Koopman-based Impulsive Model Predictive Control of BCG Immunotherapy

Bacillus of Calmette and Guerin (BCG) is the most effective immunologic treatment for non-muscle-invasive bladder cancer by stimulating the immune response of patients. The therapeutic performance of BCG treatment is limited by the dosing scheme, which is difficult to design due to nonlinear dynamics and constraints in the pharmacodynamic model. Here we present a computational method that combines linearization, impulsive control, and constrained optimization to design optimal drug dosing. We do so by first adopting Koopman theory to map the nonlinear pharmacodynamic model into linear space. Then we use model predictive control to design drug dosing schemes based on the transformed linear model with impulsive drug instillation, constrained by drug concentration. With this pipeline, we find that the Koopman-based linear system has almost identical dynamic behaviors to the original model based on numerical simulations. Also, the designed drug doses stay within the constraints and cancerous cell proliferation is effectively suppressed by driving the uninfected tumor cell population to a descending reference trajectory. Robustness tests are performed to show the proposed controller is robust to a certain level of model uncertainty. The method is expected to be generalized to the design of other model-based drug dosing schemes because of its optimality, impulsivity, and linearity.