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.

翻译：均衡流体-固体-生长（FSGe）是一种快速、开源的三维（3D）计算平台，用于模拟瞬时血流动力学与通过生长与重塑（G&R）实现的长期血管壁适应之间的相互作用。此类模型对于捕捉健康与疾病状态下的适应性变化以及临床干预后的响应至关重要。传统G&R模型中，这种反馈通过高度简化的流体模型模拟，忽略了血压和壁面剪切应力（WSS）的局部变化。FSGe通过将描述血流的3D纳维-斯托克斯方程与描述血管组织G&R的3D均衡约束混合模型（CMMe）进行强耦合，克服了这些固有局限性。CMMe允许从原始稳态出发，以与标准超弹性材料模型相当的计算成本预测长期演化的力学生物学均衡态。在示例性计算案例中，我们聚焦小鼠模型中稳定主动脉瘤的发展，突出展示了FSGe与纯固体G&R模型在生长模式和流体-固体反馈方面的关键差异。研究表明，FSGe在非对称刺激的血管中尤为重要。模拟结果揭示，流体衍生的WSS比壁内应力（IMS）呈现更大的局部变异。因此，随着WSS相对压力影响的增强，FSGe与G&R模型之间的差异变得更加显著。该方法的未来应用可涵盖高度局部的疾病过程，例如动脉粥样硬化中病变的形成，从而纳入WSS的空间和时间变化特征。