As the average age of the population has increased, the incidence of age-related bone fracture has also increased. While some of the increase of fracture incidence with age is related to loss of bone mass, a significant part of the risk is unexplained and may be caused by changes in intrinsic material properties of the hard tissue. This investigation focused on understanding how changes to the intrinsic damage properties affect bone fragility. We hypothesized that the intrinsic (μm) damage properties of bone tissue strongly and nonlinearly affect mechanical behavior at the apparent (whole tissue, cm) level. The importance of intrinsic properties on the apparent level behavior of trabecular bone tissue was investigated using voxel based finite element analysis. Trabecular bone cores from human T12 vertebrae were scanned using microcomputed tomography (μCT) and the images used to build nonlinear finite element models. Isotropic and initially homogenous material properties were used for all elements. The elastic modulus (Ei) of individual elements was reduced with a secant damage rule relating only principal tensile tissue strain to modulus damage. Apparent level resistance to fracture as a function of changes in the intrinsic damage properties was measured using the mechanical energy to failure per unit volume (apparent toughness modulus, Wa) and the apparent yield strength (σay, calculated using the 0.2% offset). Intrinsic damage properties had a profound nonlinear effect on the apparent tissue level mechanical response. Intrinsic level failure occurs prior to apparent yield strength (σay). Apparent yield strength (σay) and toughness vary strongly (1200% and 400%, respectively) with relatively small changes in the intrinsic damage behavior. The range of apparent maximum stresses predicted by the models was consistent with those measured experimentally for these trabecular bone cores from the experimental axial compressive loading (experimental: σmax = 3.0–4.3 MPa; modeling: σmax = 2–16 MPa). This finding differs significantly from previous studies based on nondamaging intrinsic material models. Further observations were that this intrinsic damage model reproduced important experimental apparent level behaviors including softening after peak load, microdamage accumulation before apparent yield (0.2% offset), unload softening, and sensitivity of the apparent level mechanical properties to variability of the intrinsic properties.

References

References
1.
Barth
,
H. D.
,
Launey
,
M. E.
,
Macdowell
,
A. A.
,
Ager
,
J. W.
, and
Ritchie
,
R. O.
,
2010
, “
On the Effect of X-Ray Irradiation on the Deformation and Fracture Behavior of Human Cortical Bone
,”
Bone
,
46
(
6
), pp.
1475
1485
.10.1016/j.bone.2010.02.025
2.
Yan
,
J.
,
Daga
,
A.
,
Kumar
,
R.
, and
Mecholsky
,
J. J.
,
2008
, “
Fracture Toughness and Work of Fracture of Hydrated, Dehydrated, and Ashed Bovine Bone
,”
J. Biomech.
,
41
(
9
), pp.
1929
1936
.10.1016/j.jbiomech.2008.03.037
3.
Burstein
,
A.
,
Zika
,
J.
,
Heiple
,
K.
, and
Klein
,
L.
,
1975
, “
Contribution of Collagen and Mineral to the Elastic-Plastic Properties of Bone
,”
J. Bone Jt. Surg., Am. Vol.
,
57
(
7
), pp.
956
961
.
4.
Vashishth
,
D.
,
Gibson
,
G. J.
,
Khoury
,
J. I.
,
Schaffler
,
M. B.
,
Kimura
,
J.
, and
Fyhrie
,
D. P.
,
2001
, “
Influence of Nonenzymatic Glycation on Biomechanical Properties of Cortical Bone
,”
Bone
,
28
(
2
), pp.
195
201
.10.1016/S8756-3282(00)00434-8
5.
Wang
,
X.
,
Li
,
X.
,
Bank
,
R. A.
, and
Agrawal
,
C. M.
,
2002
, “
Effects of Collagen Unwinding and Cleavage on the Mechanical Integrity of the Collagen Network in Bone
,”
Calcif. Tissue Int.
,
71
(
2
), pp.
186
192
.10.1007/s00223-001-1082-2
6.
Wynnyckyj
,
C.
,
Willett
,
T. L.
,
Omelon
,
S.
,
Wang
,
J.
,
Wang
,
Z.
