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Research Papers

An Analytical Approach to Investigate the Evolution of Bone Volume Fraction in Bone Remodeling Simulation at the Tissue and Cell Level

[+] Author and Article Information
Michele Colloca

Department of Biomedical Engineering,
Orthopaedic Biomechanics,
Eindhoven University of Technology,
P.O. Box 513,
Eindhoven 5600 MB, The Netherlands
e-mail: m.colloca@tue.nl

Keita Ito

Department of Biomedical Engineering,
Orthopaedic Biomechanics,
Eindhoven University of Technology,
P.O. Box 513,
Eindhoven 5600 MB, The Netherlands
e-mail: k.ito@tue.nl

Bert van Rietbergen

Department of Biomedical Engineering,
Orthopaedic Biomechanics,
Eindhoven University of Technology,
P.O. Box 513,
Eindhoven 5600 MB, The Netherlands
e-mail: b.v.rietbergen@tue.nl

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received May 2, 2013; final manuscript received November 21, 2013; accepted manuscript posted December 12, 2013; published online February 13, 2014. Assoc. Editor: Guy M. Genin.

J Biomech Eng 136(3), 031004 (Feb 13, 2014) (8 pages) Paper No: BIO-13-1213; doi: 10.1115/1.4026227 History: Received May 02, 2013; Revised November 21, 2013; Accepted December 12, 2013

Simulation of bone remodeling at the bone cell level can predict changes in bone microarchitecture and density due to bone diseases and drug treatment. Their clinical application, however, is limited since bone microarchitecture can only be measured in the peripheral skeleton of patients and since the simulations are very time consuming. To overcome these issues, we have developed an analytical model to predict bone density adaptation at the organ level, in agreement with our earlier developed bone remodeling theory at the cellular level. Assuming a generalized geometrical model at the microlevel, the original theory was reformulated into an analytical equation that describes the evolution of bone density as a function of parameters that describe cell activity, mechanotransduction and mechanical loading. It was found that this analytical model can predict changes in bone density due to changes in these cell-level parameters that are in good agreement with those predicted by the earlier numerical model that implemented a detailed micro-finite element (FE) model to represent the bone architecture and loading, at only a fraction of the computational costs. The good agreement between analytical and numerical density evolutions indicates that the analytical model presented in this study can predict well bone functional adaptation and, eventually, provide an efficient tool for simulating patient-specific bone remodeling and for better prognosis of bone fracture risk.

FIGURES IN THIS ARTICLE
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Copyright © 2014 by ASME
Topics: Bone , Simulation , Density
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References

Figures

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Fig. 1

Definition of linear apposition and resorption rates in the new formulation of the bone remodeling theory

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Fig. 2

Original discontinuous (a) and continuous (b) equations for the osteoblast (OBL) and osteoclast (OCL) activities in the new formulation of the bone remodeling theory

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Fig. 3

Three-dimensional initial bone microstructure

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Fig. 4

Evolution of bone volume fraction (b) starting from a bone regular grid (a) and final bone adapted microstructure (c)

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Fig. 5

Evolution of bone volume fraction and adaptation of the bone microstructure when increasing loading magnitude (σx, σy, σz) by 200% (a) and decreasing by 50% (b)

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Fig. 6

Evolution of bone volume fraction and adaptation of the bone microstructure when the osteoclast activation frequency (focl) is increased by a factor of 10 (a) and decreasing by a factor of 10 (b)

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Fig. 7

Evolution of bone volume fraction and adaptation of the bone microstructure when increasing bone formation rate (τ) by a factor of 10 (a) and decreasing by a factor of 10 (b)

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Fig. 8

Evolution of bone volume fraction and adaptation of the bone microstructure when osteocyte mechanosensitivity (μ) is increased by 200% (a) and decreased by 50% (b)

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