Bottega William J, Bishay Peter L, Prenner Jonathan L, Fine Howard F
Department of Mechanical & Aerospace Engineering, Rutgers University, Piscataway, NJ, USA.
Math Med Biol. 2013 Dec;30(4):287-310. doi: 10.1093/imammb/dqs024. Epub 2012 Jul 18.
A mechanics-based mathematical model for retinal detachment is developed, incorporating an energy-based criterion for propagation. Retinas with and without central tears are considered and contraction of the vitreous and extension of its fibrils, along with a pressure difference across the retina, are taken as the stimuli for detachment propagation. In addition to the equations of motion, boundary and matching conditions, the variational formulation yields the self-consistent energy release rate that governs detachment, and formulae for critical stress and critical deflections that provide a rational basis for measuring critical parameters. Exact analytical solutions are established for axisymmetric detachment of retinas with and without tears, and numerical simulations are performed based on these solutions. The results yield characteristic behaviour, including threshold levels and stability of detachment, 'dimpling' of the detaching retina, the effects of changes in material and geometric parameters, and the influence of the presence and size of the retinal tear on detachment propagation. The model predicts that once detachment ensues it does so in an unstable manner and is extensive in scope. This is in agreement with clinical observation. Results also suggest that, under appropriate conditions, the presence and size of a retinal tear or hole can have a 'stabilizing' effect with regard to detachment propagation.
建立了一种基于力学的视网膜脱离数学模型，该模型纳入了基于能量的传播准则。考虑了有无中央裂孔的视网膜，并将玻璃体的收缩及其纤维的伸展，以及视网膜上的压差作为脱离扩展的刺激因素。除了运动方程、边界条件和匹配条件外，变分公式给出了控制脱离的自洽能量释放率，以及临界应力和临界挠度的公式，这些公式为测量临界参数提供了合理依据。针对有裂孔和无裂孔视网膜的轴对称脱离建立了精确的解析解，并基于这些解进行了数值模拟。结果得出了一些特征性行为，包括脱离的阈值水平和稳定性、脱离视网膜的“凹陷”、材料和几何参数变化的影响，以及视网膜裂孔的存在和大小对脱离扩展的影响。该模型预测，一旦发生脱离，其方式是不稳定的，且范围广泛。这与临床观察结果一致。结果还表明，在适当条件下，视网膜裂孔或孔洞的存在和大小对脱离扩展可能具有“稳定”作用。