, and
Grynpas
,
M. D.
,
2011
, “
Changes in Bone Fatigue Resistance Due to Collagen Degradation
,”
J. Orthop. Res.
, pp.
197
203
.
7.
Martin
,
R. B.
,
2002
, “
Is all Cortical Bone Remodeling Initiated by Microdamage?
,”
Bone
,
30
(
1
), pp.
8
13
.10.1016/S8756-3282(01)00620-2
8.
McNamara
,
L. M.
, and
Prendergast
,
P. J.
,
2007
, “
Bone Remodelling Algorithms Incorporating Both Strain and Microdamage Stimuli
,”
J. Biomech.
,
40
(
6
), pp.
1381
1391
.10.1016/j.jbiomech.2006.05.007
9.
Burr
,
D. B.
,
Forwood
,
M. R.
,
Fyhrie
,
D. P.
,
Martin
,
R. B.
,
Schaffler
,
M. B.
, and
Turner
,
C. H.
,
1997
, “
Bone Microdamage and Skeletal Fragility in Osteoporotic and Stress Fractures
,”
J. Bone Miner. Res.
,
12
(
1
), pp.
6
15
.10.1359/jbmr.1997.12.1.6
10.
Crawford
,
R. P.
,
Cann
,
C. E.
, and
Keaveny
,
T. M.
,
2003
, “
Finite Element Models Predict In Vitro Vertebral Body Compressive Strength Better Than Quantitative Computed Tomography
,”
Bone
,
33
(
4
), pp.
744
750
.10.1016/S8756-3282(03)00210-2
11.
Bosisio
,
M. R.
,
Talmant
,
M.
,
Skalli
,
W.
,
Laugier
,
P.
, and
Mitton
,
D.
,
2007
, “
Apparent Young's Modulus of Human Radius Using Inverse Finite-Element Method
,”
J. Biomech.
,
40
(
9
), pp.
2022
2028
.10.1016/j.jbiomech.2006.09.018
12.
Chevalier
,
Y.
,
Pahr
,
D.
,
Allmer
,
H.
,
Charlebois
,
M.
, and
Zysset
,
P.
,
2007
, “
Validation of a Voxel-Based FE Method for Prediction of the Uniaxial Apparent Modulus of Human Trabecular Bone Using Macroscopic Mechanical Tests and Nanoindentation
,”
J. Biomech.
,
40
(
15
), pp.
3333
3340
.10.1016/j.jbiomech.2007.05.004
13.
Bayraktar
,
H. H.
,
Gupta
,
A.
,
Kwon
,
R. Y.
,
Papadopoulos
,
P.
, and
Keaveny
,
T. M.
,
2004
, “
The Modified Super-Ellipsoid Yield Criterion for Human Trabecular Bone
,”
J. Biomech. Eng.
,
126
(
6
), pp.
677
684
.10.1115/1.1763177
14.
Stölken
,
J. S.
, and
Kinney
,
J. H.
,
2003
, “
On the Importance of Geometric Nonlinearity in Finite-Element Simulations of Trabecular Bone Failure
,”
Bone
,
33
(
4
), pp.
494
504
.10.1016/S8756-3282(03)00214-X
15.
Van Rietbergen
,
B.
,
Odgaard
,
A.
,
Kabel
,
J.
, and
Huiskes
,
R.
,
1998
, “
Relationships Between Bone Morphology and Bone Elastic Properties Can be Accurately Quantified Using High-Resolution Computer Reconstructions
,”
J. Orthop. Res.
,
16
(
1
), pp.
23
28
.10.1002/jor.1100160105
16.
Odgaard
,
A.
,
Kabel
,
J.
,
van Rietbergen
,
B.
,
Dalstra
,
M.
, and
Huiskes
,
R.
,
1997
, “
Fabric and Elastic Principal Directions of Cancellous Bone are Closely Related
,”
J. Biomech.
,
30
(
5
), pp.
487
495
.10.1016/S0021-9290(96)00177-7
17.
