Mechanical properties of human trabecular bone play an important role in age-related bone fragility and implant stability. Microfinite element (μFE) analysis allows computing the apparent elastic properties of trabecular bone for use in homogenized FE (hFE) analysis, but the results depend unfortunately on the type of applied boundary conditions (BCs). In this study, 167 human femoral trabecular cubic regions with a side length of 5.3 mm were extracted from three proximal femora and analyzed using μFE analysis to compare systematically their stiffness with kinematic uniform BCs (KUBCs) and periodicity-compatible mixed uniform BCs (PMUBCs). The obtained elastic constants were then used in the volume fraction and fabric-based orthotropic Zysset–Curnier model to identify their respective model parameters. As expected, PMUBCs lead to more compliant apparent elastic properties than KUBCs, especially in shear. The differences in stiffness decreased with bone volume fraction and mean intercept length (MIL). Unlike KUBCs, PMUBCs were sensitive to heterogeneity of the biopsies. The Zysset–Curnier model fitted the apparent elastic constants successfully in both cases with adjusted coefficients of determination (radj2) of 0.986 for KUBCs and 0.975 for PMUBCs. The proper use of these BCs for hFE analysis of whole bones will need to be investigated in future work.

References

References
1.
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
2.
Cody
,
D. D.
,
Gross
,
G. J.
,
Hou
,
F. J.
,
Spencer
,
H. J.
,
Goldstein
,
S. A.
, and
Fyhrie
,
D. P.
,
1999
, “
Femoral Strength is Better Predicted by Finite Element Models Than QCT and DXA
,”
J. Biomech.
,
32
(
10
), pp.
1013
1020
.10.1016/S0021-9290(99)00099-8
3.
Keyak
,
J.
,
Kaneko
,
T.
,
Tehranzadeh
,
J.
, and
Skinner
,
H.
,
2005
, “
Predicting Proximal Femoral Strength Using Structural Engineering Models
,”
Clin. Orthop. Relat. Res.
,
437
, pp.
219
228
.10.1097/01.blo.0000164400.37905.22
4.
Keaveny
,
T. M.
,
2010
, “
Biomechanical Computed Tomography-Noninvasive Bone Strength Analysis Using Clinical Computed Tomography Scans
,”
Ann. N.Y. Acad. Sci.
,
1192
(
1
), pp.
57
65
.10.1111/j.1749-6632.2009.05348.x
5.
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
6.
Odgaard
,
A.
,
Hvid
,
I.
, and
Linde
,
F.
,
1989
, “
Compressive Axial Strain Distributions in Cancellous Bone Specimens
,”
J. Biomech.
,
22
(
8
), pp.
829
835
.10.1016/0021-9290(89)90066-3
7.
Hollister
,
S. J.
, and
Kikuchi
,
N.
,
1994
, “
Homogenization Theory and Digital Imaging: A Basis for Studying the Mechanics and Design Principles of Bone Tissue
,”
Biotechnol. Bioeng.
,
43
(
7
), pp.
586
596
.10.1002/bit.260430708
8.
van Rietbergen
,
B.
,
Weinans
,
H.
,
Huiskes
,
R.
, and
Odgaard
,
A.
,
1995
, “
A New Method to Determine Trabecular Bone Elastic Properties and Loading Using Micromechanical Finite-Element Models
,”
J. Biomech.
,
28
(
1
), pp.
69
81
.10.1016/0021-9290(95)80008-5
9.
Zysset
,
P. K.
,
Goullet
,
R. W.
, and
Hollister
,
S. J.
,
1998
, “
A Global Relationship Between Trabecular Bone Morphology and Homogenized Elastic Properties
,”
ASME J. Biomed. Eng.
,
120
(
5
), pp.
640
646
.10.1115/1.2834756
10.
Pahr
,
D. H.
, and
Zysset
,
P. K.
,
2009
, “
A Comparison of Enhanced Continuum FE With Micro FE Models of Human Vertebral Bodies
,”
J. Biomech.
,
42
(
4
), pp.
455
462
.10.1016/j.jbiomech.2008.11.028
11.
Hill
,
R.
,
1963
, “
Elastic Properties of Reinforced Solids: Some Theoretical Principles
,”
J. Mech. Phys. Solids
,
11
(
5
), pp.
357
372
.10.1016/0022-5096(63)90036-X
12.
Sanchez-Palencia
,
E.
,
1980
, “
Non-Homogeneous Media and Vibration Theory
,”
Lecture Notes in Physics
, Vol.
127
,
Springer-Verlag
,
Berlin, Germany
.
13.
Suquet
,
P.
,
1987
, “
Elements of Homogenization for Inelastic Solid Mechanics
,”
Homogenization Techniques for Composite Media
, Vol.
