Developing precise computational models of bone remodeling can lead to more successful types of orthopedic treatments and deeper understanding of the phenomenon. Empirical evidence has shown that bone adaptation to mechanical loading is frequency dependent, and the modal behavior of bone under vibration can play a significant role in remodeling process, particularly in the resonance region. The objective of this study is to develop a bone remodeling algorithm that takes into account the effects of bone vibrational behavior. An extended/modified model is presented based on conventional finite element (FE) remodeling models. Frequency domain analysis is used to introduce appropriate correction coefficients to incorporate the effect of bone's frequency response (FR) into the model. The method is implemented on a bovine bone with known modal/vibration characteristics. The rate and locations of new bone formation depend on the loading frequency and are consistently correlated with the bone modal behavior. Results show that the proposed method can successfully integrate the bone vibration conditions and characteristics with the remodeling process. The results obtained support experimental observations in the literature.

References

References
1.
Beaupre
,
G. S.
,
Orr
,
T. E.
, and
Carter
,
D. R.
,
1990
, “
An Approach for Time Dependent Bone Modeling and Remodeling—Theoretical Development
,”
J. Orthop. Res.
,
8
(
5
), pp.
651
661
.
2.
Lerch
,
M.
,
Kurtz
,
A.
,
Stukenborg-Colsman
,
C.
,
Nolte
,
I.
,
Weigel
,
N.
,
Bouguecha
,
A.
, and
Behrens
,
B. A.
,
2012
, “
Bone Remodeling After Total Hip Arthroplasty With a Short Stemmed Metaphyseal Loading Implant: Finite Element Analysis Validated by a Prospective DEXA Investigation
,”
J. Orthop. Res.
,
30
(
11
), pp.
1822
1829
.
3.
Thompson
,
W. R.
,
Yen
,
S. S.
, and
Rubin
,
J.
,
2014
, “
Vibration Therapy: Clinical Applications in Bone
,”
Curr. Opin. Endocrinol. Diabetes Obes.
,
21
(
6
), pp.
447
453
.
4.
Ghiasi
,
M. S.
,
Chen
,
J.
,
Vaziri
,
A.
,
Rodriguez
,
E. K.
, and
Nazarian
,
A.
,
2017
, “
Bone Fracture Healing in Mechanobiological Modeling: A Review of Principles and Methods
,”
Bone Rep.
,
6
, pp.
87
100
.
5.
Cowin
,
S. C.
, and
Van Buskirk
,
W. C.
,
1979
, “
Surface Bone Remodeling Induced by a Medullary Pin
,”
J. Biomech.
,
12
(
4
), pp.
269
276
.
6.
Jang
,
I. G.
, and
Kim
,
I. Y.
,
2010
, “
Computational Simulation of Simultaneous Cortical and Trabecular Bone Change in Human Proximal Femur During Bone Remodeling
,”
J. Biomech.
,
43
(
2
), pp.
294
301
.
7.
Pettermann
,
H. E.
,
Reiter
,
T. J.
, and
Rammerstorfer
,
F. G.
,
1997
, “
Computational Simulation of Internal Bone Remodeling
,”
Arch. Comput. Methods Eng.
,
4
(
4
), pp.
295
323
.
8.
Pereira
,
A. F.
,
Javaheri
,
B.
,
Pitsillides
,
A. A.
, and
Shefelbine
,
S. J.
,
2015
, “
Predicting Cortical Bone Adaptation to Axial Loading in the Mouse Tibia
,”
J. R. Soc. Interface
,
12
(
110
), pp. 1–14.
9.
Oftadeh
,
R.
,
Perez-Viloria
,
M.
,
Villa-Camacho
,
J. C.
,
Vaziri
,
A.
, and
Nazarian
,
A.
,
2015
, “
Biomechanics and Mechanobiology of Trabecular Bone: A Review
,”
ASME J. Biomech. Eng.
,
137
(
1
), p.
10802
.
10.
Ozcivici
,
E.
