Inaccuracies in the estimation of material properties and errors in the assignment of these properties into finite element models limit the reliability, accuracy, and precision of quantitative computed tomography (QCT)-based finite element analyses of the vertebra. In this work, a new mesh-independent, material mapping procedure was developed to improve the quality of predictions of vertebral mechanical behavior from QCT-based finite element models. In this procedure, an intermediate step, called the material block model, was introduced to determine the distribution of material properties based on bone mineral density, and these properties were then mapped onto the finite element mesh. A sensitivity study was first conducted on a calibration phantom to understand the influence of the size of the material blocks on the computed bone mineral density. It was observed that varying the material block size produced only marginal changes in the predictions of mineral density. Finite element (FE) analyses were then conducted on a square column-shaped region of the vertebra and also on the entire vertebra in order to study the effect of material block size on the FE-derived outcomes. The predicted values of stiffness for the column and the vertebra decreased with decreasing block size. When these results were compared to those of a mesh convergence analysis, it was found that the influence of element size on vertebral stiffness was less than that of the material block size. This mapping procedure allows the material properties in a finite element study to be determined based on the block size required for an accurate representation of the material field, while the size of the finite elements can be selected independently and based on the required numerical accuracy of the finite element solution. The mesh-independent, material mapping procedure developed in this study could be particularly helpful in improving the accuracy of finite element analyses of vertebroplasty and spine metastases, as these analyses typically require mesh refinement at the interfaces between distinct materials. Moreover, the mapping procedure is not specific to the vertebra and could thus be applied to many other anatomic sites.

References

References
1.
Provatidis
,
C.
,
Vossou
,
C.
,
Petropoulou
,
E.
,
Balanika
,
A.
, and
Lyritis
,
G.
, 2009, “
A Finite Element Analysis of a T12 Vertebra in Two Consecutive Examinations to Evaluate the Progress of Osteoporosis
,”
Med. Eng. Phys.
,
31
, pp.
632
641
.
2.
Tawara
,
D.
,
Sakamoto
,
J.
,
Murakami
,
H.
,
Kawahara
,
N.
,
Oda
,
J.
, and
Tomita
,
K.
, 2010, “
Mechanical Evaluation by Patient-Specific Finite Element Analyses Demonstrates Therapeutic Effects for Osteoporotic Vertebrae
,”
J. Mech. Behav. Biomed. Mater.
,
3
, pp.
31
40
.
3.
Homminga
,
J.
,
Weinans
,
H.
,
Gowin
,
W.
,
Felsenberg
,
D.
, and
Huiskes
,
R.
, 2001, “
Osteoporosis Changes the Amount of Vertebral Trabecular Bone at Risk of Fracture but Not the Vertebral Load Distribution
,”
Spine
,
26
, pp.
1555
1561
.
4.
Mirzaei
,
M.
,
Zeinali
,
A.
,
Razmjoo
,
A.
, and
Nazemi
,
M.
, 2009, “
On Prediction of the Strength Levels and Failure Patterns of Human Vertebrae Using Quantitative Computed Tomography (QCT)-Based Finite Element Method
,”
J. Biomech.
,
42
, pp.
1584
1591
.
5.
Keaveny
,
T. M.
,
Donley
,
D. W.
,
Hoffmann
,
P. F.
,
Mitlak
,
B. H.
,
Glass
,
E. V.
, and
San Martin
,
J. A.
, 2007, “
Effects of Teriparatide and Alendronate on Vertebral Strength as Assessed by Finite Element Modeling of QCT Scans in Women with Osteoporosis
,”
J. Bone Mineral Res.
,
22
, pp.
149
157
.
6.
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
, pp.
300
308
.
7.
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
, pp.
744
750
.
8.
Liebschner
,
M. A.
,
Kopperdahl
,
D. L.
,
Rosenberg
,
W. S.
, and
Keaveny
,
T. M.
, 2003, “
Finite Element Modeling of the Human Thoracolumbar Spine
,”
Spine
,
28
, pp.
559
565
.
9.
Buckley
,
J. M.
,
Loo
,
K.
, and
Motherway
,
J.
