准分子激光原位角膜磨镶术后角膜生物力学特性及其相关研究
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摘要
前言
生物力学(biomechanics)是研究生物体的力学问题，主要是生物体对力或运动的响应的学科。生物力学在医学领域有着广泛的应用，并形成了新的分支学科——临床生物力学。生物力学在实用中已对下列问题的分析和解决取得成效：①在分子、细胞和器官层次上认识生物机体的正常生理过程和病态生理过程。②医学诊断和医疗方法的发展。③矫形术的设计以及假体和仪器的设计和制造。④提高人在工作环境、体育运动以及宇宙空间里活动的效能。生物力学在眼科也有多方面的研究应用。通过眼的生物力学的基础研究，能够增强眼科手术的预测性以提高临床效果。深入了解角膜材料本身生物力学的特性，对正确评估现代屈光手术后的效果有重要意义。
手术、疾病和外伤均能引起角膜的生物力学特性的改变，而导致这种改变的主要因素有两点：(1)角膜材料的特性。(2)角膜薄壳形状的结构特性。如果要获得角膜对手术、疾病和外伤等宏观力学反应的预测，在角膜生物力学特性试验研究中，这两个因素是必须描述的重要指标。
关于角膜生物力学用于实验研究先进设备有超声弹性显微镜、单轴拉伸、共聚焦角膜显微镜、飞点扫描图像跟踪系统、动态力学分光镜、全息干涉度量仪。
生物材料的特性由本构方程来描述，广义上是一种应力-应变的方程。一种材料的本构方程只能通过实验来决定。对生物固体材料能做的最简单的实验是单轴拉伸实验。冯元桢教授通过软组织的一维拉伸实验结果提出准线性粘弹性概念。
目前，对角膜生物力学的实验研究中，大致有两种实验手段来描述角膜的生物力学特性：一种是离体角膜片的膨胀实验(也称纽扣实验)，而另一种则是离体角膜条带拉伸实验。两种方法各有优缺点，纽扣实验虽接近角膜的生理状态，但是只能够获得角膜材料的一维数据。而角膜是各向异性材料，条带拉伸实验则能够体现出角膜的各向异性生物力学特征。缺点是受初始状态的影响。两者都能够体现出角膜的非线性的弹性材料特征。
研究角膜的材料特性是为了进一步深入了解角膜对疾病外伤手术等因素的生物力学反应，有重要的临床意义。角膜的材料特性也是应用工程、数学和数字技术，建立以有限元技术为基础的角膜在手术、疾病等外部因素作用下仿真模型的基本要素。
近十年来，有限单元法(Finite element method，FEM)在国内生物力学领域不断获得发展。在方法技术与机理研究、医疗器械评价、临床问题模拟等多个方面，能及时跟踪国外研究现状，并针对国内的临床实际问题，建立了各类仿真模型及开展了相关研究工作。有限单元法是一种在工程科学技术中广泛应用的数学物理方法，用于模拟并解决各种工程力学、热学、电磁学等物理场问题。当FEM应用于人体生物力学研究时，显示了极大的优越性。经过长期的进化过程，人体形成了一个近乎完美的力学结构。由于通常的力学实验手法基本上无法直接应用于人体，对人体的力学行为进行有限元数值模拟就成为深化对人体认识的一种有效手段。
近年来，准分子激光手术矫正眼屈光不正的有效性、安全性已得到临床证实。准分子激光原位角膜磨镶术(Laser in situ keratomileusis，LASIK)手术被眼科医生普遍采用及认可。由于其安全快捷的治疗方式、术后满意的裸眼视力而使该手术目前广泛应用于临床。但是术后仍存在并发医源性圆锥角膜、远期能否引起角膜的张力性下降等潜在性问题，目前尚缺乏与之相关的、深入的基础研究，尤其是生物力学方面的研究国内报道甚少。
LASIK手术由于部分切除了角膜，人眼角膜在被部分切除后的变形状况如何，依从什么变形规律，术后角膜的受力情况怎样，每个手术参数对手术效果起到什么样的作用和影响，人眼角膜完整性受到破坏后，其整体的张应力改变是眼科学者们关心的问题。
本研究应用生物力学手段，对准分子激光原位角膜磨镶术后角膜的生物力学特性进行初步研究，并对术后角膜生物力学变化作定量分析，以及进一步行计算机有限元法模拟研究，以探讨准分子角膜屈光手术的安全阈值。
实验材料和方法
一、生物力学实验部分
1、猪眼LASIK手术模型的建立
新鲜离体猪眼共92只(46只用于应力应变实验，另46只用于应力松弛实验)，经视神经灌注维持眼压恒定，行常规LASIK手术，基质床分别切削30％、50％、70％整体角膜厚度。应力-应变实验及应力松弛实验均按切削深度分组：30％角膜厚度组、50％角膜厚度组、70％角膜厚度组，每组各10只眼，单纯切角膜瓣组10只，正常组6只。用自制的模具尺，切取哑铃型试件，20％人血白蛋白液浸泡，冰箱4℃过夜保存，次日用于力学实验测试。
2、应力-应变实验及应力松弛实验
将试样吸干蛋白液，置于自制夹具固定，于美国Tyiron250力学实验机做应力应变实验及应力松弛实验。应力-应变实验加载速度为10mm／min，而应力松弛突加载荷的加载速率为385mm／min，伸长比为1.5，松弛时间1000S，计算机自动采集数据。
二、计算机模拟部分
(一)、LASIK手术仿真三维模型的建立
1、角膜模型剖面的模拟及建立
