Numerical simulation of arterial remodeling in pulmonary autografts

Abstract

AbstractThe Ross procedure is a surgical procedure where a diseased aortic valve is replaced by the person's own pulmonary valve. The proximal segment of the pulmonary artery is thereby placed in aortic position and therefore suddenly exposed to a sevenfold increase in blood pressure. Excessive dilatation of this pulmonary autograft is a common complication and has excited interest about mechanobiological adaptation in such situations. Mathematical modelling of growth and remodelling is a relevant approach to improve insights into this phenomenon.We introduced an algorithm that models the continuous degradation and deposition of extracellular matrix in an artery according to the constrained mixture theory. To compute temporal variations of collagen and elastin mass and to deduce related mechanical properties of the remodelled artery, we discretized time and defined a finite number of cohorts for each collagen fiber family. The degradation and production rates of each cohort were mediated by the difference between ambient and homeostatic stress within each fiber cohort.We applied the algorithm to predict the adaptation of a pulmonary autograft over an extended period and compared the results to experimental data obtained in sheep. We were able to consistently reproduce the experimentally observed remodeling effects such as dilatation and delayed collagen fiber recruitment. Our simulations revealed how elastin takes up the excessive stress in overstretched regions of the tissue.In conclusion, the algorithm yields very promising results regarding autograft adaptation in overstretched conditions. Future work will focus on other situations of vascular adaptation where growth‐related deformations will be considered.