A mechanics-based mathematical model of retinal detachment due to the geometric changes of the eye associated with the evolution of myopia is developed. This includes deformation of the retina due to biological growth of the retina, as well as elastic deformation imposed on the retina by the myopic change in shape of the much stiffer choroid and sclera. The problem is formulated as a propagating boundary value problem in the calculus of variations, which yields self-consistent governing equations, boundary conditions, and transversality conditions that establish the location of the propagating boundaries that correspond to equilibrium configurations of the detaching ocular system. Axisymmetric conditions are considered, and exact, analytical solutions to the corresponding boundary value problem are obtained for detaching retinas with and without a tear. Based upon application of the model presented herein to the emmetropic retina, a value of the bond energy of the retina to retinal pigment epithelium interface is estimated using material properties found in the literature. Simulations based on the analytical solutions are performed for a detachment in the retina located at either the posterior or superior pole of the eye. The results support the clinical finding of an increased prevalence of retinal detachment in myopic eyes and provide insight into the potential causation for the increased prevalence.

中文翻译：

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关于近视的力学及其对视网膜脱离的影响。

建立了基于机械的视网膜脱离的数学模型，该模型因与近视发展有关的眼睛几何变化而引起。这包括由于视网膜的生物生长而引起的视网膜变形，以及由于刚硬的脉络膜和巩膜的近视形状改变而施加在视网膜上的弹性变形。该问题被公式化为变化演算中的传播边界值问题，产生了自洽的控制方程，边界条件和横向条件，这些条件确定了与分离的眼系统的平衡配置相对应的传播边界的位置。考虑并精确地确定了轴对称条件，获得了相应的边界值问题的解析解，用于分离有或没有泪液的视网膜。基于将本文提出的模型应用于正视视网膜，使用文献中发现的材料特性来估计视网膜与视网膜色素上皮界面的结合能值。基于分析解决方案的模拟是针对位于眼睛后极或上极的视网膜中的脱离进行的。该结果支持近视眼视网膜脱离发生率增加的临床发现，并为导致这种发生率增加的潜在原因提供了见识。视网膜与视网膜色素上皮界面的结合能的值是使用文献中发现的材料特性估算的。基于分析解决方案的模拟是针对位于眼睛后极或上极的视网膜中的脱离进行的。该结果支持近视眼视网膜脱离发生率增加的临床发现，并为导致这种发生率增加的潜在原因提供了见识。视网膜与视网膜色素上皮界面的结合能的值是使用文献中发现的材料特性估算的。基于分析解决方案的模拟是针对位于眼睛后极或上极的视网膜中的脱离进行的。该结果支持近视眼视网膜脱离发生率增加的临床发现，并为导致这种发生率增加的潜在原因提供了见识。