Howard A. Levine
Iowa State University
In this talk we present a mathematical model for the transformation of a tumor from the avascular state to the vascular state via angiogenesis as proposed by Folkman. The model combines the Michealis-Menten kinetic theory of protein transformation with the theory of reinforced random walks first introduced by Davis and exploited by many people to explain various problems in chemotaxis. We are led to a rather complex problem involving transport equations not only in the extra cellular matrix but also involving transport equations in the nearest capillary to which the former set is coupled.
We present some preliminary computations.1998-1999 Mathematics in Biology