David T, Smye S, Dabbs T, James T
School of Mechanical Engineering, University of Leeds, UK.
Phys Med Biol. 1998 Jun;43(6):1385-99. doi: 10.1088/0031-9155/43/6/001.
During saccadic motion the eyewall moves in a manner similar to a sinusoid or at least can be represented by a sine Fourier series. Motion of the vitreous is induced by the saccade and the vitreo-retinal interface is subjected to a time-dependent shear. This force may be a significant factor for retinal tearing in the neighbourhood of small retinal holes or tears. An analytical viscoelastic model and a numerical, Newtonian model of the motion of the vitreous are presented and compared. Under sinusoidal boundary motion the analytical model shows that a viscous wave propagates inward toward the axis of rotation and the characteristic length of this wave is a function of the Womersley number. The numerical solution indicates that the vitreous moves similarly to the analytical result with small secondary motion; however, this motion allows complete recirculation of the vitreous over large timescales. Excellent agreement is found between the analytical and numerical models. The time-dependent fluid shear is evaluated and from the analytical solution the maximum value of this is found to be proportional to R0 square root of v(omega)3, where R0 is the eye radius, v the modified complex viscosity and omega the sinusoidal frequency. This indicates that myopes have a larger shear force exerted on them by virtue of the larger eye size. Further work is directed toward a model which links the stress found in the sclera to that exerted on the vitreo-retinal interface by the vitreous fluid motion.
在扫视运动期间，眼壁以类似于正弦曲线的方式移动，或者至少可以用正弦傅里叶级数表示。扫视会引起玻璃体运动，玻璃体 - 视网膜界面会受到随时间变化的剪切力。对于小视网膜裂孔或撕裂附近的视网膜撕裂，这种力可能是一个重要因素。本文提出并比较了玻璃体运动的解析粘弹性模型和数值牛顿模型。在正弦边界运动下，解析模型表明粘性波向旋转轴向内传播，且该波的特征长度是沃默斯利数的函数。数值解表明玻璃体的运动与解析结果相似，伴有小的二次运动；然而，这种运动允许玻璃体在大时间尺度上完全再循环。解析模型和数值模型之间具有极好的一致性。对随时间变化的流体剪切力进行了评估，从解析解中发现其最大值与(R_0\sqrt{v(\omega)^3})成正比，其中(R_0)是眼球半径，(v)是修正的复数粘度，(\omega)是正弦频率。这表明近视患者由于眼球尺寸较大而受到更大的剪切力。进一步的工作旨在建立一个模型，将巩膜中的应力与玻璃体流体运动施加在玻璃体 - 视网膜界面上的应力联系起来。
