In 1987, Seymour Glagov observed that arteries went through a two-stage remodeling process as a result of plaque growth: first, a compensatory phase where the lumen area remains approximately constant and second, an encroachment phase where the lumen area decreases over time. In this paper, we investigate the effect of growth anisotropy on Glagov remodeling in five different cases: pure radial, pure circumferential, pure axial, isotropic and general anisotropic growth where the elements of the growth tensor are chosen to minimize the total energy. We suggest that the nature of anisotropy is inclined towards the growth direction that requires the least amount of energy. Our framework is the theory of morphoelasticity on an axisymmetric arterial domain. For each case, we explore their specific effect on the Glagov curves. For the latter two cases, we also provide the changes in collagen fiber orientation and length in the intima, media and adventitia. In addition, we compare the total energy produced by growth in radial, circumferential and axial direction and deduce that using a radially dominant anisotropic growth leads to lower strain energy than isotropic growth.

中文翻译：

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圆柱动脉粥样硬化的简单模型：各向异性生长对格拉戈夫重塑的影响

1987 年，Seymour Glagov 观察到，由于斑块的生长，动脉经历了两个阶段的重塑过程：首先，管腔面积保持大致恒定的补偿阶段，其次，管腔面积随时间减少的侵蚀阶段。在本文中，我们研究了五种不同情况下生长各向异性对 Glagov 重塑的影响：纯径向、纯圆周、纯轴向、各向同性和一般各向异性生长，其中选择生长张量的元素以最小化总能量。我们认为各向异性的性质倾向于需要最少能量的生长方向。我们的框架是轴对称动脉域上的形态弹性理论。对于每种情况，我们都会探讨它们对格拉戈夫曲线的具体影响。对于后两种情况，我们还提供了内膜、中膜和外膜中胶原纤维取向和长度的变化。此外，我们比较了径向、周向和轴向生长产生的总能量，并推断使用径向主导的各向异性生长导致比各向同性生长更低的应变能。