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.

中文翻译：

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FSGe：一种快速、强耦合的 3D 流体-固体-生长相互作用方法


平衡流体-固体生长 (FSGe) 是一种快速、开源、三维 (3D) 计算平台，用于通过机械生物学平衡生长和重塑 (G&R) 模拟瞬时血流动力学与长期血管壁适应之间的相互作用。这些模型可以捕捉健康和疾病以及临床干预中不断变化的几何形状、成分和材料特性。在传统的 G&R 模型中，这种反馈是通过高度简化的流体解决方案进行建模的，忽略了血压和壁剪切应力 (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，克服了这些固有的局限性。 CMMe 允许人们以相当于标准超弹性材料模型的计算成本来预测从原始稳态开始的长期进化的机械生物学平衡。在说明性计算示例中，我们重点关注小鼠模型中稳定主动脉瘤的发展，以突出 FSGe 和纯 G&R 模型之间生长模式的关键差异。我们证明 FSGe 在具有不对称刺激的血管中尤其重要。模拟结果表明，流体衍生的 WSS 的局部变化比壁内应力 (IMS) 的局部变化更大。因此，随着 WSS 相对于压力的影响不断增强，FSGe 和 G&R 模型之间的差异变得更加明显。未来在高度局部化的疾病过程中的应用，例如动脉粥样硬化中的病变形成，现在可以包括 WSS 的空间和时间变化。