Bayraktar
,
H. H.
,
Morgan
,
E. F.
,
Niebur
,
G. L.
,
Morris
,
G. E.
,
Wong
,
E. K.
, and
Keaveny
,
T. M.
,
2004
, “
Comparison of the Elastic and Yield Properties of Human Femoral Trabecular and Cortical Bone Tissue
,”
J. Biomech.
,
37
(
1
), pp.
27
35
.10.1016/S0021-9290(03)00257-4
18.
Verhulp
,
E.
,
van Rietbergen
,
B.
,
Muller
,
R.
, and
Huiskes
,
R.
,
2008
, “
Indirect Determination of Trabecular Bone Effective Tissue Failure Properties Using Micro-Finite Element Simulations
,”
J. Biomech.
,
41
(
7
), pp.
1479
1485
.10.1016/j.jbiomech.2008.02.032
19.
Fantner
,
G. E.
,
Hassenkam
,
T.
,
Kindt
,
J. H.
,
Weaver
,
J. C.
,
Birkedal
,
H.
,
Pechenik
,
L.
,
Cutroni
,
J. A.
,
Cidade
,
G. A.
,
Stucky
,
G. D.
,
Morse
,
D. E.
, and
Hansma
,
P. K.
,
2005
, “
Sacrificial Bonds and Hidden Length Dissipate Energy as Mineralized Fibrils Separate During Bone Fracture
,”
Nature Mater.
,
4
, pp.
612
616
.10.1038/nmat1428
20.
Fantner
,
G. E.
,
Adams
,
J.
,
Turner
,
P.
,
Thurner
,
P. J.
,
Fisher
,
L. W.
, and
Hansma
,
P. K.
,
2007
, “
Nanoscale Ion Mediated Networks in Bone: Osteopontin Can Repeatedly Dissipate Large Amounts of Energy
,”
Nano Lett.
,
7
(
8
), pp.
2491
2498
.10.1021/nl0712769
21.
Dong
,
X. N.
,
Guda
,
T.
,
Millwater
,
H. R.
, and
Wang
,
X.
,
2009
, “
Probabilistic Failure Analysis of Bone Using a Finite Element Model of Mineral-Collagen Composites
,”
J. Biomech.
,
42
(
3
), pp.
202
209
.10.1016/j.jbiomech.2008.10.022
22.
Nalla
,
R. K.
,
Kinney
,
J. H.
, and
Ritchie
,
R. O.
,
2003
, “
Mechanistic Fracture Criteria for the Failure of Human Cortical Bone
,”
Nature Mater.
,
2
(
3
), pp.
164
168
.10.1038/nmat832
23.
Fratzl
,
P.
,
2008
, “
Bone Fracture: When the Cracks Begin to Show
,”
Nature Mater.
,
7
(
8
), pp.
610
612
.10.1038/nmat2240
24.
Vashishth
,
D.
,
Koontz
,
J.
,
Qiu
,
S. J.
,
Lundin-Cannon
,
D.
,
Yeni
,
Y. N.
,
Schaffler
,
M. B.
, and
Fyhrie
,
D. P.
,
2000
, “
In Vivo Diffuse Damage in Human Vertebral Trabecular Bone
,”
Bone
,
26
(
2
), pp.
147
152
.10.1016/S8756-3282(99)00253-7
25.
Lemaître
,
J.
, and
Desmorat
,
R.
,
2005
,
Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures
,
Springer
,
New York.
26.
Ural
,
A.
, and
Vashishth
,
D.
,
2006
, “
Cohesive Finite Element Modeling of Age-Related Toughness Loss in Human Cortical Bone
,”
Journal of Biomech.
,
39
(
16
), pp.
2974
2982
.10.1016/j.jbiomech.2005.10.018
27.
Wenzel
,
T. E.
,
Schaffler
,
M. B.
, and
Fyhrie
,
D. P.
,
1996
, “
In Vivo Trabecular Microcracks in Human Vertebral Bone
,”
Bone
,
19
(
2
), pp.
89
95
.10.1016/8756-3282(96)88871-5
28.
Zauel
,
R.
