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978-3-8439-0300-4, Reihe Mathematik
A Multiscale Approach to Cell Migration in Tissue Networks
112 Seiten, Dissertation Universität Stuttgart (2011), Softcover, A5
The migration of tumour cells through the surrounding tissue is a crucial step in the formation of metastatic tumours. The cells are influenced in their movement by the tissue but can also modify it when it impedes their migration. This interaction between the cells and their environment is mostly mediated through receptors on the cell surface called integrins. Starting from basic principles, a multiscale model is derived that allows to account for the integrin-mediated movement of cancer cells, the degradation of tissue fibers and the subsequent production of soluble tissue fragments whose concentration gradient then acts together with the distribution of tissue fibers as a directional cue for the cells.
Global existence and uniqueness is then proven for this new model which consists of a kinetic equation for the cell population density, an ODE for tissue fibers and a parabolic equation for digested fibers, all of them coupled via integral operators. Based on techniques from fluid dynamics, a new numerical scheme is designed and subsequently employed to investigate the behavior of the model for realistic tissue data.