BCG immunotherapy optimization on an isoperimetric optimal control problem for the treatment of superficial bladder cancer

Abstract

The Bacillus Calmette-Guerin immunotherapy (BCG) is a clinical procedure used as the treatment by success for superficial bladder cancer. However, the toxicity of BCG, its maintenance schedule, optimal amount of dosage sufficient for the destruction of cancerous cells and its efficiency remain all unclear due to the lack of published data. We serve in this paper the optimization of BCG treatment by seeking the optimal dose we inject in the bladder during the intravesical therapy for a hypothetical patient. We outline the different steps of resolution of an optimal control problem resolved using the Pontryagin’s maximum principle. The theoretical approach lead us to use the forward-backward sweep method and the secant-method as the appropriate numerical technique to solve a two-point boundary value problem with an isoperimetric constraint on the control process function representing the optimal concentration suggested to use in each instillation of BCG.