Trabecular bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. Studying the mechanical properties of trabecular bone is important, since trabecular bone is the main load bearing bone in vertebral bodies and also transfers the load from joints to the compact bone of the cortex of long bones. This review article highlights the high dependency of the mechanical properties of trabecular bone on species, age, anatomic site, loading direction, and size of the sample under consideration. In recent years, high resolution micro finite element methods have been extensively used to specifically address the mechanical properties of the trabecular bone and provide unique tools to interpret and model the mechanical testing experiments. The aims of the current work are to first review the mechanobiology of trabecular bone and then present classical and new approaches for modeling and analyzing the trabecular bone microstructure and macrostructure and corresponding mechanical properties such as elastic properties and strength.

References

1.
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
2.
Chevalier
,
Y.
,
Pahr
,
D.
, and
Zysset
,
P. K.
,
2009
, “
The Role of Cortical Shell and Trabecular Fabric in Finite Element Analysis of the Human Vertebral Body
,”
ASME J. Biomech. Eng.
,
131
(
11
), p.
111003
.10.1115/1.3212097
3.
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
4.
Vanderoost
,
J.
,
Jaecques
,
S. V.
,
Van der Perre
,
G.
,
Boonen
,
S.
,
D'hooge
,
J.
,
Lauriks
,
W.
, and
van Lenthe
,
G. H.
,
2011
, “
Fast and Accurate Specimen-Specific Simulation of Trabecular Bone Elastic Modulus Using Novel Beam—Shell Finite Element Models
,”
J. Biomech.
,
44
(
8
), pp.
1566
1572
.10.1016/j.jbiomech.2011.02.082
5.
Hamed
,
E.
,
Jasiuk
,
I.
,
Yoo
,
A.
,
Lee
,
Y.
, and
Liszka
,
T.
,
2012
, “
Multi-Scale Modelling of Elastic Moduli of Trabecular Bone
,”
J. R. Soc., Interface
,
9
(
72
), pp.
1654
1673
.10.1098/rsif.2011.0814
6.
Stauber
,
M.
,
Rapillard
,
L.
,
van Lenthe
,
G. H.
,
Zysset
,
P.
, and
Müller
,
R.
,
2006
, “
Importance of Individual Rods and Plates in the Assessment of Bone Quality and Their Contribution to Bone Stiffness
,”
J. Bone Miner. Res.
,
21
(
4
), pp.
586
595
.10.1359/jbmr.060102
7.
Stauber
,
M.
, and
Müller
,
R.
,
2006
, “
Volumetric Spatial Decomposition of Trabecular Bone Into Rods and Plates—A New Method for Local Bone Morphometry
,”
Bone
,
38
(
4
), pp.
475
484
.10.1016/j.bone.2005.09.019
8.
Liu
,
X. S.
,
Sajda
,
P.
,
Saha
,
P. K.
,
Wehrli
,
F. W.
, and
Guo
,
X. E.
,
2006
, “
Quantification of the Roles of Trabecular Microarchitecture and Trabecular Type in Determining the Elastic Modulus of Human Trabecular Bone
,”
J. Bone Miner. Res.
,
21
(
10
), pp.
1608
1617
.10.1359/jbmr.060716
9.
Parfitt
,
A. M.
,
2001
, “
The Bone Remodeling Compartment: A Circulatory Function for Bone Lining Cells
,”
J Bone Miner. Res.
,
16
(
9
), pp.
1583
1585
.10.1359/jbmr.2001.16.9.1583
10.
Parfitt
,
A. M.
,
2002
, “
Targeted and Nontargeted Bone Remodeling: Relationship to Basic Multicellular Unit Origination and Progression
,”
Bone
,
30
(
1
), pp.
5
7
.10.1016/S8756-3282(01)00642-1
11.
Canalis
,
E.
,
2005
, “
The Fate of Circulating Osteoblasts
,”
N. Engl. J. Med.
,
352
(
19
), pp.
2014
2016
.10.1056/NEJMe058080
12.
Harada
,
S.
, and
Rodan
,
G. A.
,
2003
, “
Control of Osteoblast Function and Regulation of Bone Mass
,”
Nature
,
423
, pp.
349
355
.10.1038/nature01660
13.
Barragan-Adjemian
,
C.
,
Nicolella
,
D.
,
Dusevich
,
V.
,
Dallas
,
M. R.
,
Eick
,
J. D.
, and
Bonewald
,
L. F.
,
2006
, “
Mechanism by Which MLO-A5 Late Osteoblasts/Early Osteocytes Mineralize in Culture: Similarities With Mineralization of Lamellar Bone
,”
Calcif. Tissue Int.
,
79
(
5
), pp.
340
353
.10.1007/s00223-006-0107-2
14.
Karsenty
,
G.
, and
Wagner
,
E. F.
,
2002
, “
Reaching a Genetic and Molecular Understanding of Skeletal Development
,”
Dev. Cell
,
2
(
4
), pp.
389
406
.10.1016/S1534-5807(02)00157-0
15.
Franz-Odendaal
,
T. A.
,
Hall
,
B. K.
, and
Witten
,
P. E.
,
2006
,
Buried Alive: How Osteoblasts Become Osteocytes, Developmental Dynamics
, Vol.
235
,
American Association of Anatomists
, 235, pp.
176
190
.
16.
Kamioka
,
H.
,
Honjo
,
T.
, and
Takano-Yamamoto
,
T.
,
2001
, “
A Three-Dimensional Distribution of Osteocyte Processes Revealed by the Combination of Confocal Laser Scanning Microscopy and Differential Interference Contrast Microscopy
,”
Bone
,
28
(
2
), pp.
145
149
.10.1016/S8756-3282(00)00421-X
17.
Sugawara
,
Y.
,
Kamioka
,
H.
,
Honjo
,
T.
,
Tezuka
,
K.
, and
Takano-Yamamoto
,
T.
,
2005
, “
Three-Dimensional Reconstruction of Chick Calvarial Osteocytes and Their Cell Processes Using Confocal Microscopy
,”
Bone
,
36
(
5
), pp.
877
883
.10.1016/j.bone.2004.10.008
18.
Han
,
Y.
,
Cowin
,
S. C.
,
Schaffler
,
M. B.
, and
Weinbaum
,
S.
,
2004
, “
Mechanotransduction and Strain Amplification in Osteocyte Cell Processes
,”
Proc. Natl. Acad. Sci. U. S. A.
,
101
(
47
), pp.
16689
16694
.10.1073/pnas.0407429101
19.
Lanyon
,
L. E.
,
1993
, “
Osteocytes, Strain Detection, Bone Modeling and Remodeling
,”
Calcif. Tissue Int.
,
53
(
Suppl 1
), pp.
S102
106
[Discussion S106–107].10.1007/BF01673415
20.
Tatsumi
,
S.
,
Ishii
,
K.
,
Amizuka
,
N.
,
Li
,
M.
,
Kobayashi
,
T.
,
Kohno
,
K.
,
Ito
,
M.
,
Takeshita
,
S.
, and
Ikeda
,
K.
,
2007
, “
Targeted Ablation of Osteocytes Induces Osteoporosis With Defective Mechanotransduction
,”
Cell Metab.
,
5
(
6
), pp.
464
475
.10.1016/j.cmet.2007.05.001
21.
Dallas
,
S. L.
,
Prideaux
,
M.
, and
Bonewald
,
L. F.
,
2013
, “
The Osteocyte: An Endocrine Cell and More
,”
Endocr. Rev.
,
34
(
5
), pp.
658
690
.10.1210/er.2012-1026
22.
Burr
,
D. B.
,
Robling
,
A. G.
, and
Turner
,
C. H.
,
2002
, “
Effects of Biomechanical Stress on Bones in Animals
,”
Bone
,
30
(
5
), pp.
781
786
.10.1016/S8756-3282(02)00707-X
23.
Ehrlich
,
P. J.
,
Noble
,
B. S.
,
Jessop
,
H. L.
,
Stevens
,
H. Y.
,
Mosley
,
J. R.
, and
Lanyon
,
L. E.
,
2002
, “
The Effect of in Vivo Mechanical Loading on Estrogen Receptor Alpha Expression in Rat Ulnar Osteocytes
,”
J. Bone Miner. Res.
,
17
(
9
), pp.
1646
1655
.10.1359/jbmr.2002.17.9.1646
24.
Klein-Nulend
,
J.
,
Bakker
,
A. D.
,
Bacabac
,
R. G.
,
Vatsa
,
A.
, and
Weinbaum
,
S.
,
2013
, “
Mechanosensation and Transduction in Osteocytes
,”
Bone
,
54
(
2
), pp.
182
190
.10.1016/j.bone.2012.10.013
25.
Vatsa
,
A.
,
Breuls
,
R. G.
,
Semeins
,
C. M.
,
Salmon
,
P. L.
,
Smit
,
T. H.
, and
Klein-Nulend
, J.
2008
, “
Osteocyte Morphology in Fibula and Calvaria—Is There a Role for Mechanosensing?
,”
Bone
,
43
(
3
), pp.
452
458
.10.1016/j.bone.2008.01.030
26.
Vatsa
,
A.