,
Yeni
,
Y. N.
,
Bay
,
B. K.
,
Dong
,
X. N.
, and
Fyhrie
,
D. P.
,
2006
, “
Comparison of the Linear Finite Element Prediction of Deformation and Strain of Human Cancellous Bone to 3D Digital Volume Correlation Measurements
,”
J. Biomech. Eng.
,
128
(
1
), pp.
1
6
.10.1115/1.2146001
29.
Chavassieux
,
P.
,
Seeman
,
E.
, and
Delmas
,
P. D.
,
2007
, “
Insights into Material and Structural Basis of Bone Fragility From Diseases Associated With Fractures: How Determinants of the Biomechanical Properties of Bone are Compromised by Disease
,”
Endocr. Rev.
,
28
(
2
), pp.
151
164
.10.1210/er.2006-0029
30.
Avery
,
N. C.
, and
Bailey
,
A. J.
,
2008
, “
Restraining Cross-Links Responsible for the Mechanical Properties of Collagen Fibers: Natural and Artificial
,”
Collagen
,
P.
Fratzl
, ed.,
Springer
,
New York
, pp.
81
110
.
31.
Gautieri
,
A.
,
Uzel
,
S.
,
Vesentini
,
S.
,
Redaelli
,
A.
, and
Buehler
,
M. J.
,
2009
, “
Molecular and Mesoscale Mechanisms of Osteogenesis Imperfecta Disease in Collagen Fibrils
,”
Biophys. J.
,
97
(
3
), pp.
857
865
.10.1016/j.bpj.2009.04.059
32.
Hernandez
,
C. J.
,
Tang
,
S. Y.
,
Baumbach
,
B. M.
,
Hwu
,
P. B.
,
Sakkee
,
A. N.
,
van der Ham
,
F.
,
DeGroot
,
J.
,
Bank
,
R. A.
, and
Keaveny
,
T. M.
,
2005
, “
Trabecular Microfracture and the Influence of Pyridinium and Non-Enzymatic Glycation-Mediated Collagen Cross-Links
,”
Bone
,
37
(
6
), pp.
825
832
.10.1016/j.bone.2005.07.019
33.
Shen
,
Z. L.
,
Dodge
,
M. R.
,
Kahn
,
H.
,
Ballarini
,
R.
, and
Eppell
,
S. J.
,
2008
, “
Stress-Strain Experiments on Individual Collagen Fibrils
,”
Biophys. J.
,
95
(
8
), pp.
3956
3963
.10.1529/biophysj.107.124602
34.
Busse
,
B.
,
Hahn
,
M.
,
Soltau
,
M.
,
Zustin
,
J.
,
Püschel
,
K.
,
Duda
,
G. N.
, and
Amling
,
M.
,
2009
, “
Increased Calcium Content and Inhomogeneity of Mineralization Render Bone Toughness in Osteoporosis: Mineralization, Morphology and Biomechanics of Human Single Trabeculae
,”
Bone
,
45
(
6
), pp.
1034
1043
.10.1016/j.bone.2009.08.002
35.
Kopperdahl
,
D. L.
, and
Keaveny
,
T. M.
,
1998
, “
Yield Strain Behavior of Trabecular Bone
,”
J. Biomech.
,
31
(
7
), pp.
601
608
.10.1016/S0021-9290(98)00057-8
36.
E28 Committee
,
2009
, “
Test Methods for Compression Testing of Metallic Materials at Room Temperature
,”
ASTM International, West Conshohocken, PA
.
37.
Keaveny
,
T. M.
,
Morgan
,
E. F.
,
Niebur
,
G. L.
, and
Yeh
,
O. C.
,
2001
, “
Biomechanics of Trabecular Bone
,”
Annu. Rev. Biomed. Eng.
,
3
, pp.
307
333
.10.1146/annurev.bioeng.3.1.307
38.
Niebur
,
G. L.
,
Feldstein
,
M. J.
,
Yuen
,
J. C.
,
Chen
,
T. J.
, and
Keaveny
,
T. M.
,
2000
, “
High-Resolution Finite Element Models With Tissue Strength Asymmetry Accurately Predict Failure of Trabecular Bone
,”
J. Biomech.
,
33
(
12
), pp.
1575
1583
.10.1016/S0021-9290(00)00149-4
39.
