# Investigating the influence of growth arrest mechanisms on tumour responses to radiotherapy

## TL;DR

This study models how different growth arrest mechanisms in tumors influence their responses to radiotherapy, revealing that tumors limited by space respond best, while bistable tumors respond worst, guiding personalized treatment strategies.

## Contribution

It extends an existing tumor growth model to include two growth arrest mechanisms and analyzes their impact on radiotherapy effectiveness across different regimes.

## Key findings

- Tumors in the space-limited regime respond best to radiotherapy.
- Bistable regime tumors respond worst to radiotherapy.
- Optimal dosing regimens vary depending on the growth arrest mechanism.

## Abstract

Cancer is a heterogeneous disease and tumours of the same type can differ greatly at the genetic and phenotypic levels. Understanding how these differences impact sensitivity to treatment is an essential step towards patient-specific treatment design. In this paper, we investigate how two different mechanisms for growth control may affect tumour cell responses to fractionated radiotherapy (RT) by extending an existing ordinary differential equation model of tumour growth. In the absence of treatment, this model distinguishes between growth arrest due to nutrient insufficiency and competition for space and exhibits three growth regimes: nutrient-limited (NL), space limited (SL) and bistable (BS), where both mechanisms for growth arrest coexist. We study the effect of RT for tumours in each regime, finding that tumours in the SL regime typically respond best to RT, while tumours in the BS regime typically respond worst to RT. For tumours in each regime, we also identify the biological processes that may explain positive and negative treatment outcomes and the dosing regimen which maximises the reduction in tumour burden.