Pinsky P M, Datye D V
Department of Civil Engineering, Stanford University, CA 94305-4020.
J Biomech. 1991;24(10):907-22. doi: 10.1016/0021-9290(91)90169-n.
A mechanical model of the human cornea is proposed and employed in a finite element formulation for simulating the effects of surgical procedures, such as radial keratotomy, on the cornea. The model assumes that the structural behavior of the cornea is governed by the properties of the stroma. Arguments based on the microstructural organization and properties of the stroma lead to the conclusion that the human cornea exhibits flexural and shear rigidities which are negligible compared to its membrane rigidity. Accordingly, it is proposed that to a first approximation, the structural behavior of the cornea is that of a thick membrane shell. The tensile forces in the cornea are resisted by very fine collagen fibrils embedded in the ground substance of the stromal lamellae. When the collagen fibrils are cut, as in radial keratotomy, it is argued that they become relaxed since there is negligible transfer of load between adjacent fibrils due to the low shear modulus of the ground substance. The forces in the cornea are then resisted only by the remaining uncut fibrils. The cutting of fibrils induces an anisotropy and inhomogeneity in the membrane rigidity. By assuming a uniform angular distribution of stromal lamellae through the corneal thickness, geometric arguments lead to a quantitative representation for the anisotropy and inhomogeneity. All material behavior is assumed to be in the linear elastic regime and with no time-dependency. The resulting constitutive model for the incised cornea has been employed in a geometrically non-linear finite element membrane shell formulation for small strains with moderate rotations. A number of numerical examples are presented to illustrate the effectiveness of the proposed constitutive model and finite element formulation. The dependence of the outcome of radial keratotomy, measured in terms of the immediate postoperative shift in corneal power, on a number of important factors is investigated. These factors include the value of the elastic moduli of the stromal lamellae (dependent on the patient's age), the incision depth, the optic zone size, the number of incisions and their positions, and the intraocular pressure. Results have also been compared with expected surgical corrections predicted by three expert surgeons and show an excellent correspondence.
提出了一种人眼角膜的力学模型，并将其应用于有限元公式中，以模拟诸如放射状角膜切开术等外科手术对角膜的影响。该模型假定角膜的结构行为受基质特性的支配。基于基质的微观结构组织和特性的论据得出结论：与角膜的膜刚度相比，人眼角膜表现出的弯曲刚度和剪切刚度可忽略不计。因此，有人提出，初步近似来看，角膜的结构行为类似于厚膜壳。角膜中的拉力由嵌入基质板层的非常细的胶原纤维抵抗。当胶原纤维被切断时，如在放射状角膜切开术中那样，有人认为它们会松弛，因为由于基质的低剪切模量，相邻纤维之间的载荷传递可忽略不计。此时角膜中的力仅由剩余未切断的纤维抵抗。纤维的切断会在膜刚度中引起各向异性和不均匀性。通过假设基质板层在角膜厚度上呈均匀的角分布，几何论据可得出各向异性和不均匀性的定量表示。假定所有材料行为都处于线弹性状态且与时间无关。所得的切开角膜本构模型已应用于几何非线性有限元膜壳公式中，用于小应变和适度旋转的情况。给出了一些数值示例来说明所提出的本构模型和有限元公式的有效性。研究了以角膜屈光力术后即时变化衡量的放射状角膜切开术结果对一些重要因素的依赖性。这些因素包括基质板层的弹性模量值（取决于患者年龄）、切口深度、视区大小、切口数量及其位置以及眼内压。结果还与三位专家外科医生预测的预期手术矫正结果进行了比较，显示出极佳的一致性。
