Abstract

Patient-specific high order finite-element (FE) models of human femurs based on quantitative computer tomography (QCT) with inhomogeneous orthotropic and isotropic material properties are addressed. The point-wise orthotropic properties are determined by a micromechanics (MM) based approach in conjunction with experimental observations at the osteon level, and two methods for determining the material trajectories are proposed (along organs outer surface, or along principal strains). QCT scans on four fresh-frozen human femurs were performed and high-order FE models were generated with either inhomogeneous MM-based orthotropic or empirically determined isotropic properties. In vitro experiments were conducted on the femurs by applying a simple stance position load on their head, recording strains on femurs’ surface and head’s displacements. After verifying the FE linear elastic analyses that mimic the experimental setting for numerical accuracy, we compared the FE results to the experimental observations to identify the influence of material properties on models’ predictions. The strains and displacements computed by FE models having MM-based inhomogeneous orthotropic properties match the FE-results having empirically based isotropic properties well, and both are in close agreement with the experimental results. When only the strains in the femoral neck are being compared a more pronounced difference is noticed between the isotropic and orthotropic FE result. These results lay the foundation for applying more realistic inhomogeneous orthotropic material properties in FEA of femurs.

References

1.
Keyak
,
J. H.
,
Meagher
,
J. M.
,
Skinner
,
H. B.
, and
Mote
,
J. C. D.
, 1990, “
Automated Three-Dimensional Finite Element Modelling of Bone: A New Method
,”
ASME J. Biomech. Eng.
,
12
, pp.
389
397
.
2.
Martelli
,
S.
,
Taddei
,
F.
,
Varini
,
E.
,
Cristofolini
,
L.
,
Gill
,
H. S.
, and
Viceconti
,
M.
,. 2005, “
Accuracy of Subject Specific Finite-Element Models of Long Bones From CT Data: An in-vitro Study
,”
Proceedings of ICCB II
, Vol.
1
, pp.
251
265
.
3.
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
.
4.
Trabelsi
,
N.
,
Yosibash
,
Z.
, and
Milgrom
,
C.
, 2009, “
Validation of Subject-Specific Automated p-FE Analysis of the Proximal Femur
,”
J. Biomech.
,
42
, pp.
234
241
.
5.
Helgason
,
B.
,
Taddei
,
F.
,
Palsson
,
F.
,
Schileo
,
E.
,
Cristofolini
,
L.
,
Viceconti
,
M.
, and
Brynjolfsson
,
S.
, 2008, “
A Modified Method for Assigning Material Properties to FE Models of Bones
,”
Med. Eng. Phys.
,
30
, pp.
444
453
.
6.
Liao
,
S. H.
,
Tong
,
R. F.
, and
Dong
,
J. X.
, 2007, “
Anisotropic Finite Element Modeling for Patient-Specific Mandible
,”
J. Comput. Meth. Prog. Biomed.
,
88(3)
, pp.
197
209
.
7.
Taddei
,
F.
,
Schileo
,
E.
,
Helgason
,
B.
,
Cristofolini
,
L.
, and
Viceconti
,
M.
, 2007, “
The Material Mapping Strategy Influences the Accuracy of CT-based Finite Element Models of Bones: An Evaluation Against Experimental Measurements
,”
Med. Eng. Phys.
,
29(9)
, pp.
973
979
.
8.
Viceconti
,
M.
,
Bellingeri
,
L.
,
Cristofolini
,
L.
, and
Toni
,
A.
, 1998, “
A Comparative Study on Different Methods of Automatic Mesh Generation of Human Femurs
,”
Med. Eng. Phys.
,
20
, pp.
1
10
.
9.
Viceconti
,
M.
,
Davinelli
,
M.
,
Taddei
,
F.
, and
Cappello
,
A.
, 2004, “
Automatic Generation of Accurate Subject-Specific Bone Finite Element Models to be Used in Clinical Studies
,”
J. Biomech.
,
37
, pp.
1597
1605
.
10.
Yosibash
,
Z.
,
Padan
,
R.
,
Joscowicz
,
L.
, and
Milgrom
,
C.
, 2007, “
A CT-Based High-Order Finite Element Analysis of the Human Proximal Femur Compared to in-vitro Experiments
,”
ASME J. Biomech. Eng.
,
129(3)
, pp.
297
309
.
11.