, 2007, “
Comparison of Quantitative Computed Tomography-Based Measures in Predicting Vertebral Compressive Strength
,”
Bone
,
40
, pp.
767
774
.
10.
Jones
,
A. C.
, and
Wilcox
,
R. K.
, 2008, “
Finite Element Analysis of the Spine: Towards a Framework of Verification, Validation and Sensitivity Analysis
,”
Med. Eng. Phys.
,
30
, pp.
1287
1304
.
11.
Faulkner
,
K. G.
,
Cann
,
C. E.
, and
Hasegawa
,
B. H.
, 1991, “
Effect of Bone Distribution on Vertebral Strength: Assessment with a Patient-Specific Nonlinear Finite Element Analysis
,”
Radiology
,
179
, pp.
669
674
.
12.
Wang
,
Z. L.
,
Teo
,
J. C.
,
Chui
,
C. K.
,
Ong
,
S. H.
,
Yan
,
C. H.
,
Wang
,
S. C.
,
Wong
,
H. K.
, and
Teoh
,
S. H.
, 2005, “
Computational Biomechanical Modelling of the Lumbar Spine Using Marching-Cubes Surface Smoothened Finite Element Voxel Meshing
,”
Comput. Methods Programs Biomed.
,
80
, pp.
25
35
.
13.
Wijayathunga
,
V. N.
,
Jones
,
A. C.
,
Oakland
,
R. J.
,
Furtado
,
N. R.
,
Hall
,
R. M.
, and
Wilcox
,
R. K.
, 2008, “
Development of Specimen-Specific Finite Element Models of Human Vertebrae for the Analysis of Vertebroplasty
,”
Proc. Inst. Mech. Eng.,. Part H: J. Eng. Med.
,
222
, pp.
221
228
.
14.
Yosibash
,
Z.
,
Trabelsi
,
N.
, and
Milgrom
,
C.
, 2007, “
Reliable Simulations of the Human Proximal Femur by High-Order Finite Element Analysis Validated by Experimental Observations
,”
J. Biomech.
,
40
, pp.
3688
3699
.
15.
Zannoni
,
C.
,
Mantovani
,
R.
, and
Viceconti
,
M.
, 1998, “
Material Properties Assignment to Finite Element Models of Bone Structures: A New Method
,”
Med. Eng. Phys.
,
20
, pp.
735
740
.
16.
Zeinali
,
A.
,
Hashemi
,
B.
, and
Akhlaghpoor
,
S.
, 2010, “
Noninvasive Prediction of Vertebral Body Compressive Strength Using Nonlinear Finite Element Method and an Image Based Technique
,”
Phys. Medica
,
26
, pp.
88
97
.
17.
Merz
,
B.
,
Niederer
,
P.
,
Muller
,
R.
, and
Ruegsegger
,
P.
, 1996, “
Automated Finite Element Analysis of Excised Human Femora Based on Precision-QCT
,”
J. Biomech. Eng.
,
118
, pp.
387
390
.
18.
Beesho
,
M.
,
Ohniski
,
I.
,
Matsuyama
,
J.
,
Matsumoto
,
T.
,
Imai
,
K.
, and
Nakamura
,
K.
, 2007, “
Prediction of Strength and Strain of the Proximal Femur by a CT-Based Finite Element Method
,”
J. Biomech.
,
40
, pp.
1745
1753
.
19.
Chen
,
G.
,
Schmutz
,
B.
,
Epari
,
D.
,
Rathnayaka
,
K.
,
Ibrahim
,
S.
,
Schuetz
,
M. A.
, and
Pearcy
,
M. J.
, 2010, “
A New Approach for Assigning Bone Material Properties from CT Images into Finite Element Models
,”
J. Biomech.
,
43
, pp.
1011
1015
.
20.
Jones
,
A. C.
, and
Wilcox
,
R. K.
, 2007, “
Assessment of Factors Influencing Finite Element Vertebral Model Predictions
,”
J. Biomech. Eng.
,
129
, pp.
898
903
.
21.
