Engineering Transactions, 64, 4, pp. 605–611, 2016

A New Model of Bone Remodelling

Cracow University of Technology

Cracow University of Technology

Cracow University of Technology

The objective of this paper is to propose a mathematical model of bone remodelling, including underload and overload resorption, equilibrium and bone grow states which can occur during healing process. A continuous function of bone density rate vs. mechanical stimulus is proposed. The created model is used to predict the stress-stimulated change in callus density. It is an extension of mathematical descriptions available in literature.
Keywords: bone remodelling; mandible; callus; mechanical stimulus
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Wolff J., The law of bone remodeling, Springer-Verlag, Berlin 1986.

Mellal A., Wiskott H.W.A, Botsis J., Scherrer S.S., Belser U.C., Stimulating effect of implant loading on surrounding bone. Comparison of three numerical models and validation by in vivo data, Clinical Oral Implant Research, 15(2): 239–248, 2004, doi: 10.1111/j.1600-0501.2004.01000.x.

Chou H-Y., Jagodnik J.J., Muftu S., Predictions of bone remodeling around dental implant system, Journal of Biomechanics, 41(6): 1365–1373, 2008, doi: 10.1016/j.jbiomech.2008.01.032.

Field C., Li Q., Li W., Thompson M., Swain M., A comparative mechanical and bone remodelling study of all-ceramic posterior inlay and onlay fixed partial dentures, Journal of Dentistry, 40(1): 48–56, 2012, doi: 10.1016/j.jdent.2011.10.003.

Lian Z.Q., Guan H., Loo Y.C., Optimum degree of bone-implant contact in bone remodelling induced by dental implant, Procedia Engineering, 14: 1972–2979, 2011, doi: 10.1016/j.proeng.2011.07.374.

Lin C-L., Lin Y-H., Chang S-H., Multi-factorial analysis of variables influencing the bone loss of an implant placed in the maxilla: Prediction using FEA and SED bone remodeling algorithm, Journal of Biomechanics, 43(4): 644–651, 2010, doi: 10.1016/j.jbiomech.2009.10.030.

Wang C., Fu G., Deng F., Difference of natural teeth and implant-supported restoration: A comparison of bone remodeling simulations, Journal of Dental Science, 10(2): 190–200, 2015, doi: 10.1016/j.jds.2014.11.001.

Wang C., Li Q., McClean C., Fan Y., Numerical simulation of dental bone remodeling induced by implant-supported fixed partial denture with or without cantilever extension, International Journal for Numerical Methods in Biomedical Engineering, 29(10): 1134–1147, 2013, DOI: 10.1002/cnm.2579.

Li J., et al., A mathematical model for simulating the bone remodeling process under mechanical stimulus, Dental Materials, 23(9): 1073–1078, 2007, doi: 10.1016/

Weinans H., Huiskes R., Grootenboer H.J., The behavior of adaptive bone-remodeling simulation models, Journal of Biomechanics, 25(12): 1425–1441, 1992, doi: 0.1016/0021-9290(92)90056-7.

Knets I., Vitins V., Cimdins R., Laizans J., Biomechanical behaviour of system bone-callus-implant, Proceedings of 10th Conference of the European Society of Biomechanics, J. Vander Sloten et al. (Ed.), p. 97, Leuven, August 28–31, 1996, 97.

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