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Research Papers

Bone Remodeling Under Vibration: A Computational Model of Bone Remodeling Incorporating the Modal Behavior of Bone

[+] Author and Article Information
A. Ostadi Moghaddam

School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 11155-4563, Iran

M. J. Mahjoob

School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 11155-4563, Iran;
Center for Advance Orthopedic Studies,
BID Medical Center,
Harvard Medical School,
Boston, MA 02215
e-mail: mmahjoob@bidmc.harvard.edu

A. Nazarian

Center for Advance Orthopedic Studies,
BID Medical Center,
Harvard Medical School,
Boston, MA 02215

1Corresponding author.

Manuscript received November 8, 2017; final manuscript received June 1, 2018; published online September 25, 2018. Assoc. Editor: James C. Iatridis.

J Biomech Eng 140(12), 121003 (Sep 25, 2018) (8 pages) Paper No: BIO-17-1511; doi: 10.1115/1.4040602 History: Received November 08, 2017; Revised June 01, 2018

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.

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Copyright © 2018 by ASME
Topics: Bone , Vibration , Density
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Figures

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Fig. 1

Schematic diagram of remodeling equations

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Fig. 6

Displacement distribution corresponding to first five natural frequencies of the bone sample: (a) 130 Hz, (b) 158 Hz, (c) 735 Hz, (d) 816 Hz, and (e) 953 Hz

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Fig. 7

Final density distribution of bone after 24 remodeling steps, for different loding frequencies

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Fig. 2

Sample CT images of bovine femur

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Fig. 3

Evenly distributed reference points in the FE model of femur

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Fig. 4

(a) Loading and boundary conditions and (b) finite element mesh

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Fig. 5

Flowchart of remodeling algorithm

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Fig. 8

Final density distribution throughout the bone section at 33% and 66% of femur's length, for applied loading frequencies of 100, 200, 800, and 1000 Hz

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Fig. 9

(a) Average and maximum bone density versus loading frequency, (b) average and maximum bone elasticity versus loading frequency, (c) average and FR coefficient versus loading frequency. Dotted lines show the resonance frequencies.

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