1．1角膜的几何模型
本文的模拟计算中，采用国内外较普遍认可的数据，具体参数见表1。
表1角膜的几何参数(单位mm)
眼轴长度26.50角膜水平直径11.20
角膜平均厚度0.67角膜垂直直径11.0
角膜中心厚度(Φ3mm) 0.55角膜旁周边(Φ3～7mm)厚度0.72
角膜周边厚度(Φ7-12mm) 1.0角膜前表面弯曲半径7.80
角膜后表面弯曲半径6.80
由上表参数可以看出角膜各个区域的厚度是平滑过渡而非分段变厚度，根据以上参数运用NURBS(Non-Uniform Rational B-Splines：非均匀有理B样条曲线)数学方法进行角膜剖面图曲线的绘制，经过分区间角膜厚度的表示，以及NURBS理论插值运算，即可得到较为理想的角膜剖面图曲线图。
1．2 NURBS(非均匀有理B样条曲线)定义几何形状
角膜剖面的两条NURBS曲线的连续性采用C2标准，角膜的建模过程中，因为角膜的几何参数是分区间定义的，采用分区间作辅助点，选适当的几个点作NURBS曲线插值得到相应曲率的曲线。利用AutoCAD软件进行角膜的剖面绘制。
1．3 AutoCAD软件系统中NURBS曲线反求算法模型
对给定的型值点{pi}i=0，1，…，n，反算曲线控制顶点{dj}，j=0，1，…，n+k-1，再由顶点{dj}构造通过{pi}的k次NURBS拟合曲线，由于节点矢量序列U=[u0，u1，…，un+2k]采用累加弦长方法。采用的三次NURBS曲线需补充k-1=2个边界条件，AutoCAD用的是矢切条件。对于wj，AutoCAD一般默认为wj=1，构造出初始曲线，再根据形状细调，此时需要用命令SPLINEDIT＼REFINE＼WEIGHT来选择进行。
2、手术实体模型的建立
LASIK手术基本操作方法是先在角膜表面切开直径为9mm，厚度约130微米的角膜瓣，然后用准分子激光对中间角膜基质进行切削，再将切开的角膜瓣复位。在实体模型的建立过程中，建模的过程基本上和手术的操作过程是一致的。在手术模拟之前首先需要建立眼球角膜的完整实体模型，以便利用布尔运算、实体修改等操作。其中完整角膜的建立需要用到前面的角膜实体模型截面图来建成完整的角膜实体模型。建成完整的角膜实体模型以后，进一步对手术进行建模模拟，具体过程是先做出角膜瓣部分，然后做基质床切削模拟，最后对角膜瓣进行修改以使其能覆盖在切削后角膜上面。
3、材料的定义
在计算中选取生理条件相似，被普遍认同的数值来作为计算依据。角膜近似地被认为是不可压缩材料，学者Woo认为其泊松比为0.49，已被广泛引用和认同。
本计算中应用的常数为：角膜，Ex=1.8MPa Ey=1.8MPaμ=0.49；巩膜，Ex=3.08MPa Ey=3.08MPaμ=0.49。
计算过程中选取的温度为人体的正常体温37摄氏度
4、单元的选择
ANSYS软件单元库中有很多不同的单元类型，因为角膜是一种比较规则的生物组织。依据其形状和特性，选取可以划分为六面体并且适合对角膜组织分析的SOLID185和SURF154单元进行计算。
(二)、有限元计算模型的建立
本研究利用软件集成的办法，但在CAD软件中并不建立实体模型，只是建立角膜及巩膜纵向截面图，这样有利于应用非均匀有理B样条曲线来根据测得的参数来模拟角膜的截面图，也有利于手动划分网格操作。
在AutoCAD软件中模拟建立角膜的剖面图，之后对角膜瓣的剖面进行模拟。按照测得的角膜数据建立的角膜瓣及角膜剖面图。
将得到的剖面图输出为ANSYS有限元分析软件能够识别的SAT格式，以备导入之用。将得到的SAT格式文件导入到ANSYS软件中，利用ANSYS软件自带的SAT接口即可实现。
文件导人之后在ANSYS软件中进行前处理操作，如定义材料特性，划分网格等操作，本文中试验采用手动分网，这样可以人为地控制分网在不同地方的精度，可以减少不必要的资源浪费，如巩膜部分不是我们考察的重点，所以就不需要划分得太密。在AutoCAD和ANSYS两软件中联合进行划分网格和计算仿真并对其进行不断地修改，以获得精确的结果数据。
为研究手术中基质消融深度等参量对手术效果的影响，须构造出这些参量不同数值的多个几何模型进行对比研究。这些参量的对比情况如下：基质切削深度30％、50％、70％角膜厚度，光学区直径5.0mm，5.5mm，6.0mm，6.5mm。修边区3.0mm。眼内压在许可的范围内选取四个值(单位：mmHgh)：15，20，25，30。换算为以Pa为单位，即：2000，2670，3330，4000。角膜模型中的几何参数参照表1，角膜的拱高取3.10mm。
由于在角膜的球面上切开不贯穿厚度切口，属三维立体构图，空间位置及坐标比较难于确定，因此需多步骤分层完成。构图中多次调用了球面单元，和其他的单元进行布尔运算，加合得到不完全切透的模型。
实验结果
一、LASIK手术后猪眼角膜的生物力学特性
