resulted in

inaccurate positioning of the prosthesis [164]; the use of cement as the method of fixation, which

among other problems, resulted in a much larger bone resection [34]; fractures of the malleoli due to

unique size design of prostheses and also because of the poor instrumentation [165, 169]; excessive

traction in the skin during surgery, which gave rise to skin complications [164]; infections, wound

healing problems and severe osteolysis [1, 34]; excessive bone resection, which resulted in the

prosthesis being seated on cancellous bone that could not support BW, and consequently, this

22

contributed to component subsidence with early loosening [1, 165]. As result, all total ankle prostheses

of the first generation were discontinued and the arthrodesis continued to be the treatment of choice

throughout the 1980s, before the possibility of TAA began to be investigated again during the 1990s

[34].

2.3.2 Second Generation

Those who had persisted with TAA identified the problems of the first generation prostheses and

designed new prostheses aiming to reproduce the anatomical and biomechanical characteristics of the

ankle joint [170]. A great improvement was the introduction of a new method of fixation, the press-fit

fixation. Almost all modern total ankle prostheses are of the uncemented type, thus avoiding the risk of

osteolysis that could be induced by the cement particles. Another important development occurred on

the instrumentation [164]. Furthermore, as it was explained before, there were other, more important

problems associated with constrained and unconstrained prosthesis. In order to overcome those

problems, an intermediate component was introduced between the tibial and talar components [169]

that works like a bearing. This intermediate component helps to absorb the forces passing through the

tibia and fibula and distributing them to the talus, and this way allowing almost normal ankle motion

after TAA [171]. Taking this new concept into account, the second generation prostheses started to be

of the semiconstrained type (two-component, fixed-bearing designs) and afterwards were also

designed to be at the same time minimally constrained and congruent (three-component, mobile-

bearing designs) [1, 164]. Consequently, the fixed-bearing prostheses work differently in absorbing the

forces within the ankle during motion than mobile-bearing prostheses [20]. Moreover, the intermediate

component of all second generation prostheses, with the exception of the TNK ceramic/metallic

prosthesis, is made of polyethylene (Ultra-High-Molecular-Weight Polyethylene, UHMWPE) [172],

which is biocompatible and low friction. Due to that, the intermediate component is typically called the

polyethylene component (as the case of the present study).

In the case of fixed-bearing prostheses, as the name suggests, the polyethylene component is

fixed to the tibial component, and thus this type of prostheses has only one articulation, placed

between the polyethylene and talar components [1]. Although consisting of three components (tibial,

talar and polyethylene), these prostheses act as two-component prostheses [172]. In order to reduce

constraint it was also necessary to reduce conformity/congruency and thus this type of prostheses is

partially conforming. As result, they have higher wear rates comparing with fully conforming/congruent

prostheses due to the high local stresses resulting from small contact areas, and they have also poor

inherent stability. Typically with less conformity, wear is greater [164]. Examples of fixed-bearing

prostheses are Agility™, INBONE® (Wright Medical Technologies, Arlington, Tennessee, USA),

Eclipse (Kinetikos Medical Inc., Carlsbad, California, USA / Integra LifeSciences Corp., Plainsboro,

New Jersey, USA) and Salto® Talaris (Tornier, Inc., Saint Ismier, France) [172, 173].

In the case of mobile-bearing prostheses, as the name also suggests, the polyethylene component

is not fixed but mobile as a meniscus, aiming to provide structural integrity by reducing the impact of

the axial and shear constraints at the bone-prosthesis interface and by this way avoiding loosening.

Also, this mobile component promotes stability by maintaining the natural ankle joint kinematics [164].

23

This is achieved by the existence of two separate congruent articulations in this type of prosthesis. On

the other hand, the addition of a second articulation may increase wear [164], but still smaller than

fixed-bearing prostheses. However, with mobile-bearing designs there is a possibility of

subluxation/dislocation of the polyethylene component [164, 174]. Examples of mobile-bearing

prostheses are S.T.A.R.™, Buechel-Pappas™ (Endotec, Inc., South Orange, New Jersey, USA) and

SALTO® (Tornier, Inc., Saint Ismier, France) [164, 172, 173].

There are currently five total ankle prostheses approved for use in the USA by the Food and Drug

Administration (FDA). These prostheses are the Agility™, INBONE™, Salto® Talaris, Eclipse and,

most recently, the S.T.A.R.™, although it has been in clinical use throughout Europe since 1981 [174].

There is also the MOBILITY™ prosthesis in clinical trials versus the Agility™ prosthesis. Although the

Eclipse has garnered approval, only a few Eclipse prostheses have been implanted and this

prosthesis is not readily available to all surgeons [175]. Moreover, all the approved prostheses, except

S.T.A.R.™, are two-component, fixed-bearing designs. The S.T.A.R.™ is the only approved three-

component, mobile-bearing system available for use in the USA [174]. Furthermore, from the second

generation prostheses there are three that have dominated the market, namely Agility™, S.T.A.R.™

and Buechel-Pappas™ [7, 32, 34, 176, 177]. In particular, the Agility™ was the first total ankle

prosthesis approved by FDA and it has been the most widely marketed and used total ankle

prosthesis in USA [34, 172]. On the other hand, the S.T.A.R.™ has become the most popular total

ankle prosthesis in Europe [34]. Additionally, of the approved total ankle prostheses by FDA, only the

Agility™ and S.T.A.R.™ have published studies documenting mid- to long-term results in the USA,

and for instance, the S.T.A.R.™ is the only prosthesis where clinical studies have been carried out by

authors without a financial interest in the product [34], which explains the amount of available

information regarding particularly this prosthesis. Thus, the choice of studying the Agility™ and

S.T.A.R.™ prostheses was based on the aforementioned facts.

2.3.2.1 Agility™

The Agility™ prosthesis designed by Dr. Frank Alvine was first implanted in 1984 [178]. This

prosthesis is a two-component, fixed-bearing design, with the polyethylene component fixed to the

tibial component [22]. In particular, the polyethylene component is concave in sagittal plane, which

increases anteroposterior stability [21]. Moreover, it is a semiconstrained prosthesis, allowing axial

rotation as well as dorsi/plantarflexion motions. This is accomplished due to the existence of a

deliberate mismatch between the tibial and the talar components. The articular surface of the tibial

component is larger than that of the talar component, which allows the talus to seek its own position

and thus the compressive and shear forces are decreased at the bone-prosthesis interface [21, 34].

Nevertheless, all this causes the prosthesis to be partially conforming, which can increase contact

stresses in the polyethylene and consequently increase wear [21].

Like other prostheses, the Agility™ has gone through several modifications since its original

design [20]. In the beginning the two prosthetic components were made of titanium (Ti) but since 1989

cobalt-chromium (Co-Cr) has been used in the talar component due to loosening of two talar

components in the first 3 years [23]. Thus, currently the Agility™ prosthesis consists of a Ti tibial

24

component with sintered Ti beads and a Co-Cr talar component with sintered Co-Cr beads [22]. At the

same time, another change occurred at the tibial component: a thicker tibial component started to be

used due to two broken components in the first 21 TAA with the Agility™ prosthesis [23]. Regarding

the design of the talar component, the early design was slightly wider anteriorly than posteriorly

(anatomically similar to the talus), which was thought to provide more stability during the stance phase

of gait [164, 172]. However, this design did not take advantage of the entire available surface area and

therefore a new design was created, which partially improves the situation [21, 179]. According to the

study [179], the new design has better performance than the early design because it reduced the

overall maximum stresses in the bone, and, in particular, at the posterior edge. Clinically, the early

design was noted to fail due posterior subsidence. This led to development of wider talar components

including the posterior augmented and revision components with more rectangular designs. A natural

extension of this evolution in design was to increase the contact area of the talar component, resulting

in the new version presented in Figure 2.8. Also, to accomplish the change of the talar component

design, the sidewalls of tibial component had to be shortened [179]. All these geometric modifications

of the tibial and talar components can be observed in Figure 2.8.

Figure 2.8 The Agility™ prosthesis: the old version (at left) and the new version (at right) [180, 181].

Furthermore, this prosthesis resurfaces the articular surfaces of the ankle joint, and the medial and

lateral talar facets. Also, it is required an arthrodesis of the distal tibiofibular joint using one or two

(more common) screws through the distal fibula into the distal tibia in order to get a better load

distribution [1, 21, 23, 181]. Additionally, the medial and lateral walls of the tibial component sit flush

against the cut surface of the medial and lateral malleoli, bridging the tibial lateral surface and the

fibula medial surface. This provides a broad base of support for the tibial component and covers

nearly all exposed cancellous bone, thus increasing the contact area and improving the load

distribution [181]. Optionally a plate can be placed on the fibula at the end of the procedure in order to

increase the load distribution along the fibula and enhance the bone fusion. Given its importance, the

plate was considered in this work. However, before inserting the screws, as it is necessary to remove

part of interosseous membrane, bone graft from the excised talar and distal tibial bones is used to fill

the space created. It is preferred a single, large, well-contoured cancellous block to perfectly fit into

the space than the use of multiple cancellous chips [182]. In conclusion, with this prosthesis the

amount of bone resection is relatively high, resulting in less bone available for support [21].

25

The most reported complications using Agility™ prosthesis were radiolucency, subsidence of

prosthetic components and non- or delayed union of fibula and tibia after the arthrodesis, which

according to Dr. Frank Alvine, increases tibial component loosening [173].

2.3.2.2 S.T.A.R.™

The S.T.A.R.™ prosthesis was developed by Dr. Hakon Kofoed in Denmark, where it was first

implanted in 1981 [183]. The initial S.T.A.R.™ was a two-component, fixed-bearing prosthesis and

cement was used as the method of fixation [1, 34, 164]. The talar component was made of stainless

steel (SS) and the tibial component of polyethylene [34]. However, due to the poor results, the

prosthesis was revised in order to become a three-component, mobile-bearing design with the method

of fixation remaining the same until 1990 [1, 164]. Since then, uncemented methods of fixation started

to be used [1, 164]. The S.T.A.R.™ prosthesis is presented in Figure 2.9.

Figure 2.9 The S.T.A.R.™ prosthesis [184].

The talar component has near anatomical shape, covering completely the talar dome [174, 184],

whereas the tibial component has a flat geometry, which may reduce anteroposterior stability and

consequently expose the ligaments to forces that they cannot withstand [82]. Besides the anatomical

differences, both talar and tibial components are made of cobalt-chromium-molybdenum (Co-Cr-Mo)

with Ti plasma spray coating [184]. Moreover, there are two anchorage bars on the tibial component in

order to enhance fixation to the tibial bone. The talar component has a longitudinal ridge that is

congruent with a groove in the distal surface of polyethylene component [34, 172]. This configuration

provides medial-lateral stability for the polyethylene component toward the talar component [34].

Hence, dorsi/plantarflexion motions are allowed at the polyethylene-talar and polyethylene-tibial

interfaces but axial rotation is only allowed at the polyethylene-tibial interface [185].

The STAR™ prosthesis also resurfaces the articular surfaces of the ankle joint and the medial and

lateral talar facets but in contrast to the Agility™ prosthesis, with the STAR™ prosthesis it is not

required the arthrodesis of the distal tibiofibular joint (and so there are no additional risks associated

with that procedure) and there is also significantly less bone resection [173]. It is important to mention

that it has not been determined yet if it is necessary to resurface the medial and lateral facets.

Theoretically this may improve force distribution and long-term stability of the talar component but on

the other hand by preserving the facets, less cortical bone is removed from the talus [21]. In fact,

Rippstein [186] reported that it is not necessary to resurface the facets and therefore this aspect was

26

not considered in this study (regarding both prostheses). For each case it is necessary evaluate which

are the most important benefits, if the increased stability and fixation of the prosthesis by resurfacing

the facets or the increased bone support and resistance by preserving the strong cortical bone of the

facets [21].

Both the Agility™ and S.T.A.R.™ prostheses provide reliable plain relief and very high rates of

patient satisfaction. However, they both have high rates of complications and requirement for

secondary procedures, especially in young and PTA patients [164, 187, 188]. In published studies, the

S.T.A.R.™ prosthesis demonstrated lower rate of radiolucency and subsidence of prosthetic

components and lower failure rates at greater than 10-year follow-up, when compared with the

Agility™ prosthesis. In addition to that, the S.T.A.R.™ prosthesis avoids the complications related to

the non- or delayed union of arthrodesis [164].

2.3.3 New Designs

Currently there are about 20 total ankle prostheses available on the market worldwide [176],

including many new designs available. These new prostheses are, for instance, the HINTEGRA®

(Newdeal SA, Lyon, France/ Integra LifeSciences Corp., Plainsboro, New Jersey, USA), MOBILITY™

(DePuy International, Leeds, United Kingdom), BOX® (MatOrtho™, Leatherhead, England) and AES

(BIOMET Europe, Belgium) [176]. In these new prostheses more emphasis was placed on soft tissue

balancing, role of ligaments in stability, improving fixation, minimizing bone resection and correction of

deformity and salvage options for failed TAA [7, 34, 176]. For instance, the HINTEGRA® is an

interesting prosthesis because it uses screw fixation aiming to reduce bone resection in the ankle joint

[189], and the BOX® claims to restore the normal kinematics at the ankle joint while providing a normal

ligament tensioning [190]. Although there are few clinical studies available on these new total ankle

prostheses, the similarities between them (same basic 3-component design) indicate that an optimal

solution to replace the ankle joint is being approached [34].

2.4 Bone Remodeling

2.4.1 Bone Tissue

Bone tissue has very interesting structural properties mainly due to its composite structure. It has a

varied arrangement of material structures at many length scales which work together to perform

diverse mechanical, biological and chemical functions, such as body support, protection, assistance in

movement, mineral homeostasis (storage and release), blood cell production and triglyceride storage

[191, 192]. Regarding the mechanical functions, not only bone but also other skeletal tissues

(cartilage, ligaments, tendons, muscles) participate in the transmission of forces from one part of the

body to another while controlling strain, and this way providing the movement and the protection of

vital organs. Actually, bone essentially defines the global structural stiffness and strength of the

musculoskeletal system, whereas the transmission of loads between the bones is accomplished by

the other tissues. In particular, the mechanical properties of bone are a result of a compromise

between the stiffness (to get lower strain and more efficient kinematics) and ductility (to absorb

impacts) [193]. To achieve the best balance between these two parameters, the hierarchically

27

organized structure of bone has an irregular, but at the same time optimized, arrangement and

orientation of the components, making the material of bone multiphasic, heterogeneous and

anisotropic [191, 193]. Consequently, the mechanical properties of bone vary at different structural

levels. With this in mind, the bone structural organization can be described into the levels and

structures listed below [194-197].

Macrostructure: Cortical bone

Trabecular bone

Microstructure (from 10 to 500 µm): Haversian systems or osteons (Cortical Bone)

Single trabecula (Trabecular bone)

Sub-microstructure (1-10 µm): Lamellae

Nanostructure (from a few hundred nm to 1 µm): Collagen fibrils

Embedded mineral

Sub-nanostructure (below a few hundred nm): Mineral

Collagen

Proteoglycans and glycoproteins

Bone is a specialized connective tissue that contains an extracellular matrix (55% of crystallized

mineral salts; 30% of collagen fibers and 15% of water) surrounding widely separated cells [192].

Besides not included in the list above, there are four types of bone cells (10-100 µm), namely

osteogenic cells, osteoblasts, osteocytes, and osteoclasts. Osteogenic cells are unspecialized stem

cells, in particular, the only bone cells to undergone cell division and that can develop into osteoblasts,

which in turn are bone-building cells, responsible for the synthesis of extracellular bone matrix and for

initiate calcification. As osteoblasts surround themselves with extracellular matrix, they become

trapped in their secretions and become osteocytes, which are mature and the main cells in bone

responsible for maintaining its daily metabolism. On the other hand, osteoclasts release enzymes and

acids that digest the organic and inorganic components of the extracellular bone matrix, in a process

designated by bone resorption. The bone resorption is part of the normal development, maintenance,

and repair of bone [192], as it is explained further on.

As listed above, at the macroscopic level there are two types of bone: cortical (also called compact

or dense) and trabecular (also called cancellous or spongy). Overall, about 80% of the skeleton is

cortical bone and 20% is trabecular bone [192]. The main difference between them is the degree of

porosity or density [198, 199]. Cortical bone is heavy and strong. It has a very low porosity (5-10%),

which in turn is reflected by the measurement of the apparent density (mass/total volume). In the

human skeletal, the apparent density of cortical bone is about 1.8g/cm3 [200]. Regarding its structural

organization (Figure 2.10), cortical bone consists of repeating structural units called osteons or

Haversian systems, which in turn are composed of concentric lamellae (rings of calcified extracellular

matrix) arranged around a central canal known as Haversian canal. In these canals, there is a small

network of blood and lymphatic vessels and nerves which provide nutrients and oxygen to the

osteocytes and help in removing of wastes. Between the lamellae are small places called lacunae,

28

which contain osteocytes. From the lacunae there are tiny canaliculi radiating in all directions.

