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

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 growth and remodeling (G&R). Such models are crucial for capturing adaptations in health and disease and following clinical interventions. In traditional G&R models, this feedback is modeled through highly simplified fluid models, 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 and fluid-solid feedback 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.

平衡流 - 固 - 生长（FSGe）是一个快速的开源三维（3D）计算平台，用于模拟瞬时血流动力学与通过生长和重塑（G&R）实现的长期血管壁适应性之间的相互作用。此类模型对于捕捉健康和疾病状态下的适应性以及跟踪临床干预至关重要。在传统的G&R模型中，这种反馈是通过高度简化的流体模型来建模的，忽略了血压和壁面剪应力（WSS）的局部变化。FSGe通过将血流的3D纳维 - 斯托克斯方程与血管组织G&R的3D平衡约束混合模型（CMMe）强耦合，克服了这些固有局限性。CMMe能够以等同于标准超弹性材料模型的计算成本，从原始的内稳态预测长期演化的力学生物学平衡。在说明性计算示例中，我们专注于小鼠模型中稳定主动脉瘤的发展，以突出FSGe与仅固体的G&R模型在生长模式和流 - 固反馈方面的关键差异。我们表明，FSGe在受到不对称刺激的血管中尤为重要。模拟结果显示，流体衍生的WSS比壁内应力（IMS）具有更大的局部变化。因此，随着WSS相对于压力的影响增大，FSGe和G&R模型之间的差异变得更加明显。在高度局部化的疾病过程（如动脉粥样硬化中的病变形成）中的未来应用现在可以包括WSS的时空变化。