Modeling and Control of Tumor Growth

The effects of radiotherapy (as well as those of chemotherapy [7]) on the growth of solid tumors, while the subject of intensive experimental and clinical research in recent years, involve as yet unidentified and poorly understood biophysical mechanisms. Thus the choice of “best” therapy programs is a matter which involves great difficulties. To this date no one has proposed a cellular kinetic model that has gained wide acceptance. However, there have been numerous attempts at deriving mathematical models for tumor growth and general cell population kinetics (e.g., see the surveys [7,49,172] and their bibliographies). We shall present here a partial review (this is certainly not an exhaustive survey) of some of these mathematical models along with an account of recent efforts in this area which involve the use of control theory.