Currently, specimen-specific micro finite element (μFE) analysis based micro computed tomography (μCT) images have become a major computational tool for the assessment of the mechanical properties of human trabecular bone. Despite the fine characterization of the three-dimensional (3D) trabecular microstructure based on high-resolution μCT images, conventional μFE models with each voxel converted to an element are not efficient in predicting the nonlinear failure behavior of bone due to a prohibitive computational cost. Recently, a highly efficient individual trabecula segmentation (ITS)-based plate and rod (PR) modeling technique has been developed by substituting individual plates and rods with shell and beam elements, respectively. In this technical brief, the accuracy of novel PR μFE models was examined in idealized microstructure models over a broad range of trabecular thicknesses. The Young's modulus and yield strength predicted by simplified PR models strongly correlated with those of voxel models at various voxel sizes. The conversion from voxel models to PR models resulted in an ∼762-fold reduction in the largest model size and significantly accelerated the nonlinear FE analysis. The excellent predictive power of the PR μFE models, demonstrated in an idealized trabecular microstructure, provided a quantitative mechanical basis for this promising tool for an accurate and efficient assessment of trabecular bone mechanics and fracture risk.

References

References
1.
NIH Consensus Development Panel on Osteoporosis Prevention
,
1991
, “
Consensus Development Conference Report: Prophylaxis and Treatment of Osteoporosis
,”
Osteoporosis Int.
,
1
(
2
), pp.
114
117
.10.1007/BF01880454
2.
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
3.
Muller
,
R.
,
Hildebrand
,
T.
,
Hauselmann
,
H. J.
, and
Ruegsegger
,
P.
,
1996
, “
In Vivo Reproducibility of Three-Dimensional Structural Properties of Noninvasive Bone Biopsies Using 3D-pQCT
,”
J. Bone Miner. Res.
,
11
(
11
), pp.
1745
1750
.10.1002/jbmr.5650111118
4.
Chung
,
H. W.
,
Wehrli
,
F. W.
,
Williams
,
J. L.
, and
Wehrli
,
S. L.
,
1995
, “
Three-Dimensional Nuclear Magnetic Resonance Microimaging of Trabecular Bone
,”
J. Bone Miner. Res.
,
10
(
10
), pp.
1452
1461
.10.1002/jbmr.5650101005
5.
Kinney
,
J. H.
,
Lane
,
N. E.
, and
Haupt
,
D. L.
,
1995
, “
In Vivo, Three-Dimensional Microscopy of Trabecular Bone
,”
J. Bone Miner. Res.
,
10
(
2
), pp.
264
270
.10.1002/jbmr.5650100213
6.
Morgan
,
E. F.
,
Bayraktar
,
H. H.
,
Yeh
,
O. C.
,
Majumdar
,
S.
,
Burghardt
,
A.
, and
Keaveny
,
T. M.
,
2004
, “
Contribution of Inter-Site Variations in Architecture to Trabecular Bone Apparent Yield Strains
,”
J. Biomech.
,
37
(
9
), pp.
1413
1420
.10.1016/j.jbiomech.2003.12.037
7.
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
8.
Liu
,
X. S.
,
Sajda
,
P.
,
Saha
,
P. K.
,
Wehrli
,
F. W.
,
Bevill
,
G.
,
Keaveny
,
T. M.
, and
Guo
,
X. E.
,
2008
, “
Complete Volumetric Decomposition of Individual Trabecular Plates and Rods and Its Morphological Correlations With Anisotropic Elastic Moduli in Human Trabecular Bone
,”
J. Bone Miner. Res.
,
23
(
2
), pp.
223
235
.10.1359/jbmr.071009
9.
van Lenthe
,
G. H.
,
Stauber
,
M.
, and
Muller
,
R.
,
2006
, “
Specimen-Specific Beam Models for Fast and Accurate Prediction of Human Trabecular Bone Mechanical Properties
,”
Bone
,
39
(
6
), pp.
