Control of a 3-D solid tumor model using optimal dynamic inversion

This paper deals with designing a feedback control strategy for drug release in treatment of solid tumors. The dynamical model comprises three coupled reaction diffusion equations governing the spatio-temporal dynamics of tumor cells, normal tissues and drug concentration. The control input is the rate of drug injection. By combining the merits of nonlinear dynamic inversion and variational optimization, a control law has been synthesized. This law ensures that the tumor follows an exponential decay while minimizing the spatial drug concentration in the tumor site. The proposed method exploits the structure of the cancer dynamics to formulate a hierarchical control strategy. First the drug concentration is taken to be a pseudo-control for the tumor and normal cell dynamics which is then controlled via the rate of drug injection. The drug injection is assumed to be spatially discrete with finitely many temporally varying actuators (catheters). Contrary to existing methods which assume spatially continuous actuation, the proposed approach is more realistic in cancer therapy. A 3-D brain tumor problem has been studied to demonstrate the effectiveness of the proposed control strategy.