Design of Nonlinear Controller for Chemotherapeutic Drug in Leukemia Therapy

Abstract

Leukemia is a type of cancer that affects the white blood cells in the bone marrow. The basic cause of this disease is the inability of the bone marrow to produce healthy cells. Instead, abnormal white blood cells are being produced that are called leukocytes. The rate of production of these leukocytes is very high and eventually they leave the bone marrow and spill into the circulatory system. Chemotherapy is the most common treatment for Leukemia. It naturally kills the rapidly growing cells in the human body so normal or healthy cells are also killed along with leukemic or cancer cells. A mathematical model of Acute Leukemia is considered in this research. The effect of chemotherapeutic drug on normal and leukemic cells is represented by a therapy function that are of two types namely monotonic therapy and non-monotonic therapy. The monotonic therapy represents a direct relation ship with the therapeutic drug whereas non-monotonic therapy represents a relationship which increases in the beginning and reaches a maximum level at a point and then decreases after that point. The main objective of the thesis is to design a controller for the therapeutic agent in order to minimize the leukemic cells, maintain a safe amount of normal cells and ensure minimum amount of drug during the therapy process. Three nonlinear controllers have been designed for this purpose; 1) Backstepping Controller 2) Integral Backstepping Controller 3) Synergetic Controller. The nonlinear controllers use Lyapunov based stability theory to analyze the system’s asymptotic sta bility and convergence of the leukemic cells to their desired reference. The simulations have been performed in Matlab/Simulink and the results show that both the therapies are effective enough to reduce the leukemic cells to zero while a safe amount of normal cells has been retained using minimum amount of therapeutic agent.