Weighted scenario-based model predictive control for cancer treatment using a spatial evolutionary game framework

Tumor growth is governed by complex interactions among heterogeneous cancer cell populations that exhibit distinct behavioral phenotypes. Accurately modeling these dynamics is essential for designing effective and personalized treatment strategies. This work presents a mathematical model for simulating tumor growth and treatment response based on the probabilistic interactions between two types of cancer cells: proliferative and motile. The objective is to develop a predictive framework that serves as a first step in achieving therapy design tools that maintain treatment effectiveness under varying tumor behaviors and biological uncertainties.

Cancer cell dynamics are modeled as a spatial game on a dynamic graph, where nodes represent cells and links depict their interactions. A weighted scenario-based model predictive control (MPC) strategy is employed to determine the optimal treatment across multiple tumor growth scenarios under uncertainty, including a worst-case scenario representing a highly aggressive tumor. This controller is compared with an average-scenario predictive controller and a min-max approach, all of which aim to balance tumor suppression with treatment burden while ensuring robust performance.

Each controller was simulated 100 times, with all simulations starting from the same initial conditions. The average-scenario controller proved ineffective in constraining tumor growth, as the cancerous cell population increased from 1000 to 1796 at a significant cumulative cost of 5.54⋅10⁶. The min-max controller adopted an overly conservative control law, resulting in a final cell population of 69 and a cumulative cost of 1.38⋅10⁶. The proposed weighted scenario approach also substantially reduced the number of tumor cells, ranging from 72 to 88 depending on the scenario, while maintaining, even in its most conservative configuration, a lower cumulative cost of 1.29⋅10⁵.

Integrating spatial evolutionary game modeling with scenario-based model predictive control provides an in silico framework for comparing treatment strategies under uncertainty in tumor dynamics. The proposed weighted scenario-based MPC captures the interaction-driven dynamics of two fixed cancer cell phenotypes and provides a tunable trade-off between tumor reduction and treatment burden within the considered uncertainty scenarios. However, the model does not explicitly represent mutation, phenotypic switching, resistant clones, clinically defined tumor-burden thresholds, or pharmacokinetic/pharmacodynamic mechanisms. Therefore, the results should be interpreted as a methodological proof of concept within a simplified computational framework, rather than as evidence of clinical applicability.