Journal of Biomechanics 40

Short commu

poin tension

, Je

n Ant

Febr

rgy d

unlo

ys: r

h er ness i h

depends on the age-related changes in the post-yieldbehavior of bone (McCalden et al., 1993). However,

associated with several pathways. Thus, partitioningthe energy dissipation during the post-yield deformation

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Corresponding author. Tel.: +1 210 458 5565;

fax: +1 210 458 6504.

Using a loadunloadreload scheme as shown in

Fig. 1, we proposed to partition post-yield energy into

0021-9290/$ - see front matter r 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jbiomech.2006.02.002

E-mail addresses: xwang@utsa.edu, xiaodu.wang@utsa.edu

(X. Wang).underlying mechanisms of post-energy dissipation inbone is still not clear. Previous studies have reportedthat microdamage accumulation (including both linearmicrocrack and diffuse damage) may be major mechan-isms in energy dissipation during the post-yield defor-mation of bone (Courtney et al., 1996; Jepsen and Davy,1997; Kotha and Guzelsu, 2003; Martin et al., 1997;Zioupos and Currey, 1998). In addition, age- or disease-related changes in the collagen network may also

of bone may help elucidate the underlying mechanism ofage-related bone fractures. To address this issue, weproposed a novel methodology to assess the energydissipation pathways during the post-yield deformationof bone.

2. Materials and methods

2.1. Loading procedurecadaveric femurs of middle-aged and elderly donors were tested using this approach. The results of this study indicate that there

exist age-related differences in post-yield energy dissipation and modulus degradation. These results implicate that this novel

approach could detect the age-related differences in energy dissipation of bone and may aid in understanding the underlying

mechanisms of such changes.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Bone; Toughness; Energy dissipation; Tension; Microdamage

1. Introduction

Age-related degradation in toughness makes bonemore susceptible to fracture (Burstein et al., 1976). Theobserved decrease in bone toughness with age likely

contribute to the reduced bone toughness (Jepsenet al., 1996; Wang et al., 2002; Zioupos et al., 1999),indicating the involvement of collagen in post-yieldenergy dissipation. These previous studies implicate thatthe post-yield energy dissipation in bone may bechanges in the viscoelastic behavior of bone in the process of post-yield deformation. As an example, bone specimens from humanA novel approach to assessof bone

Xiaodu Wang

Department of Mechanical Engineering, University of Texas at Sa

Accepted 2

Abstract

In this study, we proposed a novel approach to assess the ene

the stressstrain behavior in an incremental and cyclic loading

post-yield energy dissipation of bone into three distinct pathwa

hysteresis energy (U ). Among them, U depends on the stiffffry S. Nyman

onio, 6900 North Loop 1604 West, San Antonio, TX 78249, USA

uary 2006

issipation during the post-yield deformation of bone. Based on

adingreloading scheme in uniaxial tension, we partitioned the

eleased elastic strain energy (Uer); irreversible energy (Ui); and

loss, U is the energy permanently consumed, and U reects(2007) 674677

nication

st-yield energy dissipation

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www.JBiomech.com

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Strain

Fig. 2. The cyclic loading scheme was used with a displacement

increment of 0.05mm (approximately 0.5% strain) at each successive

cycle. The energy terms could be calculated for each cycle. In this

example, failure occurred after the fourth cycle, but before the fth

cycle. UI is estimated as the gray shaded area for the last cycle. The

toughness (UT UI+Uer+Uh+Ue0+UL) was calculated as a sum-mation of all energy terms including UL.

Table 1

Number of survival specimens (no failure) at incremental displacement

is greater in middle-aged bone as indicated by the greater number of

surviving specimens at greater displacement

of Bithree components during the cycle: the released elasticstrain energy (i.e., the area enclosed in HEF or Uer),hysteresis energy (i.e., the area enclosed in the unloading

A

B

Load

EiE0

E

Unload

C

D

Ui Uh

Uer

FG

H

Stre

ss

Ue0

Fig. 1. Partitioning the energy capacity of bone: nominal elastic strain

energy (Ue0) depending on the initial elastic modulus (E0); released

elastic strain energy (Uer) relating to modulus degradation; hysteresis

energy (Uh) reecting the viscoelastic nature of bone; and irreversible

energy (Ui) dissipation, which reects the free surface energy released

by microdamage formation (Uer) and the permanent strain energy

(Up).

