Gradual loading ameliorates maladaptation in computational simulations of vein graft growth and remodelling

Vein graft failure is a prevalent problem in vascular surgeries, including bypass grafting and arteriovenous fistula procedures in which veins are subjected to severe changes in pressure and flow. Animal and clinical studies provide significant insight, but understanding the complex underlying coupled mechanisms can be advanced using computational models. Towards this end, we propose a new model of venous growth and remodelling (G&R) based on a constrained mixture theory. First, we identify constitutive relations and parameters that enable venous adaptations to moderate perturbations in haemodynamics. We then fix these relations and parameters, and subject the vein to a range of combined loads (pressure and flow), from moderate to severe, and identify plausible mechanisms of adaptation versus maladaptation. We also explore the beneficial effects of gradual increases in load on adaptation. A gradual change in flow over 3 days plus an initial step change in pressure results in fewer maladaptations compared with step changes in both flow and pressure, or even a gradual change in pressure and flow over 3 days. A gradual change in flow and pressure over 8 days also enabled a successful venous adaptation for loads as severe as the arterial loads. Optimization is used to accelerate parameter estimation and the proposed framework is general enough to provide a good starting point for parameter estimations in G&R simulations.