Constrained mixture models of soft tissue growth and remodeling can simulate many evolving conditions in health as well as in disease and its treatment, but they can be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium that yields fully resolved solutions and allows computation of quasi-equilibrated evolutions when imposed perturbations are slow relative to the adaptive process. We demonstrate quadratic convergence and verify the model via comparisons with semi-analytical solutions for arterial mechanics. We further examine the enlargement of aortic aneurysms for which we identify new mechanobiological insights into factors that affect the nearby non-aneurysmal segment as it responds to the changing mechanics within the diseased segment. Because this new 3D approach can be implemented within many existing finite element solvers, constrained mixture models of growth and remodeling can now be used more widely.

中文翻译：

---

软组织生长和重塑的 3D 约束混合模型的快速、与速率无关的有限元实现


软组织生长和重塑的约束混合模型可以模拟健康以及疾病及其治疗中的许多不断变化的条件，但它们的计算成本可能很高。在本文中，我们基于机械生物学平衡的概念推导了一种新的快速、鲁棒的有限元实现，该实现产生完全解析的解决方案，并允许在施加的扰动相对于自适应过程缓慢时计算准平衡演化。我们展示了二次收敛性，并通过与动脉力学的半解析解进行比较来验证模型。我们进一步研究了主动脉瘤的扩大，为此我们确定了新的力学生物学见解，以了解影响附近非动脉瘤部分的因素，因为它对患病部分内不断变化的力学作出反应。由于这种新的 3D 方法可以在许多现有的有限元求解器中实现，因此增长和重构的约束混合模型现在可以得到更广泛的使用。