A numerical approach for a 1D tumor-angiogenesis simulations model

Abstract

Angiogenesis, the formation of new blood vessels, is critical in both normal and pathological contexts, especially cancer. This process involves complex interactions among endothelial cells, tumor angiogenic factors, matrix metalloproteinases, angiogenic inhibitors, and neoplastic tissues. Different mathematical and computational models have been proposed for representing the tumor angiogenesis process. Among these, we focus on partial differential equations models which are able to capture the dynamic and spatial complexities in tumor growing. Our starting point is a PDE system which mimics the angiogenesis evolution. The aim of this work is to combine both spatial and time discretization methods for designing a matrix-based model. This approach allows us to observe some error properties of numerical schema proposed, by deducing the cumulative error among space and time. Experimental tests include convergence studies, for validating the reliability of the method. Results confirm our approach is useful for addressing real angiogenesis problem.