Prescheduling graphic displays for optimal cancer therapies to reveal possible tumor regression or stabilization

The paper describes an adaptive control approach to the problem of the treatment of solid tumors. The evolution with time t of the state of a tumor is modelled by a two-compartment system, governed by two differential equations forming an autonomous system under therapy control u, (formula; see text) where y1 and y2 are the number of proliferating and nonproliferating cells, respectively. The output is analyzed in the phase plane y1y2. The control problem is that of restricting the tumor state to a predetermined region of the plane by selecting a suitable change in therapy control u, e.g., modality and dosage, when the state solution intersects the boundary of this region and the ratio y1/y2 of proliferating to nonproliferating cells is displayed together with an elapsed time scale. Then, consequent selection of a suitable therapeutic sequence may be assisted by the use of a data base as part of an expert system. The process is repeated at each intersection of the prescribed boundary. Such sequences may lead to stabilization of the system through the appearance on a computer display screen of a stable equilibrium point or a limit cycle.