Computational bone remodeling simulations have recently received significant attention with the aid of state-of-the-art high-resolution imaging modalities. They have been performed using localized finite element (FE) models rather than full FE models due to the excessive computational costs of full FE models. However, these localized bone remodeling simulations remain to be investigated in more depth. In particular, applying simplified loading conditions (e.g., uniform and unidirectional loads) to localized FE models have a severe limitation in a reliable subject-specific assessment. In order to effectively determine the physiological local bone loads for the volume of interest (VOI), this paper proposes a novel method of estimating the local loads when the global musculoskeletal loads are given. The proposed method is verified for the three VOI in a proximal femur in terms of force equilibrium, displacement field, and strain energy density (SED) distribution. The effect of the global load deviation on the local load estimation is also investigated by perturbing a hip joint contact force (HCF) in the femoral head. Deviation in force magnitude exhibits the greatest absolute changes in a SED distribution due to its own greatest deviation, whereas angular deviation perpendicular to a HCF provides the greatest relative change. With further in vivo force measurements and high-resolution clinical imaging modalities, the proposed method will contribute to the development of reliable patient-specific localized FE models, which can provide enhanced computational efficiency for iterative computing processes such as bone remodeling simulations.

References

References
1.
Cowin
,
S. C.
, and
Hegedus
,
D. H.
,
1976
, “
Bone Remodeling I: Theory of Adaptive Elasticity
,”
J. Elast.
,
6
(
3
), pp.
313
326
.
2.
Carter
,
D. R.
,
Orr
,
T. E.
, and
Fyhrie
,
D. P.
,
1989
, “
Relationships Between Loading History and Femoral Cancellous Bone Architecture
,”
J. Biomech.
,
22
(
3
), pp.
231
244
.
3.
Huiskes
,
R.
,
Ruimerman
,
R.
,
van Lenthe
,
G. H.
, and
Janssen
,
J. D.
,
2000
, “
Effects of Mechanical Forces on Maintenance and Adaptation of Form in Trabecular Bone
,”
Nature
,
405
(
6787
), pp.
704
706
.
4.
Adachi
,
T.
,
Tsubota
,
K.
,
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
), p.
403
.
5.
Ruimerman
,
R.
,
Hilbers
,
P.
,
Van Rietbergen
,
B.
, and
Huiskes
,
R.
,
2005
, “
A Theoretical Framework for Strain-Related Trabecular Bone Maintenance and Adaptation
,”
J. Biomech.
,
38
(
4
), pp.
931
941
.
6.
Jang
,
I. G.
, and
Kim
,
I. Y.
,
2010
, “
Application of Design Space Optimization to Bone Remodeling Simulation of Trabecular Architecture in Human Proximal Femur for Higher Computational Efficiency
,”
Finite Elem. Anal. Des.
,
46
(
4
), pp.
311
319
.
7.
Jang
,
I. G.
, and
Kim
,
I. Y.
,
2010
, “
Computational Study on the Effect of Loading Alteration Caused by Disc Degeneration on the Trabecular Architecture in Human Lumbar Spine
,”
J. Biomech.
,
43
(
3
), pp.
492
499
.
8.
Schulte
,
F. A.
,
Lambers
,
F. M.
,
Webster
,
D. J.
,
Kuhn
,
G.
, and
Müller
,
R.
,
2011
, “
In Vivo Validation of a Computational Bone Adaptation Model Using Open-Loop Control and Time-Lapsed Micro-Computed Tomography
,”
Bone
,
49
(
6
), pp.
1166
1172
.
9.
Christen
,
P.
,
Ito
,
K.
,
dos Santos
,
A. A.
,
Müller
,
R.
, and
Bert
van Rietbergen
,
2013
, “
Validation of a Bone Loading Estimation Algorithm for Patient-Specific Bone Remodelling Simulations
,”
J. Biomech.
,
46
(
5
), pp.
941
948
.
10.
Levchuk
,
A.
,
Zwahlen
,
A.
,
Weigt
,
C.
,
Lambers
,
F. M.
,
Badilatti
,
S. D.
,
Schulte
,
F. A.
,
Kuhn
,
G.
, and
Müller
,
R.
,
2014
, “
The Clinical Biomechanics Award 2012—Presented by the European Society of Biomechanics: Large Scale Simulations of Trabecular Bone Adaptation to Loading and Treatment
,”
Clin. Biomech.
,
29
(
4
), pp.
355
362
.
11.
Christen
,
P.
,
Ito
,
K.
,
Müller
,
R.