1、随角膜切削深度增加，其断裂时的应力减小，发生屈服的应力减小。当角膜的30％整体厚度被部分切削时，角膜的弹性模量和单纯切瓣时无明显统计学差异(P＞0.05)，接近正常角膜组织的弹性模量。当基质层被部分切除50％和70％时，角膜的弹性模量明显降低(P＜0.05)，加载很小的载荷即被拉断。角膜材料发生屈服的临界点对应的应变在30％左右。角膜材料没有明显的屈服阶段。基质消融50％以上时，角膜的垂直轴向屈服强度明显小于水平轴向的屈服强度(P＜0.01)。
2、LASIK手术中，单纯切开角膜瓣即导致了角膜的应力松弛程度降低，P＜0.05，可能角膜依然保持其粘弹特性。当激光消融30％角膜整体厚度及大于此值时，角膜的应力松弛程度几乎下降了一倍，P＜0.01。在LASIK手术中角膜的纵向应力松弛程度不如横向的变化明显，尤其是在70％切削深度条件下，角膜的横向应力松弛程度小于纵向应力松弛程度，有显著的统计学差异(P＜0.001)
二、LASIK手术有限元计算机模拟
1、建立三维立体仿真LASIK手术模型
在利用软件集成成功建立角膜、巩膜模型基础上，构建LASIK手术实体模型，相对于每一种几何情况，因几何形状不同建立的有限元模型都会有一些差别，以切削深度为30％(0.165mm)光学区直径5.0mm为例：本次建模共建立节点数为6051个，共建立单元数为5154。建立SOLID185单元4032个，其中角膜部分为2304个，巩膜部分为1728个；建立SURF154单元共1152个。
2、LASIK手术中各手术参数变化对手术效果的影响模拟
LASIK手术中，切削30％角膜厚度及以下时，同一光学切削区直径、同一眼压条件下，角膜的应力有随切削深度增加而增加的趋势，但是应变在同一水平上。眼压不变条件下，光学切削区直径增加，角膜的应力增加，应变则维持不变。光学切削区直径不变条件下，不同的眼压作用下引起的角膜变形量是不同的，当眼压值达20mmHg时，应变增加了32.0％左右，当眼压增至25mmHg时，应变增加了65.0％左右；而当眼压升高到30mmHg，角膜应变增加98.0％左右，6.0mm的光学切削区直径，在不同的眼压条件下引起的角膜变形最小，在光学切削区直径6.5mm时，在不同的眼压条件下，导致的角膜的变形量最大。
结论
1、LASIK手术中，当30％整体角膜厚度的基质激光消融时，角膜仍维持其粘弹性材料特征。
2、应用有限元方法能够成功建立角膜的三维仿真实体模型；应用手工分网及单元拆分技术能够成功模拟LASIK手术过程。
3、20mmHg的眼内压引起的角膜变形在33％左右，是保持角膜弹性变形的临界眼压值。
4、6.0mm的光学切削区直径，在不同的眼压条件下引起的角膜变形最小，是LASIK手术的首选光学切削区。
Preface
Biomechanics is the science which concerns about the mechanical aspects of organism, that is, the response of a certain organ or tissue to force or locomotion. Biomechanics had been widely used in medical field, and formed a new branch-clinical biomechanics. Biomechanics had its effects in dealing with the problems as following: (1) in understanding the physiological and pathological process of life-form in the level of molecule, cell, and organ. (2) in promoting the development of clinical diagnosis and treatment. (3) in the design of rectify and manufacture of substitute, (4) in the exaltation of effectiveness of human activity in different circumstances. Biomechanics had also been used in Ophthalmology. The basal researches can help to improve the prediction and clinical effect of refractive surgery. The important characteristics of cornea are the transparency and with no blood vessels, and its major function is to refract light. The deep understand of material properties of cornea is of great importance for evaluation of results of modern refractive surgery.
