0
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
<>
Copyright © 2014 by ASME
Topics: Bone , Simulation , Density
Your Session has timed out. Please sign back in to continue.

References

Eriksen, E., 2010, “Cellular Mechanisms of Bone Remodeling,” Rev. Endocr. Metab. Disord., 11(4), pp. 219–227. [CrossRef] [PubMed]
Firoozbakhsh, K., and Aleyaasin, M., 1989, “The Effect of Stress Concentration on Bone Remodeling: Theoretical Predictions,” ASME J. Biomech. Eng., 111(4), pp. 355–360. [CrossRef]
Cowin, S. C., Moss-Salentijn, L., and Moss, M. L., 1991, “Candidates for the Mechanosensory System in Bone,” ASME J. Biomech. Eng., 113(2), pp. 191–197. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
Beaupré, G. S., Orr, T. E., and Carter, D. R., 1990, “An Approach for Time-Dependent Bone Modeling and Remodeling—Application: A Preliminary Remodeling Simulation,” J. Orthop. Res., 8(5), pp. 662–670. [CrossRef] [PubMed]
Fernandes, P., Rodrigues, H., and Jacobs, C., 1999, “A Model of Bone Adaptation Using a Global Optimisation Criterion Based on the Trajectorial Theory of Wolff,” Comput. Methods Biomech. Biomed. Eng., 2(2), pp. 125–138. [CrossRef]
Coelho, P. G., Fernandes, P. R., Rodrigues, H. C., Cardoso, J. B., and Guedes, J. M., 2009, “Numerical Modeling of Bone Tissue Adaptation—A Hierarchical Approach for Bone Apparent Density and Trabecular Structure,” J. Biomech., 42(7), pp. 830–837. [CrossRef] [PubMed]
Andreaus, U., Colloca, M., and Iacoviello, D., 2012, “An Optimal Control Procedure for Bone Adaptation Under Mechanical Stimulus,” Control Eng. Pract., 20(6), pp. 575–583. [CrossRef]
Doblare, M., and Garcia, J. M., 2001, “Application of an Anisotropic Bone-Remodelling Model Based on a Damage-Repair Theory to the Analysis of the Proximal Femur Before and After Total Hip Replacement,” J. Biomech., 34(9), pp. 1157–1170. [CrossRef] [PubMed]
Hambli, R., 2010, “Application of Neural Networks and Finite Element Computation for Multiscale Simulation of Bone Remodeling,” ASME J. Biomech. Eng., 132(11), p. 114502. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
Komarova, S. V., 2006, “Bone Remodeling in Health and Disease: Lessons From Mathematical Modeling,” Ann. N.Y. Acad. Sci, 1068(1), pp. 557–559. [CrossRef] [PubMed]
Buenzli, P. R., Pivonka, P., Gardiner, B. S., and Smith, D. W., 2012, “Modelling the Anabolic Response of Bone Using a Cell Population Model,” J. Theor. Biol., 307, pp. 42–52. [CrossRef] [PubMed]
Pivonka, P., Buenzli, P. R., Scheiner, S., Hellmich, C., and Dunstan, C. R., 2013, “The Influence of Bone Surface Availability in Bone Remodeling—A Mathematical Model Including Coupled Geometrical and Biomechanical Regulations of Bone Cells,” Eng. Struct., 47, pp. 134–147. [CrossRef]
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. [CrossRef] [PubMed]
van Rietbergen, B., Huiskes, R., Eckstein, F., and Rüegsegger, P., 2003, “Trabecular Bone Tissue Strains in the Healthy and Osteoporotic Human Femur,” J. Bone Miner. Res., 18(10), pp. 1781–1788. [CrossRef] [PubMed]
Martin, R. B., 1984, “Porosity and Specific Surface of Bone,” Crit. Rev. Biomed. Eng., 10(3), pp. 179–222. [PubMed]
Currey, J. D., 1988, “The Effect of Porosity and Mineral Content on the Young's Modulus of Elasticity of Compact Bone,” J. Biomech., 21(2), pp. 131–139. [CrossRef] [PubMed]
Burger, E. H., and Klein-Nulend, J., 1999, “Mechanotransduction in Bone-Role of the Lacuno-Canalicular Network,” FASEB J., 13(9001), pp. S101–S112. [PubMed]
Martin, R. B., 2000, “Toward a Unifying Theory of Bone Remodeling,” Bone, 26(1), pp. 1–6. [CrossRef] [PubMed]
Fazzalari, N. L., Kuliwaba, J. S., and Forwood, M. R., 2002, “Cancellous Bone Microdamage in the Proximal Femur: Influence of Age and Osteoarthritis on Damage Morphology and Regional Distribution,” Bone, 31(6), pp. 697–702. [CrossRef] [PubMed]
Eriksen, E. F., and Kassem, M., 1992, “The Cellular Basis of Bone Remodeling,” Triangle, 31(2), pp. 45–57.
Mullender, M. G., Huiskes, R., Versleyen, H., and Buma, P., 1996, “Osteocyte Density and Histomorphometric Parameters in Cancellous Bone of the Proximal Femur in Five Mammalian Species,” J. Orthop. Res., 14(6), pp. 972–979. [CrossRef] [PubMed]
