Mathematical Modeling of Immuno-Radiotherapy Treatments
Abstract
Purpose
This study aims to develop a mathematical model to understand the dynamics of immunotherapy and radiotherapy interactions for non-small cell lung cancer (NSCLC), focusing on how tumor and immune cells interact under the effects of radiation and immune checkpoint inhibitors (ICIs). The model is embedded in an uncertainty-aware optimization framework to compute the optimal scheduling strategy for immuno-radiotherapy (IRT) treatments.
Methods
A compartmental model is constructed using a system of stochastic ordinary differential equations (ODEs) to capture the population dynamics of primary and metastatic tumor cells and their interactions with naive and activated T cells. The model incorporates the cytotoxic effects of radiotherapy and the immune-modulatory influence of ICIs to simulate how these treatments jointly shape cell population trajectories over time. The proposed compartmental model is calibrated using parameter values obtained from the literature for stage III NSCLC and further refined to reproduce the Kaplan-Meier survival curves reported in relevant clinical trials. The calibrated model is integrated into a surrogate optimization framework to identify the timing and sequencing of radiotherapy and ICI therapy.
Results
Proof-of-concept results are obtained to demonstrate the feasibility of the proposed framework for uresectable locally advanced NSCLC. In particular, results are obtained by solving the calibrated ODE system for both an average patient and a virtual patient cohort. Additionally, optimal IRT treatment schedules calculated for this disease site favor adjuvant ICI therapy with a moderate gap in between treatments.
Conclusion
In this study, we develop an IRT treatment optimization framework to generate treatment regimens that are promising not just for a single nominal patient, but across a biologically plausible patient population. The proposed framework supports the design of new clinical trials by generating hypotheses about promising treatment schedules and highlighting those regimens that merit further preclinical or clinical evaluation.