A cellular automaton model for spheroid response to radiation and hyperthermia treatments

Thermo-radiosensitisation is a promising approach for treatment of radio-resistant tumours such as those containing hypoxic subregions. Response prediction and treatment planning should account for tumour response heterogeneity, e.g. due to microenvironmental factors, and quantification of the biological effects induced. 3D tumour spheroids provide a physiological in vitro model of tumour response and a systems oncology framework for simulating spheroid response to radiation and hyperthermia is presented. Using a cellular automaton model, 3D oxygen diffusion, delivery of radiation and/or hyperthermia were simulated for many (104−107\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{1}}{{\bf{0}}}^{{\bf{4}}}{\boldsymbol{-}}{\bf{1}}{{\bf{0}}}^{{\bf{7}}}$$\end{document}) individual cells forming a spheroid. The iterative oxygen diffusion model was compared to an analytical oxygenation model and simulations were calibrated and validated against experimental data for irradiated (0–10 Gy) and/or heated (0–240 CEM43) HCT116 spheroids. Despite comparable clonogenic survival, spheroid growth differed significantly following radiation or hyperthermia. This dynamic response was described well by the simulation (R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf{R}}}^{{\bf{2}}}$$\end{document} > 0.85). Heat-induced cell death was implemented as a fast, proliferation-independent process, allowing reoxygenation and repopulation, whereas radiation was modelled as proliferation-dependent mitotic catastrophe. This framework stands out both through its experimental validation and its novel ability to predict spheroid response to multimodality treatment. It provides a good description of response where biological dose-weighting based on clonogenic survival alone was insufficient.