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

TL;DR

FSGe introduces a fast, open-source platform that tightly couples 3D Navier–Stokes hemodynamics with an equilibrated constrained mixture model (CMMe) to capture long-term, mechanobiologically driven vascular remodeling. By employing a strongly coupled partitioned framework with IQN-ILS, FSGe achieves equilibrated growth predictions with computational efficiency far less burdensome than fully dynamic histories, enabling local WSS-driven remodeling to be studied in 3D. In a mouse aortic aneurysm scenario, FSGe diverges from solid-only G&R by predicting asymmetric growth and collagen remodeling driven by local WSS, including inward thickening in regions with preserved elastin, underscoring the importance of incorporating spatially varying hemodynamics. The work also discusses stability, the concept of original homeostasis, and the influence of pulsatility, providing open-source tools and performance benchmarks for future vascular disease modeling.

Abstract

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.

Figures (14)

• Figure 1: Negative feedback characteristics of mechanical homeostasis, including hemodynamics $\mathcal{F}$ and solid mechanics $\mathcal{S}$ . Stimuli consist of deviations of intramural stress, $\Delta\sigma_I$, and wall shear stress, $\Delta\tau_w$, from homeostatic set-point values. Tissue changes are modulated by gain factors $K^\alpha_{\sigma_I}$ and $K^\alpha_{\tau_w}$, which capture cell sensitivity to the particular stimulus. gr are influenced further by degradation rate $k^\alpha$, homeostatic prestretch $G^\alpha$, and orientation angle $\alpha^\alpha$. In this work, tissue constituents $\alpha$ are elastin $e$, four collagen fiber families $c$, and smooth muscle $m$, which are visualized in Figure \ref{['fig_constituents']}. Figure adapted from humphrey21.
• Figure 2: Blood vessel with length $l$, inner radius $a$, and thickness $h$. Its constituents are elastin $e$ (isotropic), smooth muscle $m$ (red, circumferential), and four collagen fiber families $c_i$ (circumferential, axial, diagonal angle $\alpha_0$). Image created by Sebastian L. Fuchs and licensed under the Creative Commons Attribution 4.0 International License.
• Figure 3: Mesh (left) with fluid domain $\mathcal{F}$ (yellow) and solid domain $\mathcal{S}$, colored by the spatial insult profile $f_\theta \, f_z$ (white healthy, purple initiating insult profile). Plot locations (right), top, right, bottom, left, with a cylindrical coordinate system $(r,\theta,z)$.
• Figure 4: Cumulative number of fsge coupling iterations per load step for different gain ratios $K_{\tau\sigma,o}$.
• Figure 5: Long-term evolved solid domains in gr (left) vs. fsge (right) for different original gain ratios $K_{\tau\sigma,o}\in[0,1]$ (from top to bottom). The geometries are colored by the evolved gain ratio $K_{\tau\sigma,h}$.