In this study, the changes in the bone density of human femur model as a result of different loadings were investigated. The model initially consisted of a solid shell representing cortical bone encompassing a cubical network of interconnected rods representing trabecular bone. A computationally efficient program was developed that iteratively changed the structure of trabecular bone by keeping the local stress in the structure within a defined stress range. The stress was controlled by either enhancing existing beam elements or removing beams from the initial trabecular frame structure. Analyses were performed for two cases of homogenous isotropic and transversely isotropic beams. Trabecular bone structure was obtained for three load cases: walking, stair climbing and stumbling without falling. The results indicate that trabecular bone tissue material properties do not have a significant effect on the converged structure of trabecular bone. In addition, as the magnitude of the loads increase, the internal structure becomes denser in critical zones. Loading associated with the stumbling results in the highest density; whereas walking, considered as a routine daily activity, results in the least internal density in different regions. Furthermore, bone volume fraction at the critical regions of the converged structure is in good agreement with previously measured data obtained from combinations of dual X-ray absorptiometry (DXA) and computed tomography (CT). The results indicate that the converged bone architecture consisting of rods and plates are consistent with the natural bone morphology of the femur. The proposed model shows a promising means to understand the effects of different individual loading patterns on the bone density.

References

References
1.
Parfitt
,
A.
,
1983
, “
The Physiologic and Clinical Significance of Bone Histomorphometric Data
,”
Bone Histomorphometry: Techniques and Interpretation
,
CRC
,
Boca Raton, FL
, p. 143.
2.
Wolff
,
J.
,
Maquet
,
P.
, and
Furlong
,
R.
,
1986
,
The Law of Bone Remodelling
,
Springer
,
Berlin, Germany
.10.1007/978-3-642-71031-5
3.
Brekelmans
,
W.
,
Poort
,
H.
, and
Slooff
,
T.
,
1972
, “
A New Method to Analyse the Mechanical Behaviour of Skeletal Parts
,”
Acta Orthop.
,
43
(
5
), pp.
301
317
.10.3109/17453677208998949
4.
Hart
,
R.
,
Davy
,
D.
, and
Heiple
,
K.
,
1984
, “
Mathematical Modeling and Numerical Solutions for Functionally Dependent Bone Remodeling
,”
Calcif. Tissue Int.
,
36
(
1
), pp.
S104
S109
.10.1007/BF02406142
5.
Carter
,
D.
,
Fyhrie
,
D.
, and
Whalen
,
R.
,
1987
, “
Trabecular Bone Density and Loading History: Regulation of Connective Tissue Biology by Mechanical Energy
,”
J. Biomech.
,
20
(
8
), pp.
785
794
.10.1016/0021-9290(87)90058-3
6.
Huiskes
,
R.
,
Weinans
,
H.
,
Grootenboer
,
H.
,
Dalstra
,
M.
,
Fudala
,
B.
, and
Slooff
,
T.
,
1987
, “
Adaptive Bone-Remodeling Theory Applied to Prosthetic-Design Analysis
,”
J. Biomech.
,
20
(
11
), pp.
1135
1150
.10.1016/0021-9290(87)90030-3
7.
Marzban
,
A.
,
Canavan
,
P.
,
Warner
,
G.
,
Vaziri
,
A.
, and
Nayeb-Hashemi
,
H.
,
2012
, “
Parametric Investigation of Load-Induced Structure Remodeling in the Proximal Femur
,”
Proc. Inst. Mech. Eng., Part H
,
226
(
6
), pp.
450
460
.10.1177/0954411912444067
8.
Bitsakos
,
C.
,
Kerner
,
J.
,
Fisher
,
I.
, and
Amis
,
A. A.
,
2005
, “
The Effect of Muscle Loading on the Simulation of Bone Remodelling in the Proximal Femur
,”
J. Biomech.
,
38
(
1
), pp.
133
139
.10.1016/j.jbiomech.2004.03.005
9.
Turner
,
A.
,
Gillies
,
R.
