Optimization of radiation therapy in a model for a heterogeneous population of tumor cells

In terms of the state-of-art data of clinical radiobiology a mathematical model of X-ray therapy is designed which includes two different subpopulations of cancer cells; The method of Lagrangeans leads to an analytical (in a simple case) and a numerical solution of the optimal treatment control problem. Optimal procedures of fractioning radiation are studied for various dynamics of tumor cell distribution. Possible applicalions of the modeling results are discussed.