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Mathematical modelling of tissue formation in chondrocyte filter cultures

Mathematical modelling of tissue formation in chondrocyte filter cultures
Mathematical modelling of tissue formation in chondrocyte filter cultures
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.
cartilage, tissue engineering, mathematical modelling, filter culture
377-392
Catt, C.J.
1cb6cc43-4bed-4dbf-aea8-95ad9677af7a
Schuurman, W.
4abb8255-753f-4f34-aa89-467d25709551
Sengers, B.G.
d6b771b1-4ede-48c5-9644-fa86503941aa
van Weeren, P.R.
644649ac-6958-426a-855e-d83bcd9b3fc4
Dhert, W.J.A.
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Please, C.P.
118dffe7-4b38-4787-a972-9feec535839e
Malda, J.
90c2ebf4-fb4b-4d69-8431-9e227018058f
Catt, C.J.
1cb6cc43-4bed-4dbf-aea8-95ad9677af7a
Schuurman, W.
4abb8255-753f-4f34-aa89-467d25709551
Sengers, B.G.
d6b771b1-4ede-48c5-9644-fa86503941aa
van Weeren, P.R.
644649ac-6958-426a-855e-d83bcd9b3fc4
Dhert, W.J.A.
53cc6982-5415-4243-9215-435ac1f9ad28
Please, C.P.
118dffe7-4b38-4787-a972-9feec535839e
Malda, J.
90c2ebf4-fb4b-4d69-8431-9e227018058f

Catt, C.J., Schuurman, W., Sengers, B.G., van Weeren, P.R., Dhert, W.J.A., Please, C.P. and Malda, J. (2011) Mathematical modelling of tissue formation in chondrocyte filter cultures. European Cells & Materials, 22, 377-392. (PMID:22179936)

Record type: Article

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.

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More information

Published date: 2011
Keywords: cartilage, tissue engineering, mathematical modelling, filter culture
Organisations: Mathematical Sciences, Faculty of Engineering and the Environment

Identifiers

Local EPrints ID: 334352
URI: https://eprints.soton.ac.uk/id/eprint/334352
PURE UUID: c9728b79-78f5-4796-bfad-e8f7a4d1d572
ORCID for B.G. Sengers: ORCID iD orcid.org/0000-0001-5859-6984

Catalogue record

Date deposited: 08 Mar 2012 10:26
Last modified: 06 Jun 2018 12:40

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Contributors

Author: C.J. Catt
Author: W. Schuurman
Author: B.G. Sengers ORCID iD
Author: P.R. van Weeren
Author: W.J.A. Dhert
Author: C.P. Please
Author: J. Malda

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