Mathematical modelling of the dynamics of image-informed tumor habitats in a murine model of glioma

Abstract Tumors are highly heterogeneous with unique sub-regions termed “habitats”. We evaluate the ability of a mathematical model built on coupled ordinary differential equations (ODEs) to describe and predict tumor habitat dynamics in a murine model of glioma. Female Wistar rats (N = 21) were inoculated intracranially with 10 6 C6 glioma cells, a subset of which received 20 (N = 5) or 40 Gy (N = 8) of radiation. All rats underwent diffusion-weighted (DW) and dynamic contrast-enhanced magnetic (DCE) resonance imaging (MRI) at up to seven time points. All MRI data at each visit were subsequently clustered using k -means to identify physiological tumor habitats. A family of four models consisting of three coupled ODEs were developed and calibrated to the habitat time series of eight control rats and eight treated rats and evaluated for predictive capability. The Akaike Information Criterion (AIC) was used for model selection, and the normalized sum-of-square-error (SSE) was used to evaluate goodness-of-fit in model calibration and prediction. Three tumor habitats with significantly different imaging data characteristics ( p < 0.05) were identified: high-vascularity high-cellularity, low-vascularity high-cellularity, and low-vascularity low-cellularity. Model selection yielded a five-parameter model whose predictions of habitat dynamics yielded SSEs that were similar to the SSEs from the calibrated model. It is thus feasible to mathematically describe habitat dynamics in a preclinical model of glioma using biology-based ODEs, showing promise for forecasting heterogeneous tumor behavior.