Marom
,
S. A.
, and
Linden
,
M. J.
, 1990, “
Computer Aided Stress Analysis of Long Bones Utilizing Computed Tomography
,”
J. Biomech.
,
23
, pp.
399
404
.
22.
Taddei
,
F.
,
Pancanti
,
A.
, and
Viceconti
,
M.
, 2004, “
An Improved Method for the Automatic Mapping of Computed Tomography Numbers onto Finite Element Models
,”
Med. Eng. Phys.
,
26
, pp.
61
69
.
23.
Kopperdahl
,
D. L.
,
Morgan
,
E. F.
, and
Keaveny
,
T. M.
, 2002, “
Quantitative Computed Tomography Estimates of the Mechanical Properties of Human Vertebral Trabecular Bone
,”
J. Orthop. Res.
,
20
, pp.
801
805
.
24.
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
, pp.
55
60
.
25.
Mosekilde
,
L.
,
Mosekilde
,
L.
, and
Danielsen
,
C. C.
, 1987, “
Biomechanical Competence of Vertebral Trabecular Bone in Relation to Ash Density and Age in Normal Individuals
,”
Bone
,
8
, pp.
79
85
.
26.
Li
,
H.
, and
Wang
,
Z.
, 2006, “
Intervertebral Disc Biomechanical Analysis Using the Finite Element Modeling Based on Medical Images
,”
Comput. Med. Imaging Graph.
,
30
, pp.
363
370
.
27.
Fazzalari
,
N.
,
Costi
,
J. J.
, and
Hearn
,
T. C.
, 2003, “
Structure and Function of Normal, Degenerate, and Surgically Fixed Spinal Segments
,” in
Advances in Spinal Fusion: Molecular Science, BioMechanics and Clinical Management
,
K.-U.
Lewandrowski
,
D. L.
Wise
,
D. J.
Trantolo
,
M. J.
Yaszemski
, and
A. A.
White
III
, eds.,
CRC Press
,
Boca Raton, FL
.
28.
Adams
,
M. A.
, and
Hutton
,
W.C.
, 1985, “
The Effect of Posture on the Lumbar Spine
,”
J. Bone Joint Surg. Br.
,
67-B
(
4
), pp.
625
629
.
29.
Morgan
,
E. F.
, and
Keaveny
,
T. M.
, 2001, “
Dependence of Yield Strain of Human Trabecular Bone on Anatomic Site
,”
J. Biomech.
,
34
, pp.
569
577
.
30.
Keyak
,
J. H.
,
Meagher
,
J. M.
,
Skinner
,
H. B.
, and
Mote
,
C. D.
, Jr.
, 1990, “
Automated Three-Dimensional Finite Element Modelling of Bone: A New Method
,”
J. Biom. Eng.
,
12
, pp.
389
397
.
31.
Yosibash
,
Z.
,
Padan
,
R.
,
Joskowicz
,
L.
, and
Milgrom
,
C.
, 2007, “
A CT-Based High-Order Finite Element Analysis of the Human Proximal Femur Compared to In-Vitro Experiments
,”
J. Biomech. Eng.
,
129
, pp.
297
309
.
32.
Tschirhart
,
C. E.
,
Roth
,
S. E.
, and
Whyne
,
C. M.
, 2005, “
Biomechanical Assessment of Stability in the Metastatic Spine Following Percutaneous Vertebroplasty: Effects of Cement Distribution Patterns and Volume
,”
J. Biomech.
,
38
, pp.
1582
1590
.
33.
Whyne
,
C. M.
,
Hu
,
S. S.
, and
Lotz
,
J. C.
, 2003, “
Burst Fracture in the Metastatically Involved Spine: Development, Validation, and Parametric Analysis of a Three-Dimensional Poroelastic Finite-Element Model
,”
Spine
,
28
(
7
), pp.
652
660
.
34.
Tschirhart
,
C. E.
,
Nagpurkar
,
A.
, and
Whyne
,
C. M.
, 2004, “
Effects of Tumor Location, Shape and Surface Serration on Burst Fracture Risk in the Metastatic Spine
,”
J. Biomech.
,
37
, pp.
653
660
.
You do not currently have access to this content.