,
Luu
,
Y. K.
,
Adler
,
B.
,
Qin
,
Y.-X.
,
Rubin
,
J.
,
Judex
,
S.
, and
Rubin
,
C. T.
,
2010
, “
Mechanical Signals as Anabolic Agents in Bone
,”
Nat. Rev. Rheumatol.
,
6
(
1
), pp.
50
59
.
11.
Frost
,
H. M.
,
1990
, “
Skeletal Structural Adaptations to Mechanical Usage (SATMU)—Part 1: Redefining Wolff's Law: The Bone Modeling Problem
,”
Anat. Rec.
,
226
(
4
), pp.
403
413
.
12.
Carter
,
D. R.
,
Fyhrie
,
D. P.
, and
Whalen
,
R. T.
,
1987
, “
Trabecular Bone Density and Loading History: Regulation of Connective Tissue Biology by Mechanical Energy
,”
J. Biomech.
,
20
(
8
), pp.
785
794
.
13.
Kourtis
,
L. C.
,
Carter
,
D. R.
,
Kesari
,
H.
, and
Beaupre
,
G. S.
,
2008
, “
A New Software Tool (VA-BATTS) to Calculate Bending, Axial, Torsional and Transverse Shear Stresses Within Bone Cross Sections Having Inhomogeneous Material Properties
,”
Comput. Methods Biomech. Biomed. Eng.
,
11
(
5
), pp.
463
476
.
14.
Marzban
,
A.
,
Canavan
,
P.
,
Warner
,
G.
,
Vaziri
,
A.
, and
Nayeb-Hashimi
,
H.
,
2012
, “
Parametric Investigation of Load-Induced Structure Remodeling in the Proximal Femur
,”
Proc. Inst. Mech. Eng. Part H: J. Eng. Med.
,
226
(
6
), pp.
450
460
.
15.
Huiskes
,
R.
,
Weinans
,
H.
,
Grootenboer
,
H. J.
,
Dalstra
,
M.
,
Fudala
,
B.
, and
Slooff
,
T. J.
,
1987
, “
Adaptive Bone-Remodeling Theory Applied to Prosthetic-Design Analysis
,”
J. Biomech.
,
20
(
11–12
), pp.
1135
1150
.
16.
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
.
17.
Coelho
,
P. G.
,
Rodrigues
,
H. C.
, and
Fernandes
,
P. R.
,
2008
, “
Bone Tissue Adaptation—A Hierarchical Approach for Apparent Density and Trabecular Structure
,”
J. Biomech.
,
41
(S1), p.
S125
.
18.
Sadegh
,
A. M.
,
Luo
,
G. M.
, and
Cowin
,
S. C.
,
1993
, “
Bone Ingrowth: An Application of the Boundary Element Method to Bone Remodeling at the Implant Interface
,”
J. Biomech.
,
26
(
2
), pp.
167
182
.
19.
Viceconti
,
M.
,
Ricci
,
S.
,
Pancanti
,
A.
, and
Cappello
,
A.
,
2004
, “
Numerical Model to Predict the Longterm Mechanical Stability of Cementless Orthopaedic Implants
,”
Med. Biol. Eng. Comput.
,
42
(
6
), pp.
747
753
.
20.
Hsieh
,
Y.
, and
Turner
,
C. H.
,
2001
, “
Effects of Loading Frequency on Mechanically Induced Bone Formation
,”
J. Bone Miner. Res.
,
16
(
5
), pp.
918
924
.
21.
Warden
,
S. J.
, and
Turner
,
C. H.
,
2004
, “
Mechanotransduction in the Cortical Bone Is Most Efficient at Loading Frequencies of 5–10 Hz
,”
Bone
,
34
(
2
), pp.
261
270
.
22.
Kameo
,
Y.
,
Adachi
,
T.
, and
Hojo
,
M.