,
Semeins
,
C. M.
,
Smit
,
T. H.
, and
Klein-Nulend
,
J.
,
2008
, “
Paxillin Localisation in Osteocytes—Is it Determined by the Direction of Loading?
,”
Biochem. Biophys. Res. Commun.
,
377
(
4
), pp.
1019
1024
.10.1016/j.bbrc.2007.12.174
27.
Pavalko
,
F. M.
,
Norvell
,
S. M.
,
Burr
,
D. B.
,
Turner
,
C. H.
,
Duncan
,
R. L.
, and
Bidwell
,
J. P.
,
2003
, “
A Model for Mechanotransduction in Bone Cells: The Load-Bearing Mechanosomes
,”
J. Cell. Biochem.
,
88
(
1
), pp.
104
112
.10.1002/jcb.10284
28.
You
,
J.
,
Yellowley
,
C. E.
,
Donahue
,
H. J.
,
Zhang
,
Y.
,
Chen
,
Q.
, and
Jacobs
,
C. R.
,
2000
, “
Substrate Deformation Levels Associated With Routine Physical Activity Are Less Stimulatory to Bone Cells Relative to Loading-Induced Oscillatory Fluid Flow
,”
ASME J. Biomech. Eng.
,
122
(
4
), pp.
387
393
.10.1115/1.1287161
29.
Weinbaum
,
S.
,
Cowin
,
S. C.
, and
Zeng
,
Y.
,
1994
, “
A Model for the Excitation of Osteocytes by Mechanical Loading-Induced Bone Fluid Shear Stresses
,”
J. Biomech.
,
27
(
3
), pp.
339
360
.10.1016/0021-9290(94)90010-8
30.
Cowin
,
S. C.
,
Weinbaum
,
S.
, and
Zeng
,
Y.
,
1995
, “
A Case for Bone Canaliculi as the Anatomical Site of Strain Generated Potentials
,”
J. Biomech.
,
28
(
11
), pp.
1281
1297
.10.1016/0021-9290(95)00058-P
31.
Hung
,
C. T.
,
Allen
,
F. D.
,
Pollack
,
S. R.
, and
Brighton
,
C. T.
,
1996
, “
Intracellular Ca2+ Stores and Extracellular Ca2+ Are Required in the Real-Time Ca2+ Response of Bone Cells Experiencing Fluid Flow
,”
J. Biomech.
,
29
(
11
), pp.
1411
1417
.10.1016/0021-9290(96)84536-2
32.
Hung
,
C. T.
,
Pollack
,
S. R.
,
Reilly
,
T. M.
, and
Brighton
,
C. T.
,
1995
, “
Real-Time Calcium Response of Cultured Bone Cells to Fluid Flow
,”
Clin. orthop. Relat. Res.
,
313
, pp.
256
269
.
33.
Lu
,
X. L.
,
Huo
,
B.
,
Park
,
M.
, and
Guo
,
X. E.
,
2012
, “
“Calcium Response in Osteocytic Networks Under Steady And Oscillatory Fluid Flow
,”
Bone
,
51
(
3
), pp.
466
473
.10.1016/j.bone.2012.05.021
34.
Zhang
,
D.
,
Weinbaum
,
S.
, and
Cowin
,
S. C.
,
1998
, “
Electrical Signal Transmission in a Bone Cell Network: The Influence of a Discrete Gap Junction
,”
Ann. Biomed. Eng.
,
26
(
4
), pp.
644
659
.10.1114/1.123
35.
Fritton
,
S. P.
, and
Weinbaum
,
S.
,
2009
, “
Fluid and Solute Transport in Bone: Flow-Induced Mechanotransduction
,”
Annu. Rev. Fluid Mech.
,
41
, pp.
347
374
.10.1146/annurev.fluid.010908.165136
36.
Owan
,
I.
,
Burr
,
D. B.
,
Turner
,
C. H.
,
Qiu
,
J.
,
Tu
,
Y.
,
Onyia
,
J. E.
, and
Duncan
,
R. L.
,
1997
, “
Mechanotransduction in Bone: Osteoblasts Are More Responsive to Fluid Forces Than Mechanical Strain
,”
Am. J. Physiol.
,
273
, pp.
C810
815
.
37.
Smalt
,
R.
,
Mitchell
,
F. T.
,
Howard
,
R. L.
, and
Chambers
,
T. J.
,
1997
, “
Induction of NO and Prostaglandin E2 in Osteoblasts by Wall-Shear Stress But Not Mechanical Strain
,”
Am. J. Physiol.
,
273
, pp.
E751
758
.
38.
Burr
,
D. B.
,
Milgrom
,
C.
,
Fyhrie
,
D.
,
Forwood
,
M.
,
Nyska
,
M.
,
Finestone
,
A.
,
Hoshaw
,
S.
,
Saiag
,
E.
, and
Simkin
,
A.
,
1996
, “
In Vivo Measurement of Human Tibial Strains During Vigorous Activity
,”
Bone
,
18
(
5
), pp.
405
410
.10.1016/8756-3282(96)00028-2
39.
Fritton
,
S. P.
,
McLeod
,
K. J.
, and
Rubin
,
C. T.
,
2000
, “
Quantifying the Strain History of Bone: Spatial Uniformity and Self-Similarity of Low-Magnitude Strains
,”
J. Biomech.
,
33
(
3
), pp.
317
325
.10.1016/S0021-9290(99)00210-9
40.
You
,
L.
,
Cowin
,
S. C.
,
Schaffler
,
M. B.
, and
Weinbaum
,
S.
,
2001
, “
A Model for Strain Amplification in the Actin Cytoskeleton of Osteocytes Due to Fluid Drag on Pericellular Matrix
,”
J. Biomech.
,
34
, pp.
1375
1386
.10.1016/S0021-9290(01)00107-5
41.
McNamara
,
L. M.
,
Majeska
,
R. J.
,
Weinbaum
,
S.
,
Friedrich
,
V.
, and
Schaffler
,
M. B.
,
2009
, “
Attachment of Osteocyte Cell Processes to the Bone Matrix
,”
Anat. Rec.
,
292
(
3
), pp.
355
363
.10.1002/ar.20869
42.
Wang
,
Y.
,
McNamara
,
L. M.
,
Schaffler
,
M. B.
, and
Weinbaum
,
S.
,
2007
, “
A Model for the Role of Integrins in Flow Induced Mechanotransduction in Osteocytes
,”
Proc. Natl. Acad. Sci. U. S. A.
,
104
(
4
), pp.
15941
15946
.10.1073/pnas.0707246104
43.
Santos
,
A.
,
Bakker
,
A. D.
, and
Klein-Nulend
,
J.
,
2009
, “
The Role of Osteocytes in Bone Mechanotransduction
,”
Osteoporosis Int.
,
20
(
6
), pp.
1027
1031
.10.1007/s00198-009-0858-5
44.
Adachi
,
T.
,
Aonuma
,
Y.
,
Tanaka
,
M.
,
Hojo
,
M.
,
Takano-Yamamoto
,
T.
, and
Kamioka
,
H.
,
2009
, “
Calcium Response in Single Osteocytes to Locally Applied Mechanical Stimulus: Differences in Cell Process and Cell Body
,”
J. Biomech.
,
42
(
12
), pp.
1989
1995
.10.1016/j.jbiomech.2009.04.034
45.
Thi
,
M. M.
,
Suadicani
,
S. O.
,
Schaffler
,
M. B.
,
Weinbaum
,
S.
, and
Spray
,
D. C.
,
2013
, “
Mechanosensory Responses of Osteocytes to Physiological Forces Occur Along Processes and Not Cell Body and Require AlphaVbeta3 Integrin
,”
Proc. Natl. Acad. Sci. U. S. A.
,
110
(
52
), pp.
21012
21017
.10.1073/pnas.1321210110
46.
Nicolella
,
D. P.
,
Feng
,
J. Q.
,
Moravits
,
D. E.
,
Bonivitch
,
A. R.
,
Wang
,
Y.
,
Dusecich
,
V.
,
Yao
,
W.
,
Lane
,
N.
, and
Bonewald
,
L. F.
,
2008
, “
Effects of Nanomechanical Bone Tissue Properties on Bone Tissue Strain: Implications for Osteocyte Mechanotransduction
,”
J. Musculoskeletal Neuronal Interact.
,
8
(
4
), pp.
330
331
.
47.
Malone
,
A. M.
,
Anderson
,
C. T.
,
Tummala
,
P.
,
Kwon
,
R. Y.
,
Johnston
,
T. R.
,
Stearns
,
T.
, and
Jacobs
,
C. R.
,
2007
, “
Primary Cilia Mediate Mechanosensing in Bone Cells by a Calcium-Independent Mechanism
,”
Proc. Natl. Acad. Sci. U. S. A.
,
104
(
33
), pp.
13325
13330
.10.1073/pnas.0700636104
48.
Xiao
,
Z.
,
Zhang
,
S.
,
Mahlios
,
J.
,
Zhou
,
G.
,
Magenheimer
,
B. S.
,
Guo
,
D.
,
Dallas
,
S. L.
,
Maser
,
R.
,
Calvet
,
J. P.
,
Bonewald
,
L.
