Un modelo de ecuaciones diferenciales parciales para el tratamiento de la leucemia

Abstract

This paper will discuss a mathematical model focused on the treatment of L1210 Leukemia and Burger's equation. In its development, descriptions of the growth rate, kinetic parameters on maturity and the effects of cell cycle specific therapy on tumor growth are taken; combined with simple pharmacokinetic models to complete the cell-drug interaction system justified by the conservation law. Simulations of cancer cell populations under treatment with cell cycle specific drugs (Ara-C) will be demostrated, arriving at the description of cell maturation and cell death by means of a partial differential equation. Then it was generalized by a quasilinear equation thought by varying the velocity of a particle. This corresponds to the rate of change of cell maturation. Considering Cauchy's method and varying the cell maturation, function; given its nature, a shock point is found where the entropy condition, the degree of molecular disorder of a system, occurs.