Moreover, osteons are aligned with the long axis of the bone and because of that, the shaft of a long

bone resists bending or fracturing even when a considerable force is applied from either extremity.

Therefore, cortical bone tends to be thicker in those bone parts where stresses are applied in relatively

few directions. These features make the cortical bone ideal to form the external shell of all bones and

the bulk of the diaphysis of long bones, providing protection, support and resisting stresses produced

by weight and movement. Furthermore, the blood and lymphatic vessels and nerves from the

periosteum (fibrous layer covering all bones) penetrate the cortical bone through transverse

perforating canals known as Volkmann’s canals, and this way, the vessels and nerves from the

periosteum connect with those of the medullary (marrow) cavity and Haversian canals [192].

Figure 2.10 Sections through the diaphysis of a long bone. From left to right: medullary cavity, trabecular bone,

cortical bone and periosteum. The repetitive structural unit of cortical bone is the osteon while of trabecular bone

is the trabecula (adapted from [192]).

Contrary to cortical bone, trabecular bone is very light, reducing the overall weight of the bone

tissue. It has a high porosity (50-95%) [193] and an apparent density that ranges from approximately

0.1 to 1.0 g/cm3 [200], providing elasticity, flexibility and resilience to the global bone structure [192].

This makes easier its adaptation to the mechanical solicitations, due to its capability of energy

absorption originated from impacts [192]. Regarding its structural organization, trabecular bone

consists of trabeculae (irregular latticework of thin columns of bone), which in turn are composed of

lamellae, as shown in Figure 2.10. The spaces between the trabeculae are filled with red bone marrow

(a connective tissue that produces the basic blood cells) or yellow bone marrow (adipose tissue) [192],

both of them containing several small bloods vessels that supply osteocytes with nutrients and oxygen

and help in removing of wastes. This way, trabecular bone provides support and protection to the

bone marrow. Lastly, it is important to mention that besides the irregular pattern of trabeculae,

29

trabecular bone is precisely oriented along lines of stresses, which helps bone resisting stresses and

transferring forces without breaking. Thus, contrary to cortical bone, trabecular bone is usually located

where bones are not heavily stressed or where stresses are applied from many directions. In

particular, it composes the epiphyses (the proximal and distal ends of long bones) and most of the

bone tissue of short, flat, and irregularly shaped bones [192].

2.4.2 Bone Remodeling Process

Contrary to the common view, bone is a dynamic tissue that constantly undergoes substantial

changes in structure, shape and composition according to the mechanical, hormonal and physiological

environment and in order to maintain stability and integrity (bone homeostasis). This process is called

bone turnover or bone remodeling, which is the ongoing replacement of damaged or old bone tissue

by new bone tissue throughout life. At any given time, about 5% of the total bone mass in the body is

being remodeled. In particular, the renewal rate for cortical bone is about 4% per year, and for

trabecular bone it is about 20% per year. Moreover, the strength of bone is related to the degree to

which it is stressed, and due to that, if newly formed bone is subjected to heavy loads, it will grow

thicker and become stronger than the old bone [192] – this is explained in more detail further on.

Bone remodeling involves bone formation that results from the action of osteoblasts by the

addition of minerals and collagen fibers to bone (formation of bone extracellular matrix) and bone

resorption that results from the action of osteoclasts by the removal of minerals and collagen fibers

from bone (destruction of bone extracellular matrix) [192]. Moreover, the remodeling process is not

performed individually by each cell, but by groups of cells functioning as organized units, which are

called basic multicellular units (BMUs) [201]. They operate on bone periosteum, endosteum,

trabecular surfaces and cortical bone, replacing old bone by new bone in discrete packets [193].

As stated before, mechanical loading has profound influences on bone remodeling. However, the

pathway by which mechanical forces are expressed in bone cells is currently one of the main studied

issues in bone mechanobiology [202]. The current concept is that the bone architecture is controlled

by a local regulatory mechanism. This idea originates from Roux [202, 203] in 1881, who proposed

that bone remodeling is a self-organizing process, which provides the capability of self-repair to bone.

Later, in 1892 Wolff [75] proposed that the morphology and structure of bone depend on applied

loads. In particular, what has become known as Wolff’s law is based on the observation that

trabeculae tend to align with principal stress directions. The trabecular alignment explains why bone is

anisotropic, i.e., the strength and stiffness of bone varies with direction. This way, trabecular bone is

stiffer and stronger in the direction of trabecular alignment. Due to this anisotropic structural property,

trabecular bone can support a great load without increasing mass and this way improving structural

efficiency. Moreover, as it is known, the lines of stress in a bone are not static but change during

growth, in response to repeated strenuous physical activity (e.g. weight training), due to fractures or

physical deformity, among others. Therefore, the structure and morphology of osteons and trabeculae

are not static but change over time in response to the physical demands placed on the skeleton [192].

Thereafter, these concepts were captured by Frost [202, 204, 205], and in his theory it was assumed

that local strains regulate bone mass. In particular, if strain levels exceed a mechanical threshold there

30

is bone formation. On the other hand, if strain levels are below a mechanical threshold there is bone

resorption. In spite of the fact that this was only a qualitative theory, it was the theoretical basis for

several mathematical and computational theories that were developed to study bone adaptation [206-

210]. Moreover, the development of new computational tools and mathematical concepts associated

with structural optimization have motivated many authors to propose new mathematical models of

bone remodeling that simulate more reliably the biomechanical behaviour of the bone, as is the case

of the model developed by Fernandes et al. [71] that is used in the present work.

In a homeostatic equilibrium, resorption and formation are balanced. However, in some conditions

of disuse, such as during immobility, space flight and long term bed rest there is more resorption than

formation and thus bone is lost [202, 211-213]. Another critical situation occurs when a prosthesis is

inserted into bone. In this case, there is a redistribution of stresses resulting from the phenomenon of

stress shielding (stress is mainly carried by the prosthesis and so the stress in bone decreases) [70].

This may cause an increase in resorption in comparison to formation, leading to a weakened bone,

more prone to the occurrence of fractures [71]. To conclude, understanding the bone remodeling

process with respect to the mechanical behaviour is a very important issue, particularly in the design

of new prostheses and helping to choose the right prosthesis for a given patient. Moreover, models

describing bone behaviour according to the load conditions are of particular value, allowing the

estimation of the amount of bone resorption related to a specific prosthesis design, as is the case of

the model used in the present work [71].

2.4.3 Bone Remodeling Model

The model used in the present work is based on a topology optimization criterion for 3-D linear

elastic bodies in contact. It is an extension of the model developed by Fernandes et al. in [71, 72], with

the equilibrium equation expressed for the contact problem being introduced by Folgado et al. [73, 74].

A porous material with a periodic microstructure is obtained by the repetition in space of a cubic cell

with rectangular holes (open cell) [73] instead of the cubic cell with a parallelepiped inclusion (closed

cell) initially developed in [69]. The equivalent elastic properties (effective elastic constants) of the

material are obtained using the method of homogenization [214]. Using a multiple loading criterion that

considers different load conditions at different temporal instants, the optimal topology is obtained by

minimizing the work of the applied forces, which in turn maximizes the overall stiffness of the structure.

This is influenced by an additional term, k, that is related to the biological cost of the organism in

maintaining bone homeostasis. This additional term is included in the cost function of the model since

bone formation requires a constant vascularity in that particular region and therefore higher energy is

spent by the body. This way, the model can take into account both mechanical and metabolic

parameters, which makes the model more reliable and closer to physiological condition of bone [71].

The necessary conditions for optimum are derived analytically using an augmented Lagrangian

formulation of the optimization problem. This methodology is similar to the one proposed by Rodrigues

[215] for shape optimization of mechanical components. Finally, the model is approximated

numerically through a suitable FE discretization [74]. The bone remodeling process follows the node-

31

based approach proposed by Jacobs et al. [216], which was implemented by Quental et al. [217] in the

present model.

The model used in the present work has been successful in predicting the optimal distribution of

bone density, enhancing our understanding about underlying biological mechanisms. Besides this, the

model also predicts bone adaptation after the implantation of a prosthesis, revealing the phenomenon

of stress-shielding and identifying the most affected regions. Therefore, it is a very useful tool to

understand both the biomechanics of bone and the influence of different prosthesis designs. In fact, it

has the potential to become a viable tool for pre-clinical testing of prostheses, taking into account

different geometries, constituent materials, etc. [202, 218, 219].

2.4.3.1 Material Model

Bone is modeled as a porous material with a periodic microstructure, which is obtained by the

repetition in space of a standard cell, whose dimensions are characterized by a1, a2, a3. This periodic

microstructure is illustrated in Figure 2.11.

Figure 2.11 Material model for bone (adapted from [73, 217]).

The relative density (µ) at each point of the bone depends on the dimensions of the holes/inclusion

(ai) and can be explicitly calculated. For the open cell, the relative density is calculated by µ = 1 – a1.a2

– a2.a3 – a1.a3 + 2 a1.a2.a3, for ai ϵ [0,1], i =1,2,3. This way, ai = 1 (for i =1,2,3) corresponds to the

absence of bone (µ = 0) whereas ai = 0 (for i =1,2,3) corresponds to cortical bone (µ = 1). In

conclusion, maximum relative density values correspond to cortical bone whereas intermediate values

correspond to trabecular bone. Also, the proposed formulation considers the bone as an orthotropic

material since it takes into account the orientation of each unit cell. Thus, at each point, bone is

characterized by both the parameters of the microstructure, a = (a1, a2, a3)T, that define the relative

density, and the orientation of the cell, using the Euler angles (θ) [73]. To summarize, the model used

in the present work calculates the relative density and orientation (the design variables) at each point

of the bone. These parameters are the solution of the topology optimization problem formulated for the

3-D linear elastic bodies in contact. However, it is important to mention that only the parameters of the

microstructure (ai) were taken into account since the objective is the analysis of bone density.

32

Then, the equivalent elastic properties of the bone are obtained by the method of homogenization.

The purpose of this method is to find for a porous and consequently heterogeneous material, a

homogeneous material with equivalent macroscopic properties without needing to represent each

individual microstructure [214]. This method considers that for each point in space there is a standard

cell that is periodically repeated and whose dimensions are much smaller than the global dimension of

the material/structure. For each point, the equivalent elastic properties reflect in average the behaviour

of the cell/microstructure, as well as the effect of the material heterogeneity. For a more detailed

description of this method see [214].

2.4.3.2 Mathematical Formulation

The bone-prosthesis group is considered as a structure, occupying a volume Ω=Ωb∪Ωp, with

fixed boundary Γu and subjected to a set of surface loads in the boundary Γf. The contact interface

is denoted by Γc (see Figure 2.11) [220]. Considering for each point the parameters a = (a1, a2, a3)T

as described above, and using a multiple load optimization criterion, the problem can be formulated

using the following objective function:

*∑ (∫

)

∫( ( ))

+ (1)

subjected to

(2)

∫ ( ) (

) ( )

∫

∫

( )

( )

(3)

{

( )

((

) )

| | |

| ,| | |

| ⇒

| | |

| ⇒

(4)

where NC corresponds to the number of load cases with the respectively load weight factors ,

satisfying ∑ .

In the previous problem statement, equations (3) and (4) correspond to the set of equilibrium

equations for two bodies in contact, in the form of a virtual displacement principle. In equation (3),

represents the homogenised material properties tensor (the superscript H denotes

homogenized), is the strain field, is the displacement field while corresponds to the virtual

displacement field, and and

are the contributions of normal and tangential contact stresses,

33

respectively. In equation (4), is the gap between the two bodies, is the friction coefficient and is

a positive parameter that guarantees the opposite direction between the displacement and force [220].

The objective function (equation (1)) is based on the balance of two terms: the first term

represents the weighted average of the work of applied forces whereas the second term characterizes

the metabolic cost of maintaining bone ( represents the metabolic cost per unit of bone volume). In

particular, the cost parameter does not depend on the location; it is constant throughout the bone

remodeling process [221]. This is a very important parameter since the resulting bone mass will

depend strongly on its value [71]. For higher values of , the resulting optimal structure presents a

lower bone mass, as expected, since the maintenance of bone homeostasis exhibits a higher cost to

the organism. Moreover, the bone remodeling process is complex, varying from individual to

individual, even in the presence of the same loading conditions. Therefore, the cost parameter

includes biological factors such as age, hormonal status, and disease, among others. As such,

determination of a precise value for a given individual is difficult [70, 218]. Finally, the parameter

also included in the second term of the objective function represents a corrective factor for the

preservation of the intermediate densities [222].

For the resolution of the optimization problem is used an augmented Lagrangian formulation,

described in detail in [223]. The law of bone remodeling results from the stationarity condition of the

Lagrangian formulation with respect to the parameters ai, and is expressed by:

∑(

(

) ( ))

(5)

These equations are solved by a suitable numerical procedure (presented as follows).

2.4.3.3 Computational Implementation

Briefly, the sequence of steps that are involved in the numerical process is presented next. Initially,

the homogenised elastic properties are computed for an initial solution ( ). To minimise

computational cost the properties are obtained for each new iteration by a polynomial

interpolation on the interval ai ϵ [0,1], i =1,2,3 [220]. Then, the displacement field ( ) and the virtual

displacement field ( ) are calculated by FEM using ABAQUS®, according to the loading conditions.

Based on the FE approximation, the optimality condition, i.e., the stationary condition present in

equation (5) is checked. When the stationarity condition is equal to zero the model is in equilibrium,

which means that the solution of the problem (the optimal distribution of bone density) was found. This

equilibrium condition reflects the balance between bone resorption and bone formation. In other

words, this corresponds to the stiffest structure of bone for given loading conditions [218, 220]. On the

other hand, if the stationarity condition is not satisfied (not equal to zero), improved values of the

design variables and Lagrange multipliers are computed, the contact conditions are updated and the

process restarts. This process only ends when the equation (5) is satisfied [74, 220]. The flow diagram

of the process is shown in Figure 2.12.

34

Figure 2.12 Computational model flow diagram (adapted from [220]).

In a more detailed description, the relative density (µ) is constant on each node, which means that

each node delimits a region of porous material with the same microstructure. The design variables that

characterize the distribution of material correspond to the parameters of the microstructure, a = (a1, a2,

a3)T at each node. By the discretization of the problem using the FEM it is possible to obtain the

optimality condition independently to each node [69]. The solution can then be obtained by means of

an iterative procedure based on a first order Lagrangian method [224]. The formulas to update the cell

design variables at the kth iteration are (for i = 1,2,3):

( ) ,

[( ) ( ) ] (

) ( ) [( ) (

) ]

( ) (

) [( ) ( ) ] (

) ( ) [( ) (

) ]

[( ) ( ) ] [( ) (

) ] ( ) (

)

(6)

where e ranges over all the finite nodes and represents the component of the descent direction

vector with respect to the parameters of the microstructure ( ), which is given by the negative of the

Lagrangian gradient with respect to the parameters :

∑(

(

) ( ))

(7)

The parameter defines the active upper and lower bound constraints in order to restrict the

changes in density to small transitions between iterations and thus allowing a smoother iterative

process. The real number d is the length of the step, which is constant and selected by the user at the

beginning of the process. In conclusion, in order to find a local minimum of the function, steps

proportional to the negative of the gradient are considered (method of steepest descent). For a more

detailed description of the model see [69-74].

35

Chapter 3

Computational Modeling

This chapter describes the steps involved in the development of the 3-D FE models of the AJC

before and after the simulation of a TAA using Agility™ and S.T.A.R.™ prostheses. In particular, the

steps followed to create the 3-D solid models of the intact AJC, including the bones (calcaneus, talus,

fibula and talus), cartilages and interosseous membrane are explained, as well as the fundamental

steps on geometric modeling of the Agility™ and S.T.A.R.™ prostheses. Then, it is explained how was

performed the assembly of the AJC with each prosthesis. Afterwards, the set of steps involved in FEA,

which includes the definition of materials properties, interaction between the parts, loading and

boundary conditions, and mesh generation, is explained. Lastly, as explained before, FEM is

integrated with the model of bone remodeling.

Once again, the geometric modeling (including the assembly of the parts) was performed by using

SolidWorks® and for the FEA it was used ABAQUS

®.

3.1 Geometric Modeling

3.1.1 Geometric Modeling of the Bones

The 3-D solid models of each intact bone, namely tibia, fibula, talus and calcaneus, were obtained

from the VAKHUM project [225]. In general, the 3-D bone reconstructive procedure follows a set of

steps, namely acquisition of medical CT images, segmentation of the CT images, processing of the

surface mesh for each bone and finally the solid construction of each bone. From the VAKHUM

project’s data base it was possible to get directly the 3-D solid models of the bones. Afterwards it was

also necessary to reprocess the surface mesh because of the “stair-step” effect presents in each

surface (which does not correspond to the natural surface curvature) and also because of the excess

of nodes and elements that give irrelevant information for the future computational processes,

increasing the computational cost. Thus, in order to obtain a smoother, more natural and simple

surface for each bone, the following sequence of filters was applied to each bone: smooth, decimation,

smooth. This was done using the open source software ParaView v3.12.0 [226]. The smoothing

technique corresponds to the adjustment of the nodes’ coordinates. The number of elements remains

the same, what changes is the position of the nodes relatively to each other, and thus the geometry of

the elements. By this procedure, the surface mesh presents a better visual appearance (see Figure

3.1). On the other hand, the decimation technique reduces the total number of nodes at each step,

until the reduction percentage of nodes established by the user is reached (in this case, 80%). As

result of the smoother surface mesh, the geometry of the resulting bone becomes more similar to the

original bone geometry. However, the surface mesh presents a worse visual appearance (see Figure

3.1). In order to improve the visual appearance of the surface mesh and to remove some decimation

36

artefacts, the smoothing technique was used again after the decimation. The Figure 3.1 shows the

result at each step of the sequence of filters applied to the particular case of talus (for exemplification

purposes).

