初始残余应力对层状主动脉生长和图案形成的影响
Influence of Initial Residual Stress on Growth and Pattern Creation for a Layered Aorta
摘要：
残余应力在大多数生物和人工材料中普遍存在且不可或缺，它维持和优化了许多生物和功能机制。从无应力初始状态开始的体积生长理论被广泛用于解释生长诱导的残余应力的产生和演变以及由此产生的形状变化，并对生长中的生物组织（如动脉和实体瘤）如何根据几何和材料参数开发图案创建策略进行建模。这种建模为设计和指导给定组织或器官的一些适当形态并实现一些目标生物医学功能提供了有希望的途径。在本文中，我们依靠一个修改后的，增强的理论，揭示我们如何可以获得生长诱导的残余应力和图案演变的分层动脉从现有的，非零的初始残余应力状态。我们使用实验确定的残余应力分布的老年人双层骨关节炎和量化其影响的幅度因子。我们的研究结果表明，初始残余应力有更显着的影响，残余应力的积累和随后的演变模式比几何和材料参数。此外，我们提供了一个必要的解释生长诱导模式驱动的差分生长耦合到初始残余应力。最后，我们表明，初始残余应力是一个现成的方法来控制生长诱导的图案创建的组织，从而可能提供一个很有前途的启发生物医学工程。
英文摘要：
Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stress-free initial state, is widely used to explain the creation and evolution of growth-induced residual stress and the resulting changes in shape, and to model how growing bio-tissues such as arteries and solid tumors develop a strategy of pattern creation according to geometrical and material parameters. This modelling provides promising avenues for designing and directing some appropriate morphology of a given tissue or organ and achieve some targeted biomedical function. In this paper, we rely on a modified, augmented theory to reveal how we can obtain growth-induced residual stress and pattern evolution of a layered artery by starting from an existing, non-zero initial residual stress state. We use experimentally determined residual stress distributions of aged bi-layered human aortas and quantify their influence by a magnitude factor. Our results show that initial residual stress has a more significant impact on residual stress accumulation and the subsequent evolution of patterns than geometry and material parameters. Additionally, we provide an essential explanation for growth-induced patterns driven by differential growth coupled to an initial residual stress. Finally, we show that initial residual stress is a readily available way to control growth-induced pattern creation for tissues and thus may provide a promising inspiration for biomedical engineering.
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