Shim
,
V. B.
,
Pitto
,
R. P.
,
Streicher
,
R. M.
,
Hunter
,
P. J.
, and
Anderson
,
I. A.
, 2007, “
The Use of Sparse CT Datasets for Auto-Generating Accurate FE Models of the Femur and Pelvis
,”
J. Biomech.
,
40
, pp.
26
35
.
12.
Keyak
,
J.
, and
Skinner
,
H.
, “
Three-Dimensional Finite Element Modelling of Bone: Effect of Element Size
,”
ASME J. Biomech. Eng.
,
14
, pp.
483
489
.
13.
Peng
,
L.
,
Bai
,
J.
,
Zeng
,
Z.
, and
Zhou
,
Y.
, 2006, “
Comparison of Isotropic and Orthotropic Material Property Assignments on Femoral Finite Element Models Under Two Loading Conditions
,”
Med. Eng. Phys.
,
28
, pp.
227
233
.
14.
Schileo
,
E.
,
Taddei
,
F.
,
Malandrino
,
A.
,
Cristofolini
,
L.
, and
Viceconti
,
M.
, 2007, “
Subject-Specific Finite Element Models can Accurately Predict Strain Levels in Long Bones
,”
J. Biomech.
,
40
, pp.
2982
2989
.
15.
Schileo
,
E.
,
DallAra
,
E.
,
Taddei
,
F.
,
Malandrino
,
A.
,
Schotkamp
,
T.
,
Baleani
,
M.
, and
Viceconti
,
M.
, 2008, “
An Accurate Estimation of Bone Density Improves the Accuracy of Subject-Specific Finite Element Models
,”
J. Biomech.
,
41
, pp.
2483
2491
.
16.
Duchemin
,
L.
,
Boussonb
,
V.
,
Raossanaly
,
C.
,
Bergot
,
C.
,
Laredob
,
J. D.
,
Skalli
,
W.
,
Mitton
,
D.
, 2008, “
Prediction of Mechanical Properties of Cortical Bone by Quantitative Computed Tomography
,”
Med. Eng. Phys.
,
30
, pp.
321
328
.
17.
Baca
,
V.
,
Horak
,
Z.
,
Mikulenka
,
P.
, and
Dzupa
,
V.
, 2008, “
Comparison of an Inhomogeneous Orthotropic and Isotropic Material Models Used for FE Analyses
,”
J. Med. Eng. Phys.
,
30
, pp.
924
930
.
18.
Yang
,
H.
,
Ma
,
X.
,
Guo
,
T.
, 2010, “
Some Factors That Affect the Comparison Between Isotropic and Orthotropic Inhomogeneous Finite Element Material Models of Femur
,”
Med. Eng. Phys.
,
32
, pp.
553
560
.
19.
Lotz
,
J. C.
,
Gerhart
,
T. N.
, and
Hayes
,
W. C.
, 1991, “
Mechanical Properties of Metaphyseal Bone in the Proximal Femur
,”
J. Biomech.
,
24
, pp.
317
329
.
20.
Wirtz
,
D.
,
Schiffers
,
N.
,
Pandorf
,
T.
,
Radermacher
,
K.
,
Weichert
,
D.
, and
Forst
,
R.
, 2000, “
Critical Evaluation of Known Bone Material Properties to Realize Anisotropic FE-Simulation of the Proximal Femur
,”
J. Biomech.
,
33
, pp.
1325
1330
.
21.
Taylor
,
W. R.
,
Roland
,
E.
,
Ploeg
,
H.
,
Hertig
,
D.
,
Klabunde
,
R.
,
Warner
,
M. D.
,
Hobatho
,
M. C.
,
Rakotomanana
,
L.
, and
Clift
,
S. E.
, 2002, “
Determination of Orthotropic Bone Elastic Constants Using FEA and Modal Analysis
,”
J. Biomech.
,
35
, pp.
767
773
.
22.
Wirtz
,
D. C.
,
Pandorf
,
T.
,
Portheine
,
F.
,
Radermacher
,
K.
,
Schiffers
,
N.
,
Prescher
,
A.
,
Weichert
,
D.
, and
Fritz
,
U. N.
, 2003, “
Concept and Development of an Orthotropic FE Model of the Proximal Femur
,”
J. Biomech.
,
36
, pp.
289
293
.
23.
Shahar
,
R.
,
Zaslansky
,
P.
,
Barak
,
M.
,
Friesem
,
A.
,
Currey
,
J.
