The Mathematical Institute, University of Oxford, Eprints Archive

A Mathematical Model of Liver Cell Aggregation In Vitro

Green, J E F and Waters, S. L. and Shakesheff, K M and Byrne, H. M. (2009) A Mathematical Model of Liver Cell Aggregation In Vitro. Bulletin of Mathematical Biology .



The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:909
Deposited By: Ruth Preston
Deposited On:25 Mar 2010 14:50
Last Modified:29 May 2015 18:35

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