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.

翻译：FSGe（流体-固体-生长平衡模型）是一个快速、开源的三维计算平台，用于通过力学生物学平衡的生长与重塑过程模拟瞬时血流动力学与长期血管壁适应性之间的相互作用。此类模型能够捕捉健康与疾病状态下以及临床干预后几何形态、组织成分和材料属性的演化过程。传统生长与重塑模型通过高度简化的流体解来模拟这种反馈机制，忽略了血压和壁面剪应力的局部变化。FSGe通过将描述血流的三维Navier-Stokes方程与描述血管组织生长重塑的三维平衡约束混合模型强耦合，克服了这些固有局限。CMMe模型使得在计算成本等同于标准超弹性材料模型的前提下，能够从原始稳态出发预测长期演化的力学生物学平衡状态。在示例计算中，我们聚焦于小鼠模型中稳定主动脉瘤的发展过程，以凸显FSGe与纯固体生长重塑模型在生长模式上的关键差异。研究表明，FSGe对于存在非对称刺激的血管尤为重要。模拟结果显示流体衍生的壁面剪应力比壁内应力具有更强的局部变异性。因此，随着壁面剪应力相对于压力影响的增长，FSGe与传统生长重塑模型间的差异愈加显著。未来在高度局部化疾病过程（如动脉粥样硬化斑块形成）的应用中，现已可纳入壁面剪应力的时空变异特征。