Figure 3.1 Process of surface mesh adjustments for the talus: 1 – Talar surface mesh obtained from VAKHUM

project; 2 – Talar surface mesh after applying the smooth filter (300 iterations); 3 – Previous modified talar surface

mesh after applying decimate filter (80% reduction percentage); 4 – Previous modified talar surface mesh after

applying the smooth filter (300 iterations). Software used: ParaView.

Then, all the bones were imported to SolidWorks® and their assembly was performed (Figure 3.2).

Figure 3.2 At left, individual solid models of the fibula, calcaneus, talus, tibia. At right, the assembly of all the

bones. Software used: SolidWorks®.

37

Additionally, the cartilage of each bone was also incorporated in the model. This was done taking

into account the information provided by anatomical books [81, 227]. Firstly, a copy of each bone was

obtained. Then, one of each group of bones was scale by a specified factor (1.2-1.3). At that time,

there were two distinct groups of bones: the scaled/enlarged and the “normal sized”. Thus, to each

scaled/enlarged bone was subtracted the corresponding “normal-sized” bone and a thin shell of 1-2

mm was obtained for each bone. The thickness of the shell is consistent with the normal thickness of

the AJC (1.6 mm). However, as the cartilage only exists in some areas of the bone, the last step was

to define those areas and remove the shell from the areas where there is no cartilage. Moreover, it

was also included the interosseous membrane, a broad and thin (1.5 mm thickness) plane of fibrous

tissue that connects the tibia and fibula. Furthermore, it is important to notice that the object of study of

this work is the AJC, which, as it was already mentioned, is constituted by the ankle, subtalar and,

according to some authors, distal tibiofibular joints [79, 80]. Once again, the ankle joint is formed by

the inferior extremity of the fibula and tibia, and the dorsum of the talus [35]. Thus, there is no need to

have the superior extremity of the tibia and fibula in the model since the prosthesis is placed in the

inferior extremity of the tibia and in the dorsum of the talus, and so the changes in stress distribution

and bone density after a TAA occur mainly in the areas adjacent to the prosthesis. For that reason, a

cut was performed through the middle of the tibia and fibula. This was also done in order to reduce the

computational cost by having a lower number of FEs for a particular level of discretization. To

summarize, the model of the AJC, as presented in Figure 3.3, consists of the inferior extremities of

tibia and fibula, the entire bones, talus and calcaneus, the interosseous membrane and the cartilage of

each bony segment/bone. This model is then imported to the FEA software, ABAQUS®.

Figure 3.3 The model of the AJC is constituted by the inferior extremities of tibia and fibula, the entire bones, talus

and calcaneus, the interosseous membrane and the cartilage of each bony segment/bone. Software used:

SolidWorks®.

38

3.1.2 Geometric Modeling of the Prostheses

Subsequently, the solid models of the Agility™ and S.T.A.R.™ prostheses were developed based

on informative documents provided by the DePuy Orthopaedics, Inc. [181] and Small Bone

Innovations, Inc. [184] companies, respectively. However, it is important to mention that there is much

more available information concerning the S.T.A.R.™ prosthesis than the Agility™ prosthesis. In

particular, there are not available the components’ sizes of the Agility™ prosthesis, and so their

geometric modeling was done taking into account the descriptions and images included in the only two

informative documents available in the literature [181, 182]. Furthermore, it is also important to

mention that the final size of each prosthetic component for both prostheses was chosen during the

assembly of the models/virtual surgical procedure (Section 3.1.3) in order to provide an optimal

adjustment between the prosthetic components and the respective bones (as it is done during the

surgical procedure). In fact, there is a wide range of sizes available for the components of both

prostheses [20, 184], despite not being available the exact sizes of the components of Agility™.

3.1.2.1 Agility™

As described before, the Agility™ prosthesis is constituted by three components: the tibial, fixed-

bearing and talar (see above Figure 2.8). The TAA using this prosthesis requires an arthrodesis of the

distal tibiofibular joint using one or two (more common) screws through the distal fibula into the distal

tibia and optionally a plate can be placed on the fibula at the end of procedure. Given its importance,

the plate was considered in this work. In order to obtain the geometric model of the Agility™

prosthesis, firstly the geometric modeling of each component was done and once all the components

were modeled, it was just needed to assemble them. The results are presented further on.

The plate and screws used in arthrodesis – There were modeled two Ti screws of 2.9 mm

diameter, one longer than the other, and a 5 hole, 1/3 semi-tubular Ti plate [181]. The plate showing

the 5 holes and the final assembly of the plate with the screws are both present in Figure 3.4.

Figure 3.4 The 5 hole, 1/3 semi-tubular Ti plate (at left) and the same plate with the two Ti screws of 2.9 mm

diameter (at right). Software used: SolidWorks®.

39

Tibial component – This component is made of Ti alloy with sintered Ti beads covering the places

where the component is in touch with the bone to allow press-fit fixation, instead of the use of cement

[22, 181]. As can be observed below in Figure 3.6, the tibial component has a rectangular shape. For

a more detailed analysis of the geometric model of this component see Appendix A.

Fixed-bearing – This component is made of UHMWPE. It has a distal concave surface, and as can

be observed below in Figure 3.6, it has a proximal flat surface that is fixed to the tibial component. For


Talar component – This component is made of Co-Cr alloy with sintered Co-Cr beads covering the

places where the component is in touch with the bone to allow press-fit fixation, instead of the use of

cement [22, 181]. Also, it sits perpendicular to the articular surface of the tibial component [181].

Regarding the old and new talar component designs, the old design is slightly wider anteriorly than

posteriorly while the new design is uniformly wider and it has a larger contact area (see Figure 2.8).

Finally, the geometric models of the old and new talar component designs are shown in Figure 3.5.

For a more detailed analysis of the geometric models of these two components see Appendix A.

Figure 3.5 The old talar component design (at left) and the new talar component design (at right). Software used:

SolidWorks®.

Assembly of the prosthetic components: Agility™ – The results presented in Figures 3.6 and 3.7

are only for the case of the new talar component design (for exemplification purposes), since the

results when using the old talar component design were similar. For a more detailed analysis of the

geometric model of the Agility™ prosthesis for both talar component designs see Appendix A.

Figure 3.6 Assembly of all the prosthetic components of Agility™ prosthesis. Software used: SolidWorks®.

40

Lastly, a very important aspect in geometric modeling of this type of prosthesis is to ensure the

congruency in the sagittal plane between the talar and polyethylene components. This feature was

strictly respected, as can be observed in Figure 3.7.

Figure 3.7 Congruency in the sagittal plane between the talar component and fixed-bearing of Agility™

prosthesis. Software used: SolidWorks®.

3.1.2.2 S.T.A.R.™

As described before, the S.T.A.R.™ prosthesis is constituted by three components: the tibial,

mobile-bearing and talar (see Figure 2.9). Like it was done in the case of Agility™ prosthesis, in order

to obtain the geometric model of the S.T.A.R.™ prosthesis, firstly the geometric modeling of each

component was done and once all the components were modeled it was just needed to assemble

them. The results are presented further on.

Tibial component – This component is made of Co-Cr-Mo with Ti plasma spray coating on the places

where the component is in touch with the bone to allow press-fit fixation, instead of the use of cement

[184]. As can be observed below in Figure 3.8, the tibial component has a distal flat surface and a

proximal surface with two raised cylindrical barrels oriented in the anterior/posterior direction, which

serve to fix the prosthesis to bone at the distal tibia. When viewed from the top, the tibial component

has a trapezoidal shape with rounded corners (see Appendix A). This component is available in five

sizes with varying widths and lengths: X-Small (30 mm x 30 mm), Small (32 mm x 30 mm), Medium

(32.5 mm x 35 mm), Large (33 mm x 40 mm), and X-Large (33.5 mm x 45 mm), but it is always 2.5

mm thick [184]. In this work, the Medium size (32.5 mm x 35 mm) was chosen. For a more detailed

analysis of the geometric model of this component see Appendix A.

Mobile-bearing – This component is made of UHMWPE. As can be observed below in Figure 3.8, it

has a proximal flat surface and a distal concave surface. Moreover, the height of the mobile-bearing

varies from 6 mm to 10 mm and there are also available revision mobile-bearings in sizes of 11mm, 12

mm, 13 mm, and 14 mm. In this work, it was chosen the height of 9 mm. Despite not visible in Figure

3.8, the distal surface has a central radial groove oriented in the anterior-posterior direction [184]. For


Talar component – Like the tibial component, this component is made of Co-Cr-Mo with Ti plasma

spray coating on the places where the component is in touch with the bone to allow press-fit fixation,

instead of the use of cement [184]. The talar component has near anatomical shape, covering

41

completely the talar dome and thus minimizing the amount of bone that must be removed. Despite not

visible below in Figure 3.8, it has a longitudinal ridge that is congruent with a groove in the distal

surface of mobile-bearing, whose purpose is to constrain the medial/lateral motion of the mobile-

bearing. This component is also available in five sizes with varying widths and lengths: XX-Small (28

mm x 29 mm), X-Small (30 mm x 31 mm), Small (34 mm x 35 mm), Medium (36 mm x 35 mm), and

Large (38 mm x 35 mm), and in both left and right-sided configurations [184]. In this work, the XX-

Small size (28 mm x 29 mm) right-sided configuration was chosen. For a more detailed analysis of the

geometric model of this component see Appendix A.

Assembly of the prosthetic components: S.T.A.R.™ – The result is presented in Figure 3.8. For a

more detailed analysis of the geometric model of the S.T.A.R.™ prosthesis see Appendix A..

Figure 3.8 Assembly of all the prosthetic components of S.T.A.R.™ prosthesis. Software used: SolidWorks®.

Lastly, as stated before, a very important aspect in geometric modeling of this type of prosthesis is

to ensure the congruency in the sagittal plane between the talar and polyethylene components. This

feature was strictly respected, as can be observed in Figure 3.9.

Figure 3.9 Congruency in the sagittal plane between the talar component and mobile-bearing of S.T.A.R.™


3.1.3 Assembly of the Models – Virtual Surgical Procedure

When a TAA is performed, the ankle joint’s articular surfaces are resected and then replaced with

especially designed prosthetic components. Thus, the intention at this stage was to create the models

in which the ankle joint’s articular surfaces are substituted by prosthetic components, which may be

termed by virtual surgical procedure. This procedure was performed for Agility™ and S.T.A.R.™

42

prostheses, and based on surgical technique manuals provided by the DePuy Orthopaedics, Inc. [182]

and Small Bone Innovations, Inc. [228] companies, respectively. Moreover, this procedure was also

performed according to what was advised by Dr. Nuno Ramiro (experienced orthopaedic surgeon) and

Prof. Dr. Jacinto Monteiro (experienced orthopaedic surgeon, external supervisor of this work), both of

whom clinical collaborators from Faculty of Medicine of the University of Lisbon.

In clinical protocol, after the foot and ankle joint have been correctly positioned at the neutral

position, the surgical procedure usually starts with an anterior incision through the skin (anterior

approach to the ankle). Then, the nerves, tendons and blood vessels are protected and moved to the

side. After that, another incision is made into the joint capsule that encloses the ankle joint. At this

level, the surgeon can look at the articular surfaces of the joint while preparing the bone to be resected

with precise instrumentation. It is important to notice that each prosthesis has a unique

instrumentation system that supports accurate and reproducible tibial, fibular (in the case of Agility™

prosthesis) and talar cuts. In fact, the bones need to be shaped so that the prosthetic components

could be inserted and fit in place. Thus the next step of the procedure is to cut the bones. After that, it

is the moment to insert the prosthetic components and make sure that all components are well

positioned and fit properly. In the case of Agility™ prosthesis, the ankle joint is implanted under

distraction (separation of the bones), and so an external ankle joint distractor is required, which

increases the difficulty of the procedure [182]. Also, as stated before, it is required an arthrodesis of

the distal tibiofibular joint to make sure that the Agility™ prosthesis fits tightly. To create a fusion

between the fibula and the tibia, two screws are inserted through the bones just above the artificial

joint, and optionally a plate is placed on the fibula at the end of procedure. Also, bone graft is taken

from the bone that was removed from the ankle joint and is placed between the tibia and fibula to

create the fusion. When all the components are well-positioned, the joint capsule is sutured back

together, as well as the skin [229, 230].

To conclude, the surgical procedure is specific for each prosthesis. The surgical techniques for

implantation of Agility™ and S.T.A.R.™ prostheses are illustrated in Appendix B. To a full description

of each procedure see, respectively, [182, 228]. It is important to notice that TAA is a very difficult

surgical procedure, and so the creation of the models in which the ankle joint’s articular surfaces are

substituted by prosthetic components is also a very difficult modeling procedure. As result, the final

models show some modeling limitations, but are still very reliable, as it is possible to confirm below.

Finally, the results of the virtual surgical procedure when using Agility™ and S.T.A.R.™ prostheses

are presented further on.

3.1.3.1 Agility™

In order to assemble the prosthetic components previously modeled into the intact bone, it was

necessary to make some changes to the bone. Thus, the bone was accurately cut into a shape that

matches the corresponding surfaces of tibial and talar components (Figure 3.10-A). According to [20,

182], 1/3 and 1/2 of the lateral and medial malleoli, respectively, are resected. The last stage was to

incorporate the tibial and talar components into the tibia and talus, respectively, with the accurate

component alignment concern (Figures 3.10-B and 3.10-C). As can be confirmed by Figure 3.10-B,

43

the medial and lateral walls of the tibial component sit flush against the cut surface of the medial and

lateral malleoli, bridging the tibial lateral surface and the fibula medial surface, as it is described in

surgical technique manual [181]. Regarding the talar component, as can be confirmed by Figure 3.10-

C, it was aligned perpendicular to the axis of the tibia and centered medial-lateral in the flat surface of

the talus. It is important to ensure that the posterior edge of the talar component lies on the posterior

surface of the talus, and although not visible in Figure 3.10-C, this aspect was respected in this work.

Figure 3.10 The most important steps during virtual surgical procedure using Agility™ prosthesis: A – The model

after the bone resection; B – The model after the insertion of the tibial component and fixed-bearing; C – The

model after the insertion of the three components of the Agility™ prosthesis. Software used: SolidWorks®.

As stated before, using the Agility™ prosthesis it is required an arthrodesis of the distal tibiofibular

joint using one or two screws through the distal fibula into the distal tibia and optionally a plate can be

placed on the fibula at the end of the procedure. As described above, two screws and a plate were

modeled in the present work. Moreover, before inserting the screws and the plate, as it was necessary

to remove part of interosseous membrane, bone graft from the excised tibial and talar articular

surfaces was used to fill the space created. In a real surgical procedure it is preferred a single, large,

well-contoured cancellous block to perfectly fit into the space than the use of multiple cancellous chips

[182], and so a well-contoured cancellous block was created for the virtual surgical procedure. The

model after both the removal of part of the interosseous membrane and the insertion of the bone graft

is presented in Figure 3.11-A. Then, the screws and the plate were inserted. In particular, the first

screw was placed 1 cm above the top of the tibial component, and the second screw 1 cm above the

first screw. Also, the distal end of the plate was placed at the level of the tibial component, according

to [182]. Finally, the final model with the bones, cartilages, interosseous membrane, Agility™

44

prosthesis, bone graft, two screws and fibular plate is presented in Figures 3.11-B and 3.11-C. During

this work, this model is called TAA+Agility™.

Figure 3.11 The most important steps during virtual surgical procedure using Agility™ prosthesis: A – The model

after the removal of part of the interosseous membrane and the insertion of the bone graft; B – The final model

with the bones, cartilages, interosseous membrane, Agility™ prosthesis, bone graft, two screws and fibular plate;

C – Magnification of the area of interest. Software used: SolidWorks®.