, and
Quarles
,
L. D.
,
2006
, “
Cilia-Like Structures and Polycystin-1 in Osteoblasts/Osteocytes and Associated Abnormalities in Skeletogenesis and Runx2 Expression
,”
J. Biol. Chem.
,
281
, pp.
30884
30895
.10.1074/jbc.M604772200
49.
Bonewald
,
L. F.
,
2011
, “
The Amazing Osteocyte
,”
J. Bone Miner. Res.
,
26
(
2
), pp.
229
238
.10.1002/jbmr.320
50.
Gardinier
,
J. D.
,
Townend
,
C. W.
,
Jen
,
K. P.
,
Wu
,
Q.
,
Duncan
,
R. L.
, and
Wang
,
L.
,
2010
, “
In Situ Permeability Measurement of the Mammalian Lacunar–Canalicular System
,”
Bone
,
46
(
4
), pp.
1075
1081
.10.1016/j.bone.2010.01.371
51.
Kamioka
,
H.
,
Miki
,
Y.
,
Sumitani
,
K.
,
Tagami
,
K.
,
Terai
,
K.
,
Hosoi
,
K.
, and
Kawata
,
T.
,
1995
, “
Extracellular Calcium Causes the Release of Calcium From Intracellular Stores in Chick Osteocytes
,”
Biochem. Biophys. Res. Commun.
,
212
(
2
), pp.
692
696
.10.1006/bbrc.1995.2024
52.
Hung
,
C. T.
,
Allen
,
F. D.
,
Pollack
,
S. R.
, and
Brighton
,
C. T.
,
1996
, “
What is the Role of the Convective Current Density in the Real-Time Calcium Response of Cultured Bone Cells to Fluid Flow?
J. Biomech.
,
29
(
11
), pp.
1403
1409
.10.1016/0021-9290(96)84535-0
53.
Klein-Nulend
,
J.
,
van der Plas
,
A.
,
Semeins
,
C. M.
,
Ajubi
,
N. E.
,
Frangos
,
J. A.
,
Nijweide
,
P. J.
, and
Burger
,
E. H.
,
1995
, “
Sensitivity of Osteocytes to Biomechanical Stress In Vitro
,”
FASEB J.
,
9
(
5
), pp.
441
445
.
54.
Bakker
,
A. D.
,
Soejima
,
K.
,
Klein-Nulend
,
J.
, and
Burger
,
E. H.
,
2001
, “
The Production of Nitric Oxide and Prostaglandin E(2) by Primary Bone Cells is Shear Stress Dependent
,”
J. Biomech
,
34
(
5
), pp.
671
677
.10.1016/S0021-9290(00)00231-1
55.
Bakker
,
A. D.
,
Silva
, V
. C.
,
Krishnan
,
R.
,
Bacabac
,
R. G.
,
Blaauboer
,
M. E.
,
Lin
,
Y. C.
,
Marcantonio
,
R. A.
,
Cirelli
,
J. A.
, and
Klein-Nulend
,
J.
,
2009
, “
Tumor Necrosis Factor Alpha and Interleukin-1beta Modulate Calcium and Nitric Oxide Signaling in Mechanically Stimulated Osteocytes
,”
Arthritis Rheum.
,
60
(
11
), pp.
3336
3345
.10.1002/art.24920
56.
Tan
,
S. D.
,
Bakker
,
A. D.
,
Semeins
,
C. M.
,
Kuijpers-Jagtman
,
A. M.
, and
Klein-Nulend
,
J.
,
2008
, “
Inhibition of Osteocyte Apoptosis by Fluid Flow is Mediated by Nitric Oxide
,”
Biochem. Biophys. Res. Commun.
,
369
(
4
), pp.
1150
1154
.10.1016/j.bbrc.2008.03.007
57.
Xia
,
X.
,
Batra
,
N.
,
Shi
,
Q.
,
Bonewald
,
L. F.
,
Sprague
,
E.
, and
Jiang
,
J. X.
,
2010
, “
Prostaglandin Promotion of Osteocyte Gap Junction Function Through Transcriptional Regulation of Connexin 43 by Glycogen Synthase Kinase 3/Beta-Catenin Signaling
,”
Mol. Cell. Biol.
,
30
(
24
), pp.
206
219
.10.1128/MCB.01844-08
58.
Kitase
,
Y.
,
Barragan
,
L.
,
Qing
,
H.
,
Kondoh
,
S.
,
Jiang
,
J. X.
,
Johnson
,
M. L.
, and
Bonewald
,
L. F.
,
2010
, “
Mechanical Induction of PGE2 in Osteocytes Blocks Glucocorticoid-Induced Apoptosis Through Both the Beta-Catenin and PKA Pathways
,”
J. Bone Miner. Res.
,
25
(
12
), pp.
2657
2668
.10.1002/jbmr.168
59.
Krishnan
,
V.
,
Bryant
,
H. U.
, and
Macdougald
,
O. A.
,
2006
, “
Regulation of Bone Mass by Wnt Signaling
,”
J. Clin. Invest.
,
116
(
5
), pp.
1202
1209
.10.1172/JCI28551
60.
Canalis
,
E.
,
Giustina
,
A.
, and
Bilezikian
,
J. P.
,
2007
, “
Mechanisms of Anabolic Therapies for Osteoporosis
,”
N. Engl. J. Med.
,
357
(
9
), pp.
905
916
.10.1056/NEJMra067395
61.
Gong
,
Y.
,
Slee
,
R. B.
,
Fukai
,
N.
,
Rawadi
,
G.
,
Roman-Roman
,
S.
,
Reginato
,
A. M.
,
Wang
,
H.
,
Cundy
,
T.
,
Glorieux
,
F. H.
,
Lev
,
D.
,
Zacharin
,
M.
,
Oexle
,
K.
,
Marcelino
,
J.
,
Suwairi
,
W.
,
Heeger
,
S.
,
Sabatakos
,
G.
,
Apte
,
S.
,
Adkins
,
W. N.
,
Allgrove
,
J.
,
Arslan-Kirchner
,
M.
,
Batch
,
J. A.
,
Beighton
,
P.
,
Black
,
G. C.
,
Boles
,
R. G.
,
Boon
,
L. M.
,
Borrone
,
C.
,
Brunner
,
H. G.
,
Carle
,
G. F.
,
Dallapiccola
,
B.
,
De Paepe
,
A.
,
Floege
,
B.
,
Halfhide
,
M. L.
,
Hall
,
B.
,
Hennekam
,
R. C.
,
Hirose
,
T.
,
Jans
,
A.
,
Juppner
,
H.
,
Kim
,
C. A.
,
Keppler-Noreuil
,
K.
,
Kohlschuetter
,
A.
,
LaCombe
,
D.
,
Lambert
,
M.
,
Lemyre
,
E.
,
Letteboer
,
T.
,
Peltonen
,
L.
,
Ramesar
,
R. S.
,
Romanengo
,
M.
,
Somer
,
H.
,
Steichen-Gersdorf
,
E.
,
Steinmann
,
B.
,
Sullivan
,
B.
,
Superti-Furga
,
A.
,
Swoboda
,
W.
,
van den Boogaard
,
M. J.
,
Van Hul
,
W.
,
Vikkula
,
M.
,
Votruba
,
M.
,
Zabel
,
B.
,
Garcia
,
T.
,
Baron
,
R.
,
Olsen
,
B. R.
, and
Warman
,
M. L.
,
2001
, “
LDL Receptor-Related Protein 5 (LRP5) Affects Bone Accrual and Eye Development
,”
Cell
,
107
(
4
), pp.
513
523
.10.1016/S0092-8674(01)00571-2
62.
Babij
,
P.
,
Zhao
,
W.
,
Small
,
C.
,
Kharode
,
Y.
,
Yaworsky
,
P. J.
,
Bouxsein
,
M. L.
,
Reddy
,
P. S.
,
Bodine
,
P. V.
,
Robinson
,
J. A.
,
Bhat
,
B.
,
Marzolf
,
J.
,
Moran
,
R. A.
, and
Bex
,
F.
,
2003
, “
High Bone Mass in Mice Expressing a Mutant LRP5 Gene
,”
J. Bone Miner. Res.
,
18
(
6
), pp.
960
974
.10.1359/jbmr.2003.18.6.960
63.
Boyden
,
L. M.
,
Mao
,
J.
,
Belsky
,
J.
,
Mitzner
,
L.
,
Farhi
,
A.
,
Mitnick
,
M. A.
,
Wu
,
D.
,
Insogna
,
K.
, and
Lifton
,
R. P.
,
2002
, “
High Bone Density Due to a Mutation in LDL-Receptor-Related Protein 5
,”
N. Engl. J. Med.
,
346
, pp.
1513
1521
.10.1056/NEJMoa013444
64.
Dyson
,
E.
, and
Whitehouse
,
W.
,
1968
, “
Composition of Trabecular Bone in Children and Its Relation to Radiation Dosimetry
,”
Nature
,
217
, pp.
576
578
.10.1038/217576a0
65.
Gong
,
J.
,
Arnold
,
J.
, and
Cohn
,
S.
