Lyashko N. Mathematical models of pharmacological correction of functional state of an organism and their analysis.

The mathematical model of pharmacological antihypoxic agent transport in structures of respiratory system, blood circulatory system and tissues is developed. Its influence on compensation of hypoxic states is investigated. The Tzafriri's model of convection-diffusion of chemotherapeutic agent in malignant tumor is reduced to the pseudo-hyperbolical equation. The optimal control problem connected with distribution of an agent in a tumor in order to reach desirable and acceptable average concentration is formulated. The conditions of existence of generalized solutions of differential pseudo-parabolical equations describing the distribution of agent concentration in a tumor are founded. The regularization of the model of state determination and optimal control problem which is necessary to provide the correctness of the model under impulse disturbance of the system state is implemented. The iterative algorithms for solving regularized optimal control problem for distribution of drugs in tumor are developed.