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Diffusion-based degeneration of the collagen reinforcement in the pathologic human cornea
Journal of Engineering Mathematics ( IF 1.3 ) Pub Date : 2021-02-24 , DOI: 10.1007/s10665-020-10088-x
Alessio Gizzi , Maria Laura De Bellis , Marcello Vasta , Anna Pandolfi

We describe a multiphysics model of the collagen structure of the cornea undergoing a progressive localized reduction of the stiffness, preluding to the development of ectasia and keratoconus. The architecture of the stromal collagen is assumed to follow the simplified two-family model proposed in Pandolfi et al. (A microstructural model of cross-link interaction between collagen fibrils in the human cornea. Philos Trans R Soc A 377:20180079, 2019), where the mechanical stiffness of the structure is supplied by transversal bonds within the fibrils of the same family (inter-crosslink bonds) and across the fibrils of the two families (intra-crosslink bonds). In Pandolfi et al. (A microstructural model of cross-link interaction between collagen fibrils in the human cornea. Philos Trans R Soc A 377:20180079, 2019), it was shown that the loss of the spherical shape due to the protrusion of a cone can be ascribed to the mechanical weakening of the intra-crosslink bonds in the central region of the collagen structure. In the present study, the reduction of bond stiffness is coupled to an evolutive pathologic phenomenon, modeled as a reaction–diffusion process of a normalized scalar field. We assume that the scalar field is a concentration-like measure of the degeneration of the chemical bonds stabilizing the structural collagen. We follow the evolution of the mechanical response of the system in terms of shape change, according to the propagation of the degeneration field, and identify the critical loss of mechanical stability resulting in the typical bulging of keratoconus corneas.



中文翻译:

基于扩散的病理性人类角膜中胶原蛋白的变性

我们描述了角膜的胶原蛋白结构的多物理场模型,该结构经历了刚度的逐渐局部降低,这预示着扩张和圆锥角膜的发展。假设基质胶原的结构遵循Pandolfi等人提出的简化的两族模型。(人类角膜中胶原纤维之间交联相互作用的微观结构模型.Philos Trans R Soc A 377:20180079,2019),其中结构的机械刚度由同一家族的纤维内部的横向键提供-交联键)和两个家族的原纤维(交联内键)。在Pandolfi等人。(人角膜中胶原纤维之间交联相互作用的微观结构模型.Philos Trans R Soc A 377:20180079,2019),结果表明,由于锥体的突出而导致的球形损失可归因于胶原结构中心区域内交联键的机械削弱。在本研究中,结合刚度的降低与演化的病理现象耦合,建模为标准化标量场的反应扩散过程。我们假设标量场是稳定结构胶原蛋白的化学键退化的浓度类似度量。我们根据退化场的传播情况,根据形状变化跟踪系统机械响应的演变,并确定导致典型圆锥角膜膨出的机械稳定性的关键损失。

更新日期:2021-02-24
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