,
Rubin
,
M. R.
,
Dempster
,
D. W.
,
Bilezikian
,
J. P.
, and
van Rietbergen
,
B.
,
2012
, “
Patient-Specific Bone Modelling and Remodelling Simulation of Hypoparathyroidism Based on Human Iliac Crest Biopsies
,”
J. Biomech.
,
45
(
14
), pp.
2411
2416
.
12.
Liu
,
X. S.
,
Huang
,
A. H.
,
Zhang
,
X. H.
,
Sajda
,
P.
,
Ji
,
B.
, and
Guo
,
X. E.
,
2008
, “
Dynamic Simulation of Three Dimensional Architectural and Mechanical Alterations in Human Trabecular Bone During Menopause
,”
Bone
,
43
(
2
), pp.
292
301
.
13.
Müller
,
R.
,
2005
, “
Long-Term Prediction of Three-Dimensional Bone Architecture in Simulations of Pre-, Peri- and Post-Menopausal Microstructural Bone Remodeling
,”
Osteoporos. Int.
,
16
(
S02
), pp.
S25
S35
.
14.
Wang
,
H.
,
Ji
,
B.
,
Liu
,
X. S.
,
Guo
,
X. E.
,
Huang
,
Y.
, and
Hwang
,
K.-C.
,
2012
, “
Analysis of Microstructural and Mechanical Alterations of Trabecular Bone in a Simulated Three-Dimensional Remodeling Process
,”
J. Biomech.
,
45
(
14
), pp.
2417
2425
.
15.
Tsubota
,
K. I.
,
Suzuki
,
Y.
,
Yamada
,
T.
,
Hojo
,
M.
,
Makinouchi
,
A.
, and
Adachi
,
T.
,
2009
, “
Computer Simulation of Trabecular Remodeling in Human Proximal Femur Using Large-Scale Voxel FE Models: Approach to Understanding Wolff's Law
,”
J. Biomech.
,
42
(
8
), pp.
1088
1094
.
16.
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
.
17.
Fischer
,
K. J.
,
Jacobs
,
C. R.
, and
Carter
,
D. R.
,
1995
, “
Computational Method for Determination of Bone and Joint Loads Using Bone Density Distributions
,”
J. Biomech.
,
28
(
9
), pp.
1127
1135
.
18.
Fischer
,
K. J.
,
Jacobs
,
C. R.
,
Levenston
,
M. E.
,
Cody
,
D. D.
, and
Carter
,
D. R.
,
1998
, “
Bone Load Estimation for the Proximal Femur Using Single Energy Quantitative CT Data
,”
Comput. Methods Biomech. Biomed. Engin.
,
1
(
3
), pp.
233
245
.
19.
Fischer
,
K. J.
,
Jacobs
,
C. R.
,
Levenston
,
M. E.
,
Cody
,
D. D.
, and
Carter
,
D. R.
,
1999
, “
Proximal Femoral Density Patterns are Consistent With Bicentric Joint Loads
,”
Comput. Methods Biomech. Biomed. Eng.
,
2
(
4
), pp.
271
283
.
20.
Fischer
,
K. J.
,
Eckstein
,
F.
, and
Becker
,
C.
,
1999
, “
Density-Based Load Estimation Predicts Altered Femoral Load Directions for Coxa Vara and Coxa Valga
,”
J. Musculoskelet. Res.
,
3
(
2
), pp.
83
92
.
21.
Christen
,
P.
,
Van Rietbergen
,
B.
,
Lambers
,
F. M.
,
Müller
,
R.
, and
Ito
,
K.
,
2012
, “
Bone Morphology Allows Estimation of Loading History in a Murine Model of Bone Adaptation
,”
Biomech. Model. Mechanobiol.
,
11
(
3–4
), pp.
483
492
.
22.
Christen
,
P.
,
Ito
,
K.
,
Knippels
,
I.
,
Müller
,
R.
,
van Lenthe
,
G. H.
, and
van Rietbergen
,
B.
,
2013
, “
Subject-Specific Bone Loading Estimation in the Human Distal Radius
,”
J. Biomech.
,
46
(
4
), pp.
759
766
.
23.
Campoli
,
G.
,
Weinans
,
H.
, and
Zadpoor
,
A. A.
,
2012
, “
Computational Load Estimation of the Femur
,”
J. Mech. Behav. Biomed. Mater.
,
10
, pp.
108
119
.
24.
Zadpoor
,
A. A.
,
Campoli
,
G.
, and
Weinans
,
H.
,
2013
, “
Neural Network Prediction of Load From the Morphology of Trabecular Bone
,”
Appl. Math. Model.