,
1964
, “
Composition of Trabecular and Cortical Bone
,”
Anat. Rec.
,
149
(
3
), pp.
325
331
.10.1002/ar.1091490303
66.
Jee
,
W.
,
1983
, “
The Skeletal Tissues
,”
Histol. Cell Tissue Biol.
,
5
, pp.
206
254
.
67.
Fritsch
,
A.
, and
Hellmich
,
C.
,
2007
, “
‘Universal’ Microstructural Patterns in Cortical and Trabecular, Extracellular and Extravascular Bone Materials: Micromechanics-Based Prediction of Anisotropic Elasticity
,”
J. Theor. Biol.
,
244
(
4
), pp.
597
620
.10.1016/j.jtbi.2006.09.013
68.
McNamara
,
L.
,
Van der Linden
,
J.
,
Weinans
,
H.
, and
Prendergast
,
P.
,
2006
, “
Stress-Concentrating Effect of Resorption Lacunae in Trabecular Bone
,”
J. Biomech.
,
39
(
4
), pp.
734
741
.10.1016/j.jbiomech.2004.12.027
69.
Runkle
,
J.
, and
Pugh
,
J.
,
1975
, “
The Micro-Mechanics of Cancellous Bone. II. Determination of the Elastic Modulus of Individual Trabeculae by a Buckling Analysis
,”
Bull. Hosp. Jt. Dis.
,
36
(
1
), pp.
2
10
.
70.
Townsend
,
P. R.
,
Rose
,
R. M.
, and
Radin
,
E. L.
,
1975
, “
Buckling Studies of Single Human Trabeculae
,”
J. Biomech.
,
8
(
3-4
), pp.
199
201
.10.1016/0021-9290(75)90025-1
71.
Hoffler
,
C. E.
,
Guo
,
X. E.
,
Zysset
,
P. K.
, and
Goldstein
,
S. A.
,
2005
, “
An Application of Nanoindentation Technique to Measure Bone Tissue Lamellae Properties
,”
ASME J. Biomech. Eng.
,
127
(
7
), pp.
1046
1053
.10.1115/1.2073671
72.
Rho
,
J.-Y.
,
Tsui
,
T. Y.
, and
Pharr
,
G. M.
,
1997
, “
Elastic Properties of Human Cortical and Trabecular Lamellar Bone Measured by Nanoindentation
,”
Biomaterials
,
18
(
20
), pp.
1325
1330
.10.1016/S0142-9612(97)00073-2
73.
Zysset
,
P.
,
Guo
,
X.
,
Hoffler
,
C.
,
Moore
,
K.
, and
Goldstein
,
S.
,
1998
, “
Mechanical Properties of Human Trabecular Bone Lamellae Quantified by Nanoindentation
,”
Technol. Health Care
,
6
(
5-6
), pp.
429
432
.10.1046/j.1365-2524.1998.00153.x
74.
Zysset
,
P. K.
,
Edward Guo
,
X.
,
Edward Hoffler
,
C.
,
Moore
,
K. E.
, and
Goldstein
,
S. A.
,
1999
, “
Elastic Modulus and Hardness of Cortical and Trabecular Bone Lamellae Measured by Nanoindentation in the Human Femur
,”
J. Biomech.
,
32
(
10
), pp.
1005
1012
.10.1016/S0021-9290(99)00111-6
75.
Turner
,
C. H.
,
Rho
,
J.
,
Takano
,
Y.
,
Tsui
,
T. Y.
, and
Pharr
,
G. M.
,
1999
, “
The Elastic Properties of Trabecular and Cortical Bone Tissues Are Similar: Results From Two Microscopic Measurement Techniques
,”
J. Biomech.
,
32
(
4
), pp.
437
441
.10.1016/S0021-9290(98)00177-8
76.
Ko
,
C.-C.
,
Douglas
,
W. H.
, and
Cheng
,
Y.-S.
,
1995
, “
Intrinsic Mechanical Competence of Cortical and Trabecular Bone Measured by Nanoindentation and Microindentation Probes
,”
BED
,
29
, pp.
415
415
.
77.
Roy
,
M.
,
Rho
,
J.-Y.
,
Tsui
,
T. Y.
, and
Pharr
,
G. M.
,
1996
, “
Variation of Young's Modulus and Hardness in Human Lumbar Vertebrae Measured by Nanoindentation
,”
BED
,
33
, pp.
385
386
.
78.
Fan
,
Z.
,
Swadener
,
J.
,
Rho
,
J.
,
Roy
,
M.
, and
Pharr
,
G.
,
2002
, “
Anisotropic Properties of Human Tibial Cortical Bone as Measured by Nanoindentation
,”
J. Orthop. Res.
,
20
(
4
), pp.
806
810
.10.1016/S0736-0266(01)00186-3
79.
Rho
,
J. Y.
,
Roy
,
M. E.
,
Tsui
,
T. Y.
, and
Pharr
,
G. M.
,
1999
, “
Elastic Properties of Microstructural Components of Human Bone Tissue as Measured by Nanoindentation
,”
J. Biomed. Mater. Res.
,
45
(
1
), pp.
48
54
.10.1002/(SICI)1097-4636(199904)45:1<48::AID-JBM7>3.0.CO;2-5
80.
Rho
,
J.
,
Zioupos
,
P.
,
Currey
,
J.
, and
Pharr
,
G.
,
2002
, “
Microstructural Elasticity and Regional Heterogeneity in Human Femoral Bone of Various Ages Examined by Nano-Indentation
,”
J. Biomech.
,
35
(
2
), pp.
189
198
.10.1016/S0021-9290(01)00199-3
81.
Rho
,
J. Y.
,
Ashman
,
R. B.
, and
Turner
,
C. H.
,
1993
, “
Young's Modulus of Trabecular and Cortical Bone Material: Ultrasonic and Microtensile Measurements
,”
J. Biomech.
,
26
(
2
), pp.
111
119
.10.1016/0021-9290(93)90042-D
82.
Ryan
,
S. D.
, and
Williams
,
J. L.
,
1989
, “
Tensile Testing of Rodlike Trabeculae Excised From Bovine Femoral Bone
,”
J. Biomech.
,
22
(
4
), pp.
351
355
.10.1016/0021-9290(89)90049-3
83.
Choi
,
K.
,
Kuhn
,
J. L.
,
Ciarelli
,
M. J.
, and
Goldstein
,
S. A.
,
1990
, “
The Elastic Moduli of Human Subchondral, Trabecular, and Cortical Bone Tissue and the Size-Dependency of Cortical Bone Modulus
,”
J. Biomech.
,
23
(
11
), pp.
1103
1113
.10.1016/0021-9290(90)90003-L
84.
Kuhn
,
J. L.
,
Goldstein
,
S. A.
,
Choi
,
R.
,
London
,
M.
,
Feldkamp
,
L.
, and
Matthews
,
L. S.
,
1989
, “
Comparison of the Trabecular and Cortical Tissue Moduli From Human Iliac Crests
,”
J. Orthop. Res.
,
7
(
6
), pp.
876
884
.10.1002/jor.1100070614
85.
Choi
,
K.
, and
Goldstein
,
S. A.
,
1992
, “
A Comparison of the Fatigue Behavior of Human Trabecular and Cortical Bone Tissue
,”
J. Biomech.
,
25
(
12
), pp.
1371
1381
.10.1016/0021-9290(92)90051-2
86.
Nicholson
,
P.
,
Cheng
,
X.
,
Lowet
,
G.
,
Boonen
,
S.
,
Davie
,
M.
,
Dequeker
,
J.
, and
Van der Perre
,
G.
,
1997
, “
Structural and Material Mechanical Properties of Human Vertebral Cancellous Bone
,”
Med. Eng. Phys.
,
19
(
8
), pp.
729
737
.10.1016/S1350-4533(97)00030-1
87.
Shieh
,
S.-J.
,
Zimmerman
,
M.
, and
Langrana
,
N.
,
1995
, “
The Application of Scanning Acoustic Microscopy in a Bone Remodeling Study
,”
ASME J. Biomech. Eng.
,
117
(
3
), pp.
286
292
.10.1115/1.2794183
88.
Ladd
,
A. J.
,
Kinney
,
J. H.
,
Haupt
,
D. L.
, and
Goldstein
,
S. A.
,
1998
, “
Finite-Element Modeling of Trabecular Bone: Comparison With Mechanical Testing and Determination of Tissue Modulus
,”
J. Orthop. Res.
,
16
(
5
), pp.
622
628
.10.1002/jor.1100160516
89.
Hou
,
F. J.
,
Lang
,
S. M.
,
Hoshaw
,
S. J.
,
Reimann
,
D. A.
, and
Fyhrie
,
D. P.
,
1998
, “
Human Vertebral Body Apparent and Hard Tissue Stiffness
,”
J. Biomech.
,
31
(
11
), pp.
1009
1015
.10.1016/S0021-9290(98)00110-9
90.
Jensen
,
K.
,
Mosekilde
,
L.
, and
Mosekilde
,
L.
,
1990
, “
A Model of Vertebral Trabecular Bone Architecture and Its Mechanical Properties
,”
Bone
,
11
(
6
), pp.