3.1.3.2 S.T.A.R.™

Once again, in order to assemble the prosthetic components previously modeled into the intact

bone, it was necessary to make some changes to the bone. Thus, as it was done for Agility™

prosthesis, the bone was accurately cut into a shape that matches the corresponding surfaces of tibial

and talar components (Figure 3.12-A). According to [228], a maximum of 5 and 4 mm of bone should

be removed from the distal tibia and talar dome, respectively. However, in this work, it was necessary

to resect 7 mm of bone from both the talar and distal tibial bones. The last stage was to incorporate

the talar and tibial components into the tibia and talus, respectively, with the accurate component

alignment concern (Figures 3.12-B and 3.12-C). Then, the mobile-bearing was inserted between the

talar and tibial components (Figure 3.13-A). Finally, the final model with the bones, cartilages,

interosseous membrane and S.T.A.R.™ prosthesis is presented in Figures 3.13-A and 3.13-B. During

this work, this model is called TAA+S.T.A.R.™.

45

Figure 3.12 The most important steps during virtual surgical procedure using S.T.A.R.™ prosthesis: A – The

model after the bone resection; B – The model after the insertion of the talar component; C – The model after the

insertion of the talar and tibial components. Software used: SolidWorks®.

Figure 3.13 The most important steps during virtual surgical procedure using S.T.A.R.™ prosthesis: A – The

model after the insertion of the three components of the S.T.A.R.™ prosthesis, which corresponds to the final

model with the bones, cartilages, interosseous membrane and S.T.A.R.™ prosthesis; B – Magnification of the

area of interest. Software used: SolidWorks®.

46

3.2 FE Modeling

3.2.1 Importation of the Models and Insertion of the Ligaments

The three models under study (intact, TAA+Agility™ and TAA+S.T.A.R.™) were imported from the

SolidWorks® to ABAQUS

® and then eight major ligaments of the AJC were included in each model,

namely, three LCL (ATaFi, PTaFi and CaFi), three MCL (DATiTa, DPTiTa and TiCa) and two

ligaments of the SLC (ATiFi and PTiFi), as shown in Figure 3.14. This choice was based on the

studies of Reggiani et al. [54] and Corazza et al. [231], which in turn took into account the study of

Pankovich and Shivaram [97]. The insertion of these ligaments, in particularly the CaFi and TiCa

ligaments, was a very important step because, as stated before, these ligaments have a particular and

important role in guiding passive motion, while other ligaments limit but do not guide motion [127].

Figure 3.14 Representation of the eight ligaments included in the model: 1 – DATiTa; 2 – TiCa; 3 – DPTiTa; 4 –

CaFi; 5 – PTaFi; 6 – PTiFi; 7 – ATaFi; 8 – ATiFi. Software used: ABAQUS®.

Firstly, the attachment surfaces of the ligaments on the bones were carefully selected. The idea

was to keep the same area for each attachment surface in the three models under study (intact,

TAA+Agility™ and TAA+S.T.A.R.™). In [88] was reported that among ligaments some have bigger

attachment surfaces than others, and so some attachment surfaces have a greater area than others.

All this was done taking into account the anatomical descriptions and images provided in [88], since it

was not possible to find the 3-D coordinates of the attachment points. Then, to each attachment

surface was associated a reference point (RP) (Coupling approach). Finally, each ligament was

defined by connecting the two corresponding RPs. However, it is important to notice that due to the

existing “coupling” between the attachment surface and the corresponding RP, each ligament is

actually associated to the attachment surfaces and this way the forces are uniformly distributed to

47

these surfaces, acting on them as naturally happens in a physiological condition and also avoiding

stress concentration artefacts.

It is important to state that the length of each ligament was strictly maintained for the three

positions under study (neutral, dorsiflexion and plantarflexion; explained in Section 3.2.4). This is

naturally a limitation of this work, because, for instance, in dorsiflexion the PTaFi and CaFi ligaments

are tensed and the ATaFi ligament is relaxed whereas in plantarflexion, the ATaFi ligament is tensed,

and the CaFi and PTaFi ligaments are relaxed [98, 232, 233]. Thus, the length of some ligaments in

neutral, dorsiflexion and plantarflexion positions may not be the same. However, due to insufficient

information, the better solution was to maintain the length of each ligament in all positions. Also, as

described above, some ligaments are under pre-tension or laxity conditions, but these assumptions

were also not considered in this work. To conclude, each of the eight ligaments was modeled as a

tension-only truss element. As the ligaments are assumed to sustain tensile force only, the “no

compression” option in ABAQUS® was used to modify the elastic behaviour of the material so that

compressive stress cannot be generated.

3.2.2 Material Properties

The biological tissues, in particular the bone, have a combination of properties that are difficult to

reproduce in FE models. The material of bone is viscoelastic, heterogeneous (in terms of mechanical

resistance, stiffness and density) and anisotropic, which means that bone is directionally dependent

[191, 234]. Except for the bone, all other tissues were idealized as linearly elastic, homogeneous and

isotropic. Initially, for the stress analysis, the bone was considered linearly elastic, heterogeneous

(divided in cortical and trabecular bone) and isotropic. In particular, the Young’s modulus and

Poisson’s ratio for the cortical bone were assigned as 19 GPa and 0.3, respectively, according to [235,

236], while for the trabecular bone the values were 500 MPa and 0.3, respectively, according to [237].

The cortical bone was defined as being the external surface of each bone, i.e., only the elements

present at the external surface of each bone were defined with a Young’s modulus of 19 GPa. This is

a limitation of this work because the cortical bone has a specific and different thickness according to

each section of the bone. For instance, the thickness of the cortical bone is greater in the diaphysis

than in the metaphysis/epiphysis. However, as explained before, this was not considered in this work.

Afterwards, for the bone remodeling analysis, the bone was modeled as a cellular material with an

orthotropic microstructure, in which the relative density can vary along the domain and is given by the

material optimization process, i.e., it results from the solution of the optimization problem. The elastic

equivalent properties for bone are computed using the homogenization method (for more details about

this method see [214]). The Young’s modulus for dense cortical bone was established as 19 GPa,

which means that 19 GPa is the maximum that may exist, for µ = 1 (maximum relative density). All the

other intermediate values of the relative density correspond to other intermediate values of the

Young’s modulus. In this case, the elastic properties are functions of relative density. Moreover, as

initial condition, all the nodes corresponding to the elements present in the external surface of the

talus and tibia – bones subjected to bone remodeling analysis – were assigned with a minimum

relative density of 0.75 and a maximum of 0.99, starting the process of bone remodeling with a relative

48

density of 0.9. For the remaining nodes, a relative density of 0.3 was considered at the initial stage of

the simulation, ranging from a minimum of 0.05 and a maximum of 0.99.

The Young’s modulus of the cartilage, 1 MPa, was selected from [238] and was assigned with a

Poisson’s ratio of 0.4 for its nearly incompressible nature. As far as the interosseous membrane and

bone graft are concerned, their material properties were not found in the literature. For the

interosseous membrane, the values of Young’s modulus and Poisson’s ratio were assumed to be

similar to those corresponding to the ligament with smaller stiffness (DPTiTa), and so 99.5 MPa and

0.49, respectively, were assigned to interosseous membrane. Regarding the bone graft, it was

assumed to be similar but weaker than trabecular bone (200 MPa). To summarize, Table 3.1 presents

the material properties defined in the three models (intact, TAA+Agility™ and TAA+S.T.A.R.™).

Table 3.1 Material properties defined in the three models under study (intact, TAA+Agility™ and TAA+S.T.A.R™).

Component Material Young’s modulus, E

(MPa)

Poisson’s ratio, ν

Cortical Bone [235, 236] 19000 0.3

Trabecular Bone [237] 500 0.3

Cartilage [238] 1 0.4

Interosseous Membrane 99.5* 0.49*

Bone Graft 200** 0.3**

Plate and Screws (Agility™) Ti [50] 110000 0.33

Tibial component (Agility™) Ti [50] 110000 0.33

Polyethylene component (Agility™) UHMWPE [239] 557 0.46

Talar component (Agility™) Co-Cr [50] 193000 0.29

Tibial component (S.T.A.R.™) Co-Cr-Mo [68] 210000 0.3

Polyethylene component (S.T.A.R.™) UHMWPE [239] 557 0.46

Talar component (S.T.A.R.™) Co-Cr-Mo [68] 210000 0.3

* Not found in literature, it was assumed to be similar to the ligament with smaller stiffness (DPTiTa)

** Not found in literature, it was assumed to be similar but weaker than trabecular bone

The material properties of most ligaments were chosen from the data provided in the study of

Corazza et al. [231], which in turn was taken from other studies [240, 241]. Regarding the material

properties of PTiFi and ATiFi ligaments, they were taken from [242, 243], respectively. To summarize,

Table 3.2 presents the material properties of the ligaments used in this work. All ligaments were

assumed to be incompressible (ν = 0.49).

49

Table 3.2 Material properties of the ligaments used in the present work.

Ligament Length (mm) Elastic Modulus, E

(MPa)

Poisson’s ratio, ν Cross-sectional area

(mm2)

ATaFi [231] 10.5 255.5 0.49 12.9

PTaFi [231] 15.3 216.5 0.49 21.9

CaFi [231] 17.5 512 0.49 9.7

DATiTa [231] 5.1 184.5 0.49 13.5

DPTiTa [231] 5.1 99.5 0.49 22.6

TiCa [231] 23.1* 512 0.49 9.7

ATiFi [243] 15.2 160 0.49 12.6

PTiFi [242] 13.8 160 0.49 12.6

* Not found in literature; it was defined by comparison with the data of other ligaments and taking into account [244]

3.2.3 Interaction between the Parts

To simulate the surface interactions among the cartilages, the automated surface-to-surface

contact algorithm provided by ABAQUS® was used. Due to the lubricating nature of these articular

surfaces, the contact behaviour between them can be considered almost frictionless [58]. Taking this

into account and the information from [245], the coefficient of friction of 0.01 was used. Moreover, the

surface interactions between the cartilage and bone were naturally considered rigidly bonded (tied), as

well as the interactions between the interosseous membrane and bones (fibula and tibia). Assuming a

successful fixation of both prostheses (Agility™ and S.T.A.R.™) on bone, the surface interactions

between both tibial and talar components and bone was considered rigidly bonded (tied). Regarding

the surface interactions among the prosthetic components, it was defined again a surface-to-surface

contact behaviour, and the friction coefficient between the talar and polyethylene components (for both

prostheses) and between the tibial and polyethylene components (only for S.T.A.R.™ prosthesis) was

defined to be 0.04, according to [54], which in turn took the data from [246].

For the contact modeling the “small-sliding” option available in ABAQUS® was selected. This way,

the contacting surfaces can undergo only relatively small sliding relative to each other. Also, as the

contacting surfaces are very close, the “adjust only to remove overclosure” option was used in order to

prevent any overclosure that could occur. Moreover, it was assigned a contact control with the

“automatic stabilization” option selected and the frictional behaviour was modeled with the penalty

friction formulation with the specified friction coefficients.

As stated before, it is necessary to perform an arthrodesis during the TAA with the Agility™

prosthesis, and so, in this particular case, bone graft, two screws and a plate were included in the

TAA+Agility™ model. The surface interactions between the bone graft and bones (fibula and tibia)

were considered rigidly bonded (tied), as well as the interactions “screw-bone” and “plate-bone”. The

two screws were also rigidly bonded to the plate.

3.2.4 Loading and Boundary Conditions

The applied loading conditions were based on the data provided by Reggiani et al. [54], which in

turn was based on force predictions reported by Seireg and Arvikar [156] and Procter and Paul [37].

50

As mentioned before, Reggiani et al. [54] used the compressive (axial) and anterior-posterior

tangential forces from the former work, and the internal-external torque and plantar-dorsiflexion

rotation from the later. Also, they found that the force predictions reported by Seireg and Arkvikar [156]

may be overestimated by a factor of 2.25 and so these forces were proportionally scaled. However, as

the study of Reggiani et al. [54] was a 2-D analysis and the present study is a 3-D analysis, it was

necessary to find the missing components. The third component of the concentrated force was taken

from the study of Seireg and Arvikar [156] and it was proportionally scaled. Nevertheless, it was

impossible to find the other components of the moment reported by Procter and Paul [37], and so only

one component was applied. This is a limitation of the work, but it is believed that the other

components would be much smaller than the one included. To summarize, the loading conditions

applied in the three models under study (intact, TAA+Agility™ and TAA+S.T.A.R.™) correspond to the

neutral, dorsiflexion and plantarflexion positions of the ankle joint and are presented in Table 3.3.

These three selected load cases correspond to discrete times of the stance phase of gait.

Table 3.3 The concentrated forces proportionally scaled and the moment/internal-external torque used as loading

conditions in the present work – Reference: coordinate system used in the study of Seireg and Arvikar [156].

Position Dorsiflexion (-10º) Neutral (0º) Plantarflexion (+15º)

Concentrated Force (N)

Z-component (axial force) 1600 600 400

Y-component (interior-exterior force) 185 -150 -100

X-component (anterior-posterior

force)

-185 -280 -245

Moment (N)

Y-component (interior-exterior torque) 6.2 2.85 -0.1

However, these forces represent the contact forces at the ankle joint, and so for the present

models it was necessary to find the forces that would produce those contact forces at the ankle joint.

Also, the literature review revealed no conclusive results about the percentage of weight-bearing

capacity of the fibula. So, in order to know the exact load carried by the fibula and tibia that would

produce the contact forces at the ankle joint described above, for each position, the FEM was used. At

first, the proximal ends of the fibula and tibia were separately constrained, as shown in Figure 3.15 (at

left). Then, the talus and calcaneus were omitted from the calculations and the reversed forces

proportionally scaled (and for each of the three positions) were applied on the tibia. It was defined a

new coordinate system in order to apply the forces at the ankle joint in the same/similar position that

they were determined in the study of Seireg and Arvikar [156]. Then, the forces were applied in a RP

that coincides to the center of the new coordinate system. As result, the reaction forces from the

constrained distal ends of the fibula and tibia were used as loading conditions, for each of the three

positions (see Tables 3.4 and 3.5). To simplify, a RP was associated to the end of each bone (fibula

and tibia) and thus the reaction forces were easily accessed later on.

51

Figure 3.15 At left, model used for determination of the loading conditions for the three models under study

(intact, TAA+Agility™ and TAA+S.T.A.R.™) at the neutral, dorsiflexion and plantarflexion positions. At right, for

exemplification purposes, the intact model of the AJC at the neutral position with the applied loading and

boundary conditions. Software used: ABAQUS®.

Table 3.4 Forces applied to the fibula in the three models under study (intact, TAA+Agility™ and TAA+S.T.A.R.™)

at the neutral, dorsiflexion and plantarflexion positions – Reference: global coordinate system of ABAQUS®.



Z-component (axial force) 385.137 -741.908 -544.748

Y-component (anterior-posterior force) 121.068 -167.375 -128.450

X-component (interior-exterior force) 147.731 -173.072 -129.061

Moment (N)

Z-component (axial torque) -1265.88 -2125.42 -1856.35

Y-component (anterior-posterior

torque)

12306.7 6515.09 6525.27

X-component (interior-exterior torque) 9463.67 11171.0 10137.2

52

Table 3.5 Forces applied to the tibia in the three models under study (intact, TAA+Agility™ and TAA+S.T.A.R.™)

at the neutral, dorsiflexion and plantarflexion positions – Reference: global coordinate system of ABAQUS®.



Z-component (axial force) 1189.77 1343.27 943.960

Y-component (anterior-posterior force) -182.079 -144.116 -130.809

X-component (interior-exterior force) 232.260 220.303 187.705

Moment (N)

Z-component (axial torque) -1531.41 -2172.71 -1902.34

Y-component (anterior-posterior

torque)

27603.6 10103.8 11022.9

X-component (interior-exterior torque) 15860.7 31151.1 26802.6

Regarding the boundary conditions, the calcaneus was fixed in three parts. The elements that

constitute these three surfaces were assigned with the “encastre” boundary condition, which means

that those elements are completed fixed. The selection of these three surfaces was based on the work

of Giddings et al. [154]. This work was developed to examine the loading on the calcaneus during

walking and running throughout the gait cycle. In this work they included a simplified free-body

diagram of the calcaneus showing the ligament, tendon and joint forces acting on it at 70% of the

stance phase during walking, as shown in Figure 3.16. The three surfaces assigned with the

“encastre” boundary condition are represented by red ellipses in Figure 3.16. The plantar fascia and

the plantar ligaments were grouped in just one surface to simplify the model.

Figure 3.16 A simplified free-body diagram of the forces acting on calcaneus at 70% of the stance phase during

walking. Vectors are shown slightly offset from the location of the force application, which in turn is indicated by a

dot. The red ellipses represent the surfaces assigned with the “encastre” boundary condition (adapter from [154]).

Finally, for exemplification purposes, the intact model of the AJC at the neutral position is

presented above in Figure 3.15 (at right), as well as the applied loading and boundary conditions.

53

To conclude, three different load cases (according to plantarflexion, neutral and dorsiflexion

positions) were considered for each model (intact, TAA+Agility™ and TAA+S.T.A.R.™).

