Cardiovascular Fluid-Solid-Growth Interaction
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The interaction between hemodynamics and growth and remodeling (G&R) of blood vessels plays a vital role in cardiovascular development, homeostasis, and disease progression [1]. Traditional G&R models rely on scalar Poiseuille fluid solutions, neglecting local variations in blood pressure and wall shear stress (WSS). We present FSGe, a fast, open-source, three-dimensional computational platform that strongly couples the Navier-Stokes equations for blood flow with an equilibrated constrained mixture model (CMMe) for vascular tissue G&R [2,3]. FSGe overcomes the disparate timescales of fluid dynamics (milliseconds) and tissue remodeling (weeks to months) through a partitioned coupling scheme using the Interface Quasi-Newton with Inverse Jacobian from Least-Squares model (IQN-ILS) [4]. The CMMe predicts long-term mechanobiological equilibria at computational costs comparable to those of standard hyperelastic materials [5]. In illustrative examples of asymmetric aortic aneurysm development, we demonstrate that FSGe captures growth patterns inaccessible to solid-only G\&R models. Key findings reveal greater local variation in fluid-derived WSS than in intramural stress, with differences becoming pronounced as the shear-to-intramural gain ratio increases. The FSGe model predicts inward growth and significant wall thickening in regions where traditional G\&R models show none. Looking ahead, we outline critical challenges including: 1) extension to pulsatile flow conditions, 2) development of robust prestressing algorithms for patient-specific geometries, and 3) addressing computational stability of constrained mixture models in a continuum formulation. These advances will enable FSG applications in atherosclerosis, tissue-engineered vascular grafts, and personalized treatment planning.
