Abstract
Key factors in the formation of cell aggregates in tissue engineering and other fields are the cell–cell and cell–matrix interactions. Other important factors are culture conditions such as nutrient and oxygen supply and the characteristics of the environment (medium versus hydrogel). As mathematical models are increasingly used to investigate biological phenomena, it is important that processes such as cell adhesion are adequately described in the models. Recently a technique was developed to incorporate cell–cell and cell–matrix adhesion in continuum models through the use of non-local terms. In this study we apply this technique to model adhesion in a cell-in-gel culture set-up often found in tissue engineering applications. We briefly describe the biological issues underlying this study and the various modelling techniques used to capture adhesive behaviour. We furthermore elaborate on the numerical techniques that were developed in the course of this study. Finally, we consider a tissue engineering model that describes the spatiotemporal evolution of the concentration of cells, matrix, hydrogel, matrix degrading enzymes and oxygen/nutrients in a cell-in-gel culture system. Sensitivity analyses indicate a clear influence of the different adhesive processes on the final cell and collagen density and distribution, demonstrating the significance of cell adhesion in tissue engineering and the potential of the proposed mathematical technique.
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Acknowledgments
L.G. is a postdoctoral research fellow of the Research Foundation Flanders (FWO). This work is part of Prometheus, the Leuven Research & Development Division of Skeletal Tissue Engineering of the Katholieke Universiteit Leuven: http://www.kuleuven.be/prometheus. A.G. gratefully acknowledges financial support by the Division of Mathematics, University of Dundee during a long-term visit in 2007 introducing him to the topic.
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Geris, L., Gerisch, A. (2010). Mathematical Modelling of Cell Adhesion in Tissue Engineering using Continuum Models. In: Gefen, A. (eds) Cellular and Biomolecular Mechanics and Mechanobiology. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/8415_2010_33
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DOI: https://doi.org/10.1007/8415_2010_33
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