1182
1189
.10.1016/j.bone.2006.06.033
10.
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
11.
Liu
,
X. S.
,
Bevill
,
G.
,
Keaveny
,
T. M.
,
Sajda
,
P.
, and
Guo
,
X. E.
,
2009
, “
Micromechanical Analyses of Vertebral Trabecular Bone Based on Individual Trabeculae Segmentation of Plates and Rods
,”
J. Biomech.
,
42
(
3
), pp.
249
256
.10.1016/j.jbiomech.2008.10.035
12.
Liu
,
X. S.
,
Zhang
,
X. H.
, and
Guo
,
X. E.
,
2009
, “
Contributions of Trabecular Rods of Various Orientations in Determining the Elastic Properties of Human Vertebral Trabecular Bone
,”
Bone
,
45
(
2
), pp.
158
163
.10.1016/j.bone.2009.04.201
13.
Liu
,
X. S.
,
Zhang
,
X. H.
,
Sekhon
,
K. K.
,
Adams
,
M. F.
,
McMahon
,
D. J.
,
Bilezikian
,
J. P.
,
Shane
,
E.
, and
Guo
,
X. E.
,
2010
, “
High-Resolution Peripheral Quantitative Computed Tomography Can Assess Microstructural and Mechanical Properties of Human Distal Tibial Bone
,”
J. Bone Miner. Res.
,
25
(
4
), pp.
746
756
.10.1359/jbmr.090822
14.
Liu
,
X. S.
,
Shane
,
E.
,
McMahon
,
D. J.
, and
Guo
,
X. E.
,
2011
, “
Individual Trabecula Segmentation (ITS)–Based Morphological Analysis of Microscale Images of Human Tibial Trabecular Bone at Limited Spatial Resolution
,”
J. Bone Miner. Res.
,
26
(
9
), pp.
2184
2193
.10.1002/jbmr.420
15.
Liu
,
X. S.
,
Cohen
,
A.
,
Shane
,
E.
,
Stein
,
E.
,
Rogers
,
H.
,
Kokolus
,
S. L.
,
Yin
,
P. T.
,
McMahon
,
D. J.
,
Lappe
,
J. M.
,
Recker
,
R. R.
, and
Guo
,
X. E.
,
2010
, “
Individual Trabeculae Segmentation (ITS)–Based Morphological Analysis of High-Resolution Peripheral Quantitative Computed Tomography Images Detects Abnormal Trabecular Plate and Rod Microarchitecture in Premenopausal Women With Idiopathic Osteoporosis
,”
J. Bone Miner. Res.
,
25
(
7
), pp.
1496
1505
.10.1002/jbmr.50
16.
Liu
,
X. S.
,
Stein
,
E. M.
,
Zhou
,
B.
,
Zhang
,
C. A.
,
Nickolas
,
T. L.
,
Cohen
,
A.
,
Thomas
,
V.
,
McMahon
,
D. J.
,
Cosman
,
F.
,
Nieves
,
J.
,
Shane
,
E.
, and
Guo
,
X. E.
,
2012
, “
Individual Trabecula Segmentation (ITS)-Based Morphological Analyses and Microfinite Element Analysis of HR-pQCT Images Discriminate Postmenopausal Fragility Fractures Independent of DXA Measurements
,”
J. Bone Miner. Res.
,
27
(
2
), pp.
263
272
.10.1002/jbmr.562
17.
Beaupre
,
G. S.
, and
Hayes
,
W. C.
,
1985
, “
Finite Element Analysis of a Three-Dimensional Open-Celled Model for Trabecular Bone
,”
ASME J. Biomech. Eng.
,
107
(
3
), pp.
249
256
.10.1115/1.3138550
18.
Gibson
,
L. J.
,
1985
, “
The Mechanical Behaviour of Cancellous Bone
,”
J. Biomech.
,
18
(
5
), pp.
317
328
.10.1016/0021-9290(85)90287-8
19.
