research article a hertzian integrated contact model of...

Research ArticleA Hertzian Integrated Contact Model of the Total KneeReplacement Implant for the Estimation of Joint Contact Forces

Tien Tuan Dao and Philippe Pouletaut

Sorbonne Universites Universite de Technologie de Compiegne CNRS UMR 7338 Biomecanique et BioingenierieCentre de Recherche Royallieu CS 60 319 60 203 Compiegne France

Correspondence should be addressed to Tien Tuan Dao tien-tuandaoutcfr

Received 26 August 2015 Revised 17 September 2015 Accepted 29 September 2015

Academic Editor Darryl D DrsquoLima

Copyright copy 2015 T T Dao and P Pouletaut This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The prediction of lower limb muscle and contact forces may provide useful knowledge to assist the clinicians in the diagnosis aswell as in the development of appropriate treatment for musculoskeletal disorders Research studies have commonly estimatedjoint contact forces using model-based muscle force estimation due to the lack of a reliable contact model and material propertiesThe objective of this present study was to develop a Hertzian integrated contact model Then in vivo elastic properties of the TotalKnee Replacement (TKR) implant were identified using in vivo contact forces leading to providing reliable material properties formodeling purposes First a patient specific rigidmusculoskeletalmodel was built Second a STL-based implantmodel was designedto compute the contact area evolutions during gait motions Finally a Hertzian integrated contact model was defined for the in vivoidentification of elastic properties (Youngrsquos modulus and Poisson coefficient) of the instrumented TKR implant Our study showeda potential use of a new approach to predict the contact forces without knowledge of muscle forces Thus the outcomes may leadto accurate and reliable prediction of human joint contact forces for new case study

1 Introduction

Total Knee Replacement (TKR) implant has been commonlyprescribed for patients with severe knee joint damage (egosteoarthritis) associated with progressive pain and impairedfunction [1 2] The implant with distal femoral and proximaltibial compartments is usually created with biocompatiblematerials [3 4] Besides TKR implant may include patella-femoral interaction which helps the knee joint to be func-tionally stabilized It is important to emphasize that the kneecontact force behaviors are activity-specific and the optimaldesign of the TKR may lead to maximizing the clinicaloutcomes However the implant design may be optimizedwhen its effect on the musculoskeletal tissues and structurescould be elucidated [5] Joint contact forces play an importantrole in the understanding of the effect of the implant on thejoint behavior and musculoskeletal load [6] Finite elementmodeling may provide reliable information on the jointcontact force behavior However the lack of accurate musclemodeling and reliable definition of boundary and loading

conditions may affect the contact force computation [7 8]Research studies demonstrated a deeper knowledge of hipimplant effect thanks to computational rigid-body modelsand available in vivo experimental data measured directlywithin the instrumented hip implant [9ndash11] Recently invivo knee contact forces can be measured from a new kneedevice [12 13] Thus for the first time computational rigidmusculoskeletal models used to facilitate the surgical andfunctional rehabilitation treatments of the musculoskeletaldisorders may be evaluated for their predictive capacitiesrelated to muscle force estimation and knee contact loadby using these available experimental data [14 15] Thusthese models may be potentially accepted in a clinical routineprocedure in the future [9 16] Moreover an open and freeaccess database (httpwwwortholoadcom) of the ortho-pedic implant loads was also provided leading to promotingextensive research activities in this field of study

The prediction of in vivo muscle and contact forcesespecially within a Total Knee Replacement is a challengingtask for biomechanical engineersresearchers Model-based

Hindawi Publishing CorporationJournal of Computational MedicineVolume 2015 Article ID 945379 9 pageshttpdxdoiorg1011552015945379

2 Journal of Computational Medicine

estimation of these forces has been commonly performed[17ndash19]Thus the redundant phenomena of the humanneuralcontrol (ie the number of muscles is greater than thenumber of degrees of freedom) may be computationallysolved using optimization techniques even if the best opti-mization strategy remains unknownHowever the predictionaccuracy of such forces depends on the accurate modelingof musculoskeletal tissues (eg muscles bone tendonsligaments and cartilage) and structures (eg joint) as wellas appropriate formulation of physical behaviors (eg jointcontact or multi-body dynamics) [19 20] Model validationhas been a challenging issue Qualitative pattern of themuscle force was commonly validated against the EMG-based muscle activities

In vivo knee contact forces may be computationallyestimated with or without contact model On the one handmodel-based efforts related to the use of inverse dynamicsapproach coupled with an elastic contact model Withinthe scope of this vision Kim et al [21] developed two-stage simulation to compute the muscle forces and thencombine them with ground reaction forces and fluoroscopicdata within a Hertzian contact model to predict the kneecontact forces Moreover Hast and Piazza [22] used acoupling between inverse dynamics forward dynamics andcomputed muscle control (CMC) algorithm within a spring-based contact model to compute the nodes-to-surface kneecontact forces On the other hand knee contact forceshave been predicted without contact model Based on themuscle forces estimated from pseudoinverse method andconstrained static optimization with Lagrange multipliersformulation and parameter reduction strategy [23] con-tact forces were computed Moreover Electromyography-(EMG-) driven muscle force estimation approach coupledwith moment balancing algorithm has been used to predictthe medial contact force [24 25] Furthermore a parametricnumerical model including 9 equilibrium equations reflect-ing muscle activation levels passive structure activationjoint moments external joint forces maximum physiologicalmuscle moments and forces has been also developed topredict the knee contact forces [26] In fact without contactmodel the problem formulation and computational cost maybe more advantageous than the use of a contact modelA recent comparison of predicted contact forces in theframework of the Knee Grand Challenge showed that theuse of a contact model does not guarantee their accuracy[15] However a deformable contact model may provideuseful knowledge about the interactions between the implantcomponents and also those at bone-to-implant surface It isimportant to note that the Knee Grand Challenge has beencreated to open a new dimension on the prediction of invivo muscle and contact forces [14 15] Almost all availablemeasurements ranging from medical imaging data to gaitanalysis and experimental contact forces were provided toenhance the research activities related to the prediction ofthese forces