Surgery, disease and injury can cause biomechanical changes in cornea, and the major factors on this changes are the material property and thin shell property of cornea. These two important factors must be descriptive in biomechanical studies for prediction of surgery, disease and injury in cornea in macro level.
There are a kind of methods applied in research of biomechanics of cornea, including ultrasound elastic microscope, monoaxial extension, confocal microscope, laser scanning track system, dynamic mechanical spectroscope, holographic interferometer.
Material property are described with structural equation, it is generally a stress-strain equation. The structural equation of a certain material can only be determined by experiment. The most simple experiment for solid tissue material is the monoaxial extension. Professor Feng yuanzheng had put forward the concept of sub-linear visco-elasticity by plane-extension text of soft tissue.
At present, there are two methods in describing material properties of cornea in biomechanical researches; inflate test (button test), and strip extension test. Inflate test can only provide plane data though it is close to the physiological status of cornea; whereas strip extension test can reflect the property of ani-sotropy of cornea, though it is affected by original status of material. Both methods can prove the non-linear elastic material behavior. It is clinically important to understand deeply the biomechanical response of cornea to disease, injury and surgery by finding out the material property of cornea which is the basic factor in constitution of imitate model based on finite element technology with the application of engineering, mathematical and digital techniques.
For the past decade, Finite element method (FEM) had been widely used in the field of biomechanics in our country. The international status has been concerned in the aspects of study methods of mechanism, evaluation of medical equipment, clinical simulation, and so on. Imitate modeling and relative studies had been performed.
Finite element method is a mathematical-physical technique, which is used to simulate and solve problems in engineering mechanics, calorifics, electromagnetics and etc. FEM had shown huge advantages when used in the study of biomechanics of human body which is a perfect mechanical structure. FEM will also be a effective method in the study of mechanical behavior, for common methods can not be used directly in human body.
Up to now, refractive correction with excimer laser has been proved to be effective and safe. Laser in situ keratomileusis (LASIK) has been ratified and applied worldwide in an increasing population with satisfied postoperative result. But we still face with problems such as operation-induced keratoconus, decrease of corneal tensility. However, there are still a few correlative basic researches, especially in the field of biomechanics.
After partial ablation by LASIK, what status on distortion the cornea is in, what rule it will obey, what force the cornea will endure,what impact on the outcome each parameter will have, and what change on stress-strain the cornea will meet, all these are necessarily concerned. we put up a pilot study on biomechanical behavior of cornea after LASIK with Finite Element Method, analyze post-operative biomechanical changes quantificationally, and setup a mathematical model in an attempt to obtain a safety-threshold of laser ablation.
Material and Method
一、Experiment on biomechanics
1、Constitutive models of ablated porcine cornea
Usual LASIK was performed on 92 fresh porcine eyes (42 for stress-strain test, 42 for strain relaxation test respectively) with stable intraocular pressure (IOP) maintained through optic nerve irrigation. The ablation depth on stromal side is 30%、50%、70% respectively(10 eyes each depth). 10 eyes had only flap-cutting procedure, anther 6 eyes without management for control. Then the dumbbell-shaped corneal strip segments were cut and stored in 20% Human Albumin solution for use (about 12 hr).
2、Stress-strain test and stress relaxation test
Corneal specimens were mounted onto a specially designed bracket attached on to Tytron250 machine equipped with a 50 N capacity load cell. For stressstrain test, the loading speed was 10mm/min; and for stress relaxation test, the loading speed was 385mm/min, with elongation rate of 1. 5 and relaxation time of 1000s. The data were collected electronically.
