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Mathematical Medicine and Biology Advance Access originally published online on July 6, 2009
Mathematical Medicine and Biology 2009 26(3):241-262; doi:10.1093/imammb/dqp013
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A continuum model for the development of tissue-engineered cartilage around a chondrocyte

Abbey J. Trewenack

Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia

Colin P. Please

Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, UK

Kerry A. Landman{dagger}

Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia

{dagger} Email: k.landman{at}ms.unimelb.edu.au

Received on September 29, 2008. Revised on February 19, 2009. Accepted on May 7, 2009.

The limited ability of cartilage to repair when damaged has led to the investigation of tissue engineering as a method for reconstructing cartilage. We propose a continuum multispecies model for the development of cartilage around a single chondrocyte. As in healthy cartilage, the model predicts a balance between synthesis, transport, binding and decay of matrix components. Two mechanisms are investigated for the transport of soluble matrix components: diffusion and advection, caused by displacement of the scaffold medium. Numerical results indicate that a parameter defined by the ratio of the flux of soluble components out of the chondrocyte and its diffusive flux determines which of these mechanisms is dominant. We investigate the diffusion-dominated and advection-dominated limiting cases using perturbation analysis. Using parameter values from the literature, our modelling results suggest that both diffusion and advection are significant mechanisms in developing cartilage. Moreover, in this parameter regime, results are particularly sensitive to parameter values. These two observations could explain differences observed experimentally between various scaffold media. Modelling results are also used to predict the minimum chondrocyte seeding density required to produce functional cartilage.

Keywords: tissue engineering; cartilage; advection; chondrocyte; diffusion


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