Regarding the bone remodeling analysis, the three load cases were included in the same

computer simulation (considering the three positions under study at once), using the multiple load

criteria with equal weights (1/3). These selected load cases correspond to discrete times of the stance

phase of gait and are considered representative of the range of loads developed during the stance

phase. However, it is important to mention that the activity included in this work (walking) does not

represent the complex spectrum of physiological movements of daily life. Nevertheless, everyone

agrees that walking corresponds to the most frequent activity of daily life. Hence, it is assumed that

these three loading conditions simulate the daily loading history of the tibia and talus and so are

valuable for the bone remodeling analysis. Also, there are not enough computational resources to

consider the entire range of loading data associated to the stance phase of gait. Moreover, there is no

information in the literature about the muscular forces and so they were not included in the present

work.

For the stress analysis, each of the three load cases was considered individually for each model

(intact, TAA+Agility™ and TAA+S.T.A.R.™) according to the position.

Moreover, for the stress analysis, another two loading conditions were included in this work. In one

case, an axial force of 600 N was applied to the three positions while in other case the axial forces of

1600 N, 600 N and 400 N were applied to dorsiflexion, neutral and plantarflexion positions,

respectively. Only an axial force was included each time aiming to compare the results with the

available studies in the literature that included the same loading condition. In this case, the axial force

was applied in the proximal ends of the fibula and tibia as a single surface, i.e., an RP was

constrained to both surfaces (Coupling approach) and then the axial force was applied in the RP. The

coupling option provided by ABAQUS® has the purpose of coupling the motion of a group of nodes on

a surface to the motion of a RP, and this way, as it was already described before, the forces are

uniformly distributed to the selected surfaces, acting on them as naturally happens in a physiological

condition and also avoiding stress concentration artefacts. Thus, every time a force or an “encastre”

boundary condition was applied, it was always applied in a RP, and this RP was associated to a

specific surface. The coupling approach is a good way to mimic the physiological condition because in

reality the forces are not applied only in single points but rather in a specific area.

In order to know which loading condition was considered in each analysis, this information is given

at the beginning, before presenting the results of each analysis (Chapter 4 – Results and Discussion).

3.2.5 Mesh Generation

The wide range of elements in ABAQUS® provides flexibility in modeling different geometries and

structures. Among all the elements, the hexahedral are the recommended ones due to the fact that

these elements provide solution with a higher accuracy at less cost especially with analysis

considering geometrically complex structures, like the present work [247]. However, due to the

limitation for the automatic-meshing algorithms in ABAQUS® to produce hexahedral meshes, 4-noded

tetrahedral elements were used for meshing all the constituent parts of the three models under study.

54

Moreover, the accuracy of the results derived from the FEA depends not only on the type of elements

but also on the mesh refinement, which is controlled by indicating the element size [248, 249]. Taking

this into consideration, an adequate mesh refinement was selected without compromising too much

the computational cost. Even so, the resulting FE meshes for the three models under study have a

good anatomical detail, as shown in Figure 3.17 (for a more detailed analysis see Appendix C). The

number of elements and nodes for each FE meshed model under study is also shown in Appendix C.

Finally, it was only after the mesh generation that the plantarflexion, dorsiflexion and neutral

positions were considered to each model (intact, TAA+Agility™ and TAA+S.T.A.R.™) – also shown in

Appendix C. This was done at the end in order to get the same mesh in the three positions for each

model, which will be helpful in the bone remodeling analysis. The parts that were rotated in the intact

model were the calcaneus, talus and corresponding cartilages. Although many studies have reported

that ankle joint presents a changing axis of rotation, it was not possible to simulate it, and therefore it

was considered a fixed axis of rotation, similar to the one postulated by Inman [116]. Regarding the

models with prosthesis, for each talar component was found the center of rotation and then the talar

component, cut talus, calcaneus and cartilages were rotated around that center. As visible in Figure

3.17, the axis of rotation changes drastically after the insertion of a prosthesis, and this may be one of

the most important reasons for the great rate of failure in TAA.

Figure 3.17 Ankle joint axes (yellow) before and after TAA using S.T.A.R.™ and Agility™ prostheses. Software

used: ABAQUS®.

55

Chapter 4

Results and Discussion

In this chapter the results of both stress and bone remodeling analyses are presented and

discussed to each model under study (intact, TAA+Agility™ and TAA+S.T.A.R.™). Then, these results

are compared with clinical and experimental results obtained by other authors.

4.1 Stress Analysis

4.1.1 Contact Stress Distribution in the Intact Ankle Joint

4.1.1.1 Results

The FE-computed contact stresses in the ankle joint for dorsiflexion, neutral and plantarflexion

positions are displayed on the cartilages of the intact tibia and talus, in Figures 4.1, 4.2 and 4.3. Three

loading conditions were considered in this analysis. At first, only an axial load was included aiming to

compare the results with the available studies in the literature that included the same loading

condition. In one case, the axial load of 600 N was applied to the three positions (Figure 4.1).

Figure 4.1 Inferior and superior views of the tibia and talus’s cartilages, respectively, overlaid with FE-computed

contact stresses (MPa) for the dorsiflexion, neutral and plantarflexion positions, considering only an axial force of

600 N to the three positions. Legend: A – Anterior; P – Posterior; L – Lateral; M – Medial. Software used:

ABAQUS®.

In the other case, the axial loads of 1600 N, 600 N and 400 N were applied to dorsiflexion, neutral

and plantarflexion positions, respectively (Figure 4.2).

56


contact stresses (MPa) for the dorsiflexion, neutral and plantarflexion positions, considering only an axial force of

1600 N, 600 N and 400 N to each position, respectively. Legend: A – Anterior; P – Posterior; L – Lateral; M –

Medial. Software used: ABAQUS®.

Then, the contact stresses for the same three positions and including all components of the

concentrated force and the internal-external torque were also computed (Figure 4.3).


contact stresses (MPa) for the dorsiflexion, neutral and plantarflexion positions, considering all the components of

the concentrated force and the internal-external torque. Legend: A – Anterior; P – Posterior; L – Lateral; M –

Medial. Software used: ABAQUS®.

By analysing the Figures 4.1, 4.2 and 4.3, it is possible to identify a consistent contact pattern on

the articular surfaces. For the contact area only a qualitative analysis was performed. Compared with

neutral position, in dorsiflexion there was a slight increase in the contact area while in plantarflexion

there was a decrease in the contact area. There were greater changes in contact area from neutral to

57

plantarflexion than to dorsiflexion. Also, the contact area occurred in the anterior lateral side for both

articular surfaces in dorsiflexion and for tibial surface in plantarflexion, whereas it occurred in the

posterior lateral side for talar surface in plantarflexion. Thus, for the three loading conditions it is

possible to state that the contact stresses spanned most of the lateral half of the tibial and talar

surfaces. Moreover, there was an increasing contact area with loading.

Regarding the contact stress, a quantitative analysis was accomplished. The maximum and mean

FE-computed contact stresses in the tibial surface for the three loading conditions are summarized in

Table 4.1.

Table 4.1 The maximum and mean FE-computed contact stresses in the tibial surface for the three loading

conditions under study. Legend: D – Dorsiflexion; N – Neutral; PF – Plantarflexion.

Loading

condition

Axial force – 600 N Axial force –

1600 N, 600 N, 400 N

Concentrated force +

Torque

Position D N PF D N PF D N PF

Mean contact

stress (MPa) 1.10 1.15 1.24 2.17 1.15 0.95 2.42 1.23 1.20

Maximum

contact stress

(MPa)

3.52 3.95 4.33 6.16 3.95 3.61 7.38 3.22 3.81

The maximum contact stresses were in the range of 3.22-7.38 MPa, while the mean contact

stresses were in the range of 0.95-2.42 MPa. Using the same axial force for the three positions, the

maximum and mean contact stresses increased from the dorsiflexion to plantarflexion positions. This

feature was not found for the other two loading conditions because it was possible to identify

increasing contact stresses with loading, and so the higher magnitude of the loads applied in

dorsiflexion position – which corresponds to the most demanding loading condition during gait cycle –

resulted in higher mean and maximum contact stresses.

In conclusion, using the same axial force for the three positions, in plantarflexion the contact area

was lower and the contact stress was higher, indicating a greater force per unit area as compared with

dorsiflexion and neutral positions. On the other hand, in dorsiflexion the contact area was higher and

the contact stress was lower as compared with neutral position.

4.1.1.2 Discussion

The analysis of the magnitude and distribution of contact stresses at the ankle joint as a function of

loading condition and ankle position is important to understand the pathogenesis of arthritis and other

abnormalities in order to prevent their existence. In fact, the understanding of load distribution is the

baseline for biomechanics of the ankle joint since changes in ankle biomechanics lead to altered load

transmission through the ankle joint, which in turn may predispose the joint to pathologic conditions,

such as OA. Also, data quantifying the ankle joint contact stress distribution is helpful for the design of

total ankle prostheses. Furthermore, the contact stress distribution in the articular surfaces is

commonly used to validate FE models, which is a very important step before any further investigation.

58

Thus, the comparison between experimental and FE results obtained by other authors and the FE

results presented before could help establishing the validity of the present computational model.

The qualitative analysis of the contact area showed that, compared with neutral position, in

dorsiflexion there was a slight increase in the contact area while in plantarflexion there was a

decrease in the contact area, which was also reported by Calhoun et al. [63]. There were greater

changes in contact area from neutral to plantarflexion than to dorsiflexion, which was also documented

by Michelson et al. [250]. Moreover, in the three loading conditions, the contact stresses spanned

most of the lateral half of the tibial and talar surfaces, which was also reported by Anderson et al. [55].

It was also observed an increasing contact area with loading, in agreement with the studies of

Kimizuka et al. [251] and Calhoun et al. [63]. Regarding the magnitude of contact stress, using the

same axial force for the three positions under study, the maximum and mean contact stresses

increased from the dorsiflexion to plantarflexion positions, which was also observed by Calhoun et al.

[63]. This feature was not found for the other two loading conditions because it was possible to identify

increasing contact stresses with loading – also reported by Calhoun et al. [63] – and so the higher

magnitude of the loads applied in dorsiflexion position resulted in higher mean and maximum contact

stresses.

In the literature there is rare data describing the contact pattern in the tibial surface. Only a recent

study of Anderson et al. [55] presents the FE-computed contact stress distribution in the tibial surface

with the ankle in neutral position and using an axial load of 600 N. This study was conducted to

determine the agreement between experimental and FE-computed results of contact stress

distribution in the ankle joint. The FE-computed results of the present study show good comparison

among the global magnitude of the contact stresses reported in the study of Anderson et al. [55], as

shown in Table 4.2.

Table 4.2 Comparison of the contact stresses reported in the study of Anderson et al. [55] and the FE-computed

results of the present study.

Source Load (N) Joint

Orientation

Method Maximum

contact stress

(MPa)

Mean contact

stress (MPa)

Anderson et al. [55] 600 Neutral FEM 3.74 (ankle 1) 2.02 (ankle 1)

2.74 (ankle 2) 1.36 (ankle 2)

Tekscan 3.69 (ankle 1) 1.96 (ankle 1)

2.92 (ankle 2) 1.15 (ankle 2)

Present study 600 Neutral FEM 3.95 1.15

However, the spatial distribution of the contact stresses differs slightly in terms of the maximum

contact stress’s position. In the study of Anderson et al. [55] the maximum contact stress was found in

the anterior lateral side of the tibial surface while in the present study it was found in posterior lateral

side, as shown in Figure 4.4. Nevertheless, when all components of the concentrated force and the

internal-external torque were used as loading condition, the maximum contact stress moved to the

anterior lateral side of the tibial surface, as shown in Figure 4.4.

59

Figure 4.4 Comparison of the spatial distributions of the contact stresses (MPa) in the tibial surface determined in

the study of Anderson et al. [55] (at left) and in the present study (at right) for neutral position and using an axial

force of 600 N. Only for the present study, it was also included the result when all components of the

concentrated force and the internal-external torque were used as loading condition (adapted from [55]).

It should be stated that there is a high inter-specimen variability in ankle joint contact distribution.

For instance, in the study of Kura et al. [65] a typical contact pattern of the tibial surface with the ankle

in neutral position and using an axial load of 667 N was shown. As can be confirmed below by Figure

4.5, the typical contact pattern of the tibial surface provided in the study of Kura et al. [65] is very

different from the one observed in the study of Anderson et al. [55] and the present study, and the

slight difference in the magnitude of the applied loads in both studies does not seem to be the main

responsible for these changes. In conclusion, the present study agrees that the complex geometry of

the articular surfaces of the ankle joint influences the load distribution and consequently the contact

pattern.

However, despite the existence of a high inter-specimen variability in ankle joint contact

distribution, there are several plausible explanations for the discrepancies observed in spatial

distribution of contact stresses in the present study. For instance, an imperfect segmentation of the

bones and/or the degree of smoothing utilized in going from CT-derived segmentations to smooth

bone surfaces and/or inadequate replication of the cartilage thickness and/or the definition of a fixed

ankle joint’s axis of rotation and/or the inclusion of the interosseous membrane and ligaments in the

present study – which were not included in the study of Anderson et al. [55] – may influence the

spatial distribution of the FE-computed contact stresses. Moreover, another parameter that could

influence the contact stress distribution at the ankle joint is the motion at the subtalar joint. In this

study, the calcaneus was moved along with the talus according to the ankle joint axis, and not

according to the subtalar joint axis. This is a limitation of the present study. However, on the other

hand, Beaudoin et al. [252] reported that the ankle joint contact was similar before and after subtalar

fusion, and therefore it is not clear how much this simplifying approach could affect the contact stress

distribution.

60

Figure 4.5 A typical contact pattern of the tibial surface with the ankle in neutral position and using an axial load of

667 N – provided in study of Kura et al. [65]. Black regions correspond to articular contact while white regions

represent no contact between the tibia and talus.

To conclude, the analysis of the contact stress distribution is not the focus of this work and

therefore, besides the limitations of this study, these results show reasonable comparison and are, for

the most part, consistent with previous studies. Thus, this validation establishes confidence in results

from the FE models.

4.1.2 Contact Stress Distribution in the Polyethylene Component

4.1.2.1 Preliminary Test

Firstly, the contact stress distribution was investigated in the polyethylene component’s surface

that contacts with the talar component of the Agility™ prosthesis, taking into account the old and new

talar component designs. Then, the contact stresses were also determined for the polyethylene

component’s upper and lower surfaces of the S.T.A.R.™ prosthesis. This was done considering only

an axial force of 600 N with respect to the neutral position. Table 4.3 presents the maximum and mean

FE-computed contact stresses in the polyethylene component’s surfaces that contact with the old and

new talar component designs of Agility™ prosthesis and with the tibial and talar components of the

S.T.A.R.™ prosthesis.

Table 4.3 The maximum and mean FE-computed contact stresses in the polyethylene component’s surfaces that

contact with the old and new talar component designs of Agility™ prosthesis and with the tibial and talar

components of the S.T.A.R.™ prosthesis, considering only an axial force of 600 N with respect to the neutral

position.

Model Agility™

(the old talar

component design)

Agility™

(the new talar

component design)

S.T.A.R.™

(talar

component)

S.T.A.R.™

(tibial

component)

Mean contact

stress (MPa)

17.59 5.32 3.07 2.03

Maximum contact

stress (MPa)

68.81 31.75 9.74 5.10

As expected, the wider shape of the new talar component design of Agility™ prosthesis at the

posterior edge and the increased contact area provided by it led to a decrease of both the maximum

61

and mean FE-computed contact stresses in the polyethylene component’s surface. In particular, the

mean contact stress decreased from 17.59 MPa (using the old talar component design) to 5.32 MPa

(using the new talar component design) while the maximum contact stress decreased from 68.81 MPa

(using the old talar component design) to 31.75 MPa (using the new talar component design).

Furthermore, the maximum and mean FE-computed contact stresses for both talar component

designs were higher than those determined for the S.T.A.R.™ prosthesis (considering both upper and

lower surfaces). This was also expected since the S.T.A.R.™ is a three-component, mobile-bearing

design, which means that it is at the same time a congruent and minimally constrained prosthesis,

whereas Agility™ is a two-component, fixed-bearing design, i.e., it is a partially conforming and

semiconstrained prosthesis, which in turn potentially increases the contact stresses and consequently

the wear rate.

At first sight, the contact stresses calculated for the old talar component design seem

unreasonably high. However, it is important to mention that three times larger stresses at the Agility™

prosthesis (considering the old talar component design) than at the S.T.A.R.™ prosthesis were

estimated by McIff et al. [253], which may confirm the great difference observed in this study.

To conclude, these results indicate that the new talar component design has better performance

than the old talar component design. As result, only the new talar component design was considered

in a more detailed analysis of the contact stresses, as described further on.

4.1.2.2 Results

With the results from preliminary test in mind, the FE-computed contact stress distributions in the

polyethylene component’s surfaces for Agility™ (considering only the new talar component design)

and S.T.A.R.™ prostheses and for dorsiflexion, neutral and plantarflexion positions are displayed in

Figures 4.6, 4.7 and 4.8. Once again, as done for the intact ankle joint, three loading conditions were

considered in the study. At first, only an axial load was included. In one case, the axial load of 600 N

was applied to three positions (Figure 4.6) while in other case the axial loads of 1600 N, 600 N and

400 N were applied to dorsiflexion, neutral and plantarflexion positions, respectively (Figure 4.7).

Then, the contact stress distributions for the same three positions and including all components of the

concentrated force and the internal-external torque were also computed (Figure 4.8).