,
37
(
7
), pp.
5260
5276
.
25.
Zadpoor
,
A. A.
,
2013
, “
Open Forward and Inverse Problems in Theoretical Modeling of Bone Tissue Adaptation
,”
J. Mech. Behav. Biomed. Mater.
,
27
, pp.
249
261
.
26.
Bergmann
,
G.
,
Deuretzbacher
,
G.
,
Heller
,
M.
,
Graichen
,
F.
,
Rohlmann
,
A.
,
Strauss
,
J.
, and
Duda
,
G. N.
,
2001
, “
Hip Contact Forces and Gait Patterns From Routine Activities
,”
J. Biomech.
,
34
(
7
), pp.
859
871
.
27.
Lloyd
,
D. G.
, and
Besier
,
T. F.
,
2003
, “
An EMG-Driven Musculoskeletal Model to Estimate Muscle Forces and Knee Joint Moments In Vivo
,”
J. Biomech.
,
36
(
6
), pp.
765
776
.
28.
Jinha
,
A.
,
Ait-Haddou
,
R.
, and
Herzog
,
W.
,
2006
, “
Predictions of Co-Contraction Depend Critically on Degrees-of-Freedom in the Musculoskeletal Model
,”
J. Biomech.
,
39
(
6
), pp.
1145
1152
.
29.
Kim
,
H. J.
,
Fernandez
,
J. W.
,
Akbarshahi
,
M.
,
Walter
,
J. P.
,
Fregly
,
B. J.
, and
Pandy
,
M. G.
,
2009
, “
Evaluation of Predicted Knee-Joint Muscle Forces During Gait Using an Instrumented Knee Implant
,”
J. Orthop. Res.
,
27
(
10
), pp.
1326
1331
.
30.
Phillips
,
A. T. M.
,
Villette
,
C. C.
, and
Modenese
,
L.
,
2015
, “
Femoral Bone Mesoscale Structural Architecture Prediction Using Musculoskeletal and Finite Element Modelling
,”
Int. Biomech.
,
2
(
1
), pp.
43
61
.
31.
Cook
,
R. D.
,
Malkus
,
D. S.
,
Plesha
,
M. E.
, and
Witt
,
R. J. W.
,
2002
,
Concept and Applications of Finite Element Analysis
,
Wiley
,
New York
.
32.
Morgan
,
E. F.
,
Bayraktar
,
H. H.
, and
Keaveny
,
T. M.
,
2003
, “
Trabecular Bone Modulus–Density Relationships Depend on Anatomic Site
,”
J. Biomech.
,
36
(
7
), pp.
897
904
.
33.
Snyder
,
S. M.
, and
Schneider
,
E.
,
1991
, “
Estimation of Mechanical Properties of Cortical Bone by Computed Tomography
,”
J. Orthop. Res.
,
9
(
3
), pp.
422
431
.
34.
Heller
,
M. O.
,
Bergmann
,
G.
,
Kassi
,
J. P.
,
Claes
,
L.
,
Haas
,
N. P.
, and
Duda
,
G. N.
,
2005
, “
Determination of Muscle Loading at the Hip Joint for Use in Pre-Clinical Testing
,”
J. Biomech.
,
38
(
5
), pp.
1155
1163
.
35.
Verhulp
,
E.
,
van Rietbergen
,
B.
, and
Huiskes
,
R.
,
2008
, “
Load Distribution in the Healthy and Osteoporotic Human Proximal Femur During a Fall to the Side
,”
Bone
,
42
(
1
), pp.
30
35
.
36.
Adachi
,
T.
,
Osako
,
Y.
,
Tanaka
,
M.
,
Hojo
,
M.
, and
Hollister
,
S. J.
,
2006
, “
Framework for Optimal Design of Porous Scaffold Microstructure by Computational Simulation of Bone Regeneration
,”
Biomaterials
,
27
(
21
), pp.
3964
3972
.
37.
Shefelbine
,
S. J.
,
Augat
,
P.
,
Claes
,
L.
, and
Simon
,
U.
,
2005
, “
Trabecular Bone Fracture Healing Simulation With Finite Element Analysis and Fuzzy Logic
,”
J. Biomech.
,
38
(
12
), pp.
2440
2450
.
38.
Kim
,
J. J.
, and
Jang
,
I. G.
, “
Image Resolution Enhancement for Healthy Weight-Bearing Bones Based on Topology Optimization
,”
J. Biomech.
, (submitted).
39.
Magland
,
J. F.
,
Zhang
,
N.
