Orssengo G J, Pye D C
School of Optometry, University of New South Wales, Sydney, NSW 2052, Australia.
Bull Math Biol. 1999 May;61(3):551-72. doi: 10.1006/bulm.1999.0102.
The purpose of this study was to determine the true intraocular pressure and modulus of elasticity of the human cornea in vivo. The cornea was modeled as a shell, and the equations for the deformations of a shell due to applanating and intraocular pressures were combined to model the behavior of the cornea during applanation tonometry. At certain corneal dimensions called the calibration dimensions, the applanating and intraocular pressures are considered to be equal. This relationship was used to determine the modulus of elasticity of the cornea and the relationship between the applanating and intraocular pressures. The true intraocular pressure (IOPT) was found to be related to Goldmann's applanating pressure (IOPG) as IOPT = IOPG/K, where K is a correction factor. For the calibration corneal thickness of 0.52 mm, the modulus of elasticity E in MPa of the human cornea was found to be related to the true intraocular pressure IOPT in mmHg as E = 0.02291OPT. The generalization of the Imbert-Fick law that takes into account the effect of corneal dimensions and stiffness was found to be given by IOPT = 73.5W/(K A), where W is the applanating weight in gf (gram force) and A is the applanated area in mm2. The calculated true intraocular pressure and modulus of elasticity were found to agree with published experimental results. The mathematical model developed may therefore be used to improve results from applanation tonometry and to estimate the mechanical property of the cornea in vivo.
本研究的目的是确定人眼角膜在体内的真实眼压和弹性模量。将角膜建模为一个壳，并结合由于压平压力和眼压引起的壳变形方程，以模拟压平眼压测量过程中角膜的行为。在某些被称为校准尺寸的角膜尺寸下，压平压力和眼压被认为是相等的。利用这种关系来确定角膜的弹性模量以及压平压力和眼压之间的关系。发现真实眼压（IOPT）与戈德曼压平眼压（IOPG）的关系为IOPT = IOPG/K，其中K是一个校正因子。对于校准角膜厚度为0.52 mm的情况，发现人眼角膜以MPa为单位的弹性模量E与以mmHg为单位的真实眼压IOPT的关系为E = 0.0229IOPT。考虑角膜尺寸和硬度影响的伊姆伯特 - 菲克定律的推广形式为IOPT = 73.5W/(K A)，其中W是以gf（克力）为单位的压平重量，A是以mm²为单位的压平面积。计算得到的真实眼压和弹性模量与已发表的实验结果一致。因此，所建立的数学模型可用于改善压平眼压测量的结果，并估计体内角膜的力学性能。