62

Figure 4.6 Inferior view of the polyethylene component’s lower surfaces that articulate with the talar component of

the Agility™ and S.T.A.R.™ prostheses and also the superior view of the polyethylene component’s upper

surface that articulates with the tibial component of the S.T.A.R.™ prosthesis, overlaid with FE-computed contact

stresses (MPa) for the dorsiflexion, neutral and plantarflexion positions, considering only an axial force of 600 N to

the three positions. Legend: A – Anterior; P – Posterior; L – Lateral; M – Medial. Software used: ABAQUS®.

63




stresses (MPa) for the dorsiflexion, neutral and plantarflexion positions, considering only an axial force of 1600 N,

600 N and 400 N to each position, respectively. Legend: A – Anterior; P – Posterior; L – Lateral; M – Medial.

Software used: ABAQUS®.

64




stresses (MPa) for the dorsiflexion, neutral and plantarflexion positions, considering all the components of the

concentrated force and the internal-external torque. Legend: A – Anterior; P – Posterior; L – Lateral; M – Medial.

Software used: ABAQUS®.

By analysing the Figures 4.6, 4.7 and 4.8, it is possible to clearly identify the problem of edge-

loading in Agility™ prosthesis for the three loading conditions, and also for S.T.A.R.™ prosthesis in

some loading conditions. In fact, in spite of the fact that the S.T.A.R.™ is a fully conforming/congruent

prosthesis, a non-uniform contact stress distribution was observed in the polyethylene component’s

lower and upper surfaces. Moreover, in the three loading conditions, the contact stresses spanned

most of the medial half of the upper and lower surfaces of the S.T.A.R.™ prosthesis, in contrast to

what happened in the intact ankle joint.

A quantitative analysis of the contact stresses was also performed. The maximum and mean FE-

computed contact stresses in the polyethylene component’s lower surfaces that articulate with the

talar component of the Agility™ and S.T.A.R.™ prostheses and in the polyethylene component’s

upper surface that articulates with the tibial component of the S.T.A.R.™ prosthesis are summarized

in Tables 4.4, 4.5 and 4.6 for the three loading conditions.

65

Table 4.4 The maximum and mean FE-computed contact stresses in the polyethylene component’s lower surface

of the Agility™ prosthesis for the three loading conditions under study. Legend: D – Dorsiflexion; N – Neutral; PF

– Plantarflexion.

Loading

condition


1600 N, 600 N, 400 N


Torque


Mean contact

stress (MPa)

4.20 5.32 8.21 9.79 5.32 6.61 15.82 3.39 2.97

Maximum

contact

stress (MPa)

22.71 31.75 55.85 52.08 31.75 40.33 63.45 14.74 17.92

Table 4.5 The maximum and mean FE-computed contact stresses in the polyethylene component’s lower surface

of the S.T.A.R.™ prosthesis for the three loading conditions under study. Legend: D – Dorsiflexion; N – Neutral.

PF – Plantarflexion.

Loading

condition


1600 N, 600 N, 400 N


Torque


Mean contact

stress (MPa)

3.09 3.07 3.63 7.21 3.07 2.45 7.38 7.65 6.13

Maximum

contact

stress (MPa)

10.11 9.74 17.99 25.87 9.74 10.73 23.05 25.26 20.63

Table 4.6 The maximum and mean FE-computed contact stresses in the polyethylene component’s upper surface

of the S.T.A.R.™ prosthesis for the three loading conditions under study. Legend: D – Dorsiflexion; N – Neutral;

PF – Plantarflexion.

Loading

condition


1600 N, 600 N, 400 N


Torque


Mean contact

stress (MPa)

1.86 2.03 2.12 4.92 2.03 1.44 5.17 5.96 5.15

Maximum

contact

stress (MPa)

4.59 5.10 4.53 10.30 5.10 3.03 10.82 13.34 12.36

For Agility™ prosthesis, the maximum contact stresses were in the range of 14.74-63.45 MPa,

while the mean contact stresses were in the range of 2.97-15.82. On the other hand, for S.T.A.R.™

prosthesis these values decreased: maximum contact stresses were in the range of 9.74-25.87 MPa

(lower surface) and 3.03-13.34 MPa (upper surface), while the mean contact stresses were in the

range of 2.45-7.65 (lower surface) and 1.44-5.96 MPa (upper surface). Like in the ankle joint, using

the same axial force (600 N) for the three positions, the maximum and mean contact stresses

increased from the dorsiflexion to plantarflexion positions, except for the maximum contact stresses in

66

the polyethylene component’s upper surface of the S.T.A.R.™ prosthesis. Once again, this feature

was not found with the other loading conditions because it was possible to identify increasing contact

stresses with loading in some cases. In particular, the higher magnitude of the loads applied in

dorsiflexion position – which corresponds to the most demanding loading condition during gait cycle –

resulted in the highest mean and maximum contact stresses observed in the study.

4.1.2.3 Discussion

Among other factors, the success of the TAA depends on the contact stresses generated in

prosthetic surfaces. Due to the high loads observed in the ankle joint and the experience gained from

hip and knee arthroplasties, concerns have arisen about the long-term wear and ultimate survival of

the total ankle prostheses. In particular, excessive and non-uniform contact stresses may lead to

instability and poor function in the short-term and increased wear, which in turn may lead to a

catastrophic failure of the TAA in the long-term. Currently there is a lack of suitable tools capable of

analysing the performance of the TAA in vivo. Therefore, FE models are an excellent tool to assess

the magnitude and distribution of contact stresses in a replaced ankle when subjected to forces typical

of a gait cycle. As result, a FEA of contact stress distribution was undertaken for the purpose of

predicting the extent of wear for two different types of prostheses (Agility™ and S.T.A.R.™).

Some studies [21, 254] have indicated that to achieve a successful TAA the contact stresses

should not exceed 10 MPa in the polyethylene component. The present results show that the mean

contact stresses were always less than 10 MPa in the polyethylene component for both prostheses

and considering the three loading conditions, except when considering all the components of the

concentrated force and the internal-external torque in dorsiflexion position – which corresponds to the

most demanding loading condition during gait cycle – for Agility™ prosthesis. On the other hand, the

maximum contact stresses were always higher than 10 MPa in the polyethylene component for both

prosthesis and for the three loading conditions, except in some cases when considering only the upper

surface of S.T.A.R.™ prosthesis.

The comparison of the present results with previous studies from the literature is difficult because

of the different designs analysed, the different boundary and loading conditions applied and

particularly the ligamentous apparatus included or not in the models. Most of the previous studies

have only included simplified loading and boundary conditions. These previous studies and the

corresponding results are summarized below in Table 4.7.

In particular, McIff et al. [255] examined the contact stresses using S.T.A.R.™ prosthesis under a

3650 N axial force. They reported a maximum contact stress in the polyethylene component’s upper

surface of approximately 10 MPa. Regarding the polyethylene component’s lower surface, a value

ranging between 8 and 10 MPa was observed on most of the surface, except for the anterior, posterior

and internal edges where a 20 MPa contact stress was determined. In another study, Nicholson et al.

[67] examined the contact stress distribution in the polyethylene component’s surface of Agility™

prosthesis considering a 700 N axial force in neutral position. They measured a mean contact stress

of 5.6 MPa and a maximum contact stress of 21 MPa. Later, Miller et al. [52] performed a FEA of two

different talar component designs of Agility™ prosthesis under a 3330N axial force applied to the

67

proximal tibia and fibula. The maximum and mean contact stresses dropped from 36 to 25 MPa and

from 23 to 19 MPa, respectively, when the wider shape of the talar component was analysed. In the

study of Reggiani et al. [54] the contact stress distribution was analysed for the BOX® prosthesis over

the stance phase of gait cycle. In spite of the fact that a non-uniform distribution was observed,

contact stresses in the polyethylene component’s upper and lower surfaces less than 10 MPa were

determined during most of the stance phase of gait. The maximum contact stresses reported during

dorsiflexion (the most demanding loading condition during gait cycle) were: 16.1 MPa for the

polyethylene component’s lower surface and 10.3 MPa for the polyethylene component’s upper

surface.

By analysing the Table 4.7 presented below, it is possible to conclude that the predicted contact

stresses for different types of prostheses are highly variable, which in turn is due to different

measurement techniques, prosthesis’s geometry, loading and boundary conditions, etc. The reported

maximum and mean contact stresses from the literature are in the range of 5.7-36 MPa and 5.6-23

MPa, respectively. In the present study, as presented before, for Agility™ prosthesis, the maximum

contact stresses were in the range of 14.74-63.45 MPa, while the mean contact stresses were in the

range of 2.97-15.82 MPa. On the other hand, for S.T.A.R.™ prosthesis these values decreased:

maximum contact stresses were in the range of 9.74-25.87 MPa (lower surface) and 3.03-13.34 MPa

(upper surface), while the mean contact stresses were in the range of 2.45-7.65 MPa (lower surface)

and 1.44-5.96 MPa (upper surface).

Larger values for the contact stresses were observed in the present study, mostly for the Agility™

prosthesis. As explained before, there are many plausible explanations for these relatively small

discrepancies. However, the main reason is probably related to the loading conditions considered in

the present study. For the first time, at the present state of knowledge, a 3-D concentrated force and

an internal-external torque were applied in a contact stress analysis of a replaced ankle and in

particular, for the Agility™ and S.T.A.R.™ prostheses. As it has been confirmed, there is an increased

contact stress with loading, and so the larger values observed in the present study may be related to

that fact. In general, the FE-computed contact stresses in the present study show good comparison

among the reported contact stresses from the literature, as can be confirmed by analysing and

comparing the Tables 4.3, 4.4, 4.5, 4.6 and 4.7.

To conclude, the polyethylene component’s lower surface of the Agility™ prosthesis presented the

highest contact stresses, followed by the polyethylene component’s lower surface of the S.T.A.R.™

prosthesis. The lowest contact stresses were determined for the polyethylene component’s upper

surface of the S.T.A.R.™ prosthesis. Moreover, the problem of edge-loading was evident in Agility™

prosthesis for the three loading conditions, and also for S.T.A.R.™ prosthesis in some loading

conditions. This problem have been reported in several studies [21, 24, 256, 257]. In fact, in spite of

the fact that the S.T.A.R.™ is a fully conforming/ congruent prosthesis, it is possible to observe a non-

uniform contact stress distribution in the polyethylene component’s surfaces, which was also reported

in [253, 258]. One possible solution to the problem of edge-loading in Agility™ prosthesis would be to

make the profile in the frontal plane to be “curved-on-curved type” [259]. However, this would restrict

the motion of the prosthesis to the sagittal plane, making the implant highly constrained. Furthermore,

68

both prostheses (especially Agility™) exceeded the contact stress recommended for the polyethylene

component (10 MPa) and its compressive yield point (13-25 MPa [21]). In fact, these prostheses still

have some untested features and the optimal articulation configuration is currently not known. On the

one hand, mobile-bearing designs (such as S.T.A.R.™) theoretically offer less wear and loosening

because of full conformity and minimal constraint, respectively. On the other hand, fixed-bearing

designs (such as Agility™) avoid the dislocation of the polyethylene component and the potential

increased wear from a second articulation/contact surface.

Table 4.7 Contact stress data from the literature for total ankle prostheses. Legend: D – Dorsiflexion; N – Neutral;

PF – Plantarflexion; AF – Axial force; APF – Anterior-posterior force; T – Interior-exterior torque; PC –

Polyethylene component; US – Upper surface; LS – Lower surface; TC – Talar component.

Source Prosthesis Load (N) Joint

Orientation

Method Maximum

contact

stress

(MPa)

Mean

contact

stress

(MPa)

Reggiani et

al. [54]

BOX® PC’s US 1600 (AF)

-185 (APF)

6.2 (T)

D FEA 9* –

600 (AF)

-280 (APF)

2.85 (T)

N 5*

400 (AF)

-245 (APF)

-0.1 (T)

PF 4*

PC’s LS 1600 (AF)

-185 (APF)

6.2 (T)

D 15* –

600 (AF)

-280 (APF)

2.85 (T)

N 10*

400 (AF)

-245 (APF)

-0.1 (T)

PF 8*

Miller et al.

[52]

Agility™ PC’s LS

(Narrowed

shape of

TC)

3330 (AF) N FEA 36 23

PC’s LS

(Wider

shape of

TC)

25 19

McIff et al.

[255]

S.T.A.R.™ PC’s UP 3650 (AF) N FEA 10 –

PC’s LS 20 –

Nicholson

et al. [67]

Agility™ PC’s LS 700 (AF) N Tekscan 21 5.6

Fukuda et

al. [66]

Agility™ PC’s LS 740 (AF) N Tekscan 5.7 –

* These values are approximations based on the time-history of the maximum contact stresses during the stance phase of gait

plotted in a graphic in [54]

69

4.1.3 Internal Stress Distribution in the Talus

4.1.3.1 Results

Firstly, the internal stress distribution was investigated in the talus for the intact, TAA+Agility™

(including the old and new talar component designs) and TAA+S.T.A.R.™ models, considering only an

axial force of 600 N with respect to the neutral position. Figure 4.9 presents Von Mises stresses in the

talus for the intact, TAA+Agility™ (including the old and new talar component designs) and

TAA+S.T.A.R.™ models, considering only an axial force of 600 N.

Figure 4.9 The Von Mises stress distribution (MPa) in the talus for the intact, TAA+Agility™ (including the old and

new talar component designs) and TAA+S.T.A.R.™ models, considering only an axial force of 600 N with respect

to the neutral position. Three cuts in the transverse plane at the talus for each model are shown (superior view).

From left to right: the cut is further from the surface where the talar component is placed. Legend: A – Anterior; P

– Posterior; L – Lateral; M – Medial. Software used: ABAQUS®.

70

By analysing the Figure 4.9, it is possible to notice that the intact talus distributes stresses evenly

throughout the bone, and that there is a preferential area for the transmission of force from talus to the

calcaneus. After the insertion of both prostheses (taking into account the two talar components for

Agility™) major changes occurred in the talus, in particular, in its internal stress distribution. There was

an increase of the magnitude of stresses in trabecular bone for the three models. When comparing the

two talar components of Agility™ prosthesis, the wider shape of the new talar component design at

the posterior edge and the increased contact area provided by it led to a decrease of the maximum

internal stresses in the talus. In particular, the maximum Von Mises stresses decreased from 54.25

MPa (using the old talar component design) to 40.96 MPa (using the new talar component design).

Moreover, the old talar component design originated larger stresses at the posterior edge, which can

explain the early loosening and subsidence of this component. In fact, clinically, the old design was

noted to fail due to posterior subsidence, which is in accordance with the present results. These

results show once again that the new talar component design has better performance than the old

talar component design. Furthermore, when comparing the stress distribution in the talus using the

new talar component design of Agility™ prosthesis and the talar component of S.T.A.R.™ prosthesis,

it is possible to identify an improvement in the stress distribution in the case of S.T.A.R.™, despite the

slight increase in stresses at the anterior medial side of the talus. In the case of Agility™ a clearly

marked area of larger stresses around the prosthesis was identified, despite not being so significant

when comparing with the area originated by the old talar component design. This was also expected

since the S.T.A.R.™ is a three-component, mobile-bearing design, which means that it is at the same

time a congruent and minimally constrained prosthesis (providing great mobility), whereas Agility™ is

a two-component, fixed-bearing design, i.e., it is a partially conforming and semiconstrained

prosthesis, which may originate high axial and shear constrains at the bone-prosthesis interface.

Then, the internal stress distribution was also investigated for the intact, TAA+Agility™ (including

only the new talar component design) and TAA+S.T.A.R.™ models, considering all components of the

concentrated force and the internal-external torque with respect to the neutral position. Besides not

shown here, the internal stress distributions in the talus were similar for each model, with an

increasing on the maximum stresses.

4.1.3.2 Discussion

The stress analysis allows the assessment of the internal stresses at the ankle joint before and

after a TAA, which in turn helps in understanding the influence of a particular prosthesis in host bone.