417
423
.10.1016/8756-3282(90)90137-N
91.
Hodgskinson
,
R.
,
Currey
,
J.
, and
Evans
,
G.
,
1989
, “
Hardness, an Indicator of the Mechanical Competence of Cancellous Bone
,”
J. Orthop. Res.
,
7
(
5
), pp.
754
758
.10.1002/jor.1100070518
92.
Cyganik
,
Ł.
,
Binkowski
,
M.
,
Kokot
,
G.
,
Rusin
,
T.
,
Popik
,
P.
,
Bolechała
,
F.
,
Nowak
,
R.
,
Wróbel
,
Z.
, and
John
,
A.
,
2014
, “
Prediction of Young's Modulus of Trabeculae in Microscale Using Macro-Scale’s Relationships Between Bone Density and Mechanical Properties
,”
J. Mech. Behav. Biomed. Mater.
,
36
, pp.
120
134
.10.1016/j.jmbbm.2014.04.011
93.
Gillard
,
F.
,
Boardman
,
R.
,
Mavrogordato
,
M.
,
Hollis
,
D.
,
Sinclair
,
I.
,
Pierron
,
F.
, and
Browne
,
M.
,
2014
, “
The Application of Digital Volume Correlation (DVC) to Study the Microstructural Behaviour of Trabecular Bone During Compression
,”
J. Mech. Behav. Biomed. Mater.
,
29
, pp.
480
499
.10.1016/j.jmbbm.2013.09.014
94.
Timoshenko
,
S.
,
1983
,
History of Strength of Materials: With a Brief Account of the History of Theory of Elasticity and Theory of Structures,
Courier Dover Publications
,
Mineola, NY
.
95.
Haiat
,
G.
,
Padilla
,
F.
,
Svrcekova
,
M.
,
Chevalier
,
Y.
,
Pahr
,
D.
,
Peyrin
,
F.
,
Laugier
,
P.
, and
Zysset
,
P.
,
2009
, “
Relationship Between Ultrasonic Parameters and Apparent Trabecular Bone Elastic Modulus: A Numerical Approach
,”
J. Biomech.
,
42
(
13
), pp.
2033
2039
.10.1016/j.jbiomech.2009.06.008
96.
Ashman
,
R. B.
, and
Rho
,
J. Y.
,
1988
, “
Elastic Modulus of Trabecular Bone Material
,”
J. Biomech.
,
21
(
3
), pp.
177
181
.10.1016/0021-9290(88)90167-4
97.
Brennan
,
O.
,
Kennedy
,
O. D.
,
Lee
,
T. C.
,
Rackard
,
S. M.
, and
O’Brien
,
F. J.
,
2009
, “
Biomechanical Properties Across Trabeculae From the Proximal Femur of Normal and Ovariectomised Sheep
,”
J. Biomech.
,
42
(
4
), pp.
498
503
.10.1016/j.jbiomech.2008.11.032
98.
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
99.
Verhulp
,
E.
,
van Rietbergen
,
B.
,
Müller
,
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
100.
Ciarelli
,
M.
,
Goldstein
,
S.
,
Kuhn
,
J.
,
Cody
,
D.
, and
Brown
,
M.
,
1991
, “
Evaluation of Orthogonal Mechanical Properties and Density of Human Trabecular Bone From the Major Metaphyseal Regions With Materials Testing and Computed Tomography
,”
J. Orthop. Res.
,
9
(
5
), pp.
674
682
.10.1002/jor.1100090507
101.
Hodgskinson
,
R.
, and
Currey
,
J.
,
1993
, “
Separate Effects of Osteoporosis and Density on the Strength and Stiffness of Human Cancellous Bone
,”
Clin. Biomech.
,
8
(
5
), pp.
262
268
.10.1016/0268-0033(93)90036-H
102.
Keaveny
,
T. M.
,
Guo
,
X. E.
,
Wachtel
,
E. F.
,
McMahon
,
T. A.
, and
Hayes
,
W. C.
,
1994
, “
Trabecular Bone Exhibits Fully Linear Elastic Behavior and Yields at Low Strains
,”
J. Biomech.
,
27
(
9
), pp.
1127
1136
.10.1016/0021-9290(94)90053-1
103.
Goldstein
,
S. A.
,
Wilson
,
D. L.
,
Sonstegard
,
D. A.
, and
Matthews
,
L. S.
,
1983
, “
The Mechanical Properties of Human Tibial Trabecular Bone as a Function of Metaphyseal Location
,”
J. Biomech.
,
16
(
12
), pp.
965
969
.10.1016/0021-9290(83)90097-0
104.
Brown
,
T. D.
, and
Ferguson
,
A. B.
,
1980
, “
Mechanical Property Distributions in the Cancellous Bone of the Human Proximal Femur
,”
Acta Orthop.
,
51
(
1–6
), pp.
429
437
.10.3109/17453678008990819
105.
Renders
,
G.
,
Mulder
,
L.
,
Langenbach
,
G.
,
Van Ruijven
,
L.
, and
Van Eijden
,
T.
,
2008
, “
Biomechanical Effect of Mineral Heterogeneity in Trabecular Bone
,”
J. Biomech.
,
41
(
13
), pp.
2793
2798
.10.1016/j.jbiomech.2008.07.009
106.
Mosekilde
,
L.
,
Mosekilde
,
L.
, and
Danielsen
,
C.
,
1987
, “
Biomechanical Competence of Vertebral Trabecular Bone in Relation to Ash Density and Age in Normal Individuals
,”
Bone
,
8
(
2
), pp.
79
85
.10.1016/8756-3282(87)90074-3
107.
Galante
,
J.
,
Rostoker
,
W.
, and
Ray
,
R.
,
1970
, “
Physical Properties of Trabecular Bone
,”
Calcif. Tissue Res.
,
5
(
1
), pp.
236
246
.10.1007/BF02017552
108.
Keaveny
,
T. M.
,
Pinilla
,
T. P.
,
Crawford
,
R. P.
,
Kopperdahl
,
D. L.
, and
Lou
, A., “
Systematic and Random Errors in Compression Testing of Trabecular Bone
,”
J. Orthop. Res.
,
15
(
1
), pp.
101
110
.10.1002/jor.1100150115
109.
Linde
,
F.
,
Hvid
,
I.
, and
Madsen
,
F.
,
1992
, “
The Effect of Specimen Geometry on the Mechanical Behaviour of Trabecular Bone Specimens
,”
J. Biomech.
,
25
(
4
), pp.
359
368
.10.1016/0021-9290(92)90255-Y
110.
Jacobs
,
C.
,
Davis
,
B.
,
Rieger
,
C.
,
Francis
,
J.
,
Saad
,
M.
, and
Fyhrie
,
D.
,
1999
, “
The Impact of Boundary Conditions and Mesh Size on the Accuracy of Cancellous Bone Tissue Modulus Determination Using Large-Scale Finite-Element Modeling
,”
J. Biomech.
,
32
(
11
), pp.
1159
1164
.10.1016/S0021-9290(99)00115-3
111.
Cowin
,
S. C.
,
1985
, “
The Relationship Between The Elasticity Tensor and the Fabric Tensor
,”
Mech. Mater.
,
4
(
2
), pp.
137
147
.10.1016/0167-6636(85)90012-2
112.
Zysset
,
P.
, and
Curnier
,
A.
,
1995
, “
An Alternative Model for Anisotropic Elasticity Based on Fabric Tensors
,”
Mech. Mater.
,
21
(
4
), pp.
243
250
.10.1016/0167-6636(95)00018-6
113.
Shi
,
X.
,
Wang
,
X.
, and
Niebur
,
G. L.
,
2009
, “
Effects of Loading Orientation on the Morphology of the Predicted Yielded Regions in Trabecular Bone
,”
Ann. Biomed. Eng.
,
37
(
2
), pp.
354
362
.10.1007/s10439-008-9619-4
114.
Öhman
,
C.
,
Baleani
,
M.
,
Perilli
,
E.
,
Dall’Ara
,
E.
,
Tassani
,
S.
,
Baruffaldi
,
F.
, and
Viceconti
,
M.
,
2007
, “
Mechanical Testing of Cancellous Bone From the Femoral Head: Experimental Errors Due to Off-Axis Measurements
,”
J. Biomech.
,
40
(
11
), pp.
2426
2433
.10.1016/j.jbiomech.2006.11.020
115.
Morgan
,
E. F.
,
Bayraktar
,
H. H.
, and
Keaveny
,
T. M.
,
2003
, “
Trabecular Bone Modulus–Density Relationships Depend on Anatomic Site
,”
J. Biomech.
,
36
(
5
), pp.
897
904
.10.1016/S0021-9290(03)00071-X
116.
Morgan
,
E. F.
, and
Keaveny
,
T. M.
,
2001
, “
Dependence of Yield Strain of Human Trabecular Bone on Anatomic Site
,”
J. Biomech.
,
34
(
5
), pp.
569
577
.10.1016/S0021-9290(01)00011-2
117.
Nazarian
,
A.
,
Muller
,
J.
,
Zurakowski
,
D.
,
Müller
,
R.
