SPARSITY
The main motivation
The proposal focuses on mathematical models to predict the radiation induced biological damage, with a specific emphasis on radiotherapy in cancer treatment. Recent groundbreaking discoveries highlight an unexpected effect, named in the community FLASH effect, where ultra-high dose rates spare healthy tissue while maintaining efficacy against tumors. Current mathematical models fall short in elucidating this phenomenon, believed to be connected to spatial ion interactions and nonlocal effects on cell populations. Consequently, there arises a necessity for an innovative mathematical approach to comprehend the underlying mechanism of the FLASH effect.
This project seeks to develop a comprehensive mathematical model that addresses the inherent stochasticity, different time scales, and explicit inclusion of cell population topology associated with the biological effect of radiation. Beyond shedding light on FLASH, the project aims to contribute to a broader understanding of radiation's biological effects. The resulting mathematical theory extends its applications beyond radiotherapy, encompassing various chemical and biological systems, including chemical reaction networks and compartmental models.
Operating at the intersection of stochastic analysis, mathematical biology, and radiotherapy, this project embraces a highly interdisciplinary approach.
Stochastic spatial reaction-diffusion system with heterogeneous interaction
This proposal centers on crafting a mathematical model for the dynamics of double-strand break (DSB) formation and repair in individual cells and entire cell populations, with a specific emphasis on applications in radiotherapy. The approach involves integrating stochastic chemical reaction networks, and stochastic reaction-diffusion equations to establish a versatile multiscale mathematical framework capturing the kinetics of an irradiated chemical and biological system.
The project focuses on investigating heterogenous cell population models and their continuum limit described as general stochastic processes on infinite network. The overarching goal is to develop a mathematical theory for stochastic particle-based reaction-diffusion systems with heterogeneous interactions, surpassing traditional mean-field scaling limits. These results will be instrumental in characterizing irradiated cell populations, accounting for non-local effects and heterogenous populations.
Stochastic model for radiotherapy
Our goal is to construct a comprehensive mathematical model for radiotherapy , leveraging advancements in mathematical modeling of cell populations. Specifically, we aim to create a robust model that sheds light on the FLASH effect, utilizing insights from particle-based graphon stochastic reaction-diffusion equations. This resulting model will capture inter-track effects of radiation and accommodate variations in tissue topologies. The graphon-based population model naturally integrates non-local effects influenced by the spatial distance between individual cells.
The project aims to develop a comprehensive mathematical model, simultaneously elucidating dynamics at both the individual cell and cell-population levels.