Garnero, P., Sornay-Rendu, E., Chapuy, M.-C., and Delmas, P. D., 1996, “Increased Bone Turnover in Late Postmenopausal Women is a Major Determinant of Osteoporosis,” J. Bone Miner. Res., 11(3), pp. 337–349. [CrossRef] [PubMed]
Rubin, M. R., Dempster, D. W., Kohler, T., Stauber, M., Zhou, H., Shane, E., Nickolas, T., Stein, E., Sliney, J., Jr., Silverberg, S. J., Bilezikian, J. P., and Muller, R., 2010, “Three Dimensional Cancellous Bone Structure in Hypoparathyroidism,” Bone, 46, pp. 190–195. [CrossRef] [PubMed]
Recker, R. R., Lappe, J. M., Davies, K. M., and Kimmel, D. B., 1992, “Change in Bone Mass Immediately Before Menopause,” J. Bone Miner. Res., 7(8), pp. 857–862. [CrossRef] [PubMed]
Morita, M., Ebihara, A., Itoman, M., and Sasada, T., 1994, “Progression of Osteoporosis in Cancellous Bone Depending on Trabecular Structure,” Ann. Biomed. Eng., 22(5), pp. 532–539. [CrossRef] [PubMed]
Li, X. J., Jee, W. S. S., Chow, S.-Y., and Woodbury, D. M., 1990, “Adaptation of Cancellous Bone to Aging and Immobilization in the Rat: A Single Photon Absorptiometry and Histomorphometry Study,” Anat. Rec., 227(1), pp. 12–24. [CrossRef] [PubMed]
Fyhrie, D. P., and Schaffler, M. B., 1995, “The Adaptation of Bone Apparent Density to Applied Load,” J. Biomech., 28(2), pp. 135–146. [CrossRef] [PubMed]
Parfitt, A. M., 1994, “Osteonal and Hemi-Osteonal Remodeling: The Spatial and Temporal Framework for Signal Traffic in Adult Human Bone,” J. Cell. Biochem., 55(3), pp. 273–286. [CrossRef] [PubMed]
Colloca, M., van Rietbergen, B., Blanchard, R., Hellmich, C., and Ito, K., 2012, “From Cell Level to Organ Level: A Multiscale Approach for Bone Remodeling Simulation,” J. Biomech., 45, p. S470. [CrossRef]
Vuong, J., and Hellmich, C., 2011, “Bone Fibrillogenesis and Mineralisation: Quantitative Analysis and Implications for Tissue Elasticity,” J. Theor. Biol., 287, pp. 115–130. [CrossRef] [PubMed]
Malandrino, A., Fritsch, A., Lahayne, O., Kropik, K., Redl, H., Noailly, J. R. M., Lacroix, D., and Hellmich, C., 2012, “Anisotropic Tissue Elasticity in Human Lumbar Vertebra, by Means of a Coupled Ultrasound-Micromechanics Approach,” Mater. Lett., 78, pp. 154–158. [CrossRef]
Mulder, L., van Rietbergen, B., Noordhoek, N. J., and Ito, K., 2012,”Determination of Vertebral and Femoral Trabecular Morphology and Stiffness Using a Flat-Panel C-Arm-Based CT Approach,“Bone, 50(1), pp. 200–208. [CrossRef] [PubMed]
Rauch, F., Plotkin, H., Zeitlin, L., and Glorieux, F. H., 2003, “Bone Mass, Size, and Density in Children and Adolescents With Osteogenesis Imperfecta: Effect of Intravenous Pamidronate Therapy,” J. Bone Miner. Res., 18(4), pp. 610–614. [CrossRef] [PubMed]
Glorieux, F. H., Bishop, N. J., Plotkin, H., Chabot, G., Lanoue, G., and Travers, R., 1998, “Cyclic Administration of Pamidronate in Children With Severe Osteogenesis Imperfect,” New Engl. J. Med., 339(14), pp. 947–952. [CrossRef]
Boivin, G. Y., Chavassieux, P. M., Santora, A. C., Yates, J., and Meunier, P. J., 2000, “Alendronate Increases Bone Strength by Increasing the Mean Degree of Mineralization of Bone Tissue in Osteoporotic Women,” Bone, 27(5), pp. 687–694. [CrossRef] [PubMed]
Weinstein, R. S., Nicholas, R. W., Manolagas, S. C., 2000, “Apoptosis of Osteocytes in Glucocorticoid-Induced Osteonecrosis of the Hip,” J. Clin. Endocrinol. Metab., 85(8), pp. 2907–2912. [CrossRef] [PubMed]
Lin, B. Y., Jee, W. S. S., Ma, Y. F., Ke, H. Z., Kimmel, D. B., and Li, X. J.,1994, “Effects of Prostaglandin E2 and Risedronate Administration on Cancellous Bone in Older Female Rats,” Bone, 15(5), pp. 489–496. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 3

Three-dimensional initial bone microstructure

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
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)

Grahic Jump Location
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)

Grahic Jump Location
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)

Grahic Jump Location
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)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In