Adaptive finite element methodology for tumour angiogenesis modelling

In this paper, we consider an adaptive finite element approach for reliable, efficient solution of a class of continuum models for tumour-induced angiogenesis. The ideas are demonstrated using an established three equation reaction/transport model that simulates aspects of tumour-induced angiogenesis in a deterministic manner. The weak variational formulation and finite element approximation scheme for the model are developed, and a statistical approach for concurrent adaptive mesh refinement and coarsening is described. The appropriate form of the model and solution dependence on choice of parameters are explored. Computational results are presented for 1D, 2D and 3D geometry models. The effectiveness of the open-source, parallel adaptive software library (LibMesh) that is being developed in the CFDLab at the University of Texas is also demonstrated. Copyright q 2006 John Wiley & Sons, Ltd