, and
Weiner
,
S.
, 2007, “
Anisotropic Poisson’s Ratio and Compression Modulus of Cortical Bone Determined by Speckle Interferometry
,”
J. Biomech.
,
40
, pp.
252
264
.
24.
Tabor
,
Z.
, and
Rokita
,
E.
, 2007, “
Quantifying Anisotropy of Trabecular Bone From Gray-Level Images
,”
Bone
,
40
, pp.
966
972
.
25.
Schneider
,
R.
,
Faust
,
G.
,
Hindenlang
,
U.
,
Helwig
,
P.
, 2009, “
Inhomogeneous, Orthotropic Material Model for the Cortical Structure of Long Bones Modelled on the Basis of Clinical CT or Density Data
,”
Comput. Meth. Appl. Mech. Eng.
,
198
, pp.
2167
2174
.
26.
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
, pp.
597
620
.
27.
Franzoso
,
G.
, and
Zysset
,
P.
, 2009, “
Elastic Anisotropy of Human Cortical Bone Secondary Osteons Measured by Nanoindentation
,”
ASME J. Biomech. Eng.
,
131(2)
, p.
021001
.
28.
Cowin
,
S.
, 1985, “
The Relationship Between the Elasticity Tensor and the Fabric Tensor
,”
Mech. Mater.
,
4
, pp.
137
147
.
29.
Ogdgaard
,
A.
, 1997, “
Three-Dimensional Methods for Quantification of Cancellous Bone Architecture
,”
Bone
,
20(4)
, pp.
315
328
.
30.
Chevalier
,
Y.
,
Pahr
,
D.
, and
Zysset
,
P.
, 2009, “
The Role of Cortical Shell and Trabecular Fabric in Finite Element Analysis of the Human Vertebral Body
,”
J. Biomech. Eng.
,
13
, p.
111003
.
31.
Hellmich
,
C.
,
Kober
,
C.
, and
Erdmann
,
B.
, 2008, “
Micromechanics-Based Conversion of CT Data Into Anisotropic Elasticity Tensors, Applied to FE Simulations of a Mandible
,”
Ann. Biomed. Eng.
,
36
, pp.
108
122
.
32.
Yosibash
,
Z.
,
Trabelsi
,
N.
, and
Hellmich
,
C.
, 2008, “
Subject-Specific p-FE Analysis of the Proximal Femur Utilizing Micromechanics Based Material Properties
,”
Int. J. Multiscale Comput. Eng.
,
6(5)
, pp.
483
498
.
33.
Szabó
,
B. A.
, and
Babuîska
,
I.
, 1991,
Finite Element Analysis
,
John-Wiley
,
New York
.
34.
Carter
,
D.
, and
Hayes
,
W.
, 1977, “
The Compressive Behavior of Bone as a Two-Phase Porous Structure
,”
J. Bone Joint Surg. Am.
,
59
, pp.
954
962
.
35.
Cody
,
D. D.
,
Hou
,
F. J.
,
Divine
,
G. W.
, and
Fyhrie
,
D. P.
, 2000, “
Short Term in vivo Study of Proximal Femoral Finite Element Modeling
,”
Ann. Biomed. Eng.
,
28
, pp.
408
414
.
36.
Keyak
,
J.
, and
Falkinstein
,
Y.
, 2003, “
Comparison of in situ and in vitro CT Scan-Based Finite Element Model Predictions of Proximal Femoral Fracture Load
,”
Med. Eng. Phys.
,
25
, pp.
781
787
.
37.
Keller
,
T. S.
, 1994, “
Predicting the Compressive Mechanical Behavior of Bone
,”
J. Biomech.
,
27
, pp.
1159
1168
.
38.
Morgan
,
E. F.
,
Bayraktar
,
H. H.
, and
Keaveny
,
T. M.
, 2003, “
Trabecular Bone Modulus-Density Relationships Depend on Anatomic Site
,”
J. Biomech.
,
36
, pp.
897
904
.
39.
Zaoui
,
A.
, 2002, “
Continuum Micromechanics: Survey
,”
J. Eng. Mech. (ASCE)
,
128(8)
, pp.
808
816
.
40.
Ashman
,
R. B.
,
Cowin
,
S. C.
,
van Buskirk
,
W. C.
, and
Rice
,
J. C.
, 1984, “
A Continuous Wave Technique for the Measurement of the Elastic Properties of Cortical Bone
,”
J. Biomech.
,
17
(
5
), pp.