Previous studies used only simplified representation (egone point contact or nodes-to-surface contact) of contactsurface between implant components Moreover materialproperties of the implants were commonly provided by

manufacturer However assumptions were commonly per-formed for musculoskeletal modelingThus these propertiesneed to be calibrated and fitted to the modeling assumptionfor predicting accurately the knee contact forces In factpredictive trends of numerical models are limited for clinicalapplications Thus the objectives of this present study aretwofold (1) the development of a Hertzian integrated contactmodel based on a global surface-to-surface interaction and(2) the use of in vivo contact forces and the developed contactmodel to identify the reliable and fitted elastic properties ofthe implant for modeling purpose

2 Materials and Methods

21 Computational Workflow A computational workflowwas developed to identify the elastic properties of theinstrumented TKR implant (Figure 1) The workflow consistsof the following components (1) a patient specific rigidmusculoskeletal model to compute the knee kinematics fromskin-mounted markersrsquo trajectories (2) a STL-based implantmodel to compute the contact area evolution during kneemotion and (3) aHertzian integrated contactmodel for the invivo identification of elastic properties (Youngrsquos modulus andPoisson coefficient) of the instrumented TKR implant usingcontact area information and in vivo measured joint contactforces

22 Patient Data The patient data from the fourth editionof the Knee Grand Challenge [14] was used in this presentstudy Imaging and gait data were acquired on a patient(male 88 years old 168 cm body height 667 kg body massand 236 kgm2 Body Mass Index (BMI)) with knee implantinstrumented in his right knee side (Figure 2(a)) The patienthad Rockport flat bottom sneakers shoes during the gait dataacquisition process The patient performed an overgroundnormal gait pattern which was used as reference patternThen 4 overground gait trials reflecting 4 gait modificationstrategies (bouncymedial thrustmild crouch andmtp)wereacquired using an 8-camera Vicon system (Table 1) All skin-mounted markers were posed using a modified ClevelandClinic marker protocol [14] In vivo knee contact forces werealso obtained during the gait data acquisition Four uniaxialload cell measurements (posterior-medial (PM) anterior-medial (AM) anterior-lateral (AL) and posterior-lateral(PL)) from the instrumented tibial prosthesis were performed(Figure 2(b)) The first generation of tray design (eKnee)was used The main implant components were fabricatedin CoCr polyethylene and titanium Sampling frequency is120Hz Furthermore pre- and postsurgery CT data were alsoacquired on the patient using a SiemensCTmachine the slicethickness was set up as 06mm The matrix is 512 times 512 andthe pixel resolution is 09 times 09mm2 The number of slices is1900 for the whole scanned lower limb

23 Patient Specific Rigid Musculoskeletal Model

231 Model Development To compute the knee kinematicsa patient specific musculoskeletal model which is provided

Journal of Computational Medicine 3

Patient

model Inverse kinematics

Markersrsquo trajectories

Material properties

Joint kinematics

Hertzian integrated eKnee data

Optimization block

Geometric computing

STL-based implant

(E )

F

R

d

120572Hertz

model

contact model

specific rigid

Figure 1 Workflow of the computational process to in vivo characterize the elastic properties of the instrumented TKR implant

(a)

AM

PM

AL

PL

(b)

Figure 2 Geometrical components of the TKR implant within the skeletal model (a) and locations of 4 load cells (posterior-medial (PM)anterior-medial (AM) anterior-lateral (AL) and posterior-lateral (PL)) used to measure the contact forces (b)

Table 1 Description of normal gait and gait modification strategies

Gait modifications Description Trial name gait cycle times (start gt end)(time in sec)

Ngait Normal gait Ngait og1 1699 gt 2811 (1112)

Bouncy Increased superior-inferior translation ofthe pelvis Bouncy1 2066 gt 3214 (1148)

Medial thrust Internally rotated hip of the stance leg Medthrust2 2415 gt 3571 (1156)

Midcrouch Crouched position with a mild increase inknee flexion angle Mildcrouch1 10822 gt 11901 (1079)

Mtp Gait with forefoot strike Mtpgait2 2276 gt 3421 (1145)


Dist

ance

map

(mm

)

40

30

20

10

00

0∘

15∘

30∘

45∘

Figure 3 Illustration of knee contact area evolution map

from the fourth edition of the Knee Grand Challenge [14]was used This model has 8 segments (pelvis right femurfemoral implant component patella tibial implant com-ponent right tibia right fibula and right foot) Imagesegmentation using SliceOmatic (Montreal Canada) wasperformed on the post- and presurgery CT data and laser-scan-based implant component to extract bony segmentsand implant components STL-based surface geometries werecreated and imported into OpenSIM engine [27] to developcorresponding bony segments The model has 24 degrees offreedom (DOF) (6-DOF ground-to-pelvis joint 3-DOF hipjoint 6-DOF tibiofemoral joint 6-DOF patellofemoral joint2-DOF ankle joint and 1-DOF toes joint) The interactionbetween implant components and its respective bone wasmodeled using an OpenSIM weld joint The interactionbetween implant components (femoral component tibialtray and patellafemoral component) was modeled using anOpenSIM reverse joint All segment coordinate systems werebased on the ISB recommendations [28] The model has 22skin-mounted virtual markersrsquo cluster according to the realmarket cloud used in the motion capture acquisition Thismodel has 44 lower limb muscles Each muscle was modeledas a Schutte muscle model [29] Muscle attachment pointsand wrapping surface were created using an available lowerlimbmodel [30] A transformation process using informationfrom bone-to-bone alignment was performed to morphthe patient specific musculature Some attachments pointsand unrealistic intersection of muscle lines of action weremanually adjusted