The importance of bone support was quickly recognized in TAA. Past experience with TAA has

shown that loss of support is a primary reason for failure. The problem is that most prostheses depend

primarily on bone for support, but unfortunately many patients needing prosthetic arthroplasties have

weakened or compromised bone. In particular, the first FE model of ankle joint found in the literature

was developed by Calderale et al. [46] in 1983 and is 3-D. This study showed that after the resection

of the top of the talus to the insertion of the talar component, stresses abnormally increased near the

resected surface. Moreover, an early laboratory study [260] assessed the bone support at ankle joint

by performing TAA in cadavers and subjecting these models to physiologic forces. The study showed

71

the failure of bone support around the prosthesis in just a few days. The present study is in agreement

with those findings since the stresses increased near the resected surfaces for both prostheses

(taking into account the two talar components for Agility™). Also, as stated before, there was an

increase of the magnitude of stresses in trabecular bone for the three models, which in turn increases

the chance of failure of bone support around prosthesis and consequently the subsidence of talar

component can occur, following the assumption reported by Taylor et al. [261]. They stated that there

was a relationship between the stresses in trabecular bone and the subsidence rate of some types of

femoral implants after two years of clinical use. Since subsidence is related to loosening, they stated

that the initial stresses in the trabecular bone could be used to predict clinical performance of an

implant. Furthermore, a study performed by Hvid et al. [262] showed that in talus and also tibia the

strength rapidly decreased with the increasing distance to articular surfaces. In particular, they

concluded that if talar resection was more than 4 mm deep, the new surface will be significantly less

resistant to compressive loads. This difference in bone strength was not included in the present

models but still stresses increased near the resected surfaces for both prostheses. In conclusion, the

present results agree that excessive bone resection results in the prosthesis being seated on

trabecular bone that may not support the forces at the ankle, which consequently may contribute to

early loosening and subsidence of the talar component. Thus, minimal bone resection is required in

order to remain firm the bone-prosthesis interface, as reported in [34].

4.2 Bone Remodeling Analysis

4.2.1 Intact Model

4.2.1.1 Results

The tibia and talus are the two bones considered as design area in the bone remodeling simulation.

As explained before, the parameter k represents the metabolic cost of maintaining bone, being a very

important parameter to bone remodeling process since the resulting bone mass will depend strongly

on its value. Moreover, there is another important parameter to take into account in the bone

remodeling process, the parameter m. As mentioned before, the parameter m represents a corrective

factor for the preservation of the intermediate densities. Thus, the determination of k and m is

essential for the validation of the bone remodeling results. Using the intact model of the AJC, several

bone remodeling computer simulations were performed, assuming different values for k and m, to

assess which ones best fit the real bone density distribution of the talus and tibia (physiological state).

Due to the complexity of the model, bone remodeling computer simulations were performed only for

30 iterations, which revealed to be a reasonable value to choose the best parameters without

compromising too much the time spent in each simulation. Different parameters were tested but for

reasons of synthesis, only the results of the computer simulations with the parameter k of 0,005, 0,007

and 0,009 N/mm2 and the parameter m of 1 and 2 are presented in Figure 4.10. The most appropriate

values for the parameters k and m were chosen from the comparison of the bone density distributions

resulting from the bone remodeling computer simulations and the CT scan images (qualitative

analysis). Furthermore, it is important to mention that firstly another parameter was tested for the

optimization problem, the value of step. After several tests, the step was fixed at a value of 10.

72

Figure 4.10 Comparison of the bone density distributions resulting from the bone remodeling computer simulations (after 30 iterations) and the CT scan images. Software used:

ABAQUS®.

73

All the bone density distributions resulting from the bone remodeling computer simulations reflect

some morphological features observed in actual density patterns of the tibia and talus.

For instance, it is possible to observe an inner area of lower relative densities, which corresponds

to trabecular bone, surrounded by an external layer of higher relative densities, which corresponds to

cortical bone. In particular, the cortical layer is ticker in the diaphysis and becomes thinner toward one

extremity. However, like CT scan images show (frontal plane view), the cortical layer is thicker in the

diaphysis and becomes thinner toward both extremities but the present results could not simulate

perfectly well one of the extremities. Moreover, as visible in sagittal plane, there is a thick cortical layer

in the anterior side and a thin cortical layer in the posterior side of the tibia, and the anterior and

posterior sides should be more uniform, as CT scan images show (sagittal plane view). Still, the

results for the tibia are reasonably similar when comparing to the CT scan images.

As far as talus is concerned, it is important to notice that navicular – the bone in direct contact with

the anterior side of talus – was not included in the model and due to that fact, the loads that are

originated in the talus from the contact surfaces of the talus and navicular are not observed in the

present model. With this limitation is mind, it is easy to understand the “black” area (very low densities)

present in the anterior side of the talus (sagittal plane view), which is visible in all bone remodeling

computer simulations (Figure 4.10). This result from the assumption that bone adapts itself according

to the applied loads and so, if there are no loads, there is no bone formation. Besides this, it is also

visible in the sagittal plane – considering both CT scan images and present results – a concentrated

area in the middle and distal side of talus that corresponds to the area of force transmission to the

calcaneus. On the other hand, in the frontal plane it is also noticeable small “black” areas (very low

densities) that are not visible in the CT scan images. This could be result of the ligaments’ modeling,

i.e., the real attachment sites for the ligaments into the talus may occupy a larger area than the one

that was considered, which would have a direct impact on the bone remodeling process. With this in

mind, the “white” area (very high densities) also visible in the medial side of the frontal plane may have

been caused by a concentrated attachment area of a particular ligament into the talus. To conclude

this initial analysis, the model converged to a solution with relatively high similarity to the morphology

of the tibia, reproducing the behaviour of the real bone, but with less similarity to the morphology of the

talus. The aforementioned negative points can be improved in future works.

Furthermore, among all the bone density distributions that resulted from the different bone

remodeling computer simulations there is a clear difference between the bone density distributions

that resulted from varying the parameter m. A higher value of parameter m led the solution to a more

homogeneous distribution, neglecting the nodes with extreme densities. In other words, all the nodes

tend to converge to an intermediate density, increasing the average global density, as shown in Figure

4.11. In fact, as can be observed in Figure 4.10, for m = 1 the trabecular bone has a lower average

density than for m = 2 but on the other hand, cortical bone has a more defined layer and a higher

average density. When parameter k was tested, a higher value of parameter k led the solution to a

lower average global density, as shown in Figure 4.11. This result was expected since a higher value

of parameter k means that it is more “expensive” (biological cost) for the organism to maintain bone

homeostasis, i.e., to allow bone formation.

74

Figure 4.11 Evolution of the bone mass throughout the iterative process of bone remodeling (30 iterations),

dimensionless by its initial mass, for different values of parameters k and m. Software used: MATLAB®.

For the selection of the parameters k and m that best fit the real bone density distribution of the

talus and tibia (physiological state), the following considerations were taken into account. Regarding

the parameter k, for k = 0,009 N/mm2 there is an excessive loss of relative densities in the external

layer of cortical bone, which results in a thinner cortical layer. On the other hand, for k = 0,005 N/mm2

the thickness of cortical layer in the diaphysis is almost identical to the real thickness shown in CT

scan images but it is also much more thicker in one extremity of the metaphysis/epiphysis than the

real case. Thus, there must be a compromise between the reproduction of the cortical layer in

diaphysis and in the metaphysis/epiphysis. Taking this into account, the value of 0,007 N/mm2 seems

to be the most balanced, reproducing the result more similar to the pattern of density distribution of the

real tibia. Still, there are some limitations in the result obtained, since the cortical layer should become

thinner toward both extremities, which only occurs in one extremity. Also, as visible in sagittal plane

view, there is a thick cortical layer in the anterior side and a thin cortical layer in the posterior side of

the tibia, and the anterior and posterior sides should be more uniform. As far as talus is concerned,

there are no significant differences when varying the value of parameter k. Regarding the parameter

m, as explained before, for m = 2 the bone density distribution is more homogeneous. All the nodes

tended to converge to an intermediate density but at the same time not neglecting too much the

extreme densities. The results considering m = 2 are fairly more similar to the CT scan images than

the results considering m = 1. Thus, for all the reasons pointed out before, the parameters chosen

were k = 0,007 N/mm2 and m = 2. The resulting bone density distribution is presented in Figure 4.12.

75

Figure 4.12 The bone density distribution resulting from the bone remodeling computer simulation with k = 0,007

N/mm2 and m = 2, after 100 iterations. Software used: ABAQUS

®.

Figure 4.13 Evolution of the bone mass throughout the iterative process of bone remodeling (100 iterations),

dimensionless by its initial mass, for k = 0,007 and m = 2. Software used: MATLAB®.

76

By analysing Figure 4.13 it is possible to notice that the process has reached the desired

convergence (the change in bone mass stabilized) within the number of iterations considered. This

means that the solution of the model converged to an equilibrium state between successive bone

formation and bone resorption events. It is important to notice that this iterative process of bone

remodeling took about 14 days to perform 100 iterations.

Furthermore, the bone density distributions that resulted from the bone remodeling computer

simulations considering 30 and 100 iterations (for k = 0,007 and m = 2) are not significantly different,

as can be confirmed by a comparative analysis of Figures 4.10 and 4.12. Also, Figure 4.13 shows that

the evolution of bone mass after 30th iteration is not significant. These results lead to the conclusion

that considering only 30 iterations to evaluate the performance of different values for parameters k and

m was a good option.

4.2.1.2 Discussion

As described before, the model converged to a solution with relatively high similarity to the

morphology of the tibia, reproducing the behaviour of the real bone, but with less similarity to the

morphology of the talus. The aforementioned negative points are result of some limitations of the

study that can be improved in future works.

The only study found in literature [68] that analysed the bone remodeling process in the ankle joint

considered tibia and talus as different models and applied only one static load case to each model.

However, the validation of the bone remodeling models before the insertion of the prosthesis was not

included in the study.

To conclude, it is very important to understand the bone remodeling process prior to the insertion

of a prosthesis, and so the validation of the bone remodeling models obtained for tibia and talus is

also an important step before analysing the effects of the ankle prostheses on the bones. However, if

the aim of the study was to analyse the importance on the bone remodeling process of inserting an

ankle prosthesis into the AJC, that can be done by considering the final bone density distribution

obtained from the model of the intact AJC as the initial bone density distribution of the model of the

AJC after the insertion of the prosthesis. This way, it is possible to analyse only the changes caused

by the insertion of the prosthesis. This was the strategy applied in the present study.

4.2.2 TAA+Agility™ and TAA+S.T.A.R.™ Models

Once again, the tibia and talus are the two bones considered as design area in the bone

remodeling simulation. As explained before, the initial density distributions of the tibia and talus in the

TAA+Agility™ and TAA+S.T.A.R.™ models correspond to the final density distributions of the tibia and

talus in the intact model. However, since the meshes of the tibia and talus in the three models are

different, it was necessary to develop an algorithm in MATLAB® (described in Appendix D) to transit

the nodes’ densities of the mesh of the intact model to the nodes of the mesh of the TAA+Agility™ and

TAA+S.T.A.R.™ models. Thus, tibia and talus start from an initial situation with greater resemblance

to reality and, consequently, to clinical scenario.

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4.2.2.1 Preliminary Results

The results of TAA+Agility™ and TAA+S.T.A.R.™ models are presented in Figures 4.14 and 4.15.

In order to analyse the evolution of each of the bone density distributions, the physiological and the

initial states are also presented. It is important to mention that bone remodeling processes in the

prosthetic tibia and talus occur mainly in the metaphysis/epiphysis, where the prosthesis is implanted.

For that reason, the changes in bone density distribution are only analysed in that region.

Figure 4.14 Bone density distributions in the tibia and talus before and after the insertion of Agility™ prosthesis

(frontal plane view). Software used: ABAQUS®.

Through the observation of the Figure 4.14 it is possible to identify an increase in density in

concentrated regions of the lateral and medial sides of the tibia (above the tibial component).

Moreover, a significant increase in density is observed in the site where talar component is fixed to the

talus and near the keel, and a lesser but still noticeable increase is observed beneath the keel of the

talar component. It is also visible a decrease in density in the medial region of the talus beneath the

talar component.

Figure 4.15 Bone density distributions in the tibia and talus before and after the insertion of S.T.A.R.™ prosthesis

(frontal plane view). Software used: ABAQUS®.

From Figure 4.15 it is possible to identify an increase in density above the two raised cylindrical

barrels and in the medial malleolus. Moreover, a decrease of bone mass is visible in the lateral region

of the distal tibia. For talus, the bone mass loss is also observed in the lateral region beneath the talar

78

component. A significant increase in density is observed beneath the central keel of talar component

and a lesser but still noticeable increase is observed in the lateral and medial sites where talar

component is fixed to the talus.

4.2.2.2 Discussion

Although these are preliminary results, a relatively good agreement was achieved between these

results and the results of the study of Boughecha et al. [68] for the S.T.A.R.™ prosthesis. Regarding

the Agility™ prosthesis, there was not found any study in the literature related to the bone remodeling

analysis and so the present results for TAA+Agility™ model could not be confirmed by any other

study.

Regarding the TAA+Agility™ model, the present results showed a decrease in density in the

medial region of the talus beneath the talar component, which could be associated with stress

shielding effect. However, further investigation is still needed to confirm these results.

Regarding the TAA+S.T.A.R.™ model, the present results showed an increase in density above

the two raised cylindrical barrels, which was also reported in [68]. Moreover, in [68] was also observed

a decrease in density centrally above the tibial component, which was not visible in the present

results. Instead, a decrease of bone mass was visible in the lateral region of the distal tibia. Besides

this, both results showed that forces are transmitted from the two raised cylindrical barrels into the

bone, which may lead to stress shielding in some areas near these two structures. This was also

pointed out by Hintermann in [263]. Moreover, a bone mass loss was also observed in the lateral

region beneath the talar component. This stress shielding effect may contribute to loosening and

subsidence of the tibial and/or talar component, often reported in clinical studies.

The bone remodeling model used in this study has been extensively applied in the studies of the

hip ([220, 264, 265]), the spine ([266]) and the shoulder ([217, 267]). The application of this model to

the AJC is considered to be adequate taking into account the parameters chosen before. However,

more computer simulations, and mainly a more precise quantitative analysis has to be performed in

order to proof the accuracy of the present results.

79

Chapter 5

Conclusions and Future Directions

5.1 Conclusions

This thesis analysed the internal and contact stress distributions and the bone remodeling of the

AJC before and after the simulation of a TAA using two different prostheses, Agility™ and S.T.A.R.™.

This was done using the FEM provided by the commercial software ABAQUS® together with the model

of bone remodeling developed in IDMEC/IST. In a first phase the work involved the geometric and FE

modeling of the AJC and the Agility™ and S.T.A.R.™ prostheses. The 3-D solid models of each intact

bone, namely tibia, fibula, talus and calcaneus, were obtained from the VAKHUM project while the

solid models of the Agility™ and S.T.A.R.™ prostheses were developed using SolidWorks® and based

on informative documents provided by the DePuy Orthopaedics, Inc. and Small Bone Innovations, Inc.

companies, respectively. Then, the simulation of the TAA using Agility™ and S.T.A.R.™ prostheses

was performed by assembling the AJC (after some cuts) with each prosthesis. This was also done

using SolidWorks®. In a second phase the contact stress distributions in the intact ankle joint and in

the polyethylene component of the each prosthesis were evaluated, as well as the load transfer

behaviour in the talus and the effect of the geometry of three different talar component designs – two

for Agility™ prosthesis and one for S.T.A.R.™ prosthesis – on host bone. Finally, in a third phase the

bone remodeling model was used to determine the bone density distribution in the talus and tibia

before and after a TAA.

This work determined the contact stress distribution in the intact ankle joint for dorsiflexion, neutral

and plantarflexion positions under three different loading conditions. In particular, using the same axial

force (600 N) for the three positions under study, the maximum and mean contact stresses increased

from the dorsiflexion to plantarflexion positions. This feature was not found for the other two loading

conditions because it was possible to identify increasing contact stresses with loading, and so the

higher magnitude of the loads applied in dorsiflexion position in the other two loading conditions

resulted in higher mean and maximum contact stresses. The present study agrees that the complex

geometry of the articular surfaces of the ankle joint influences the load distribution and consequently

the contact pattern. In conclusion, the analysis of the contact stress distribution was not the focus of

this work but, besides some limitations, these results showed reasonable comparison and are, for the

most part, consistent with previous studies. Thus, this validation established confidence in results from

the FE models.

Then, the contact stress distribution in the polyethylene component of the Agility™ and S.T.A.R.™

prostheses was also evaluated.

Firstly, the contact stress distribution was investigated in the polyethylene component’s surface

that contacts with the talar component of the Agility™ prosthesis, taking into account two different

designs: the old and the new talar component designs. Moreover, the contact stresses were also

determined for the polyethylene component’s upper and lower surfaces of the S.T.A.R.™ prosthesis.

80

This was done considering only an axial force of 600 N with respect to the neutral position. The wider

shape of the new talar component design of Agility™ prosthesis at the posterior edge and the

increased contact area provided by it led to a decrease of both the maximum and mean FE-computed

contact stresses in the polyethylene component’s surface. In particular, the mean contact stress

decreased from 17.59 MPa (using the old talar component design) to 5.32 MPa (using the new talar

component design) while the maximum contact stress decreased from 68.81 MPa (using the old talar

component design) to 31.75 MPa (using the new talar component design). Furthermore, the maximum

and mean FE-computed contact stresses for both talar component designs were higher than those

determined for the S.T.A.R.™ prosthesis (considering both upper and lower surfaces). This was also

expected since the S.T.A.R.™ is a three-component, mobile-bearing design, which means that it is at

the same time a congruent and minimally constrained prosthesis, whereas Agility™ is a two-

component, fixed-bearing design, i.e., it is a partially conforming and semiconstrained prosthesis,

which in turn potentially increases the contact stresses and consequently the wear rate. To conclude,

these results indicate that the new talar component design has better performance than the old

design.