, and
Snyder
,
B. D.
,
2007
, “
Densitometric, Morphometric and Mechanical Distributions in the Human Proximal Femur
,”
J. Biomech.
,
40
(
1
), pp.
2573
2579
.10.1016/j.jbiomech.2006.11.022
118.
Harrison
,
N. M.
, and
McHugh
,
P. E.
,
2010
, “
Comparison of Trabecular Bone Behavior in Core and Whole Bone Samples Using High-Resolution Modeling of a Vertebral Body
,”
Biomech. Model. Mechanobiol.
,
9
(
4
), pp.
469
480
.10.1007/s10237-009-0188-8
119.
Ün
,
K.
,
Bevill
,
G.
, and
Keaveny
,
T. M.
,
2006
, “
The Effects of Side-Artifacts on the Elastic Modulus of Trabecular Bone
,”
J. Biomech.
,
39
(
11
), pp.
1955
1963
.10.1016/j.jbiomech.2006.05.012
120.
Day
,
J.
,
Ding
,
M.
,
Van Der Linden
,
J.
,
Hvid
,
I.
,
Sumner
,
D.
, and
Weinans
,
H.
,
2001
, “
A Decreased Subchondral Trabecular Bone Tissue Elastic Modulus is Associated With Pre-Arthritic Cartilage Damage
,”
J. Orthop. Res.
,
19
(
5
), pp.
914
918
.10.1016/S0736-0266(01)00012-2
121.
Ashman
,
R.
,
Rho
,
J.
, and
Turner
,
C.
,
1989
, “
Anatomical Variation of Orthotropic Elastic Moduli of the Proximal Human Tibia
,”
J. Biomech.
,
22
(
8-9
), pp.
895
900
.10.1016/0021-9290(89)90073-0
122.
Røhl
,
L.
,
Larsen
,
E.
,
Linde
,
F.
,
Odgaard
,
A.
, and
Jørgensen
,
J.
,
1991
, “
Tensile and Compressive Properties of Cancellous Bone
,”
J. Biomech.
,
24
(
12
), pp.
1143
1149
.10.1016/0021-9290(91)90006-9
123.
Linde
,
F.
,
Hvid
,
I.
, and
Jensen
,
N. C.
,
1985
, “
Material Properties of Cancellous Bone in Repetitive Axial Loading
,”
Eng. Med.
,
14
, pp.
173
177
.10.1243/EMED_JOUR_1985_014_042_02
124.
Linde
,
F.
, and
Hvid
,
I.
,
1987
, “
Stiffness Behaviour of Trabecular Bone Specimens
,”
J. Biomech.
,
20
(
1
), pp.
83
89
.10.1016/0021-9290(87)90270-3
125.
Turner
,
C. H.
,
Cowin
,
S. C.
,
Rho
,
J. Y.
,
Ashman
,
R. B.
, and
Rice
,
J. C.
,
1990
, “
The Fabric Dependence of the Orthotropic Elastic Constants of Cancellous Bone
,”
J. Biomech.
,
23
(
6
), pp.
549
561
.10.1016/0021-9290(90)90048-8
126.
Hernandez
,
C.
,
Beaupré
,
G.
,
Keller
,
T.
, and
Carter
,
D.
,
2001
, “
The Influence of Bone Volume Fraction and Ash Fraction on Bone Strength and Modulus
,”
Bone
,
29
(
1
), pp.
74
78
.10.1016/S8756-3282(01)00467-7
127.
Martin
,
R.
, and
Ishida
,
J.
,
1989
, “
The Relative Effects of Collagen Fiber Orientation, Porosity, Density, and Mineralization on Bone Strength
,”
J. Biomech.
,
22
(
5
), pp.
419
426
.10.1016/0021-9290(89)90202-9
128.
Ciarelli
,
T.
,
Fyhrie
,
D.
,
Schaffler
,
M.
, and
Goldstein
,
S.
,
2000
, “
Variations in Three-Dimensional Cancellous Bone Architecture of the Proximal Femur in Female Hip Fractures and in Controls
,”
J. Bone Miner. Res.
,
15
(
1
), pp.
32
40
.10.1359/jbmr.2000.15.1.32
129.
Cory
,
E.
,
Nazarian
,
A.
,
Entezari
,
V.
,
Vartanians
,
V.
,
Müller
,
R.
, and
Snyder
,
B. D.
,
2010
, “
Compressive Axial Mechanical Properties of Rat Bone as Functions of Bone Volume Fraction, Apparent Density and Micro-CT Based Mineral Density
,”
J. Biomech.
,
43
(
5
), pp.
953
960
.10.1016/j.jbiomech.2009.10.047
130.
Goulet
,
R. W.
,
Goldstein
,
S. A.
,
Ciarelli
,
M. J.
,
Kuhn
,
J. L.
,
Brown
,
M.
, and
Feldkamp
,
L.
,
1994
, “
The Relationship Between the Structural and Orthogonal Compressive Properties of Trabecular Bone
,”
J. Biomech.
,
27
(
4
), pp.
375
389
.10.1016/0021-9290(94)90014-0
131.
Keller
,
T. S.
,
1994
, “
Predicting the Compressive Mechanical Behavior of Bone
,”
J. Biomech.
,
27
(
9
), pp.
1159
1168
.10.1016/0021-9290(94)90056-6
132.
Hodgskinson
,
R.
, and
Currey
,
J.
,
1992
, “
Young's Modulus, Density and Material Properties in Cancellous Bone Over a Large Density Range
,”
J. Mater. Sci.: Mater. Med.
,
3
(
5
), pp.
377
381
.10.1007/BF00705371
133.
Ulrich
,
D.
,
Van Rietbergen
,
B.
,
Laib
,
A.
, and
Ruegsegger
,
P.
,
1999
, “
The Ability of Three-Dimensional Structural Indices to Reflect Mechanical Aspects of Trabecular Bone
,”
Bone
,
25
(
1
), pp.
55
60
.10.1016/S8756-3282(99)00098-8
134.
Kabel
,
J.
,
Van Rietbergen
,
B.
,
Odgaard
,
A.
, and
Huiskes
,
R.
,
1999
, “
Constitutive Relationships of Fabric, Density, and Elastic Properties in Cancellous Bone Architecture
,”
Bone
,
25
(
4
), pp.
481
486
.10.1016/S8756-3282(99)00190-8
135.
Rüegsegger
,
P.
,
Koller
,
B.
, and
Müller
,
R.
,
1996
, “
A Microtomographic System for the Nondestructive Evaluation of Bone Architecture
,”
Calcif. Tissue Int.
,
58
(
1
), pp.
24
29
.10.1007/BF02509542
136.
Hipp
,
J. A.
,
Jansujwicz
,
A.
,
Simmons
,
C. A.
, and
Snyder
,
B. D.
,
1996
, “
Trabecular Bone Morphology From Micro-Magnetic Resonance Imaging
,”
J. Bone Miner. Res.
,
11
(
2
), pp.
286
292
.10.1002/jbmr.5650110218
137.
Ladd
,
A. J.
, and
Kinney
,
J. H.
,
1998
, “
Numerical Errors and Uncertainties in Finite-Element Modeling of Trabecular Bone
,”
J. Biomech.
,
31
(
10
), pp.
941
945
.10.1016/S0021-9290(98)00108-0
138.
Ulrich
,
D.
,
Van Rietbergen
,
B.
,
Weinans
,
H.
, and
Rüegsegger
,
P.
,
1998
, “
Finite Element Analysis of Trabecular Bone Structure: A Comparison of Image-Based Meshing Techniques
,”
J. Biomech.
,
31
(
12
), pp.
1187
1192
.10.1016/S0021-9290(98)00118-3
139.
Müller
,
R.
, and
Rüegsegger
,
P.
,
1995
, “
Three-Dimensional Finite Element Modelling of Non-Invasively Assessed Trabecular Bone Structures
,”
Med. Eng. Phys.
,
17
(
2
), pp.
126
133
.10.1016/1350-4533(95)91884-J
140.
Cowin
,
S.
, and
Mehrabadi
,
M.
,
1989
, “
Identification of the Elastic Symmetry of Bone and Other Materials
,”
J. Biomech.
,
22
(
6-7
), pp.
503
515
.10.1016/0021-9290(89)90001-8
141.
Hildebrand
,
T.
,
Laib
,
A.
,
Müller
,
R.
,
Dequeker
,
J.
, and
Rüegsegger
,
P.
,
1999
, “
Direct Three-Dimensional Morphometric Analysis of Human Cancellous Bone: Microstructural Data From Spine, Femur, Iliac Crest, and Calcaneus
,”
J. Bone Miner. Res.
,
14
(
7
), pp.
1167
1174
.10.1359/jbmr.1999.14.7.1167
142.
Kabel
,
J.
,
Odgaard
,
A.
,
Van Rietbergen
,
B.
, and
Huiskes
,
R.
,
1999
, “
Connectivity and the Elastic Properties of Cancellous Bone
,”
Bone
,
24
(
2
), pp.
115
120
.10.1016/S8756-3282(98)00164-1
143.
Kabel
,
J.
,
van Rietbergen
,
B.
,
Dalstra
,
M.
,
Odgaard
,
A.
