eCM (Eur Cell Mater / e Cells & Materials) Not-for-profit Open Access
Created by Scientists, for Scientists
 ISSN:1473-2262         NLM:100973416 (link)         DOI:10.22203/eCM

2011   Volume No 22 – pages 377-392

Title: Mathematical modelling of tissue formation in chondrocyte filter cultures

Author: CJ Catt, W Schuurman, BG Sengers, PR van Weeren, WJA Dhert, CP Please, J Malda

Address: Department of Orthopaedics, University Medical Centre Utrecht, PO Box 85500, Utrecht 3508 GA, The Netherlands

E-mail: j.malda at

Key Words: Cartilage, tissue engineering, mathematical modelling, filter culture.

Publication date: December 17th 2011

Abstract: In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

Article download: Pages 377-392 (PDF file)
DOI: 10.22203/eCM.v022a28