232 Joint Angle Computing Based on skin-mountedmarkerrsquos trajectories inverse kinematics was performed tocompute the knee joint angles of each gait pattern (normalbouncy medial thrust mild crouch and mtp) At each timestep (ie frame of motion) generalized coordinate valueswere computed to put the model in a best-fitting pose inminimizing the deviation between the experimental markersrsquo

and estimated coordinate values The deviation is expressedas a weighted least squares problem as follows

min119902[ sum119894isinmarkers119908119894

1003817100381710038171003817119909exp119894minus 119909119894(119902)10038171003817100381710038172

] (1)

where 119902 is the vector of generalized coordinates 119908119894is the

marker weight 119909exp119894

is the experimental position of themarker 119894 119909

119894(119902) is the position of the corresponding marker

on the model

24 STL-Based Implant Model and Contact Area ComputingBased on the reconstructed implant components a geometri-cal computing process was applied to compute the surface-to-surface contact area evolution according to each series of kneekinematics (eg flexionextension) Threshold-based mini-mal distance principle was used to compute the implant-to-implant contact area minimal distance map was computedand area under the threshold of 4mm was calculated [31]The threshold was calibrated using experimental data of theknee contact area [32] An illustration of contact area mapduring knee flexionextension from 0 to 90 degrees is shownin Figure 3

25 Hertzian Integrated Contact Model

251 Contact Model To describe the physical relation-ships between the applied force and the contact behaviora Hertzian linearly elastic contact model was formulatedThis model describes conservative interaction forces [33]Constitutive equation of this model is expressed as follows

119865Hertz =2

3119877

119864

(1 minus V2)(119886Hertz)

3

(2)

where 119865Hertz and 119886Hertz are applied force and its respectivecontact radius 119877 is the radius of the contact cylinder


Medial condyle Lateral condyle

F

R

120572Hertz

d

FLateralFMedial

Figure 4 Schematic representation of a Hertzian elastic contact model

(eg femoral condyle) (Figure 4) 119864 and V are Youngrsquosmodulus and Poisson coefficient respectively It is assumedthat 119877 is constant for different knee flexionextension angles

252 Elastic Property Identification To identify the appro-priate values of the implant elastic material properties (119864 andV) an optimization problem was formulated as follows

min119906

10038171003817100381710038171003817119865Hertzminus 119865

eKnee100381710038171003817100381710038172

Subject to 119864 gt 0 0 lt V lt 05

119886Hertz = radic119878

120587

(3)

where 119865eKnee is the in vivo measured contact force 119906 is a setof knee angles 119878 is the total contact area computed by themethod described in Section 24 To compute the value of 119877a cylinder-fitting process was applied The values of in vivomeasured contact forces were calculated from the load cellmeasurements (119865AM 119865PM 119865AL 119865PL) (Figure 2(b)) by using thefollowing validated regression equations [34]

119865eKnee= 119865

Medial+ 119865

Lateral

119865Medial= 09871119865AM + 09683119865PM + 00387119865AL

+ 00211119865PL

119865Lateral= 00129119865AM + 00317119865PM + 09613119865AL

+ 09789119865PL

(4)

The constrained optimization process was performed usinga quasi-Newton approach implemented in the OptimizationToolbox in Matlab R2010b (Mathworks USA)

3 Results

31 Determination of Contact Cylinder Radius 119877 The fittedcylinder used to compute the value of the radius 119877 is shown

in Figure 5 It is important to note that two physiologicalcondyles were assumed to be symmetric Thus the kneejoint behavior functions like a hinge joint A value of 37mmwas found with a mean error of 1652mm from 1024 pointsbetween the fitted cylinder and the external femoral surfaceof the implant component Note this error is relatively highdue to the assumption of constant 119877 for different kneeflexionextension angles

32 Knee Kinematics duringGaitMotions Figure 6 shows theevolution of knee flexionextension angles during the normalgait with instrumented TKR implant The total squarederror between real markersrsquo coordinates and virtual makersrsquocoordinates computed by inverse kinematics process rangesfrom000072 to 000215mm for 326 framesThe same patternwas obtained for other gait patterns with a first peak-to-peakabsolute deviation ranging from 56 to 185 degrees as well asa second peak-to-peak absolute deviation ranging from 18 to852 degrees It is important to note that these deviations aredue to temporal shifts when modifying the gait patterns

33 Implant-to-Implant Contact Area Evolution The evolu-tion of implant-to-implant contact area during the stancephase (60) of the normal and modified gaits is illustratedin Figure 7 The peak contact area values range from 1016 to1117mm2 for all gait patterns According to the normal gaitthe patterns of the contact area are different for all modifiedstrategies except for the Medthrust These differences aredirectly related to the differences in the kinematics patternsof these modified strategies

34 In Vivo Contact Forces and Implantrsquos Elastic PropertiesThe in vivo medial contact forces during the normal and4 modified gaits are shown in Figure 8 Root mean squareerrors (RMSE) between the normal gait and bouncy medialthrust mild crouch mtp gaits are 2225 1928 1323 and17777N respectively for the medial side On the other hand


Figure 5 Fitted cylinder of the femoral implant component

Gait cycle ()0 20 40 60 80 100

10

20

30

40

50

60

70

Knee

flex

ion

exte

nsio

n an

gle (

∘)

Figure 6 Evolution of knee flexionextension angles during thenormal gait with instrumented TKR implant

BouncyMedthrustMidcrouch

MtpgaitNgait

100 20 30 40 50 601040

1060

1080

1100

1120

1140

1160

Gait cycle ()

Con

tact

area

(mm2)

T Fukubayashi and H Kurosawa1980 (cadaveric testing 1000N load)

Figure 7 Implant-to-implant contact area evolutions during gait

0 20 40 60 80 100Gait cycle ()

Med

ial f

orce

(N)