Fyhrie
,
D. P.
, and
Vashishth
,
D.
,
2000
, “
Bone Stiffness Predicts Strength Similarly for Human Vertebral Cancellous Bone in Compression and for Cortical Bone in Tension.
,”
Bone
,
26
(
2
), pp.
169
173
.10.1016/S8756-3282(99)00246-X
40.
Currey
,
J. D.
,
Brear
,
K.
,
Zioupos
,
P.
, and
Reilly
,
G. C.
,
1995
, “
Effect of Formaldehyde Fixation on Some Mechanical Properties of Bovine Bone
,”
Biomaterials
,
16
(
16
), pp.
1267
1271
.10.1016/0142-9612(95)98135-2
41.
Morgan
,
E. F.
,
Bayraktar
,
H. H.
, and
Keaveny
,
T. M.
,
2003
, “
Trabecular Bone Modulus-Density Relationships Depend on Anatomic Site
,”
J. Biomech.
,
36
(
7
), pp.
897
904
.10.1016/S0021-9290(03)00071-X
42.
Verhulp
,
E.
,
Van Rietbergen
,
B.
,
Müller
,
R.
, and
Huiskes
,
R.
,
2008
, “
Micro-Finite Element Simulation of Trabecular-Bone Post-Yield Behaviour—Effects of Material Model, Element Size and Type
,”
Comput. Methods Biomech. Biomed. Eng.
,
11
(
4
), pp.
389
395
.10.1080/10255840701848756
43.
Bigley
,
R. F.
,
Gibeling
,
J. C.
,
Stover
,
S. M.
,
Hazelwood
,
S. J.
,
Fyhrie
,
D. P.
, and
Martin
,
R. B.
,
2008
, “
Volume Effects on Yield Strength of Equine Cortical Bone
,”
J. Mech. Behav. Biomed. Mater.
,
1
(
4
), pp.
295
302
.10.1016/j.jmbbm.2007.11.001
44.
Zhang
,
J.
,
Michalenko
,
M. M.
,
Kuhl
,
E.
, and
Ovaert
,
T. C.
,
2010
, “
Characterization of Indentation Response and Stiffness Reduction of Bone Using a Continuum Damage Model
,”
J. Mech. Behav. Biomed. Mater.
,
3
(
2
), pp.
189
202
.10.1016/j.jmbbm.2009.08.001
45.
Kosmopoulos
,
V.
, and
Keller
,
T. S.
,
2008
, “
Predicting Trabecular Bone Microdamage Initiation and Accumulation Using a Non-Linear Perfect Damage Model
,”
Med. Eng. Phys.
,
30
(
6
), pp.
725
732
.10.1016/j.medengphy.2007.02.011
46.
Moore
,
T. L. A.
, and
Gibson
,
L. J.
,
2002
, “
Microdamage Accumulation in Bovine Trabecular Bone in Uniaxial Compression
,”
J. Biomech. Eng.
,
124
(
1
), pp.
63
71
.10.1115/1.1428745
47.
Nagaraja
,
S.
,
Couse
,
T. L.
, and
Guldberg
,
R. E.
,
2005
, “
Trabecular Bone Microdamage and Microstructural Stresses Under Uniaxial Compression
,”
J. Biomech.
,
38
(
4
), pp.
707
716
.10.1016/j.jbiomech.2004.05.013
48.
Wang
,
C. C.
,
Deng
,
J. M.
,
Ateshian
,
G. A.
, and
Hung
,
C. T.
,
2002
, “
An Automated Approach for Direct Measurement of Two-Dimensional Strain Distributions Within Articular Cartilage Under Unconfined Compression
,”
J. Biomech. Eng.
,
124
(
5
), pp.
557
567
.10.1115/1.1503795
49.
Tomar
,
V
.,
2009
, “
Insights Into the Effects of Tensile and Compressive Loadings on Microstructure Dependent Fracture of Trabecular Bone
,”
Eng. Fract. Mech.
,
76
(
7
), pp.
884
897
.10.1016/j.engfracmech.2008.12.013
50.
Ager
,
J. W.
, III
,
Balooch
,
G.