二、computer simulation
(一)、imitate 3-dimension LASIK model
1、modeling of corneal trans-section
1.1 geometric model of cornea
Corneal geometric parameters are based on recognized data, as shown in table 1.
table 1 corneal geometric parameter (mm)
axial length 26.50 Horizontal diameter 11.20
corneal main thickness 0.67 Vertical diameter 11.0
Central thickness (Φ3.0) 0.55 Pericentral thickness (3.0～7.0) 0.72
Peripheral thickness (Φ7.0-12.0) 1.0 Corneal anterior radius 7.80
Corneal posterior radius 6. 80
NURBS (Non-Uniform Rational B-Splines) mathematical method was used to protract the ideal corneal trans-section profile curve by denotation of subarea thickness.
1. 2 definition of geometric shape with NURBS.
C2 criterion was taken in continuity of two NURBS curves of corneal transsection. because the corneal geometric parameters are regional, subarea method was chosen, some points were selected as assistance in construction of corneal medel. AutoCAD software was used in the protract of corneal section plane.
1.3 model of reverse calculation of NURBS curve with AutoCAD.
With given values in point {pi} i =0, 1,…, n, reverse calculating the apical points {dj}, j =0, 1,…, n + k-1, then construct the NURBS draft curve by {pi} passing through {dj}; because the series vector of node were U = [ u0, u1,…, un +2k], so accumulated increment of srings method was adopted. Triple NURBS curve was renewed with number of k-1=2 boundary conditions, under this circumstances, tangent vector procedure was selected in AutoCAD. With default wj = 1 for AutoCAD, SPLINEDIT\REFINE\WEIGHT instruction was chosen to refine the original curve.
2、building of actual LASIK model
In LASIK procedure, a corneal flap was firstly made with the diameter of 9mm and the depth of 130μm, then stromal ablation was performed with excimer laser, recover the flap finally. The construction of model is similar to the operation, a intact corneal model was built first with the trans-section curves described above, in order to apply Bull-calculation and modification. Then simulate the operation, beginning with the corneal flap cutting, and succedent ablation, recovery of flap.
3、definition of material
The calculation was based on recognized data. The cornea was deemed to be non-compressable. The Poisson' s ratio was 0.49 determined by Dr. Woo and recognized widely.
The constant used in this study were: Ex = 1. 8MPa Ey = 1. 8MPaμ= 0.49 for cornea;,Ex =3.08MPa Ey =3.08MPaμ=0.49 for sclera.
Normal body temperature(37℃.) was selected for working temperature.
4、select of calculation unit
There are different kinds of calculation unit for selection in ANSYS software database. Because of the regularity of cornea, SOLID18 and SURF154 unit were chosen.
(二)、construction of finite element model
In this study, we only built a corneo-scleral portrait trans-section, it is better for corneal modeling with NURBS data, and for subsequent manual net topology. After the corneal section modeling with AutoCAD, the section of flap was modeled with corneal data.
The section was transferred into SAT format which can be recognized by ANSYS analysis software, and then transmit to ANSYS through SAT meet.
Manual net topology was decided to artificially control the precision., and to decrease the analysis coast. Net plot and imitation were performed and refined with the combination of AutoCA and ANSYS.
several models should be made with different value of parameters such as ablation depth, to evaluate the effect on the result of surgery. These parameters were; ablation depth of 30%、50%、70%; the optic diameter of 5. 0mm, 5. 5mm,6. 0mm,6. 5mm; the marginal area of 3mm; the IOP of 15, 20, 25, 30mmHg(2000, 2670, 3330, 4000 Pa respectively). Corneal parameter were as in table 1, and corneal arch is 3.100mm.
Because of the non-penetrating cutting, the cornea is a 3-dimension structure, and should be built by multi-steps.
Bull-calculation was used in combined spherical unit and other kind of unit applied in this study, to create a partially ablated model.
Result
一、Biomechanical properties of porcine cornea after LASIK
1, As ablation depth increased, the Break-Stress decreased, and Stress-at-Yield also decreased. When the ablation depth was 30%, the corneal elastic modulus was similar to that of a single flap-cutting cornea as well as a normal cornea, with no statistical significance (P＞0. 05). When the ablation reached to 50% and 70%, the corneal elastic modulus decreased obviously, and it is easy to break the strip with a minimal load. The critical strain-at-yield of cornea was about 30%. The corneal material had not a relaxed phase. When the ablation depth was more than 50%, the corneal load-at-yield in vertical meridian was lower than that in horizontal direction (P＜0. 01).
2, In LASIK procedure, though a single flap-cutting can cause a little reduction of corneal stress relaxation, P＜0. 05, the cornea may still remain its property of visco-elasticity. When ablation depth was 30% or more, corneal stress relaxation decreased to almost one half, P＜0.01.
Corneal stress relaxation in vertical meridian was lower than that in horizontal direction, especially when ablation depth was 70%, and it' s statistically significant P＜0.001).
