FSGe: A fast and strongly-coupled 3D fluid-solid-growth interaction method

Equilibrated fluid-solid-growth (FSGe) is a fast, open source, three-dimensional (3D) computational platform for simulating interactions between instantaneous hemodynamics and long-term vessel wall adaptation through mechanobiologically equilibrated growth and remodeling (G&R). Such models can capture evolving geometry, composition, and material properties in health and disease and following clinical interventions. In traditional G&R models, this feedback is modeled through highly simplified fluid solutions, neglecting local variations in blood pressure and wall shear stress (WSS). FSGe overcomes these inherent limitations by strongly coupling the 3D Navier-Stokes equations for blood flow with a 3D equilibrated constrained mixture model (CMMe) for vascular tissue G&R. CMMe allows one to predict long-term evolved mechanobiological equilibria from an original homeostatic state at a computational cost equivalent to that of a standard hyperelastic material model. In illustrative computational examples, we focus on the development of a stable aortic aneurysm in a mouse model to highlight key differences in growth patterns between FSGe and solid-only G&R models. We show that FSGe is especially important in blood vessels with asymmetric stimuli. Simulation results reveal greater local variation in fluid-derived WSS than in intramural stress (IMS). Thus, differences between FSGe and G&R models became more pronounced with the growing influence of WSS relative to pressure. Future applications in highly localized disease processes, such as for lesion formation in atherosclerosis, can now include spatial and temporal variations of WSS.