PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy

Immunotherapy with Bacillus Calmette-Guérin (BCG)—an attenuated strain of Mycobacterium bovis (M. bovis) used for anti-tuberculosis immunization—is a clinically established procedure for the treatment of superficial bladder cancer. Bunimovich-Mendrazitsky et al. [16] studied the role of BCG immunotherapy in bladder cancer dynamics in a system of nonlinear ODEs. The purpose of this paper is to develop a first mathematical model that uses PDEs to describe tumor-immune interactions in the bladder as a result of BCG therapy considering the geometrical configuration of the human bladder. A mathematical analysis of the BCG as a PDE model identifies multiple equilibrium points, and their stability properties are identified so that treatment that has the potential to result in a tumor-free equilibrium can be determined. Estimating parameters and validating the model using published data are taken from in vitro, mouse, and human studies. The model makes clear that the intensity of immunotherapy must be kept within limited bounds. We use numerical analysis methods to find the solution of the PDE describing the tumor-immune interaction; in particular, analysis of the solution’s stability for given parameters is presented using Computer Vision methodologies.