The prediction of patient-specific proximal femur mechanical response to various load conditions is of major clinical importance in orthopaedics. This paper presents a novel, empirically validated high-order finite element method (FEM) for simulating the bone response to loads. A model of the bone geometry was constructed from a quantitative computerized tomography (QCT) scan using smooth surfaces for both the cortical and trabecular regions. Inhomogeneous isotropic elastic properties were assigned to the finite element model using distinct continuous spatial fields for each region. The Young’s modulus was represented as a continuous function computed by a least mean squares method. p-FEMs were used to bound the simulation numerical error and to quantify the modeling assumptions. We validated the FE results with in-vitro experiments on a fresh-frozen femur loaded by a quasi-static force of up to 1500N at four different angles. We measured the vertical displacement and strains at various locations and investigated the sensitivity of the simulation. Good agreement was found for the displacements, and a fair agreement found in the measured strain in some of the locations. The presented study is a first step toward a reliable p-FEM simulation of human femurs based on QCT data for clinical computer aided decision making.

1.
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.
1350-4533,
20
, pp.
1
10
.
2.
Taddei
,
F.
,
Cristofolini
,
L.
,
Martelli
,
S.
,
Gill
,
H. S.
, and
Viceconti
,
M.
, 2006, “
Subject-Specific Finite Element Models of Long Bones: An In vitro Evolution of the Overall Accuracy
,”
J. Biomech.
0021-9290,
39
(
18
), pp.
2457
2467
.
3.
Keaveny
,
T. M.
,
Guo
,
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.
0021-9290,
27
, pp.
1127
1136
.
4.
Cowin
,
S. C.
, and
Ashby
,
M. F.
, 2001,
Bone Mechanics Handbook
,
CRC Press
, Boca Raton, FL.
5.
Lotz
,
J. C.
,
Gerhart
,
T. N.
, and
Hayes
,
W. C.
, 1991, “
Mechanical Properties of Metaphyseal Bone in the Proximal Femur
,”
J. Biomech.
0021-9290,
24
, pp.
317
329
.
6.
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. Assist. Tomogr.
0363-8715,
14
(
1
), pp.
107
114
.
7.
Wirtz
,
D. C.
,
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.
0021-9290,
33
, pp.
1325
1330
.
8.
Morgan
,
E. F.
,
Bayraktar
,
H. H.
, and
Keaveny
,
T. M.
, 2003, “
Trabecular Bone Modulus-Density Relationships Depend on Anatomic Site
,”
J. Biomech.
0021-9290,
36
, pp.
897
904
.
9.
Keller
,
T. S.
, 1994, “
Predicting the Compressive Mechanical Behavior of Bone
,”
J. Biomech.
0021-9290,
27
, pp.
1159
1168
.
10.
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.
1350-4533,
17
, pp.
347
355
.
11.
Szabó
,
B. A.
, and
Babuška
,
I.
, 1991,
Finite Element Analysis
,
Wiley
, New York.
12.
Mueller-Karger
,
C. M.
,
Rank
,
E.
, and
Cerrolaza
,
M.
, 2004, “
p-Version of the Finite Element Method for Highly Heterogeneous Simulation of Human Bone
,”
Finite Elem. Anal. Design
0168-874X,
40
, pp.
757
770
.
13.
Keyak
,
J. H.
,
Rossi
,
S. A.
,
Jones
,
K. A.
, and
Skinner
,
H. B.
, 1998, “
Prediction of Femoral Fracture Load Using Automated Finite Element Modeling
,”
J. Biomech.
0021-9290,
31
, pp.
125
133
.
14.
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.
0021-9290,
32
, pp.
1013
1020
.
15.
Lotz
,
J. C.
,
Cheal
,
E. J.
, and
Hayes
,
W. C.
, 1991, “
Fracture Prediction for the Proximal Femur Using Finite Element Models: Part 1—Linear Analysis
,”
J. Biomech. Eng.
0148-0731,
113
, pp.
353
360
.
16.
Mertz
,
B.
,
Niederer
,
P.
,
Muller
,
R.
, and
Ruegsegger
,
P.
, 1996, “
Automated Finite Element Analysis of Excised Human Femura Based on Precision-QCT
,”
J. Biomech. Eng.
0148-0731,
118
, pp.
387
390
.
17.
Wirtz
,
D. C.
,
Pandorf
,
T.
,
Portheine
,
F.
,
Radermacher
,
K.
,
Schiffers
,
N.
,
Prescher
,
A.
,
Weichert
,
D.
, and
Firtz
,
U. N.
, 2003, “
Concept and Development of an Orthotropic FE Model of the Proximal Femur
,
J. Biomech.
0021-9290,
36
, pp.
289
293
.
18.
Couteau
,
B.
,
Payan
,
Y.
, and
Lavallee
,
S.
, 2000, “
The Mesh-Matching Algorithm: An Automatic 3d Mesh Generator for Finite Element Structures
,”
J. Biomech.
0021-9290,
33
, pp.
1005
1009
.
19.
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. Biomed. Eng.
0141-5425,
12
, pp.
389
397
.
20.
Cody
,
D. D.
,
McCubbrey
,
D. A.
,
Divine
,
G. W.
,
Gross
,
G. J.
, and
Goldstein
,
S. A.
, 1996, “
Predictive Value of Proximal Femural Bone Densiometry in Determining Local Orthogonal Material Properties
,”
J. Biomech.
0021-9290,
29
, pp.
