Modeling Medicine Propagation in Tissue: Generalized Statement

Abstract

A new generalized model of propagation of a medicine in tissue is considered. Instead of the traditional diffusion model described by a parabolic equation, the model described by a more general hyperbolic equation is postulated, which predicts finite velocity of disturbance propagation. As a result, the medicine is delivered to the invaded tissue with a finite velocity. The first disturbance (precursor) carries information from the injection to any point in the tissue and, what is important, to the affected zone, wherefrom information arrives at the brain in the form of neurological disorder. The generalized solution of the problem is considered. A brief generalization of the Bellman problem is given concerning the injection of medicine with respect to the time of injection.