Vascular Adaptation: Pattern Formation and Cross Validation between an Agent Based Model and a Dynamical System.

Myocardial infarction is the global leading cause of mortality (Go et al., 2014). Coronary artery occlusion is its main etiology and it is commonly treated by Coronary Artery Bypass Graft (CABG) surgery (Wilson et al, 2007). The long-term outcome remains unsatisfactory (Benedetto, 2016) as the graft faces the phenomenon of restenosis during the post-surgery, which consists of re-occlusion of the lumen and usually requires secondary intervention even within one year after the initial surgery (Harskamp, 2013). In this work, we propose an extensive study of the restenosis phenomenon by implementing two mathematical models previously developed by our group: a heuristic Dynamical System (DS) (Garbey and Berceli, 2013), and a stochastic Agent Based Model (ABM) (Garbey et al., 2015). With an extensive use of the ABM, we retrieved the pattern formations of the cellular events that mainly lead the restenosis, especially focusing on mitosis in intima, caused by alteration in shear stress, and mitosis in media, fostered by alteration in wall tension. A deep understanding of the elements at the base of the restenosis is indeed crucial in order to improve the final outcome of vein graft bypass. We also turned the ABM closer to the physiological reality by abating its original assumption of circumferential symmetry. This allowed us to finely replicate the trigger event of the restenosis, i.e. the loss of the endothelium in the early stage of the post-surgical follow up (Roubos et al., 1995) and to simulate the encroachment of the lumen in a fashion aligned with histological evidences (Owens et al., 2015). Finally, we cross-validated the two models by creating an accurate matching procedure. In this way we added the degree of accuracy given by the ABM to a simplified model (DS) that can serve as powerful predictive tool for the clinic.