,
Sekel
,
R.
,
Morris
,
P.
,
Bruce
,
W.
, and
Walsh
,
W.
,
2005
, “
Computational Bone Remodelling Simulations and Comparisons With DEXA Results
,”
J. Orthop. Res.
,
23
(
4
), pp.
705
712
.10.1016/j.orthres.2005.02.002
10.
Boyle
,
C.
, and
Kim
, I
. Y.
,
2011
, “
Three-Dimensional Micro-Level Computational Study of Wolff's Law via Trabecular Bone Remodeling in the Human Proximal Femur Using Design Space Topology Optimization
,”
J. Biomech.
,
44
(
5
), pp.
935
942
.10.1016/j.jbiomech.2010.11.029
11.
Hambli
,
R.
,
Lespessailles
,
E.
, and
Benhamou
,
C.-L.
,
2013
, “
Integrated Remodeling-to-Fracture Finite Element Model of Human Proximal Femur Behaviour
,”
J. Mech. Behav. Biomed. Mater.
,
17
, pp.
89
106
.10.1016/j.jmbbm.2012.08.011
12.
Fyhrie
,
D.
, and
Carter
,
D.
,
1986
, “
A Unifying Principle Relating Stress to Trabecular Bone Morphology
,”
J. Orthop. Res.
,
4
(
3
), pp.
304
317
.10.1002/jor.1100040307
13.
Carter
,
D.
,
Orr
,
T.
, and
Fyhrie
,
D.
,
1989
, “
Relationships Between Loading History and Femoral Cancellous Bone Architecture
,”
J. Biomech.
,
22
(
3
), pp.
231
244
.10.1016/0021-9290(89)90091-2
14.
Adachi
,
T.
,
Tomita
,
Y.
,
Sakaue
,
H.
, and
Tanaka
,
M.
,
1997
, “
Simulation of Trabecular Surface Remodeling Based on Local Stress Nonuniformity
,”
JSME Int. J. Ser. C
,
40
(
4
), pp.
782
792
.10.1299/jsmec.40.782
15.
Adachi
,
T.
,
Tsubota
,
K.-I.
,
Tomita
,
Y.
, and
Hollister
,
S. J.
,
2001
, “
Trabecular Surface Remodeling Simulation for Cancellous Bone Using Microstructural Voxel Finite Element Models
,”
ASME J. Biomech. Eng.
,
123
(
5
), pp.
403
409
.10.1115/1.1392315
16.
Beaupré
,
G.
,
Orr
,
T.
, and
Carter
,
D.
,
1990
, “
An Approach for Time-Dependent Bone Modeling and Remodeling—Theoretical Development
,”
J. Orthop. Res.
,
8
(
5
), pp.
651
661
.10.1002/jor.1100080506
17.
Cowin
,
S. C.
,
2001
,
Bone Mechanics Handbook
,
CRC
,
Boca Raton, FL
.
18.
Keaveny
,
T. M.
,
Morgan
,
E. F.
,
Niebur
,
G. L.
, and
Yeh
,
O. C.
,
2001
, “
Biomechanics of Trabecular Bone
,”
Annu. Rev. Biomed. Eng.
,
3
(
1
), pp.
307
333
.10.1146/annurev.bioeng.3.1.307
19.
Sarikanat
,
M.
, and
Yildiz
,
H.
,
2011
, “
Determination of Bone Density Distribution in Proximal Femur by Using the 3D Orthotropic Bone Adaptation Model
,”
Proc. Inst. Mech. Eng., Part H
,
225
(
4
), pp.
365
375
.10.1177/09544119JEIM895
20.
Miller
,
Z.
,
Fuchs
,
M. B.
, and
Arcan
,
M.
,
2002
, “
Trabecular Bone Adaptation With an Orthotropic Material Model
,”
J. Biomech.
,
35
(
2
), pp.
247
256
.10.1016/S0021-9290(01)00192-0
21.
Ashman
,
R.
,
Rho
,
J.