Then, the contact stress distribution in the polyethylene component’s surfaces for Agility™

(considering only the new talar component design) and S.T.A.R.™ prostheses were also analysed for

dorsiflexion, neutral and plantarflexion positions and under different loading conditions. The

polyethylene component’s lower surface of the Agility™ prosthesis presented the highest contact

stresses, followed by the polyethylene component’s lower surface of the S.T.A.R.™ prosthesis. The

lowest contact stresses were determined for the polyethylene component’s upper surface of the

S.T.A.R.™ prosthesis. Moreover, the problem of edge-loading was evident in Agility™ prosthesis for

the three loading conditions, and also for S.T.A.R.™ prosthesis, in some loading conditions. In fact, in

spite of the fact that the S.T.A.R.™ is a fully conforming/ congruent prosthesis, it is possible to

observe a non-uniform contact stress distribution in the polyethylene component’s surfaces.

Furthermore, both prostheses (especially Agility™) exceeded the contact stress recommended for the

polyethylene component (10 MPa) and its compressive yield point (13-25 MPa). In fact, these

prostheses still have some untested features and the optimal articulation configuration is currently not

known. On the one hand, mobile-bearing designs (such as S.T.A.R.™) theoretically offer less wear

and loosening because of full conformity and minimal constraint, respectively. On the other hand,

fixed-bearing designs (such as Agility™) avoid the dislocation of the polyethylene component and the

potential increased wear from a second articulation/contact surface.

Afterwards, the internal stress distribution was investigated in the talus for the intact,

TAA+Agility™ (including the old and new talar component designs) and TAA+S.T.A.R.™ models. The

present results showed that stresses increased near the resected surface for both prostheses (taking

into account the two talar components for Agility™). In particular, there was an increase of the

magnitude of stresses in trabecular bone for the three models, which in turn increases the chance of

failure of bone support around prosthesis and consequently the subsidence of the talar component

can occur. When comparing the two talar components of Agility™ prosthesis, the wider shape of the

new talar component design at the posterior edge and the increased contact area provided by it led to

81

a decrease of the maximum internal stresses in the talus. In particular, the maximum Von Mises

stresses decreased from 54.25 MPa (using the old talar component design) to 40.96 MPa (using the

new talar component design). Moreover, the old talar component design originated larger stresses at

the posterior edge, which can explain the early loosening and subsidence of this component. In fact,

clinically, the old talar component design was noted to fail due to posterior subsidence, which is in

accordance with the present results. These results show once again that the new talar component

design has better performance than the old talar component design. Furthermore, when comparing

the stress distribution in the talus using the new talar component design of Agility™ prosthesis and the

talar component of S.T.A.R.™ prosthesis, it is possible to identify an improvement in the stress

distribution in the case of S.T.A.R.™ prosthesis, despite the slight increase in stresses at the anterior

medial side of the talus. In the case of Agility™ a clearly marked area of larger stresses around the

prosthesis was identified, despite not being so significant when comparing with the area originated by

the old talar component design. This was also expected since the S.T.A.R.™ is a three-component,

mobile-bearing design, which means that it is at the same time a congruent and minimally constrained

prosthesis (and thus providing great mobility), whereas Agility™ is a two-component, fixed-bearing

design, i.e., it is a partially conforming and semiconstrained prosthesis, which may originate high axial

and shear constrains at the bone-prosthesis interface. In conclusion, the present results agree that

excessive bone resection results in the prosthesis being seated on trabecular bone that may not

support the forces at the ankle, which consequently may contribute to early loosening and subsidence

of the talar component. Thus, minimal bone resection is required in order to remain firm the bone-

prosthesis interface.

Lastly, the bone remodeling process was investigated in the talus and tibia. The model converged

to a solution with relatively high similarity to the morphology of the tibia, reproducing the behaviour of

the real bone, but with less similarity to the morphology of the talus. This was due to some limitations

of the study that can be improved in future works. It is very important understand the bone remodeling

process prior to the insertion of the prosthesis, and so the validation of the bone remodeling models

obtained for tibia and talus is also an important step before analysing the effects of the ankle

prostheses on these bones. However, if the aim of the study was to analyse the importance on the

bone remodeling process of inserting an ankle prosthesis into the AJC, that can be done by

considering the final bone density distribution obtained from the model of the intact AJC as the initial

bone density distribution of the model of the AJC after the insertion of the prosthesis. This way, it is

possible to analyse only the changes caused by the insertion of the prosthesis.

With this in mind, in order to evaluate the changes in the bone remodeling process that occur in

the tibia and talus after a TAA using Agility™ and S.T.A.R.™ prostheses, the initial density

distributions of the tibia and talus in the TAA+Agility™ and TAA+S.T.A.R.™ models correspond to the

final density distributions of the tibia and talus in the intact model. Regarding the TAA+Agility™ model,

the present results showed a decrease in density in the medial region of the talus beneath the talar

component, which could be associated with stress shielding effect. However, further investigation is

still needed to confirm these results. Regarding the TAA+S.T.A.R.™ model, the present results

showed an increase in density above the two raised cylindrical barrels and a decrease of bone mass

82

in the lateral region of the distal tibia. These results showed that forces are transmitted from the two

raised cylindrical barrels into the bone, which may lead to stress shielding in the area near these two

structures. Moreover, a bone mass loss was also observed in the lateral region beneath the talar

component. This stress shielding effect may contribute to loosening and subsidence of the tibial and/or

talar component, often reported in clinical studies. In conclusion, the bone remodeling model used in

this study has been extensively applied in the studies of the hip ([220, 264, 265]), the spine ([266]) and

the shoulder ([217, 267]). The application of this model to the AJC is considered to be adequate taking

into account the parameters chosen before. However, more computer simulations, and mainly a more

precise quantitative analysis has to be perform in order to proof the accuracy of the present results.

Finally, to conclude, an overall analysis of both stress and bone remodeling results from the FEA

of this work allows concluding that they show good agreement with several clinical and numerical

studies from the literature, which were described above. Moreover, it is important to mention that it

was found only one work in the literature related to the bone remodeling of the ankle joint. That work

considered the tibia and talus as two different models. In the present work, the tibia and talus were

considered in the same model. In fact, it was not found any similar work to the present work, and so

this thesis can be a complement to the previous research on ankle joint.

5.2 Limitations of the Work and Future Directions

Among the main limitations of the present study are the loading conditions considered in the

models. In the best case, only three different static load cases were applied to each model. These

selected load cases correspond to discrete times of the stance phase of gait and are considered

representative of the range of loads developed during the stance phase. However, in reality more

complex loading conditions can be expected. The applied loading conditions result from the fact that,

as mentioned before, there are not enough computational resources to consider the entire range of

loads of the stance phase of gait. Moreover, there is no information in the literature about the muscular

forces, and so they were not included in the present work. In future works, force patterns derived from

multibody simulations should be incorporated into the FE models in order to examine the influence of

the muscular forces. The research in TAA would benefit from further in vivo studies of the forces

acting across the ankle joint, such as instrumented, telemeterized prosthesis. Also, further analysis of

other gait activities, such as chair climbing, squat, among others, are required. Moreover, it is

important to notice that considering the same loading conditions to the three models (intact,

TAA+Agility™, TAA+S.T.A.R.™) is also a limitation of this work because, for instance, due to the

arthrodesis performed during the TAA with the Agility™ prosthesis it is expected a higher percentage

of the load carried by the fibula, and as mentioned before, the patients with disabling joint disease

before and even after undergoing TAA present lower loads at the ankle joint than healthy subjects.

Nevertheless, at the same time the application of the same loads to the three models would provide a

more consistent analysis of the results.

As stated before, the real attachment sites for the ligaments into talus may occupy a larger area

than the one that was considered, which would have a direct impact on the bone remodeling. To

overcome this problem, different ways of modeling the ligaments should be tested. Also, navicular was

83

not included in the model and so the loads that are originated in the talus from the contact surfaces of

the talus and navicular are not observed in the present model. It is important to mention that originally

navicular was not included in the model since the talar component is placed in the dorsum of the talus,

and so the changes in stress distribution and bone density after a TAA occur mainly in the area

adjacent to that component. Also, this was done in order to reduce the complexity of the model.

However, the conclusion is that navicular should be important to better analyse the bone density

distribution after a TAA and so in future works it would be important to include navicular or in some

way simulate the contact forces originated at the anterior side of the talus.

The solid models of the bones were obtained from the VAKHUM project and there was no access

to the CT scan images of the subject whose bones were analysed. Due to that fact, it was necessary

to use other CT scan images that could have a significantly different geometry. Moreover, all analyses

were performed with the same bone geometry (from the same subject) and the dependency of the

results on the bone geometry was not addressed. Thus, in future works it would be important to

include a greater number of bones (from different subjects) in order to sustain the results obtained.

Lastly, it is very important to notice that ankle joint axis was defined “manually” and the calcaneus

was moved along with the talus according to that ankle joint axis, and not according to the subtalar

joint axis. If the aim of the study was to analyse the exact contact stress distribution in the ankle joint it

would be important to determine by a more accurate way the exact position of the ankle joint axis.

To conclude, further investigation is still required and is actually planned regarding the previously

described limitations. Furthermore, some other possible guidelines for future works are listed below.

Determination of the forces experienced by the ligaments in dorsiflexion, plantarflexion and

neutral positions for the three models developed in this study and comparison of these forces

with the forces at failure of each ligament. This would show which prosthesis best preserves

the ligamentous configuration of the intact AJC.

Determination of the internal stress distribution in the tibia before and after the insertion of the

Agility™ and S.T.A.R.™ prostheses, like what was done in this study for talus.

Investigation of the effect of modeling the bone-prosthesis interface with contact (frictionless

and with friction), instead of bonded, and comparison of the results. The correct simulation of

the different interfaces in the models is essential to obtain more realistic results.

Validation of the bone density distributions determined for the intact tibia and talus by the bone

remodeling model. This can be done by analysing and comparing the bone remodeling results

with the real bone density of the specimen.

Quantification of the importance of the quality of the initial bone, the muscle action, among

other factors. For instance, the importance of the quality of the initial bone can be quantified

by increasing the value of the parameter k in the bone remodeling simulation for the intact

model, and then consider the final bone density distribution of the intact model as the initial

bone density distribution of the models with prostheses.

Division of the bones into regions of interest that can be separately analysed. This would allow

observing the remodelling process in more detail.

Analysis of more total ankle prosthesis, specially the new designs introduced on the market.

85

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97

Appendix A

In the following figures different views of the prosthetic components and the prostheses (after the

assembly of the components) created in the present study are shown for a more detail analysis.

Figure A.1 Different views of the geometric model of the Agility™ prosthesis, considering the new talar component

design (for exemplification purposes). Software used: SolidWorks®.

98

Figure A.2 Different views of the geometric model of the tibial component of the Agility™ prosthesis. Software

used: SolidWorks®.

Figure A.3 Different views of the geometric model of the polyethylene component/fixed-bearing of the Agility™


99

Figure A.4 Different views of the geometric model of the new talar component design of the Agility™ prosthesis.

Software used: SolidWorks®.

Figure A.5 Different views of the geometric model of the old talar component design of the Agility™ prosthesis.

Software used: SolidWorks®.

100

Figure A.6 Different views of the geometric model of the S.T.A.R.™ prosthesis. Software used: SolidWorks®.

Figure A.7 Different views of the geometric model of the tibial component of the S.T.A.R.™ prosthesis. Software

used: SolidWorks®.

101

Figure A.8 Different views of the geometric model of the polyethylene component/mobile-bearing of the

S.T.A.R.™ prosthesis. Software used: SolidWorks®.

Figure A.9 Different views of the geometric model of the talar component of the S.T.A.R.™ prosthesis. Software

used: SolidWorks®.

102

Appendix B

The surgical technique for implantation of Agility™ prosthesis is illustrated below.

Figure B.1 Illustration of the bone resection technique for implantation of Agility™ prosthesis (adapted from [182]).

Figure B.2 Illustration of the insertion of the prosthetic components of Agility™ prosthesis (3 – Tibial component

and fixed-bearing; 4 – Talar component) and of the arthrodesis performed at the end of procedure (5) (adapted

from [182]).

103

The surgical technique for implantation of S.T.A.R.™ prosthesis is illustrated below.

Figure B.3 Illustration of the bone resection technique for implantation of the tibial component of the S.T.A.R.™

prosthesis (adapted from [228]).

Figure B.4 Illustration of the bone resection technique for implantation of the talar component of the S.T.A.R.™

prosthesis (adapted from [228]).

104

Figure B.5 Illustration of the insertion of the prosthetic components of S.T.A.R.™ prosthesis: 1 – Talar

component; 2 – Tibial component; 3 – Mobile-bearing; 4 – TAA completed (adapted from [228]).

105

Appendix C

Intact model

The resulting FE meshes of the intact model are presented in Figure C.1.

Figure C.1 FE meshes of the intact model: A – Tibia (green) and the corresponding cartilage (blue); B –

Interosseous membrane (yellow); C – Fibula (green) and the corresponding cartilage (blue); D – Talus (green)

and the corresponding cartilages (blue); E – Calcaneus (green) and the corresponding cartilage (blue); F – Intact

model. Software used: ABAQUS®.

The number of elements and nodes of each FE mesh of the intact model is presented in Table

C.1.

Table C.1 Number of elements and nodes of the FE meshes of the intact model.

Part Number of elements Number of nodes

Calcaneus 88650 16888

Calcaneus’s cartilage 9519 3194

Talus 87105 16637

Talus’s up cartilage 21699 7150

Talus’s down cartilage 12280 4212

Tibia 145967 27955

Tibia’s cartilage 10239 3542

Fibula 68889 14155

Fibula’s cartilage 4939 1748

Interosseous membrane 26420 7106

Ligaments 1 2

106

Finally, the plantarflexion, neutral and dorsiflexion positions for the intact model are presented in

Figure C.2.

Figure C.2 The three positions under study for the intact model: A – Plantarflexion position; B – Neutral position;

C – Dorsiflexion position. Software used: ABAQUS®.

TAA+Agility™ model

The resulting FE meshes of the TAA+Agility™ model are presented in Figure C.3. For

exemplification purposes, it is only presented the case for the new talar component design.

Figure C.3 FE meshes of the TAA+Agility™ model: A – The two screws and the plate (purple); B – Agility™

prosthesis; C – Tibial component (blue); D – Polyethylene component (orange); E – New talar component design

(yellow); F – Cut tibia and fibula (green), the interosseous membrane (yellow) and bone graft (orange); G – Cut

talus (green) and the corresponding inferior cartilage (blue); H – TAA+Agility™ model. Software used: ABAQUS®.

107

The number of elements and nodes of each FE mesh of the TAA+Agility™ model are presented in

Table C.2.

Table C.2 Number of elements and nodes of the FE meshes of the TAA+Agility™ model.




Talus 71016 13746


New talar component design 14746 3211

Old talar component design 10775 2340

Polyethylene 15013 3286

Tibial component 18481 4115

Tibia 152862 29153

Fibula 69190 14283

Screw 1 1729 538

Screw 2 1831 575

Plate 2737 1068

Bone graft 25382 5447


Ligaments 1 2

Finally, the plantarflexion, neutral and dorsiflexion positions for the TAA+Agility™ model are

presented in Figure C.4.

Figure C.4 The three positions under study for the TAA +Agility™ model: A – Plantarflexion position; B – Neutral

position; C – Dorsiflexion position. Software used: ABAQUS®.

108

TAA+S.T.A.R.™ model

The resulting FE meshes of the TAA+S.T.A.R.™ model are presented in Figure C.5.

Figure C.5 FE meshes of the TAA+S.T.A.R.™ model: A – S.T.A.R.™ prosthesis; B – Tibial component (blue); C –

Polyethylene component (orange); D – Talar component (yellow); E – Cut tibia (green); F – Cut talus (green); G –

TAA+S.T.A.R.™ model. Software used: ABAQUS®.

The number of elements and nodes of each FE mesh of the TAA+S.T.A.R.™ model are presented

in Table C.3.

Table C.3 Number of elements and nodes of the FE meshes of the TAA+S.T.A.R.™ model.




Talus 81489 15915


Talar componente + keel 7155 + 1473 2140 + 384

Polyethylene 17089 3659

Tibial component 12601 3100

Tibia 143509 27694

Fibula 68889 14155


Ligaments 1 2

109

Finally, the plantarflexion, neutral and dorsiflexion positions for the TAA+S.T.A.R.™ model are

presented in Figure C.6.

Figure C.6 The three positions under study for the TAA+S.T.A.R.™ model: A – Plantarflexion position; B – Neutral

position; C – Dorsiflexion position. Software used: ABAQUS®.

110

Appendix D

The algorithm for transition of the tibia and talus’ densities from the intact model to the

TAA+Agility™ and TAA+S.T.A.R.™ models is schematized below.

Figure D.1 Algorithm flow diagram.