PDE based geometry model for BCG immunotherapy of bladder cancer

Abstract

BCG immunotherapy has shown significant success for bladder cancer treatment, but due to the complexity of the interaction between immunity and cancer, clinical outcomes vary significantly between patients. A possible approach to overcome this difficulty may be to develop new methodologies for personally predicting the results of therapy by integrating patient data with dynamic mathematical model. We present a model describing a BCG immunotherapy dynamic taking into consideration an approximation of the bladder's geometry using PDE. We show that the proposed model takes into account the initial distribution of the cancer cells in the geometry of the bladder and as such can provide more customized treatment by providing tumor polyp depth in the urothelium. In addition, time optimal treatment protocol for the average case and recover-rate optimal, personalized treatment protocol based on initial tumor distribution have been analyzed.

Keywords: Multiple geometrical PDE systems Dynamics; Nonlinear systems; PDE cancer Treatment model.