, and
Turner
,
C.
,
1989
, “
Anatomical Variation of Orthotropic Elastic Moduli of the Proximal Human Tibia
,”
J. Biomech.
,
22
(
8
), pp.
895
900
.10.1016/0021-9290(89)90073-0
22.
Turner
,
C. H.
,
Rho
,
J.
,
Takano
,
Y.
,
Tsui
,
T. Y.
, and
Pharr
,
G. M.
,
1999
, “
The Elastic Properties of Trabecular and Cortical Bone Tissues are Similar: Results From Two Microscopic Measurement Techniques
,”
J. Biomech.
,
32
(
4
), pp.
437
441
.10.1016/S0021-9290(98)00177-8
23.
Marzban
,
A.
,
Nayeb-Hashemi
,
H.
, and
Vaziri
,
A.
,
2013
, “
Numerical Simulation of Load-Induced Bone Structural Remodelling Using Stress-Limit Criterion
,”
Comput. Methods Biomech. Biomed. Eng.
,
18
(
3
), pp.
259
268
.10.1080/10255842.2013.792915
24.
Keyak
,
J. H.
,
Rossi
,
S. A.
,
Jones
,
K. A.
, and
Skinner
,
H. B.
,
1997
, “
Prediction of Femoral Fracture Load Using Automated Finite Element Modeling
,”
J. Biomech.
,
31
(
2
), pp.
125
133
.10.1016/S0021-9290(97)00123-1
25.
Ethier
,
C. R.
, and
Simmons
,
C. A.
,
2007
,
Introductory Biomechanics: From Cells to Organisms
,
Cambridge University
, Cambridge, UK.10.1017/CBO9780511809217
26.
Couteau
,
B.
,
Labey
,
L.
,
Hobatho
,
M.
,
Vander Sloten
,
J.
,
Arlaud
,
J.
, and
Brignola
,
J.
,
1999
, “
Validation of a Three Dimensional Finite Element Model of a Femur With a Customized Hip Implant
,”
Comput. Methods Biomech. Biomed. Eng.
,
2
(
2
), pp.
147
154
.
27.
Taylor
,
W.
,
Roland
,
E.
,
Ploeg
,
H.
,
Hertig
,
D.
,
Klabunde
,
R.
,
Warner
,
M.
,
Hobatho
,
M.
,
Rakotomanana
,
L.
, and
Clift
,
S.
,
2002
, “
Determination of Orthotropic Bone Elastic Constants Using FEA and Modal Analysis
,”
J. Biomech.
,
35
(
6
), pp.
767
773
.10.1016/S0021-9290(02)00022-2
28.
Heller
,
M.
,
Bergmann
,
G.
,
Kassi
,
J.-P.
,
Claes
,
L.
,
Haas
,
N.
, and
Duda
,
G.
,
2005
, “
Determination of Muscle Loading at the Hip Joint for Use in Pre-Clinical Testing
,”
J. Biomech.
,
38
(
5
), pp.
1155
1163
.10.1016/j.jbiomech.2004.05.022
29.
El’Sheikh
,
H.
,
MacDonald
,
B.
, and
Hashmi
,
M.
,
2003
, “
Finite Element Simulation of the Hip Joint During Stumbling: A Comparison Between Static and Dynamic Loading
,”
J. Mater. Process. Technol.
,
143
, pp.
249
255
.10.1016/S0924-0136(03)00352-2
30.
Bergmann
,
G.
,
Graichen
,
F.
, and
Rohlmann
,
A.
,
1993
, “
Hip Joint Loading During Walking and Running, Measured in Two Patients
,”
J. Biomech.
,
26
(
8
), pp.
969
990
.10.1016/0021-9290(93)90058-M
31.
Lennon
,
A.
,
McCormack
,
B.
, and
Prendergast
,
P.
,
1998
, “
Development of a Physical Model of a Cemented Hip Replacement for Investigation of Cement Damage Accumulation
,”
J. Biomech.
,
31
(Suppl. 1), p.
