GPU-based parallel simulations of the Gatenby-Gawlinski model with anisotropic, heterogeneous acid diffusion

Abstract: We introduce a variant of the Gatenby-Gawlinski model for acid-mediated tumor invasion, accounting for anisotropic and heterogeneous diffusion of the lactic acid across the surrounding healthy tissues. Numerical simulations are performed for two-dimensional data by employing finite volume schemes on staggered Cartesian grids, and parallel implementation through the modern CUDA GPUs technology is considered. The effectiveness of such approach is proven by reproducing biologically relevant results like the formation of propagating fronts and the emergence of an interstitial gap between normal and cancerous cells, which is driven by the pH lowering strategy and depends significantly on the diffusion rates. By means of a performance analysis of the serial and parallel execution protocols, we infer that exploiting highly parallel GPU-based computing devices allows to rehabilitate finite volume schemes on regularly-shaped meshes, together with explicit time discretization, for complex applications to interface diffusion problems of invasive processes.