X. Wang, J.S. Nyman / Journaland reloading loop orUh), and the irreversible energy (i.e.,the area enclosed in ABCG or Ui). The released elasticstrain energy is mainly due to the modulus loss (Fondrket al., 1999a). The hysteresis energy reects the viscoelasticbehavior of bone in the process of load bearing (Doubalet al., 2004). Finally, the irreversible energy dissipation(Ui) involves at least two possible pathways: formation ofnew cracks (Uer) and permanent deformation (Up) in thetissue Fondrk et al., 1999b). The underlying mechanismsinvolved in these pathways are still unclear. However,previous studies have shown that microdamage accumu-lation is related to the loss of the stiffness of bone (Burret al., 1998). In addition, the integrity of the collagennetwork signicantly affects the toughness (Wang et al.,2001) and the post-yield stressstrain behavior of bone(Wright et al., 1981). Moreover, a microstructural barrier(e.g., cement lines), which slows the growth of cracksduring fatigue loading, may also affect post-yield behaviorof bone (OBrien et al., 2003).To distinguish between these different pathways of

energy dissipation, a progressive loadunloadreloadscheme in uniaxial tension was implemented as shown inFig. 2. An incremental displacement of 0.05mm wasimposed on the specimen for each cycle (Table 1). Strainwas estimated as the change of the crosshead displace-ment per 10mm gage region. In each cycle, the specimenwas rst loaded under displacement control to the nextReload

UnloadCycle 1

Stre

ss

E0

Uer

Uh

Ue0

UL

max

Cycle 2

FailureX

Cycle i

EFLoad

Ui

omechanics 40 (2007) 674677 675displacement level at a rate of 5mm/min; then heldsteady for 60 s for stress relaxation (from point C to Has shown in Fig. 1). Thereafter, the specimen wasunloaded in load control to zero force, and held for 60 sfor strain relaxation (from point F to G as shown inFig. 1), and then reloaded again in displacement controlto the next strain level. This process was repeated untilfailure. All specimens that did not fail at the sixth cyclewere loaded to failure without further cycles. The bonespecimens were kept moist by wrapping them with gauzesoaked with physiological saline.In the incremental loading scheme (Fig. 2), the total

irreversible energy (Ui) absorbed by the specimen at theprevious and present cycles is actually the result ofcumulative deformation of each loading cycle, and canbe simply calculated as the summation of each Ui of all

Cycle (ith) Displacement

(mm)

Estimated

strain

Middle-aged Elderly

1 0.05 0.005 9 9

2 0.10 0.010 9 9

3 0.15 0.015 9 9

4 0.20 0.020 9 6

5 0.25 0.025 7 4

6 0.30 0.030 4 2

Final Till failure 40.030 3 2

previous and present loading cycles. On the other hand,Uer and Uh measured at each cycle already represent thecumulative effect. The permanent strain energy portion(Up) of the total irreversible energy (Ui) was estimated asUiUer. Also, we calculated the toughness (UT Ui+Uer+Uh+Ue0+UL) and the ultimate strength (smax) foreach bone specimen as shown in Fig. 2. To investigatethe contribution of each post-yield energy term to thetotal energy dissipation, we used the ratio of each energyterm (i.e., Up, Uer, and Uh) to the overall energy capacity(US Ui+Uer+Uh+Ue0 in Fig. 2) at the nal cycle.The elastic modulus after yielding was calculated as

the slope of line HG (presumably between twoequilibrium points) in order to avoid the inuence ofviscoelasticity (hysteresis). Moreover, the modulusdegradation at the each cycle was estimated as (1Ef/E0), where E0 is the initial elastic modulus and Ef is theelastic modulus at the cycle.

2.2. Bone specimen preparation

Eighteen tensile specimens were prepared each from18 male cadaveric femurs that were collected from TexasWilled Body Program and National Disease Research

Exchange. The specimens were evenly divided into twoage groups (n 9): middle-aged (4959 years) andelderly (6987 years). The dog bone specimens(10mm 5mm 2mm grip regions and a 10mm2mm 2mm gage region) were prepared longitudinallyfrom the mid-diaphysis of each femur using a diamondsaw and a CNC machine (ProLIGHT 1000, LightMachines, Manchester, NH).

2.3. Statistical analysis

Furthermore, the relative contribution of the post-yield energy terms to the energy capacity of bone did not

ARTICLE IN PRESS

0.20

0.25

cle 3

(MJ/m

3 )

Middle

Old

lure (

le-ag

70.270.070.070.971170.0

X. Wang, J.S. Nyman / Journal of Biomechanics 40 (2007) 6746776760.00

0.05

0.10

0.15

Post

-yie

ld e

nerg

y at

cy

Up Uer Uh

*

Fig. 3. Post-yield energy dissipation at the early stage of post-yield

deformation (at cycle 3) does show signicant age-related effects in

energy dissipation except for the released elastic strain energy

(p 0:027). *indicates signicant difference between the two agegroups (po0:05).

