Model predictive control for optimal treatment in a spatial cancer game

This work focuses on modeling tumorigenesis as a spatial evolutionary game and on finding optimal cancer treatment using a model predictive control approach. Extending a nonspatial cancer game from the literature into a spatial setting, we consider a solid tumor composed of cells of two different types: proliferative and motile. In our agent-based spatial game, cells represent vertices of an undirected dynamic graph where a link between any two cells indicates that these cells can interact with each other. A focal cell can reproduce only if it interacts with another cell, where the proliferation probabilities are given by the fitness matrix of the original nonspatial game. Without treatment, the cancer cells grow exponentially. Subsequently, we use nonlinear model predictive control to find an optimal time-varying treatment, with an objective representing a trade-off between minimization of the tumor mass and treatment toxicity. As for example androgen-deprivation treatment in metastatic castrate-resistant prostate cancer, this treatment is assumed to decrease the chances for interaction between the cancer cells and hereby decrease cells' proliferation rate. In case studies, we show that the optimal treatment often leads to a decrease of the tumor mass. This suggests that model predictive control has a high potential in designing cancer treatments.