200

400

600

800

1000

1200


MtpgaitNgait

Figure 8 Evolutions of in vivo contact forces at the medial side ofthe TKR implant

lateral side revealed a RMSE of 1202 1226 911 and 896Nfor comparison between the normal and the bouncy medialthrust mild crouch andmtp gaits respectivelyThemaximalRMSE of the medial contact force is 2225N between thenormal and the bouncy gaits The maximal RMSE of thelateral contact force is 1226N between the normal andthe medial thrust gaits Using the total contact forces withthe integrated contact model the optimization process wasconverged after 6 iterations (3 15 30 33 36 39 and 42function calls resp) at the minimal objective function valueof 116437119890 minus 009 Thus optimal Youngrsquos modulus was 467GPa and its respective Poisson coefficient was 025

Figure 9 shows the evolutions of predicted contact forcesusing integrated contact model and experimental eKnee datafor the normal gait A good convergence (ie error betweenpredicted results and experimental data leads nearly to 0) was


Gait cycle ()0 10 20 30 40 50 60

Tota

l con

tact

forc

es (N

)

400

600

800

1000

1200

1400

1600

1800

Hertzian elastic contact modelExperimental eKnee data

Figure 9 Comparisons between predicted contact forces usingintegrated contact model and experimental eKnee data for thenormal gait

noted over the 54 of the gait cycle However the amplitudesand trends of the predicted values were largely different inearly phase of the gait cycle This is due to the modelingassumption of the ideal symmetric contact model

4 Discussion

The prediction of in vivo muscle and contact forces playsan important role in the objective and precise diagnosis andtreatment of the musculoskeletal disorders in the future [910 14 35 36] In fact the use of computational models mayallow the clinicians to perform a series of virtual treatmenttrials without any dangerous risk for the involved patientsMoreover optimal treatment plan may be elucidated withobjective data related to its effect on the musculoskeletaltissues and structures However the validation of modelbehaviorprediction against critical experimental data isextremely a challenging task especially for in vivo estimatedmuscle and contact forces Skeletal muscle with its multiscalearchitecture revealed a complex (eg anisotropic or hetero-geneous) living material Hill-based macroscopic rheologicalmodel has been commonly used to define the physiologicalforce-length and force-velocity relationships [37] Despitemany efforts during the last several decades to estimate the invivo muscle forces using inverse dynamics and optimizationor EMG-driven approach [17 19 20 24 25 29] the lackof in vivo experimental data for direct and quantitativevalidation purposemay be one of the obstacles to promote theuse of computational musculoskeletal models in the clinicalsetting Recently technological progress allows measuringin vivo contact forces within instrumented implants (egat the hip and knee levels) [9 12 13] which could be usedto validate indirectly the muscle force estimation Howeverthese data are only available for patients with instrumentedimplant Thus the accurate and reliable prediction and itsquantitative validation of these forces on the healthy subjectsto prevent themusculoskeletal diseases remain a challenge formusculoskeletal modeling community

Regarding the Knee Grand Challenge a series of editionshas been organized and many efforts have been investigatedto predict the in vivo contact forces using different approaches[15 21ndash26] In fact contact forces may be predicted with orwithout a contact model formulation Even if the approachwithout a contact model revealed interesting results [26] thisapproach is based purely on the numerical power to find thestatistical correlation pattern between the contact forces andother physically measurable or computable quantities such asEMG-basedmuscle activation levels or maximum physiolog-ical musclemoments Besides the use of a contactmodelmayprovide more descriptive and meaningful information insidethe implant-to-implant interaction under musculoskeletalload However current approach based on Hertzian contactmodel has two disadvantages The first one relates to thestrong constraint of the use of muscle forces to predict thecontact forces due to the lack of contact area informationThe second one deals with the simplified representationof the contact interaction Thus nodes-to-surface approachis commonly used However the number and location ofnodes may be sensitive factors influencing the prediction ofthe contact forces This present study developed a Hertziancontact model integrating contact area information Indeedmuscle forces are not necessary to predict the contact forcesMoreover thanks to available in vivo contact forces elasticproperties (Youngrsquos modulus and Poisson coefficient) of theimplant were numerically identified and thenmay be used forthe further prediction of the new patient case Furthermorewhen the reliable contact forces are known muscle forcesmay be further estimated in a reliable manner In additionthe knowledge of the contact area may allow other contactproperties such as contact pressure and surface energy to becomputed leading to better understanding of the effect ofTKR implant on the musculoskeletal tissues and structures

From methodological point of view the fact that muscleforces are not required to predict the contact forces leadsto avoiding the limitations of the muscle force estima-tion approaches For example inverse dynamics and staticoptimization showed high residual results due to dynamicinconsistencies between ground reaction forces (GFR) andcaptured kinematics [17 19] Kinematical errors comingfrom anatomical representation marker registration andsoft tissue artifacts may alter the accuracy of the results[12] Moreover the inaccuracy may come from the noise inGRF or drift effect over time Furthermore the choice ofthe objective function may create nonuniqueness solutionsEMG-driven approach has computational complexity Inaddition the accuracy of estimated muscle forces dependson the accuracy of EMG signals related to electrode type andlocation Furthermore EMG signal processing approachmayalter significantly the simulation results [38]

Regarding our identification process the value of cylin-der radius (119877) fitted to the femoral implant componentis very close to the value used in the literature (119877 =40mm) [21] Moreover a good agreement was also notedbetween our contact area and the literature value acquiredfrom cadaveric testing with 1000N of load (Figure 8) [32]The contact evolution maps revealed a more descriptivesurface-to-surface interaction between implant components


The accuracy of our prediction depends strongly on the con-tact area estimation Thus the input data such as joint angleneeds to be accurately computedThe use of a patient specificmusculoskeletal model without scaling step may guaranteethe minimal errors between virtual marker coordinates andthe real marker ones during inverse kinematics process [19]However the lack of knowledge about themuscles forcesmaylead to the neglect of the contact force balance ratio betweenmedial and lateral sides [14] Moreover the present definitionof the contact model is global and its behavior is symmetricFurthermore from computational point of view this contactarea process is dissociated from the inverse kinematicsanalysis Indeed further work will be investigated for thecosimulation of these physics with asymmetric definitionof the contact model integrated side-dependent kinematicdata such as joint abductionadduction patterns In this caseadvanced computational paradigm needs to be developed[18 23] Thus available fluoroscopic data will provide preciseand local information on the translation and rotation of theimplant leading to possibly achieving this challenging goal