,
2011
, “
Effects of Loading Frequency on the Functional Adaptation of Trabeculae Predicted by Bone Remodeling Simulation
,”
J. Mech. Behav. Biomed. Mater.
,
4
(
6
), pp.
900
908
.
23.
Tanaka
,
S. M.
,
Alam
,
I. M.
, and
Turner
,
C. H.
,
2003
, “
Stochastic Resonance in Osteogenic Response to Mechanical Loading
,”
Faseb J.
,
17
(
2
), pp.
313
314
.
24.
Zhao
,
L.
,
Dodge
,
T.
,
Nemani
,
A.
, and
Yokota
,
H.
,
2014
, “
Resonance in the Mouse Tibia as a Predictor of Frequencies and Locations of Loading-Induced Bone Formation
,”
Biomech. Model. Mechanobiol.
,
13
(
1
), pp.
141
151
.
25.
Zhang
,
P.
,
Tanaka
,
S. M.
,
Sun
,
Q.
,
Turner
,
C. H.
, and
Yokota
,
H.
,
2007
, “
Frequency-Dependent Enhancement of Bone Formation in Murine Tibiae and Femora With Knee Loading
,”
J. Bone Miner. Metab.
,
25
(
6
), pp.
383
391
.
26.
Han
,
Z. H.
,
Palnitkar
,
S.
,
Rao
,
D. S.
,
Nelson
,
D.
, and
Parfitt
,
M.
,
1997
, “
Effects of Ethnicity and Age or Menopause on the Remodeling and Turnover of Iliac Bone
,”
J. Bone Min. Res.
,
12
(
4
), pp.
498
508
.
27.
Fares
,
J. E.
,
Choucair
,
M.
,
Nabulsi
,
M.
,
Salamoun
,
M.
,
Shahine
,
C. H.
, and
Fuleihan
,
G. E. H.
,
2003
, “
Effect of Gender, Puberty, and Vitamin D Status on Biochemical Markers of Bone Remodedeling
,”
Bone
,
33
(
2
), pp.
242
247
.
28.
Weinans
,
H.
,
Huiskes
,
R.
, and
Grootenboer
,
H. J.
,
1992
, “
The Behavior of Adaptive Bone-Remodeling Simulation Models
,”
J. Biomech.
,
25
(
12
), pp.
1425
1441
.
29.
Moghaddam
,
A. O.
,
Mahjoob
,
M. J.
, and
Nazarian
,
A.
,
2016
, “
Assigning Material Properties to Finite Element Models of Bone: A New Approach Based on Dynamic Behavior
,” 7th International Conference on Computational Methods (
ICCM
), Berkeley, CA, Aug. 1–4, pp.
1
9
.http://www.sci-en-tech.com/ICCM2016/PDFs/1759-6308-1-PB.pdf
30.
Wagner
,
D. W.
,
Divringi
,
K.
,
Ozcan
,
C.
,
Grujicic
,
M.
,
Pandurangan
,
B.
, and
Grujicic
,
A.
,
2010
, “
Combined Musculoskeletal Dynamics/Structural Finite Element Analysis of Femur Physiological Loads During Walking
,”
Multidiscip. Model. Mater. Struct.
,
6
(
4
), pp.
417
437
.
31.
Erdemir
,
A.
,
McLean
,
S.
,
Herzog
,
W.
, and
van den Bogert
,
A. J.
,
2007
, “
Model-Based Estimation of Muscle Forces Exerted During Movements
,”
Clin. Biomech.
,
22
(
2
), pp.
131
154
.
32.
Turner
,
C. H.
, and
Robling
,
A. G.
,
2003
, “
Designing Exercise Regimens to Increase Bone Strength
,”
Exercise Sport Sci. Rev.
,
31
(
1
), pp.
45
50
.
33.
Zhang
,
P.
,
Malacinski
,
G. M.
, and
Yokota
,
H.
,
2008
, “
Joint Loading Modality: Its Application to Bone Formation and Fracture Healing
,”
Br. J. Sports Med.
,
42
(
7
), pp.
556
560
.
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