Workshop on Pattern Formation and Functional Morphology, Wed, 09 Jan, 2008
Speaker: Mark Chaplain
Abstract
The ability of cancer cells to break out of tissue compartments and
invade locally gives solid tumours a defining deadly characteristic. The
first step of invasion is the over-expression by the cancer cells of
proteolytic enzymes, such as the urokinase-type plasminogen activator
(uPA) and matrix metalloproteinases (MMPs). Degradation of the matrix then
enables the cancer cells to migrate through the tissue and subsequently to
spread to secondary sites in the body (metastasis). In this talk we
present a mathematical model of cancer cell invasion of tissue
(extracellular matrix) which focuses on the role of the urokinase
plasminogen activation system. The model consists of a system of 5
reaction-diffusion-taxis partial differential equations describing the
interactions between cancer cells, urokinase plasminogen activator
(uPA), uPA inhibitors, plasmin and the host tissue. The spatio-temporal
dynamics of the uPA system is coupled to the cancer cells through
chemotaxis and haptotaxis. The results obtained from numerical
computations carried out on the model equations produce dynamic
heterogeneous spatio-temporal solutions and using linear stability
analysis we show that this is caused by a taxis-driven instability of a
spatially homogeneous steady-state. Finally we discuss the biological
implications of the model results and future development of the model.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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