Learning Model Parameter Dynamics in a Combination Therapy for Bladder Cancer from Sparse Biological Data

In a mathematical model of interacting biological organisms, where external interventions may alter behavior over time, traditional models that assume fixed parameters usually do not capture the evolving dynamics. In oncology, this is further exacerbated by the fact that experimental data are often sparse and sometimes are composed of a few time points of tumor volume. In this paper, we propose to learn time-varying interactions between cells, such as those of bladder cancer tumors and immune cells, and their response to a combination of anticancer treatments in a limited data scenario. We employ the physics-informed neural network (PINN) approach to predict possible subpopulation trajectories at time points where no observed data are available. We demonstrate that our approach is consistent with the biological explanation of subpopulation trajectories. Our method provides a framework for learning evolving interactions among biological organisms when external interventions are applied to their environment.