, and
Huiskes
,
R.
,
1999
, “
The Role of an Effective Isotropic Tissue Modulus in the Elastic Properties of Cancellous Bone
,”
J. Biomech.
,
32
(
7
), pp.
673
680
.10.1016/S0021-9290(99)00045-7
144.
Van Rietbergen
,
B.
,
Odgaard
,
A.
,
Kabel
,
J.
, and
Huiskes
,
R.
,
1996
, “
Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture
,”
J. Biomech.
,
29
(
12
), pp.
1653
1657
.10.1016/S0021-9290(96)80021-2
145.
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
146.
Arbenz
,
P.
,
van Lenthe
,
G. H.
,
Mennel
,
U.
,
Müller
,
R.
, and
Sala
,
M.
,
2008
, “
A Scalable Multi-Level Preconditioner for Matrix-Free μ-Finite Element Analysis of Human Bone Structures
,”
Int. J. Numer. Methods Eng.
,
73
(
7
), pp.
927
947
.10.1002/nme.2101
147.
Podshivalov
,
L.
,
Fischer
,
A.
, and
Bar-Yoseph
,
P.
,
2011
, “
3D Hierarchical Geometric Modeling and Multiscale FE Analysis as a Base for Individualized Medical Diagnosis of Bone Structure
,”
Bone
,
48
(
4
), pp.
693
703
.10.1016/j.bone.2010.12.022
148.
Podshivalov
,
L.
,
Fischer
,
A.
, and
Bar-Yoseph
,
P.
,
2011
, “
Multiscale FE Method for Analysis of Bone Micro-Structures
,”
J. Mech. Behav. Biomed. Mater.
,
4
(
6
), pp.
888
899
.10.1016/j.jmbbm.2011.03.003
149.
Wang
,
H.
,
Liu
,
X. S.
,
Zhou
,
B.
,
Wang
,
J.
,
Ji
,
B.
,
Huang
,
Y.
,
Hwang
,
K.-C.
, and
Guo
,
X. E.
,
2013
, “
Accuracy of Individual Trabecula Segmentation Based Plate and Rod Finite Element Models in Idealized Trabecular Bone Microstructure
,”
ASME J. Biomech. Eng.
,
135
(
4
), p.
044502
.10.1115/1.4023983
150.
Helgason
,
B.
,
Perilli
,
E.
,
Schileo
,
E.
,
Taddei
,
F.
,
Brynjólfsson
,
S.
, and
Viceconti
,
M.
,
2008
, “
Mathematical Relationships Between Bone Density and Mechanical Properties: A Literature Review
,”
Clin. Biomech.
,
23
(
2
), pp.
135
146
.10.1016/j.clinbiomech.2007.08.024
151.
Cheal
,
E.
,
Snyder
,
B.
,
Nunamaker
,
D.
, and
Hayes
,
W.
,
1987
, “
Trabecular Bone Remodeling Around Smooth and Porous Implants in an Equine Patellar Model
,”
J. Biomech.
,
20
(
11-12
), pp.
1121
1134
.10.1016/0021-9290(87)90029-7
152.
Fyhrie
,
D.
, and
Carter
,
D.
,
1990
, “
Femoral Head Apparent Density Distribution Predicted From Bone Stresses
,”
J. Biomech.
,
23
(
1
), pp.
1
10
.10.1016/0021-9290(90)90363-8
153.
Lotz
,
J.
,
Cheal
,
E.
, and
Hayes
,
W.
,
1991
, “
Fracture Prediction for the Proximal Femur Using Finite Element Models: Part I—Linear Analysis
,”
ASME J. Biomech. Eng.
,
113
(
4
), pp.
353
360
.10.1115/1.2895412
154.
Gibson
,
L. J.
,
1985
, “
The Mechanical Behaviour of Cancellous Bone
,”
J. Biomech.
,
18
(
5
), pp.
317
328
.10.1016/0021-9290(85)90287-8
155.
Silva
,
M. J.
, and
Gibson
,
L. J.
,
1997
, “
The Effects of Non-Periodic Microstructure and Defects on the Compressive Strength of Two-Dimensional Cellular Solids
,”
Int. J. Mech. Sci.
,
39
(
5
), pp.
549
563
.10.1016/S0020-7403(96)00065-3
156.
Yeh
,
O.
, and
Keaveny
,
T.
,
1999
, “
Biomechanical Effects of Intraspecimen Variations in Trabecular Architecture: A Three-Dimensional Finite Element Study
,”
Bone
,
25
(
2
), pp.
223
228
.10.1016/S8756-3282(99)00092-7
157.
Fyhrie
,
D. P.
, and
Hou
,
F. J.
,
1995
, “
Prediction of Human Vertebral Cancellous Bone Strength Using Non-Linear, Anatomically Accurate, Large-Scale, Finite Element Analysis
,”
BED
,
29
, pp.
301
301
.
158.
Van Rietbergen
,
B.
,
Ulrich
,
D.
,
Pistoia
,
W.
,
Huiskes
,
R.
, and
Rüegsegger
,
P.
,
1998
, “
Prediction of Trabecular Bone Failure Parameters Using a Tissue Failure Criterion
,”
Transactions of the Annual Meeting-Orthopaedic Research Society
,
Orthopaedic Research Scoiety
, pp.
550
550
.
159.
Niebur
,
G. L.
,
Hsia
,
A. C.
,
Chen
,
T. J.
, and
Keaveny
,
T.
,
1999
, “
Simulation of Trabecular Bone Yield Using Nonlinear Finite Element Analysis
,”
BED
,
43
, pp.
175
176
.
160.
Keyak
,
J.
,
Rossi
,
S.
,
Jones
,
K.
,
Les
,
C.
, and
Skinner
,
H.
,
2001
, “
Prediction of Fracture Location in the Proximal Femur Using Finite Element Models
,”
Med. Eng. Phys.
,
23
(
9
), pp.
657
664
.10.1016/S1350-4533(01)00094-7
161.
Fenech
,
C.
, and
Keaveny
,
T.
,
1999
, “
A Cellular Solid Criterion for Predicting the Axial-Shear Failure Properties of Bovine Trabecular Bone
,”
ASME J. Biomech. Eng.
,
121
(
4
), pp.
414
422
.10.1115/1.2798339
162.
Keyak
,
J. H.
, and
Rossi
,
S. A.
,
2000
, “
Prediction of Femoral Fracture Load Using Finite Element Models: An Examination of Stress-and Strain-Based Failure Theories
,”
J. Biomech.
,
33
(
2
), pp.
209
214
.10.1016/S0021-9290(99)00152-9
163.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1999
,
Cellular Solids: Structure and Properties
,
Cambridge University Press
,
New York
.
164.
Triantafillou
,
T.
, and
Gibson
,
L.
,
1990
, “
Multiaxial Failure Criteria for Brittle Foams
,”
Int. J. Mech. Sci.
,
32
(
6
), pp.
479
496
.10.1016/0020-7403(90)90154-B
165.
Keaveny
,
T.
,
Wachtel
,
E.
,
Zadesky
,
S.
, and
Arramon
,
Y.
,
1999
, “
Application of the Tsai–Wu Quadratic Multiaxial Failure Criterion to Bovine Trabecular Bone
,”
ASME J. Biomech. Eng.
,
121
(
1
), pp.
99
107
.10.1115/1.2798051
166.
Keaveny
,
T. M.
,
Wachtel
,
E. F.
,
Ford
,
C. M.
, and
Hayes
,
W. C.
,
1994
, “
Differences Between the Tensile and Compressive Strengths of Bovine Tibial Trabecular Bone Depend on Modulus
,”
J. Biomech.
,
27
(
9
), pp.
1137
1146
.10.1016/0021-9290(94)90054-X
167.
Nazarian
,
A.
,
Stauber
,
M.
,
Zurakowski
,
D.
,
Snyder
,
B. D.
, and
R.
Müller
,
2006
, “
The Interaction of Microstructure and Volume Fraction in Predicting Failure in Cancellous Bone
,”
Bone
,
39
(
6
), pp.
1196
1202
.10.1016/j.bone.2006.06.013
168.
Lotz
,
J. C.
,
Gerhart
,
T. N.
, and
Hayes
,
W. C.
,
1990
, “
Mechanical Properties of Trabecular Bone From the Proximal Femur: A Quantitative CT Study
,”
J. Comput. Assisted Tomogr.
,
14
(
1
), pp.
107
114
.10.1097/00004728-199001000-00020
169.
McCalden
,
R. W.
, and
McGeough
,
J. A.
,
1997
, “
Age-Related Changes in the Compressive Strength of Cancellous Bone. The Relative Importance of Changes in Density and Trabecular Architecture
,”
J. Bone Jt. Surg.
,
79
(
3
), pp.
421
427
.
170.
Ding
,
M.
,
Dalstra
,
M.
,
Danielsen
,
C. C.
,
Kabel
,
J.
,
Hvid
,
I.
, and
Linde
,
F.
,
1997
, “
Age Variations in the Properties of Human Tibial Trabecular Bone
,”
J. Bone Jt. Surg.
,
79
(
6
), pp.
995
1002
.10.1302/0301-620X.79B6.7538
171.