二、computer simulation of LASIK with Finite Element Method
1、construction of 3-dimension imitate LASIK model
Based on the integration function of software, the corneo-scleral model was constructed, and then, was the LASIK model. There were certainly differences in finite element modeling because of the geometric shape. For example, in the case with the ablation depth of 30% (0.165mm) and diameter of 5.0mm, 6051 nodes had been built, within these, 4032 units for SOLID185, 2304 for cornea, 1728 for sclera, and 1152 units for SURF154.
2、simulation of effects of varied parameters on LASIK
When the ablation depth was under 30% of corneal thickness, corneal stress had the trend to increase with the depth, and the strain was in the same level. When the IOP was stable, corneal stress increased with ablation diameter, the strain remained unchanged. When the ablation diameter was fixed, corneal deformation was different with different IOP, the strain increased 32. 0% under IOP of 20mmHg; when IOP was 25mmHg, the strain increased 65.0%; when IOP was 30mmHg, the strain increased 98.0%. Under different IOP With ablation diameter of 6. 0mm, corneal deformity is the least. The corneal deformation was most serious with ablation diameter of 6.5mm under different IOP.
Conclusion
1. Cornea will still maintain its visco-elastic property even if 30% of its total thickness was ablated by LASIK.
2. 3-dimension imitate true model can be built with finite element method; LASIK procedure can be simulated with manual net topology and unit split technique.
3. 20mmHg of IOP can cause corneal deformation of 33% percent, it is the critical IOP.
4. Under different IOP With ablation diameter of 6.0mm, corneal deformity is the least, it is the preferred diameter.
生物力学(biomechanics)是研究生物体的力学问题，主要是生物体对力或运动的响应的学科。生物力学在医学领域有着广泛的应用，并形成了新的分支学科——临床生物力学。生物力学在实用中已对下列问题的分析和解决取得成效：①在分子、细胞和器官层次上认识生物机体的正常生理过程和病态生理过程。②医学诊断和医疗方法的发展。③矫形术的设计以及假体和仪器的设计和制造。④提高人在工作环境、体育运动以及宇宙空间里活动的效能。生物力学在眼科也有多方面的研究应用。通过眼的生物力学的基础研究，能够增强眼科手术的预测性以提高临床效果。深入了解角膜材料本身生物力学的特性，对正确评估现代屈光手术后的效果有重要意义。
手术、疾病和外伤均能引起角膜的生物力学特性的改变，而导致这种改变的主要因素有两点：(1)角膜材料的特性。(2)角膜薄壳形状的结构特性。如果要获得角膜对手术、疾病和外伤等宏观力学反应的预测，在角膜生物力学特性试验研究中，这两个因素是必须描述的重要指标。