In addition the use of a Hertzian contact model allowsonly the description of conservative interaction forces via alinearly elastic behavior More advanced contact models needto be investigated For example Derjaguin-Muller-Toporov(DMT) model [39] may provide elastic behavior and van derWaals forces outside the contact region Moreover Johnson-Kendall-Robert (JKR) model [40] allows defining the adhe-sion (ie short-range forces in the contact area) phenomenaand this model may be used to predict infinite stress atedge of contact circle and nonconservative interaction forcesFurthermore themodel needs to be refined for other types ofimplants with different designs

In conclusion reliable elastic properties of the TKRimplants were identified using a Hertzian integrated contactmodel and in vivo contact forces The availability of contactarea information allows the in vivo prediction of contactforces without knowledge of the muscle forces Thus ourpresent study demonstrated a potential use of such approachin the accurate and reliable prediction of human joint contactforces leading to better diagnosis and a more suitable treat-ment prescription for patients with instrumented implants torecover locomotion function and to improve the quality ofdaily activities of life

Conflict of Interests

The authors declare no conflict of interests

Acknowledgment

The authors would like to thank the organizers of the KneeGrand Challenge for providing available useful data forresearch purposes

References

[1] T K Fehring S Odum W L Griffin J B Mason and MNadaud ldquoEarly failures in total knee arthroplastyrdquo ClinicalOrthopaedics and Related Research no 392 pp 315ndash318 2001

[2] E A Lingard J N Katz E A Wright and C B SledgeldquoPredicting the outcome of total knee arthroplastyrdquoThe Journalof Bone amp Joint SurgerymdashAmerican Volume vol 86 no 10 pp2179ndash2186 2004

[3] C E H Scott M J Eaton R W Nutton F A Wade PPankaj and S L Evans ldquoProximal tibial strain in medialunicompartmental knee replacements a biomechanical studyof implant designrdquo Bone and Joint Journal vol 95 no 10 pp1339ndash1347 2013

[4] P Pankaj ldquoPatient-specificmodelling of bone and bone-implantsystems the challengesrdquo International Journal for NumericalMethods in Biomedical Engineering vol 29 no 2 pp 233ndash2492013

[5] A A Oshkour N A A Osman M M Davoodi et alldquoFinite element analysis on longitudinal and radial functionallygraded femoral prosthesisrdquo International Journal for NumericalMethods in Biomedical Engineering vol 29 no 12 pp 1412ndash14272013

[6] B J Fregly ldquoDesign of optimal treatments for neuromuscu-loskeletal disorders using patient-specific multibody dynamicmodelsrdquo International Journal of Computational Vision andBiomechanics vol 2 no 2 pp 145ndash154 2009

[7] J P Halloran A J Petrella and P J Rullkoetter ldquoExplicitfinite element modeling of total knee replacement mechanicsrdquoJournal of Biomechanics vol 38 no 2 pp 323ndash331 2005

[8] M Taylor R Bryan and F Galloway ldquoAccounting for patientvariability in finite element analysis of the intact and implantedhip and knee a reviewrdquo International Journal for NumericalMethods in Biomedical Engineering vol 29 no 2 pp 273ndash2922013

[9] M O Heller G Bergmann J-P Kassi L Claes N P Haas andG N Duda ldquoDetermination of muscle loading at the hip jointfor use in pre-clinical testingrdquo Journal of Biomechanics vol 38no 5 pp 1155ndash1163 2005

[10] G Bergmann F Graichen A Rohlmann et al ldquoRealisticloads for testing hip implantsrdquo Bio-Medical Materials andEngineering vol 20 no 2 pp 65ndash75 2010

[11] V Schwachmeyer P Damm A Bender J Dymke F Graichenand G Bergmann ldquoIn vivo hip joint loading during post-operative physiotherapeutic exercisesrdquo PLOS ONE vol 8 no10 Article ID e77807 2013

[12] D D DrsquoLima C P Townsend S W Arms B A Morris andC W Colwell Jr ldquoAn implantable telemetry device to measureintra-articular tibial forcesrdquo Journal of Biomechanics vol 38 no2 pp 299ndash304 2005

[13] B Kirking J Krevolin C Townsend C W Colwell Jr andD D DrsquoLima ldquoA multiaxial force-sensing implantable tibialprosthesisrdquo Journal of Biomechanics vol 39 no 9 pp 1744ndash17512006

[14] B J Fregly T F Besier D G Lloyd et al ldquoGrand challenge com-petition to predict in vivo knee loadsrdquo Journal of OrthopaedicResearch vol 30 no 4 pp 503ndash513 2012

[15] A L Kinney T F Besier D D DrsquoLima and B J Fregly ldquoUpdateon grand challenge competition to predict in vivo knee loadsrdquoJournal of Biomechanical Engineering vol 135 no 2 Article ID021005 2013

[16] J Li A C Redmond Z Jin J Fisher M H Stone andT D Stewart ldquoHip contact forces in asymptomatic total hipreplacement patients differ from normal healthy individualsimplications for preclinical testingrdquo Clinical Biomechanics vol29 no 7 pp 747ndash751 2014


[17] A Erdemir S McLean W Herzog and A J van den BogertldquoModel-based estimation of muscle forces exerted duringmovementsrdquo Clinical Biomechanics vol 22 no 2 pp 131ndash1542007

[18] Y-C Lin J P Walter S A Banks M G Pandy and B J FreglyldquoSimultaneous prediction of muscle and contact forces in theknee during gaitrdquo Journal of Biomechanics vol 43 no 5 pp945ndash952 2010