753
761
.
21.
Fox
,
J. C.
,
Gupta
,
A.
,
Blumenkrantz
,
G.
,
Bayraktar
,
H. H.
, and
Keaveny
,
T. M.
, 2004, “
Role of Elastic Anisotropy and Failure Criterion in Femoral Fracture Strength Predictions
,”
Trans. Orthopaedic Res. Soc. Conference Proceedings
, p.
520
.
22.
Marom
,
A. S.
, and
Linden
,
M. J.
, 1990, “
Computer Aided Stress Analysis of Long Bones Utilizing Computed Tomography
,”
J. Biomech.
0021-9290,
23
, pp.
399
404
.
23.
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.
0021-9290,
37
, pp.
1597
1605
.
24.
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.
1350-4533,
26
, pp.
61
69
.
25.
Zannoni
,
C.
,
Mantovani
,
R.
, and
Viceconti
,
M.
, 1998, “
Material Properties Assignment to Finite Element Models of Bone Structure: A New Method
,”
Med. Eng. Phys.
1350-4533,
20
, pp.
735
740
.
26.
Esses
,
S. I.
,
Lotz
,
J. C.
, and
Hayes
,
W. C.
, 1989, “
Biomechanical Properties of the Proximal Femur Determined In Vitro by Single-Energy Quantitative Computed Tomography
,”
J. Bone Miner. Res.
0884-0431,
4
, pp.
715
722
.
27.
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.
0090-6964,
28
, pp.
408
414
.
28.
Yang
,
G.
,
Kabel
,
J.
,
VanRiertbergen
,
B.
,
Odgaard
,
A.
,
Huiskes
,
R.
, and
Cowin
,
S. C.
, 1999, “
The Anisotropic Hooke’s Law for Cancellous Bone and Wood
,”
J. Elast.
0374-3535,
53
, pp.
125
146
.
29.
Keyak
,
J. H.
, and
Skinner
,
H. B.
, 1992, “
Three-Dimensional Finite Element Modelling of Bone: Effect of Element Size
,”
J. Biomed. Eng.
0141-5425,
14
, pp.
483
489
.
30.
Keyak
,
J. H.
,
Fourkas
,
M. G.
,
Meagher
,
J. M.
, and
Skinner
,
H. B.
, 1993, “
Validation of Automated Method of Three-Dimensional Finite Element Modelling of Bone
,”
J. Biomed. Eng.
0141-5425,
15
, pp.
505
509
.
31.
Yeni
,
Y. N.
, and
Fyhire
,
D. P.
, 2001, “
Finite Element Calculated Uniaxial Apparent Stiffness is a Consistent Predictor of Uniaxial Apparent Strength in Human Vertebral Cancellous Bone Tested with Different Boundary Conditions
,”
J. Biomech.
0021-9290,
34
(
12
), pp.
1649
1654
.
32.
Templeton
,
A.
, and
Liebschner
,
M.
, 2004, “
A Hierarchical Approach to Finite Element Modeling of the Human Spine
,”
Crit. Rev. Eukaryot Gene Expr
1045-4403,
14
(
4
), pp.
317
328
.
33.
Hernandez
,
C. J.
,
Gupta
,
A.
, and
Keaveny
,
T. M.
, 2006, “
A Biomechanical Analysis of the Effects of Resorption Cavities on Cancellous Bone Strength
,”
J. Bone Miner. Res.
0884-0431,
21
(
8
), pp.
1248
1255
.
34.
Kenney
,
J. F.
, and
Keeping
,
E. S.
, 1962,
Mathematics of Statistics
,
Van Nostrand
, New York.
35.
Ayyub
,
B. M.
, and
McCuen
,
R. H.
, 1996,
Numerical Methods for Engineers
,
Prentice Hall
, Englewood Cliffs, NJ.
36.
Padan
,
R.
, 2006, “
Towards a Reliable Mechanical Simulation of the Proximal Femur
,” M.Sc. thesis, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
37.
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.
0021-9290,
21
, pp.
155
168
.
38.
Carter
,
D. R.
, and
Hayes
,
W. C.
, 1977, “
The Compressive Behavior of Bone as a Two-Phase Porous Structure
,”
J. Bone Jt. Surg., Am. Vol.
0021-9355,
59
, pp.
954
962
.
39.
Ciarelli
,
M. J.
,
Goldstein
,
S. A.
,
Kuhn
,
J. L.
,
Cody
,
D. D.
, and
Brown
,
M. B.
, 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.
0736-0266,
9
, pp.
674
682
.
40.
Jensen
,
J. S.
, 1978, “
A Photoelastic Study of a Model of the Proximal Femur. A Biomechanical Study of Unstable Trochanteric Fractures I
,”
Acta Orthop. Scand.
0001-6470,
49
(
1
), pp.
54
59
.
41.
Fedida
,
R.
,
Yosibash
,
Z.
,
Milgrom
,
C.
, and
Joscowicz
,
L.
, 2005, “
Femur Mechanical Simulation Using High-Order FE Analysis With Continuous Mechanical Properties
,”
Proceedings of ICCB05 - II International conference on computational bioengineering
, Lisbon, Portugal, Vol.
1
,
H.
Rodrigues
et al.
, eds.,
IST Press
, pp.
85
96
.
42.
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.
0021-9290,
33
, pp.
209
214
.
You do not currently have access to this content.