关于角膜生物力学用于实验研究先进设备有超声弹性显微镜、单轴拉伸、共聚焦角膜显微镜、飞点扫描图像跟踪系统、动态力学分光镜、全息干涉度量仪。
生物材料的特性由本构方程来描述，广义上是一种应力-应变的方程。一种材料的本构方程只能通过实验来决定。对生物固体材料能做的最简单的实验是单轴拉伸实验。冯元桢教授通过软组织的一维拉伸实验结果提出准线性粘弹性概念。
目前，对角膜生物力学的实验研究中，大致有两种实验手段来描述角膜的生物力学特性：一种是离体角膜片的膨胀实验(也称纽扣实验)，而另一种则是离体角膜条带拉伸实验。两种方法各有优缺点，纽扣实验虽接近角膜的生理状态，但是只能够获得角膜材料的一维数据。而角膜是各向异性材料，条带拉伸实验则能够体现出角膜的各向异性生物力学特征。缺点是受初始状态的影响。两者都能够体现出角膜的非线性的弹性材料特征。
研究角膜的材料特性是为了进一步深入了解角膜对疾病外伤手术等因素的生物力学反应，有重要的临床意义。角膜的材料特性也是应用工程、数学和数字技术，建立以有限元技术为基础的角膜在手术、疾病等外部因素作用下仿真模型的基本要素。
近十年来，有限单元法(Finite element method，FEM)在国内生物力学领域不断获得发展。在方法技术与机理研究、医疗器械评价、临床问题模拟等多个方面，能及时跟踪国外研究现状，并针对国内的临床实际问题，建立了各类仿真模型及开展了相关研究工作。有限单元法是一种在工程科学技术中广泛应用的数学物理方法，用于模拟并解决各种工程力学、热学、电磁学等物理场问题。当FEM应用于人体生物力学研究时，显示了极大的优越性。经过长期的进化过程，人体形成了一个近乎完美的力学结构。由于通常的力学实验手法基本上无法直接应用于人体，对人体的力学行为进行有限元数值模拟就成为深化对人体认识的一种有效手段。
近年来，准分子激光手术矫正眼屈光不正的有效性、安全性已得到临床证实。准分子激光原位角膜磨镶术(Laser in situ keratomileusis，LASIK)手术被眼科医生普遍采用及认可。由于其安全快捷的治疗方式、术后满意的裸眼视力而使该手术目前广泛应用于临床。但是术后仍存在并发医源性圆锥角膜、远期能否引起角膜的张力性下降等潜在性问题，目前尚缺乏与之相关的、深入的基础研究，尤其是生物力学方面的研究国内报道甚少。
LASIK手术由于部分切除了角膜，人眼角膜在被部分切除后的变形状况如何，依从什么变形规律，术后角膜的受力情况怎样，每个手术参数对手术效果起到什么样的作用和影响，人眼角膜完整性受到破坏后，其整体的张应力改变是眼科学者们关心的问题。
本研究应用生物力学手段，对准分子激光原位角膜磨镶术后角膜的生物力学特性进行初步研究，并对术后角膜生物力学变化作定量分析，以及进一步行计算机有限元法模拟研究，以探讨准分子角膜屈光手术的安全阈值。
实验材料和方法
一、生物力学实验部分
1、猪眼LASIK手术模型的建立
新鲜离体猪眼共92只(46只用于应力应变实验，另46只用于应力松弛实验)，经视神经灌注维持眼压恒定，行常规LASIK手术，基质床分别切削30％、50％、70％整体角膜厚度。应力-应变实验及应力松弛实验均按切削深度分组：30％角膜厚度组、50％角膜厚度组、70％角膜厚度组，每组各10只眼，单纯切角膜瓣组10只，正常组6只。用自制的模具尺，切取哑铃型试件，20％人血白蛋白液浸泡，冰箱4℃过夜保存，次日用于力学实验测试。
2、应力-应变实验及应力松弛实验
将试样吸干蛋白液，置于自制夹具固定，于美国Tyiron250力学实验机做应力应变实验及应力松弛实验。应力-应变实验加载速度为10mm／min，而应力松弛突加载荷的加载速率为385mm／min，伸长比为1.5，松弛时间1000S，计算机自动采集数据。
二、计算机模拟部分
(一)、LASIK手术仿真三维模型的建立
1、角膜模型剖面的模拟及建立
1．1角膜的几何模型
本文的模拟计算中，采用国内外较普遍认可的数据，具体参数见表1。
表1角膜的几何参数(单位mm)
眼轴长度26.50角膜水平直径11.20
角膜平均厚度0.67角膜垂直直径11.0
角膜中心厚度(Φ3mm) 0.55角膜旁周边(Φ3～7mm)厚度0.72
角膜周边厚度(Φ7-12mm) 1.0角膜前表面弯曲半径7.80
角膜后表面弯曲半径6.80
由上表参数可以看出角膜各个区域的厚度是平滑过渡而非分段变厚度，根据以上参数运用NURBS(Non-Uniform Rational B-Splines：非均匀有理B样条曲线)数学方法进行角膜剖面图曲线的绘制，经过分区间角膜厚度的表示，以及NURBS理论插值运算，即可得到较为理想的角膜剖面图曲线图。
1．2 NURBS(非均匀有理B样条曲线)定义几何形状
角膜剖面的两条NURBS曲线的连续性采用C2标准，角膜的建模过程中，因为角膜的几何参数是分区间定义的，采用分区间作辅助点，选适当的几个点作NURBS曲线插值得到相应曲率的曲线。利用AutoCAD软件进行角膜的剖面绘制。