[19] T T Dao F Marin P Pouletaut F Charleux P Aufaureand M C Ho Ba Tho ldquoEstimation of accuracy of patient-specific musculoskeletal modelling case study on a post polioresidual paralysis subjectrdquo Computer Methods in Biomechanicsand Biomedical Engineering vol 15 no 7 pp 745ndash751 2012

[20] T T Dao P Pouletaut F Charleux et al ldquoEstimation ofpatient specific lumbar spinemuscle forces usingmulti-physicalmusculoskeletal model and dynamic MRIrdquo in Knowledge andSystems Engineering vol 245 of Advances in Intelligent Systemsand Computing pp 411ndash422 Springer 2014

[21] H J Kim J W Fernandez M Akbarshahi J P Walter B JFregly and M G Pandy ldquoEvaluation of predicted knee-jointmuscle forces during gait using an instrumented knee implantrdquoJournal of Orthopaedic Research vol 27 no 10 pp 1326ndash13312009

[22] MWHast and S J Piazza ldquoDual-jointmodeling for estimationof total knee replacement contact forces during locomotionrdquoJournal of Biomechanical Engineering vol 135 no 2 Article ID021013 2013

[23] F Moissenet L Cheze and R Dumas ldquoA 3D lower limb mus-culoskeletal model for simultaneous estimation of musculo-tendon joint contact ligament and bone forces during gaitrdquoJournal of Biomechanics vol 47 no 1 pp 50ndash58 2014

[24] K Manal and T S Buchanan ldquoAn electromyogram-drivenmusculoskeletal model of the knee to predict in vivo jointcontact forces during normal and novel gait patternsrdquo Journalof Biomechanical Engineering vol 135 no 2 Article ID 0210147 pages 2013

[25] P Gerus M Sartori T F Besier et al ldquoSubject-specific kneejoint geometry improves predictions of medial tibiofemoralcontact forcesrdquo Journal of Biomechanics vol 46 no 16 pp2778ndash2786 2013

[26] H J Lundberg C Knowlton and M A Wimmer ldquoFine tuningtotal knee replacement contact force prediction algorithmsusing blinded model validationrdquo Journal of BiomechanicalEngineering vol 135 no 2 Article ID 021008 2013

[27] S L Delp F C Anderson A S Arnold et al ldquoOpenSim open-source software to create and analyze dynamic simulations ofmovementrdquo IEEE Transactions on Biomedical Engineering vol54 no 11 pp 1940ndash1950 2007

[28] G Wu S Siegler P Allard et al ldquoISB recommendation ondefinition of joint coordinate system of various joints for thereporting of human joint motionmdashpart 1 ankle hip and spinerdquoJournal of Biomechanics vol 35 no 4 pp 543ndash548 2002

[29] L M Schutte M Rodgers F E Zajac and R M GlaserldquoImproving the efficacy of electrical stimulation-induced legcycle ergometry an analysis based on a dynamic musculoskele-talmodelrdquo IEEETransactions on Rehabilitation Engineering vol1 no 2 pp 109ndash125 1993

[30] E M Arnold S R Ward R L Lieber and S L Delp ldquoA modelof the lower limb for analysis of human movementrdquo Annals ofBiomedical Engineering vol 38 no 2 pp 269ndash279 2010

[31] T T Dao P Pouletaut J-C Goebel A Pinzano P Gillet andM C Ho Ba Tho ldquoIn vivo characterization of morphological

properties and contact areas of the rat cartilage derived fromhigh-resolution MRIrdquo IRBM vol 32 no 3 pp 204ndash213 2011

[32] T Fukubayashi and H Kurosawa ldquoThe contact area andpressure distribution pattern of the knee a study of normal andosteoarthrotic knee jointsrdquo Acta Orthopaedica Scandinavicavol 51 no 1ndash6 pp 871ndash879 1980

[33] H Hertz ldquoOn the contact of rigid elastic solidsrdquo Journal fur dieReine und Angewandte Mathematik vol 92 pp 156ndash171 1896

[34] D Zhao S A Banks D D DrsquoLima C W Colwell Jr and B JFregly ldquoIn vivo medial and lateral tibial loads during dynamicand high flexion activitiesrdquo Journal of Orthopaedic Research vol25 no 5 pp 593ndash602 2007

[35] S S Blemker D S Asakawa G E Gold and S L Delp ldquoImage-based musculoskeletal modeling applications advances andfuture opportunitiesrdquo Journal of Magnetic Resonance Imagingvol 25 no 2 pp 441ndash451 2007

[36] S F Bensamoun T T Dao F Charleux and M-C Ho BaTho ldquoEstimation of muscle force derived from in vivoMR elas-tography tests a preliminary studyrdquo Journal of MusculoskeletalResearch vol 16 no 3 Article ID 1350015 10 pages 2013

[37] F E Zajac ldquoMuscle and tendon properties models scalingand application to biomechanics and motor controlrdquo CriticalReviews in Biomedical Engineering vol 17 no 4 pp 359ndash4111989

[38] D Staudenmann K Roeleveld D F Stegeman and J H vanDieen ldquoMethodological aspects of SEMG recordings for forceestimationmdasha tutorial and reviewrdquo Journal of Electromyographyand Kinesiology vol 20 no 3 pp 375ndash387 2010

[39] B V Derjaguin V M Muller and Y P Toporov ldquoEffect ofcontact deformations on the adhesion of particlesrdquo Journal ofColloid And Interface Science vol 53 no 2 pp 314ndash326 1975

[40] K L Johnson K Kendall and A D Roberts ldquoSurface energyand the contact of elastic solidsrdquo Proceedings of the Royal Societyof London Series AMathematical and Physical Sciences vol 324no 1558 pp 301ndash313 1971

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

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Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



