Manchester Applied Mathematics and Numerical Analysis Seminars

Spring 1999

July 14, 1999, 3.00 pm

Room OF/B9 in Oddfellows Hall

Mathematical Modeling of Capillary Formation and Development in Tumor Angiogenesis

Prof. Howard A Levine, Iowa State University

The purpose of this paper is to present a mathematical model based on Judah Folkman's tumor vascularization theory of tumor growth. In the simplest version of this model, an avascular tumor sends emits a tumor growth factor, (TAF) which is transported across an extracellular matrix (ECM) to the nearest capillary where it stimulates endothelial cells to produce a protease which acts as a catalyst to degrade the fibronectin of the capillary wall and the ECM. The endothelial cells then follow the trail of TAF back to the tumor, proliferating and forming a new capillary wall as they go.

In the model we present here, we also include a simple mechanism for the action of angiostatin. In this mechanism, angiostatin is presumed to stimulate endothelial cells to produce a protease inhibitor which, in its turn, binds to molecules of protease, interfering with their catalytic properties.

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For further info contact either Matthias Heil (, Mark Muldoon ( the seminar secretary (Tel. 0161 275 5800).

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