129
.10.1016/S0021-9290(98)80260-1
32.
Homminga
,
J.
,
McCreadie
,
B.
,
Ciarelli
,
T.
,
Weinans
,
H.
,
Goldstein
,
S.
, and
Huiskes
,
R.
,
2002
, “
Cancellous Bone Mechanical Properties From Normals and Patients With Hip Fractures Differ on the Structure Level, Not on the Bone Hard Tissue Level
,”
Bone
,
30
(
5
), pp.
759
764
.10.1016/S8756-3282(02)00693-2
33.
Keyak
,
J. H.
, 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
(
9
), pp.
781
787
.10.1016/S1350-4533(03)00081-X
34.
Nazarian
,
A.
,
von Stechow
,
D.
,
Zurakowski
,
D.
,
Müller
,
R.
, and
Snyder
,
B. D.
,
2008
, “
Bone Volume Fraction Explains the Variation in Strength and Stiffness of Cancellous Bone Affected by Metastatic Cancer and Osteoporosis
,”
Calcif. Tissue Int.
,
83
(
6
), pp.
368
379
.10.1007/s00223-008-9174-x
35.
Van Rietbergen
,
B.
,
Kabel
,
J.
,
Odgaard
,
A.
, and
Huiskes
,
R.
,
1997
, “
Determination of Trabecular Bone Tissue Elastic Properties by Comparison of Experimental and Finite Element Results
,”
Material Identification Using Mixed Numerical Experimental Methods
,
Springer
, Netherlands, pp.
183
192
.10.1007/978-94-009-1471-1_19
36.
Ladd
,
A. J.
,
Kinney
,
J. H.
,
Haupt
,
D. L.
, and
Goldstein
,
S. A.
,
1998
, “
Finite-Element Modeling of Trabecular Bone: Comparison With Mechanical Testing and Determination of Tissue Modulus
,”
J. Orthop. Res.
,
16
(
5
), pp.
622
628
.10.1002/jor.1100160516
37.
Hou
,
F. J.
,
Lang
,
S. M.
,
Hoshaw
,
S. J.
,
Reimann
,
D. A.
, and
Fyhrie
,
D. P.
,
1998
, “
Human Vertebral Body Apparent and Hard Tissue Stiffness
,”
J. Biomech.
,
31
(
11
), pp.
1009
1015
.10.1016/S0021-9290(98)00110-9
38.
Kabel
,
J.
,
van Rietbergen
,
B.
,
Dalstra
,
M.
,
Odgaard
,
A.
, and
Huiskes
,
R.
,
1999
, “
The Role of an Effective Isotropic Tissue Modulus in the Elastic Properties of Cancellous Bone
,”
J. Biomech.
,
32
(
7
), pp.
673
680
.10.1016/S0021-9290(99)00045-7
39.
Baum
,
T.
,
Carballido-Gamio
,
J.
,
Huber
,
M.
,
Müller
,
D.
,
Monetti
,
R.
,
Räth
,
C.
,
Eckstein
,
F.
,
Lochmüller
,
E.
,
Majumdar
,
S.
, and
Rummeny
,
E.
,
2010
, “
Automated 3D Trabecular Bone Structure Analysis of the Proximal Femur—Prediction of Biomechanical Strength by CT and DXA
,”
Osteoporosis Int.
,
21
(
9
), pp.
1553
1564
.10.1007/s00198-009-1090-z
40.
Huber
,
M. B.
,
Carballido-Gamio
,
J.
,
Bauer
,
J. S.
,
Baum
,
T.
,
Eckstein
,
F.
,
Lochmuller
,
E. M.
,
Majumdar
,
S.
, and
Link
,
T. M.
,
2008
, “
Proximal Femur Specimens: Automated 3D Trabecular Bone Mineral Density Analysis at Multidetector CT—Correlation With Biomechanical Strength Measurement 1
,”
Radiology
,
247
(
2
), pp.
472
481
.10.1148/radiol.2472070982
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