349
361
.
41.
Kober
,
C.
,
Erdmann
,
B.
,
Hellmich
,
C.
,
Sader
,
R.
, and
Zeilhofer
,
H.-F.
, 2006, “
Consideration of Anisotropic Elasticity Minimizes Volumetric Rather Than Shear Deformation in Human Mandible
,”
Comput. Meth. Biomech. Biomed. Eng.
,
9(2)
, pp.
91
101
.
42.
Pietruszczak
,
S.
,
Inglis
,
D.
, and
Pande
,
G.
, 1999, “
A Fabric-Dependent Fracture Criterion for Bone
,”
J. Biomech.
,
32(10)
, pp.
1071
1079
.
43.
Wolff
,
J.
, 1986,
The Law of Bone Remodeling,
Springer
,
Berlin
(translation of the German 1892 edition).
44.
Hert
,
J.
,
Fiala
,
P.
, and
Petrtyl
,
M.
, 1994, “
Osteon Orientation of the Diaphysis of the Long Bones in Man
,”
Bone
,
15(3)
, pp.
269
277
.
45.
Cristofolini
,
L.
,
Juszczyk
,
M.
,
Taddei
,
F.
, and
Viceconti
,
M.
, 2009, “
Strain Distribution in the Proximal Human Femoral Metaphysis
,”
Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
,
223
, pp.
273
288
.
46.
Sokolnikoff
,
I. S.
, 1956,
Mathematical Theory of Elasticity
,
McGraw-Hill
,
New York
.
47.
Bergmann
,
G.
,
Deuretzbacher
,
G.
,
Heller
,
M. O.
,
Graichenm
,
F.
,
Rohlmann
,
A.
,
Strauss
,
J.
,
Haas
,
N. P.
, and
Duda
,
G.
, 2001, “
Hip Contact Forces and Gait Patterns From Routine Activities
,”
J. Biomech.
,
34
, pp.
859
871
.
48.
Ohman
,
C.
,
Baleani
,
M.
,
Perilli
,
E.
,
DallAra
,
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
, pp.
2426
2433
.
49.
Yosibash
,
Z.
,
Tal
,
D.
, and
Trabelsi
,
N.
, 2010, “
Predicting the Yield of the Proximal Femur Using High Order Finite Element Analysis With Inhomogeneous Orthotropic Material Properties
,”
Philos. Trans. R. Soc. London, Ser. A
,
368
, pp.
2707
2723
.
50.
Heller
,
M. O.
,
Bergmann
,
G.
,
Deuretzbacher
,
G.
,
Durselen
,
L.
,
Pohl
,
M.
,
Claes
,
L.
, and
Haas
,
N. P.
,
Duda
,
G. N.
, 2001, “
Musculo-Skeletal Loading Conditions at the Hip During Walking and Stair Climbing
,”
J. Biomech.
,
34
, pp.
883
893
.
51.
Heller
,
M. O.
,
Bergmann
,
G.
,
Kassi
,
J.-P.
,
Claes
,
L.
, and
Haas
,
N. P.
,
Duda
,
G. N.
, 2005, “
Determination of Muscle Loading at the Hip Joint for Use in Pre-Clinical Testing
,”
J. Biomech.
,
38
, pp.
1155
1163
.
52.
Ting
,
T. C. T.
, 1996,
Anisotropic Elasticity Theory and Applications
,
Oxford Engineering Science Series
,
Oxford
.
53.
Rho
,
J.
, 1996, “
An Ultrasonic Method for Measuring the Elastic Properties of Human Tibial Cortical and Cancellous Bone
,”
J. Ultrasonics
,
34(8)
, pp.
777
778
.
54.
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
.
55.
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
.
56.
Yoon
,
Y.
, and
Cowin
,
S.
, 2008, “
The Estimated Elastic Constants for a Single Bone Osteonal Lamella
,”
J. Biomech. Model. Mechanobiol.
,
7
, pp.
1
11
.
57.
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 Tomography
,
14
(
1
), pp.
107
114
.
58.
Rho
,
J. Y.
,
Hobatho
,
M. C.
, and
Ashman
,
R. B.
, 1995, “
Relations of Mechanical Properties to Density and CT Numbers in Human Bone
,”
Med. Eng. Phys.
,
17
, pp.
347
355
.
You do not currently have access to this content.