Ford
,
C. M.
, and
Keaveny
,
T. M.
,
1996
, “
The Dependence of Shear Failure Properties of Trabecular Bone on Apparent Density and Trabecular Orientation
,”
J. Biomech.
,
29
(
10
), pp.
1309
1317
.10.1016/0021-9290(96)00062-0
172.
Tassani
,
S.
,
Öhman
,
C.
,
Baleani
,
M.
,
Baruffaldi
,
F.
, and
Viceconti
,
M.
,
2010
, “
Anisotropy and Inhomogeneity of the Trabecular Structure can Describe the Mechanical Strength of Osteoarthritic Cancellous Bone
,”
J. Biomech.
,
43
(
6
), pp.
1160
1166
.10.1016/j.jbiomech.2009.11.034
173.
Rice
,
J.
,
Cowin
,
S.
, and
Bowman
,
J.
,
1988
, “
On the Dependence of the Elasticity and Strength of Cancellous Bone on Apparent Density
,”
J. Biomech.
,
21
(
2
), pp.
155
168
.10.1016/0021-9290(88)90008-5
174.
Sanyal
,
A.
,
Gupta
,
A.
,
Bayraktar
,
H. H.
,
Kwon
,
R. Y.
, and
Keaveny
,
T. M.
,
2012
, “
Shear Strength Behavior of Human Trabecular Bone
,”
J. Biomech.
,
45
(
15
), pp.
2513
2519
.10.1016/j.jbiomech.2012.07.023
175.
Perilli
,
E.
,
Baleani
,
M.
,
Öhman
,
C.
,
Fognani
,
R.
,
Baruffaldi
,
F.
, and
Viceconti
,
M.
,
2008
, “
Dependence of Mechanical Compressive Strength on Local Variations in Microarchitecture in Cancellous Bone of Proximal Human Femur
,”
J. Biomech.
,
41
(
2
), pp.
438
446
.10.1016/j.jbiomech.2007.08.003
176.
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
177.
Silva
,
M. J.
,
Keaveny
,
T. M.
, and
Hayes
,
W. C.
,
1998
, “
Computed Tomography-Based Finite Element Analysis Predicts Failure Loads and Fracture Patterns for Vertebral Sections
,”
J. Orthop. Res.
,
16
(
3
), pp.
300
308
.10.1002/jor.1100160305
178.
Rennick
,
J. A.
,
Nazarian
,
A.
,
Entezari
,
V.
,
Kimbaris
,
J.
,
Tseng
,
A.
,
Masoudi
,
A.
,
Nayeb-Hashemi
,
H.
,
Vaziri
,
A.
, and
Snyder
,
B. D.
,
2013
, “
Finite Element Analysis and Computed Tomography Based Structural Rigidity Analysis of Rat Tibia With Simulated Lytic Defects
,”
J. Biomech.
,
46
(
5
), pp.
2701
2709
.10.1016/j.jbiomech.2013.06.024
179.
Turner
,
C.
,
1989
, “
Yield Behavior of Bovine Cancellous Bone
,”
ASME J. Biomech. Eng.
,
111
(
4
), pp.
256
260
.10.1115/1.3168375
180.
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
181.
Isaksson
,
H.
,
Nagao
,
S.
,
MaŁkiewicz
,
M.
,
Julkunen
,
P.
,
Nowak
,
R.
, and
Jurvelin
,
J. S.
,
2010
, “
Precision of Nanoindentation Protocols for Measurement of Viscoelasticity in Cortical and Trabecular Bone
,”
J. Biomech.
,
43
(
12
), pp.
2410
2417
.10.1016/j.jbiomech.2010.04.017
182.
Keaveny
,
T. M.
,
Wachtel
,
E. F.
, and
Kopperdahl
,
D. L.
,
1999
, “
Mechanical Behavior of Human Trabecular Bone After Overloading
,”
J. Orthop. Res.
,
17
(
3
), pp.
346
353
.10.1002/jor.1100170308
183.
Pugh
,
J.
,
Rose
,
R.
, and
Radin
,
E.
,
1973
, “
A Possible Mechanism of Wolff's Law: Trabecular Microfractures
,”
Arch. Physiol. Biochem.
,
81
(
1
), pp.
27
40
.10.3109/13813457309074441
184.
Benaissa
,
R.
,
Uhthoff
,
H. K.
, and
Mercier
,
P.
,
1989
, “
Repair of Trabecular Fatigue Fractures Cadaver Studies of the Upper Femur
,”
Acta Orthop.
,
60
(
5
), pp.
585
589
.10.3109/17453678909150127
185.
Zysset
,
P.
, and
Curnier
,
A.
,
1996
, “
A 3D Damage Model for Trabecular Bone Based on Fabric Tensors
,”
J. Biomech.
,
29
(
12
), pp.
1549
1558
.10.1016/S0021-9290(96)80006-6
186.
Fondrk
,
M.
,
Bahniuk
,
E.
,
Davy
,
D.
, and
Michaels
,
C.
,
1988
, “
Some Viscoplastic Characteristics of Bovine and Human Cortical Bone
,”
J. Biomech.
,
21
(
8
), pp.
623
630
.10.1016/0021-9290(88)90200-X
187.
Kopperdahl
,
D. L.
,
Pearlman
,
J. L.
, and
Keaveny
,
T. M.
,
2000
, “
Biomechanical Consequences of an Isolated Overload on the Human Vertebral Body
,”
J. Orthop. Res.
,
18
(
5
), pp.
685
690
.10.1002/jor.1100180502
188.
Vashishth
,
D.
,
Koontz
,
J.
,
Qiu
,
S.
,
Lundin-Cannon
,
D.
,
Yeni
,
Y.
,
Schaffler
,
M.
, and
Fyhrie
,
D.
,
2000
, “
In Vivo Diffuse Damage in Human Vertebral Trabecular Bone
,”
Bone
,
26
(
2
), pp.
147
152
.10.1016/S8756-3282(99)00253-7
189.
Haddock
,
S. M.
,
Yeh
,
O. C.
,
Mummaneni
,
P. V.
,
Rosenberg
,
W. S.
, and
Keaveny
,
T. M.
,
2004
, “
Similarity in the Fatigue Behavior of Trabecular Bone Across Site and Species
,”
J. Biomech.
,
37
(
2
), pp.
181
187
.10.1016/S0021-9290(03)00245-8
190.
Bowman
,
S.
,
Guo
,
X.
,
Cheng
,
D.
,
Keaveny
,
T.
,
Gibson
,
L.
,
Hayes
,
W.
, and
McMahon
,
T.
,
1998
, “
Creep Contributes to the Fatigue Behavior of Bovine Trabecular Bone
,”
ASME J. Biomech. Eng.
,
120
(
5
), pp.
647
654
.10.1115/1.2834757
191.
Bowman
,
S. M.
,
Keaveny
,
T. M.
,
Gibson
,
L. J.
,
Hayes
,
W. C.
, and
McMahon
,
T. A.
,
1994
, “
Compressive Creep Behavior of Bovine Trabecular Bone
,”
J. Biomech.
,
27
(
3
), pp.
301
310
.10.1016/0021-9290(94)90006-X
192.
Dendorfer
,
S.
,
Maier
,
H.
, and
Hammer
,
J.
,
2009
, “
Fatigue Damage in Cancellous Bone: An Experimental Approach From Continuum to Micro Scale
,”
J. Mech. Behav. Biomed. Mater.
,
2
(
1
), pp.
113
119
.10.1016/j.jmbbm.2008.03.003
193.
Kosmopoulos
,
V.
,
Schizas
,
C.
, and
Keller
,
T. S.
,
2008
, “
Modeling the Onset and Propagation of Trabecular Bone Microdamage During Low-Cycle Fatigue
,”
J. Biomech.
,
41
(
3
), pp.
515
522
.10.1016/j.jbiomech.2007.10.020
194.
Homminga
,
J.
,
McCreadie
,
B.
,
Ciarelli
,
T.
,
Weinans
,
H.
,
Goldstein
,
S.
, and
Huiskes
,
R.
,
2002
, “
Cancellous Bone Mechanical Properties From Normals and Patients With Hip Fractures Differ on the Structure Level, Not on the Bone Hard Tissue Level
,”
Bone
,
30
(
5
), pp.
759
764
.10.1016/S8756-3282(02)00693-2
195.
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
196.
Hoffler
,
C.
,
Moore
,
K.
,
Kozloff
,
K.
,
Zysset
,
P.
,
Brown
,
M.
, and
Goldstein
,
S.
,
2000
, “
Heterogeneity of Bone Lamellar-Level Elastic Moduli
,”
Bone
,
26
(
6
), pp.
603
609
.10.1016/S8756-3282(00)00268-4
197.
Kaneko
,
T. S.
,
Bell
,
J. S.
,
Pejcic
,
M. R.
,
Tehranzadeh
,
J.
, and
Keyak
,
J. H.
,
2004
, “
Mechanical Properties, Density and Quantitative CT Scan Data of Trabecular Bone With and Without Metastases
,”
J. Biomech.
,
37
(
4
), pp.
523
530
.10.1016/j.jbiomech.2003.08.010
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