272
,
Springer
,
Berlin, Germany
, pp.
193
278
.
14.
Hollister
,
S. J.
,
Fyhrie
,
D.
,
Jepsen
,
K.
, and
Goldstein
,
S. A.
,
1991
, “
Application of Homogenization Theory to the Study of Trabecular Bone Mechanics
,”
J. Biomech.
,
24
(
9
), pp.
825
839
.10.1016/0021-9290(91)90308-A
15.
Pahr
,
D.
, and
Zysset
,
P.
,
2008
, “
Influence of Boundary Conditions on Computed Apparent Elastic Properties of Cancellous Bone
,”
Biomech. Model. Mechanobiol.
,
7
(
6
), pp.
463
476
.10.1007/s10237-007-0109-7
16.
Hazanov
,
S.
, and
Amieur
,
M.
,
1995
, “
On Overall Properties of Elastic Heterogeneous Bodies Smaller Than the Representative Volume
,”
Int. J. Eng. Sci.
,
33
(
9
), pp.
1289
1301
.10.1016/0020-7225(94)00129-8
17.
Ostoja-Starzewski
,
M.
,
2006
, “
Material Spatial Randomness: From Statistical to Representative Volume Element
,”
Probab. Eng. Mech.
,
21
(
2
), pp.
112
132
.10.1016/j.probengmech.2005.07.007
18.
Kowalczyk
,
P.
,
2003
, “
Elastic Properties of Cancellous Bone Derived From Finite Element Models of Parameterized Microstructure Cells
,”
J. Biomech.
,
36
(
7
), pp.
961
972
.10.1016/S0021-9290(03)00065-4
19.
Anthoine
,
A.
,
1995
, “
Derivation of the In-Plane Elastic Characteristics of Masonry Through Homogenization Theory
,”
Int. J. Solids Struct.
,
32
(
2
), pp.
137
163
.10.1016/0020-7683(94)00140-R
20.
Hazanov
,
S.
, and
Huet
,
C.
,
1994
, “
Order Relationships for Boundary Conditions Effect in Heterogeneous Bodies Smaller Than the Representative Volume
,”
J. Mech. Phys. Solids
,
42
(
12
), pp.
1995
2011
.10.1016/0022-5096(94)90022-1
21.
Harrigan
,
T. P.
,
Jasty
,
M.
,
Mann
,
R. W.
, and
Harris
,
W. H.
,
1988
, “
Limitations of the Continuum Assumption in Cancellous Bone
,”
J. Biomech.
,
21
(
4
), pp.
269
275
.10.1016/0021-9290(88)90257-6
22.
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
23.
Zysset
,
P. K.
,
2003
, “
A Review of Morphology–Elasticity Relationships in Human Trabecular Bone: Theories and Experiments
,”
J. Biomech.
,
36
(
10
), pp.
1469
1485
.10.1016/S0021-9290(03)00128-3
24.
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
25.
Gross
,
T.
,
Pahr
,
D. H.
, and
Zysset
,
P. K.
,
2013
, “
Morphology–Elasticity Relationships Using Decreasing Fabric Information of Human Trabecular Bone From Three Major Anatomical Locations
,”
Biomech. Model. Mechanobiol.
,
12
(
4
), pp.
793
800
.10.1007/s10237-012-0443-2
26.
Harrigan
,
T. P.
, and
Mann
,
R. W.
,
1984
, “
Characterization of Microstructural Anisotropy in Orthotropic Materials Using a Second Rank Tensor
,”
J. Mater. Sci.
,
19
(
3
), pp.
761
767
.10.1007/BF00540446
27.
Whitehouse
,
W. J.
,
1974
, “
The Quantitative Morphology of Anisotropic Trabecular Bone
,”
J. Microsc.
,
101
(
2
), pp.
153
168
.10.1111/j.1365-2818.1974.tb03878.x
28.
Riedler
,
T. W.
, and
Calvard
,
S.
,
1978
, “
Picture Thresholding Using an Iterative Selection Method
,”
IEEE Trans. Systems, Man Cybern.
,
8
(
8
), pp.
630
632
.10.1109/TSMC.1978.4310039
29.
Pistoia
,
W.
,
Van Rietbergen
,
B.
,
Lochmüller
,
E.-M.
,
Lill
,
C.
,
Eckstein
,
F.
, and
Rüegsegger
,
P.
,
2002
, “
Estimation of Distal Radius Failure Load With Micro-Finite Element Analysis Models Based on Three-Dimensional Peripheral Quantitative Computed Tomography Images
,”
Bone
,
30
(
6
), pp.
842
848
.10.1016/S8756-3282(02)00736-6
30.
Rice
,
J. C.
,
Cowin
,
S. C.
, and
Bowman
,
J. A.
,
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
You do not currently have access to this content.