Guo
,
X. E.
, and
Kim
,
C. H.
,
2002
, “
Mechanical Consequence of Trabecular Bone Loss and Its Treatment: A Three-Dimensional Model Simulation
,”
Bone
,
30
(
2
), pp.
404
411
.10.1016/S8756-3282(01)00673-1
20.
Silva
,
M. J.
, and
Gibson
,
L. J.
,
1997
, “
Modeling the Mechanical Behavior of Vertebral Trabecular Bone: Effects of Age-Related Changes in Microstructure
,”
Bone
,
21
(
2
), pp.
191
199
.10.1016/S8756-3282(97)00100-2
21.
Yeh
,
O. C.
, and
Keaveny
,
T. M.
,
2001
, “
Relative Roles of Microdamage and Microfracture in the Mechanical Behavior of Trabecular Bone
,”
J. Orthop. Res.
,
19
(
6
), pp.
1001
1007
.10.1016/S0736-0266(01)00053-5
22.
Zysset
,
P. K.
,
Ominsky
,
M. S.
, and
Goldstein
,
S. A.
,
1998
, “
A Novel 3D Microstructural Model for Trabecular Bone: I. The Relationship Between Fabric and Elasticity
,”
Comput. Methods Biomech. Biomed. Eng.
,
1
(
4
), pp.
321
331
.10.1080/01495739808936710
23.
Saha
,
P. K.
,
Chaudhuri
,
B. B.
, and
Majumder
,
D. D.
,
1997
, “
A New Shape Preserving Parallel Thinning Algorithm for 3D Digital Images
,”
Pattern Recogn.
,
30
(
12
), pp.
1939
1955
.10.1016/S0031-3203(97)00016-2
24.
Saha
,
P. K.
, and
Chaudhuri
,
B. B.
,
1996
, “
3D Digital Topology Under Binary Transformation With Applications
,”
Comput. Vis. Image Underst.
,
63
(
3
), pp.
418
429
.10.1006/cviu.1996.0032
25.
Hollister
,
S. J.
,
1994
, “
A Homogenization Sampling Procedure for Calculating Trabecular Bone Effective Stiffness and Tissue Level Stress
,”
J. Biomech.
,
27
(
4
), pp.
433
444
.10.1016/0021-9290(94)90019-1
26.
Gupta
,
A.
,
Bayraktar
,
H.
,
Fox
,
J.
,
Keaveny
,
T.
, and
Papadopoulos
,
P.
,
2007
, “
Constitutive Modeling and Algorithmic Implementation of a Plasticity-Like Model for Trabecular Bone Structures
,”
Comput. Mech.
,
40
(
1
), pp.
61
72
.10.1007/s00466-006-0082-5
27.
Stein
,
E. M.
,
Liu
,
X. S.
,
Nickolas
,
T. L.
,
Cohen
,
A.
,
Thomas
,
V.
,
McMahon
,
D. J.
,
Zhang
,
C.
,
Yin
,
P. T.
,
Cosman
,
F.
,
Nieves
,
J.
,
Guo
,
X. E.
, and
Shane
,
E.
,
2010
, “
Abnormal Microarchitecture and Reduced Stiffness at the Radius and Tibia in Postmenopausal Women With Fractures
,”
J. Bone Miner. Res.
,
25
(
12
), pp.
2572
2581
.10.1002/jbmr.152
28.
Ghugal
,
Y. M.
, and
Sharma
,
R.
,
2011
, “
A Refined Shear Deformation Theory for Flexure of Thick Beams
,”
Lat. Am. J. Solids Struct.
,
8
(
2
), pp.
183
195
.10.1590/S1679-78252011000200005
29.
Kim
,
H. S.
, and
Al-Hassani
,
S. T.
,
2002
, “
A Morphological Model of Vertebral Trabecular Bone
,”
J. Biomech.
,
35
(
8
), pp.
1101
1114
.10.1016/S0021-9290(02)00053-2
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