, and
Ritchie
,
R. O.
,
2006
, “
Fracture, Aging, and Disease in Bone
,”
J. Mater. Res
,
21
(
8
), pp.
1878
1892
.10.1557/jmr.2006.0242
51.
Tang
,
S. Y.
,
Zeenath
,
U.
, and
Vashishth
,
D.
,
2007
, “
Effects of Non-Enzymatic Glycation on Cancellous Bone Fragility
,”
Bone
,
40
(
4
), pp.
1144
1151
.10.1016/j.bone.2006.12.056
52.
Bradke
,
B. S.
,
Tang
,
S.
, and
Vashid
,
D.
,
2009
, “
An Agent Cleaving Sugar-Derived Collagen Cross-Links Decreases Bone Fragility
,” Orthopaedic Research Society Meeting. Las Vegas, 2009,
Orthop. Res. Soc.
, Poster 695.
53.
Paschalis
,
E. P.
,
Shane
,
E.
,
Lyritis
,
G.
,
Skarantavos
,
G.
,
Mendelsohn
,
R.
, and
Boskey
,
A. L.
,
2004
, “
Bone Fragility and Collagen Cross-Links
,”
J. Bone Miner. Res.
,
19
(
12
), pp.
2000
2004
.10.1359/jbmr.040820
54.
Van Rietbergen
,
B.
,
Muller
,
R.
,
Ulrich
,
D.
,
Ruegsegger
,
P.
, and
Huiskes
,
R.
,
1999
, “
Tissue Stresses and Strain in Trabeculae of a Canine Proximal Femur can be Quantified From Computer Reconstructions
,”
J. Biomech.
,
32
(
4
), pp.
443
451
.10.1016/S0021-9290(98)00150-X
55.
Karim
,
L.
, and
Vashishth
,
D.
,
2011
, “
Role of Trabecular Microarchitecture in the Formation, Accumulation, and Morphology of Microdamage in Human Cancellous Bone
,”
J. Orthop. Res.
,
29
(
11
), pp.
1739
1744
.10.1002/jor.21448
56.
Wright
,
T. M.
, and
Vosburgh
,
F.
,
1981
, “
Permanent Deformation of Compact Bone Monitored by Acoustic Emission
,”
J. Biomech.
,
14
(
6
), pp.
405
409
.10.1016/0021-9290(81)90058-0
57.
Boyce
,
T. M.
,
Fyhrie
,
D. P.
,
Glotkowski
,
M. C.
,
Radin
,
E. L.
, and
Schaffler
,
M. B.
,
1998
, “
Damage Type and Strain Mode Associations in Human Compact Bone Bending Fatigue
,”
J. Orthop. Res.
,
16
(
3
), pp.
322
329
.10.1002/jor.1100160308
58.
Burger
,
E. H.
, and
Klein-Nulend
,
J.
,
1999
, “
Mechanotransduction in Bone—Role of the Lacuno-Canalicular Network
,”
FASEB J.
,
13
(Suppl.), pp.
101
112
.
59.
Hardisty
,
M. R.
,
Akens
,
M. K.
,
Yee
,
A. J.
, and
Whyne
,
C. M.
,
2010
, “
Image Registration Demonstrates a Variable Effect of the Growth Plate on Vertebral Strain
,”
Ann. Biomed. Eng.
,
38
(
9
), pp.
2948
2955
.10.1007/s10439-010-0052-0
60.
Nazarian
,
A.
, and
Muller
,
R.
,
2004
, “
Time-Lapsed Microstructural Imaging of Bone Failure Behavior
,”
J. Biomech.
,
37
(
1
), pp.
55
65
.10.1016/S0021-9290(03)00254-9
61.
Easley
,
S. K.
,
Jekir
,
M. G.
,
Burghardt
,
A. J.
,
Li
,
M.
, and
Keaveny
,
T. M.
,
2010
, “
Contribution of the Intra-Specimen Variations in Tissue Mineralization to PTH- and Raloxifene-Induced Changes in Stiffness of Rat Vertebrae
,”
Bone
,
46
(
4
), pp.
1162
1169
.10.1016/j.bone.2009.12.009
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