Author: Young-Bin Cho, Jacob Scott, Nara Yoon 👨🔬
Affiliation: Adelphi University, Cleveland Clinic 🌍
Purpose: The immune system plays a critical role in determining cancer prognosis. Based on our prior study (Cho et al., 2023) about the bystander effect induced by immune responses in spatially designed radiation therapy, we investigate how immune suppression impacts tumor progression. Specifically, we aim to mathematically validate the findings of the prior study regarding the mode switch (bifurcation) from immune-limited to immune-escape states as immune suppression levels vary.
Methods: A simplified mathematical model considering only tumor and immune cell populations and their interactions is derived and was used to analyze bifurcations. The study employed the trace-determinant (TD) plane of a two-dimensional discrete model to track the stability of equilibria. Phase portraits were developed to depict equilibrium transitions as immune suppression (parameterized by k) changed, comparing scenarios of relatively weak and strong immune systems.
Results: The analysis identified the moments of bifurcation from stable (immune-limited) to unstable (immune-escape) states. When immune strength is robust, stability persists until immune suppression reaches critical bifurcation points, preventing early bifurcation. Conversely, weak immune strength leads to early bifurcation and premature immune escape. The mathematical framework explains the differing patterns of tumor growth under various immune conditions, and emphasizes the importance of personalized radiation therapy.
Conclusion: This study provides a theoretical explanation for immune-limited and immune-escape transitions influenced by immune suppression. The methodological framework enhances understanding of immune responses under different treatment scenarios, offering a foundation for optimizing therapeutic strategies, particularly comparing homogeneous and spatially fractionated radiotherapy.
Reference [1] Cho Y-B, Yoon N, Suh John, Scott J, Radio-immuno Response Modelling for SFRT, Phy. Med. Biol. 68 (2023):165010. https://doi.org/10.1088/1361-6560/ace819