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Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


estimation of these forces has been commonly performed[17ndash19]Thus the redundant phenomena of the humanneuralcontrol (ie the number of muscles is greater than thenumber of degrees of freedom) may be computationallysolved using optimization techniques even if the best opti-mization strategy remains unknownHowever the predictionaccuracy of such forces depends on the accurate modelingof musculoskeletal tissues (eg muscles bone tendonsligaments and cartilage) and structures (eg joint) as wellas appropriate formulation of physical behaviors (eg jointcontact or multi-body dynamics) [19 20] Model validationhas been a challenging issue Qualitative pattern of themuscle force was commonly validated against the EMG-based muscle activities

In vivo knee contact forces may be computationallyestimated with or without contact model On the one handmodel-based efforts related to the use of inverse dynamicsapproach coupled with an elastic contact model Withinthe scope of this vision Kim et al [21] developed two-stage simulation to compute the muscle forces and thencombine them with ground reaction forces and fluoroscopicdata within a Hertzian contact model to predict the kneecontact forces Moreover Hast and Piazza [22] used acoupling between inverse dynamics forward dynamics andcomputed muscle control (CMC) algorithm within a spring-based contact model to compute the nodes-to-surface kneecontact forces On the other hand knee contact forceshave been predicted without contact model Based on themuscle forces estimated from pseudoinverse method andconstrained static optimization with Lagrange multipliersformulation and parameter reduction strategy [23] con-tact forces were computed Moreover Electromyography-(EMG-) driven muscle force estimation approach coupledwith moment balancing algorithm has been used to predictthe medial contact force [24 25] Furthermore a parametricnumerical model including 9 equilibrium equations reflect-ing muscle activation levels passive structure activationjoint moments external joint forces maximum physiologicalmuscle moments and forces has been also developed topredict the knee contact forces [26] In fact without contactmodel the problem formulation and computational cost maybe more advantageous than the use of a contact modelA recent comparison of predicted contact forces in theframework of the Knee Grand Challenge showed that theuse of a contact model does not guarantee their accuracy[15] However a deformable contact model may provideuseful knowledge about the interactions between the implantcomponents and also those at bone-to-implant surface It isimportant to note that the Knee Grand Challenge has beencreated to open a new dimension on the prediction of invivo muscle and contact forces [14 15] Almost all availablemeasurements ranging from medical imaging data to gaitanalysis and experimental contact forces were provided toenhance the research activities related to the prediction ofthese forces

Previous studies used only simplified representation (egone point contact or nodes-to-surface contact) of contactsurface between implant components Moreover materialproperties of the implants were commonly provided by

manufacturer However assumptions were commonly per-formed for musculoskeletal modelingThus these propertiesneed to be calibrated and fitted to the modeling assumptionfor predicting accurately the knee contact forces In factpredictive trends of numerical models are limited for clinicalapplications Thus the objectives of this present study aretwofold (1) the development of a Hertzian integrated contactmodel based on a global surface-to-surface interaction and(2) the use of in vivo contact forces and the developed contactmodel to identify the reliable and fitted elastic properties ofthe implant for modeling purpose

2 Materials and Methods

21 Computational Workflow A computational workflowwas developed to identify the elastic properties of theinstrumented TKR implant (Figure 1) The workflow consistsof the following components (1) a patient specific rigidmusculoskeletal model to compute the knee kinematics fromskin-mounted markersrsquo trajectories (2) a STL-based implantmodel to compute the contact area evolution during kneemotion and (3) aHertzian integrated contactmodel for the invivo identification of elastic properties (Youngrsquos modulus andPoisson coefficient) of the instrumented TKR implant usingcontact area information and in vivo measured joint contactforces

22 Patient Data The patient data from the fourth editionof the Knee Grand Challenge [14] was used in this presentstudy Imaging and gait data were acquired on a patient(male 88 years old 168 cm body height 667 kg body massand 236 kgm2 Body Mass Index (BMI)) with knee implantinstrumented in his right knee side (Figure 2(a)) The patienthad Rockport flat bottom sneakers shoes during the gait dataacquisition process The patient performed an overgroundnormal gait pattern which was used as reference patternThen 4 overground gait trials reflecting 4 gait modificationstrategies (bouncymedial thrustmild crouch andmtp)wereacquired using an 8-camera Vicon system (Table 1) All skin-mounted markers were posed using a modified ClevelandClinic marker protocol [14] In vivo knee contact forces werealso obtained during the gait data acquisition Four uniaxialload cell measurements (posterior-medial (PM) anterior-medial (AM) anterior-lateral (AL) and posterior-lateral(PL)) from the instrumented tibial prosthesis were performed(Figure 2(b)) The first generation of tray design (eKnee)was used The main implant components were fabricatedin CoCr polyethylene and titanium Sampling frequency is120Hz Furthermore pre- and postsurgery CT data were alsoacquired on the patient using a SiemensCTmachine the slicethickness was set up as 06mm The matrix is 512 times 512 andthe pixel resolution is 09 times 09mm2 The number of slices is1900 for the whole scanned lower limb

23 Patient Specific Rigid Musculoskeletal Model

231 Model Development To compute the knee kinematicsa patient specific musculoskeletal model which is provided


Patient



Material properties

Joint kinematics


Optimization block

Geometric computing

STL-based implant

(E )

F

R

d

120572Hertz

model

contact model

specific rigid


(a)

AM

PM

AL

PL

(b)










Dist

ance

map

(mm

)

40

30

20

10

00

0∘

15∘

30∘

45∘






1003817100381710038171003817119909exp119894minus 119909119894(119902)10038171003817100381710038172

] (1)





on the model




119865Hertz =2

3119877

119864


3

(2)




F

R

120572Hertz

d

FLateralFMedial




min119906

10038171003817100381710038171003817119865Hertzminus 119865

eKnee100381710038171003817100381710038172



120587

(3)


119865eKnee= 119865

Medial+ 119865

Lateral

119865Medial= 09871119865AM + 09683119865PM + 00387119865AL

+ 00211119865PL

119865Lateral= 00129119865AM + 00317119865PM + 09613119865AL

+ 09789119865PL

(4)


