A Versatile Hybrid Agent-Based, Particle and Partial Differential Equations Method to Analyze Vascular Adaptation

Abstract

Failure of peripheral endovascular interventions occurs at the intersection of vascular biology, biomechanics, and clinical decision making. It is our hypothesis that most of the endovascular treatments share the same driving mechanisms during post-surgical follow-up, and accordingly, a deep understanding of them is mandatory in order to improve the current surgical outcome. This work presents a versatile model of vascular adaptation post vein graft bypass intervention to treat arterial occlusions. The goal is to improve the computational models developed so far by effectively modeling the cell-cell and cell-membrane interactions that are recognized to be pivotal elements for the re-organization of the graft’s structure. A numerical method is here designed to combine the best features of an Agent-Based Model and a Partial Differential Equations model in order to get as close as possible to the physiological reality while keeping the implementation both simple and general.