Stability and control of a class of compartmental systems with application to cell proliferation and cancer therapy

This paper concerns a systematic application of a variety of concepts and tools of control theory to the study of the stability and control of a class of compartmental systems arising in several application areas where population kinetics are of significant importance. To provide a focus to the development, the specific area of cell proliferation kinetics is selected for detailed study. A multicompartmental model which portrays the progression of a population of cells through the different phases of the ceil cycle is developed and a model reference adaptive algorithm for estimating model parameters is presented. An exponential stability framework is developed for quantifying the control effects of an administered drug protocol and is used to design efficient treatment strategies for cancer chemotherapy by application of optimization concepts. Since the toxic effects of anticancer drugs on the normal cell populations of the body are the bottlenecks in successful chemotherapy, determination of dosing strategies that minimize toxicity while maximizing the therapeutic effects are of great importance. A mathematical formulation of this problem leads to the optimization of bilinear systems under exponential stability constraints for which a solution procedure is presented.