,
Rajapakse
,
C. S.
, and
Wehrli
,
F. W.
,
2012
, “
Computationally-Optimized Bone Mechanical Modeling From High-Resolution Structural Images
,”
PLoS One
,
7
(
4
), p.
e35525
.
40.
Bruyneel
,
M.
, and
Duysinx
,
P.
,
2005
, “
Note on Topology Optimization of Continuum Structures Including Self-Weight
,”
Struct. Multidiscip. Optim.
,
29
(
4
), pp.
245
256
.
41.
Jang
,
I. G.
, and
Kim
,
I. Y.
,
2008
, “
Computational Study of Wolff's Law With Trabecular Architecture in the Human Proximal Femur Using Topology Optimization
,”
J. Biomech.
,
41
(
11
), pp.
2353
2361
.
42.
Beck
,
T. J.
,
Ruff
,
C. B.
,
Scott
,
W. W.
,
Plato
,
C. C.
,
Tobin
,
J. D.
, and
Quan
,
C. A.
,
1992
, “
Sex Differences in Geometry of the Femoral Neck With Aging: A Structural Analysis of Bone Mineral Data
,”
Calcif. Tissue Int.
,
50
(
1
), pp.
24
29
.
43.
Heller
,
M.
,
Bergmann
,
G.
,
Deuretzbacher
,
G.
,
Dürselen
,
L.
,
Pohl
,
M.
,
Claes
,
L.
,
Haas
,
N.
, and
Duda
,
G.
,
2001
, “
Musculo-Skeletal Loading Conditions at the Hip During Walking and Stair Climbing
,”
J. Biomech.
,
34
(
7
), pp.
883
893
.
44.
Stansfield
,
B. W.
,
Nicol
,
A. C.
,
Paul
,
J. P.
,
Kelly
,
I. G.
,
Graichen
,
F.
, and
Bergmann
,
G.
,
2003
, “
Direct Comparison of Calculated Hip Joint Contact Forces With Those Measured Using Instrumented Implants. An Evaluation of a Three-Dimensional Mathematical Model of the Lower Limb
,”
J. Biomech.
,
36
(
7
), pp.
929
936
.
45.
Martelli
,
S.
,
Taddei
,
F.
,
Cappello
,
A.
,
Van Sint Jan
,
S.
,
Leardini
,
A.
, and
Viceconti
,
M.
,
2011
, “
Effect of Sub-Optimal Neuromotor Control on the Hip Joint Load During Level Walking
,”
J. Biomech.
,
44
(
9
), pp.
1716
1721
.
46.
Modenese
,
L.
,
Gopalakrishnan
,
A.
, and
Phillips
,
A. T. M.
,
2013
, “
Application of a Falsification Strategy to a Musculoskeletal Model of the Lower Limb and Accuracy of the Predicted Hip Contact Force Vector
,”
J. Biomech.
,
46
(
6
), pp.
1193
1200
.
47.
Modenese
,
L.
,
Phillips
,
A. T. M.
, and
Bull
,
A. M. J.
,
2011
, “
An Open Source Lower Limb Model: Hip Joint Validation
,”
J. Biomech.
,
44
(
12
), pp.
2185
2193
.
48.
Zhao
,
C.
,
Hobbs
,
B. E.
,
Mühlhaus
,
H. B.
, and
Ord
,
A.
,
1999
, “
A Consistent Point-Searching Algorithm for Solution Interpolation in Unstructured Meshes Consisting of 4-Node Bilinear Quadrilateral Elements
,”
Int. J. Numer. Methods Eng.
,
45
(
10
), pp.
1509
1526
.
49.
Dohrmann
,
C. R.
,
Key
,
S. W.
, and
Heinstein
,
M. W.
,
2000
, “
A Method for Connecting Dissimilar Finite Element Meshes in Two Dimensions
,”
Int. J. Numer. Methods Eng.
,
48
(
5
), pp.
655
678
.
50.
Verhulp
,
E.
,
van Rietbergen
,
B.
, and
Huiskes
,
R.
,
2006
, “
Comparison of Micro-Level and Continuum-Level Voxel Models of the Proximal Femur
,”
J. Biomech.
,
39
(
16
), pp.
2951
2957
.
51.
Lee
,
Y. H.
,
Kim
,
Y.
,
Kim
,
J. J.
, and
Jang
,
I. G.
,
2015
, “
Homeostasis-Based Aging Model for Trabecular Changes and Its Correlation With Age-Matched Bone Mineral Densities and Radiographs
,”
Eur. J. Radiol.
,
84
(
11
), pp.
2261
2268
.
You do not currently have access to this content.