3 Results








Gait cycle ()0 20 40 60 80 100

10

20

30

40

50

60

70

Knee

flex

ion

exte

nsio

n an

gle (

∘)



MtpgaitNgait

100 20 30 40 50 601040

1060

1080

1100

1120

1140

1160

Gait cycle ()

Con

tact

area

(mm2)



0 20 40 60 80 100Gait cycle ()

Med

ial f

orce

(N)

200

400

600

800

1000

1200


MtpgaitNgait





Gait cycle ()0 10 20 30 40 50 60

Tota

l con

tact

forc

es (N

)

400

600

800

1000

1200

1400

1600

1800




4 Discussion











Acknowledgment


References
















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Patient



Material properties

Joint kinematics


Optimization block

Geometric computing

STL-based implant

(E )

F

R

d

120572Hertz

model

contact model

specific rigid


(a)

AM

PM

AL

PL

(b)










Dist

ance

map

(mm

)

40

30

20

10

00

0∘

15∘

30∘

45∘






1003817100381710038171003817119909exp119894minus 119909119894(119902)10038171003817100381710038172

] (1)





on the model




119865Hertz =2

3119877

119864


3

(2)




F

R

120572Hertz

d

FLateralFMedial




min119906

10038171003817100381710038171003817119865Hertzminus 119865

eKnee100381710038171003817100381710038172



120587

(3)


119865eKnee= 119865

Medial+ 119865

Lateral

119865Medial= 09871119865AM + 09683119865PM + 00387119865AL

+ 00211119865PL

119865Lateral= 00129119865AM + 00317119865PM + 09613119865AL

+ 09789119865PL

(4)


3 Results








Gait cycle ()0 20 40 60 80 100

10

20

30

40

50

60

70

Knee

flex

ion

exte

nsio

n an

gle (

∘)



MtpgaitNgait

100 20 30 40 50 601040

1060

1080

1100

1120

1140

1160

Gait cycle ()

Con

tact

area

(mm2)



0 20 40 60 80 100Gait cycle ()

Med

ial f

orce

(N)

200

400

600

800

1000

1200


MtpgaitNgait





Gait cycle ()0 10 20 30 40 50 60

Tota

l con

tact

forc

es (N

)

400

600

800

1000

1200

1400

1600

1800




4 Discussion











Acknowledgment


References
















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Dist

ance

map

(mm

)

40

30

20

10

00

0∘

15∘

30∘

45∘






1003817100381710038171003817119909exp119894minus 119909119894(119902)10038171003817100381710038172

] (1)





on the model




119865Hertz =2

3119877

119864


3

(2)




F

R

120572Hertz

d

FLateralFMedial




min119906

10038171003817100381710038171003817119865Hertzminus 119865

eKnee100381710038171003817100381710038172



120587

(3)


119865eKnee= 119865

Medial+ 119865

Lateral

119865Medial= 09871119865AM + 09683119865PM + 00387119865AL

+ 00211119865PL

119865Lateral= 00129119865AM + 00317119865PM + 09613119865AL

+ 09789119865PL

(4)


3 Results








Gait cycle ()0 20 40 60 80 100

10

20

30

40

50

60

70

Knee

flex

ion

exte

nsio

n an

gle (

∘)



MtpgaitNgait

100 20 30 40 50 601040

1060

1080

1100

1120

1140

1160

Gait cycle ()

Con

tact

area

(mm2)



0 20 40 60 80 100Gait cycle ()

Med

ial f

orce

(N)

200

400

600

800

1000

1200


MtpgaitNgait





Gait cycle ()0 10 20 30 40 50 60

Tota

l con

tact

forc

es (N

)

400

600

800

1000

1200

1400

1600

1800




4 Discussion











Acknowledgment


References
















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















F

R

120572Hertz

d

FLateralFMedial




min119906

10038171003817100381710038171003817119865Hertzminus 119865

eKnee100381710038171003817100381710038172



120587

(3)


119865eKnee= 119865

Medial+ 119865

Lateral

119865Medial= 09871119865AM + 09683119865PM + 00387119865AL

+ 00211119865PL

119865Lateral= 00129119865AM + 00317119865PM + 09613119865AL

+ 09789119865PL

(4)


3 Results








Gait cycle ()0 20 40 60 80 100

10

20

30

40

50

60

70

Knee

flex

ion

exte

nsio

n an

gle (

∘)



MtpgaitNgait

100 20 30 40 50 601040

1060

1080

1100

1120

1140

1160

Gait cycle ()

Con

tact

area

(mm2)



0 20 40 60 80 100Gait cycle ()

Med

ial f

orce

(N)

200

400

600

800

1000

1200


MtpgaitNgait





Gait cycle ()0 10 20 30 40 50 60

Tota

l con

tact

forc

es (N

)

400

600

800

1000

1200

1400

1600

1800




4 Discussion











Acknowledgment


References
















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















Gait cycle ()0 20 40 60 80 100

10

20

30

40

50

60

70

Knee

flex

ion

exte

nsio

n an

gle (

∘)



MtpgaitNgait

100 20 30 40 50 601040

1060

1080

1100

1120

1140

1160

Gait cycle ()

Con

tact

area

(mm2)



0 20 40 60 80 100Gait cycle ()

Med

ial f

orce

(N)

200

400

600

800

1000

1200


MtpgaitNgait





Gait cycle ()0 10 20 30 40 50 60

Tota

l con

tact

forc

es (N

)

400

600

800

1000

1200

1400

1600

1800




4 Discussion











Acknowledgment


References
















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Gait cycle ()0 10 20 30 40 50 60

Tota

l con

tact

forc

es (N

)

400

600

800

1000

1200

1400

1600

1800




4 Discussion











Acknowledgment


References
















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






















Acknowledgment


References
















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















research article a hertzian integrated contact model of...

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