Table 2

Summary of experimental results obtained at the last cycle prior to fai

Properties Midd

Plastic strain energy Up (MJ/m3) 0.674

Released elastic strain energy Uer (MJ/m3) 0.298

Hysteresis energy Uh (MJ/m3) 0.320

Toughness UT (MJ/m3) 2.48

Strength smax (MPa) 88.1Final modulus degradation (1EF/E0) 0.48show signicant differences between the age groups inthe early cycles (Fig. 3), with permanent strain energy(Up) having the greatest contribution to energy dissipa-tion. However, signicant age-related differenceswere observed in the total energy dissipation of bone(Table 3). Lastly, with an increase in post-yield

N 9)

ed Elderly p-value

57 0.40370.230 0.01699 0.19970.126 0.04292 0.22970.134 0.05875 1.74070.856 0.054.4 75.6713.0 0.0235 0.4170.09 0.047Students t-tests (one tail) were performed to examinethe age-related effects on the post-yield energy dissipa-tion and other aforementioned properties of bone.Signicant differences were considered only if p-valuewas less than 0.05.

3. Results

Table 1 shows the number of survival specimens (nofailure) at each incremental loading cycle. It wasobserved that after 2.0% strain the number of survivalspecimens in the middle-aged group was consistentlyhigher than that in the elderly one. Also, it was observedthat no difference in Up exists at cycle 3 (Fig. 3), but atthe nal cycle between the age groups (Table 2). Asshown in Table 2, Up, Uer, su, and modulus degradationof bone decreased signicantly with age (po0:05). UTand Uh of bone did indicate a trend of decrease with agealthough their p-values are little higher than 0.05(po0:06). It is noteworthy that the age-related differ-ences were very similar in all energy dissipation terms(about 3035%), while the differences in strength andmodulus degradation were somewhat smaller (around1315%).

reducing the incremental loading displacement.

ARTICLE IN PRESS

Middle-aged 34.475.3 15.471.5 16.871.1

X. Wang, J.S. Nyman / Journal of Biomechanics 40 (2007) 674677 677There is one intriguing observation in the experi-mental results obtained using the proposed approach:That is, age-related decreases are more signicant in thedeformation, age rst affected Uer and then Up (Table 2and Fig. 3).

4. Discussion

The results of this study indicate that the proposedexperimental approach may be of use in distinguishingthe different pathways of energy dissipation in the post-yield deformation of bone. Conventional approaches,such as fracture toughness testing, give the bulkproperties, but cannot distinguish between contributionsof bone constituents to bone toughness. The advantageof the present approach is that it may provide morespecic information to help understand changes in thebone constituents as a function of aging or other bonediseases.There are some limitations to the current approach.

First, this approach has only been tested in uniaxialtension. While energy dissipation during tensile yieldingis informative, failure of bone certainly occurs in theother modes of loading. Diagnostic tests investigatingthe effect of damage by overload on mechanicalproperties of cortical bone indicated similar post-yieldbehavior in torsion (Jepsen and Davy, 1997) andcompression (Morgan et al., 2005), but failure appearsto occur at lower strain levels. Second, since the bonespecimens did not break exactly at prescribed strainlevels, we used the post-yield energy dissipation at thelast complete cycle as an approximation of those termsat failure. In fact, such errors could be limited by

Elderly 28.777.3a 13.572.3 16.571.9

aSignicantly less than the middle-aged group (p-valueo0.05).Table 3

Relative contribution of each nal post-yield energy term to the energy

capacity of middle-aged and elderly bone (N 9)

Properties Up/US (%) Uer/US (%) Uh/US (%)post-yield energy dissipation than in the modulusdegradation (stiffness loss) of bone, suggesting thataging has more effects on the post-yield energydissipation than on the stiffness loss of bone.

Acknowledgment

The authors would like to thank Mr. Jerrod Tyler forhis assistance in preparing and testing the bone specimens.

Zioupos, P., Currey, J.D., 1998. Changes in the stiffness, strength, and

toughness of human cortical bone with age. Bone 22, 5766.Zioupos, P., Currey, J.D., Hamer, A.J., 1999. The role of collagen in

the declining mechanical properties of aging human cortical bone.

Journal Of Biomedical Materials Research 45, 108116.This study is partially supported by a NIH/NIA GrantAG 022044 and the San Antonio Area Foundation.

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A novel approach to assess post-yield energy dissipation of bone in tensionIntroductionMaterials and methodsLoading procedureBone specimen preparationStatistical analysis

ResultsDiscussionAcknowledgmentReferences