1．3 AutoCAD软件系统中NURBS曲线反求算法模型
对给定的型值点{pi}i=0，1，…，n，反算曲线控制顶点{dj}，j=0，1，…，n+k-1，再由顶点{dj}构造通过{pi}的k次NURBS拟合曲线，由于节点矢量序列U=[u0，u1，…，un+2k]采用累加弦长方法。采用的三次NURBS曲线需补充k-1=2个边界条件，AutoCAD用的是矢切条件。对于wj，AutoCAD一般默认为wj=1，构造出初始曲线，再根据形状细调，此时需要用命令SPLINEDIT＼REFINE＼WEIGHT来选择进行。
2、手术实体模型的建立
LASIK手术基本操作方法是先在角膜表面切开直径为9mm，厚度约130微米的角膜瓣，然后用准分子激光对中间角膜基质进行切削，再将切开的角膜瓣复位。在实体模型的建立过程中，建模的过程基本上和手术的操作过程是一致的。在手术模拟之前首先需要建立眼球角膜的完整实体模型，以便利用布尔运算、实体修改等操作。其中完整角膜的建立需要用到前面的角膜实体模型截面图来建成完整的角膜实体模型。建成完整的角膜实体模型以后，进一步对手术进行建模模拟，具体过程是先做出角膜瓣部分，然后做基质床切削模拟，最后对角膜瓣进行修改以使其能覆盖在切削后角膜上面。
3、材料的定义
在计算中选取生理条件相似，被普遍认同的数值来作为计算依据。角膜近似地被认为是不可压缩材料，学者Woo认为其泊松比为0.49，已被广泛引用和认同。
本计算中应用的常数为：角膜，Ex=1.8MPa Ey=1.8MPaμ=0.49；巩膜，Ex=3.08MPa Ey=3.08MPaμ=0.49。
计算过程中选取的温度为人体的正常体温37摄氏度
4、单元的选择
ANSYS软件单元库中有很多不同的单元类型，因为角膜是一种比较规则的生物组织。依据其形状和特性，选取可以划分为六面体并且适合对角膜组织分析的SOLID185和SURF154单元进行计算。
(二)、有限元计算模型的建立
本研究利用软件集成的办法，但在CAD软件中并不建立实体模型，只是建立角膜及巩膜纵向截面图，这样有利于应用非均匀有理B样条曲线来根据测得的参数来模拟角膜的截面图，也有利于手动划分网格操作。
在AutoCAD软件中模拟建立角膜的剖面图，之后对角膜瓣的剖面进行模拟。按照测得的角膜数据建立的角膜瓣及角膜剖面图。
将得到的剖面图输出为ANSYS有限元分析软件能够识别的SAT格式，以备导入之用。将得到的SAT格式文件导入到ANSYS软件中，利用ANSYS软件自带的SAT接口即可实现。
文件导人之后在ANSYS软件中进行前处理操作，如定义材料特性，划分网格等操作，本文中试验采用手动分网，这样可以人为地控制分网在不同地方的精度，可以减少不必要的资源浪费，如巩膜部分不是我们考察的重点，所以就不需要划分得太密。在AutoCAD和ANSYS两软件中联合进行划分网格和计算仿真并对其进行不断地修改，以获得精确的结果数据。
为研究手术中基质消融深度等参量对手术效果的影响，须构造出这些参量不同数值的多个几何模型进行对比研究。这些参量的对比情况如下：基质切削深度30％、50％、70％角膜厚度，光学区直径5.0mm，5.5mm，6.0mm，6.5mm。修边区3.0mm。眼内压在许可的范围内选取四个值(单位：mmHgh)：15，20，25，30。换算为以Pa为单位，即：2000，2670，3330，4000。角膜模型中的几何参数参照表1，角膜的拱高取3.10mm。
由于在角膜的球面上切开不贯穿厚度切口，属三维立体构图，空间位置及坐标比较难于确定，因此需多步骤分层完成。构图中多次调用了球面单元，和其他的单元进行布尔运算，加合得到不完全切透的模型。
实验结果
一、LASIK手术后猪眼角膜的生物力学特性
1、随角膜切削深度增加，其断裂时的应力减小，发生屈服的应力减小。当角膜的30％整体厚度被部分切削时，角膜的弹性模量和单纯切瓣时无明显统计学差异(P＞0.05)，接近正常角膜组织的弹性模量。当基质层被部分切除50％和70％时，角膜的弹性模量明显降低(P＜0.05)，加载很小的载荷即被拉断。角膜材料发生屈服的临界点对应的应变在30％左右。角膜材料没有明显的屈服阶段。基质消融50％以上时，角膜的垂直轴向屈服强度明显小于水平轴向的屈服强度(P＜0.01)。
2、LASIK手术中，单纯切开角膜瓣即导致了角膜的应力松弛程度降低，P＜0.05，可能角膜依然保持其粘弹特性。当激光消融30％角膜整体厚度及大于此值时，角膜的应力松弛程度几乎下降了一倍，P＜0.01。在LASIK手术中角膜的纵向应力松弛程度不如横向的变化明显，尤其是在70％切削深度条件下，角膜的横向应力松弛程度小于纵向应力松弛程度，有显著的统计学差异(P＜0.001)
二、LASIK手术有限元计算机模拟
1、建立三维立体仿真LASIK手术模型
在利用软件集成成功建立角膜、巩膜模型基础上，构建LASIK手术实体模型，相对于每一种几何情况，因几何形状不同建立的有限元模型都会有一些差别，以切削深度为30％(0.165mm)光学区直径5.0mm为例：本次建模共建立节点数为6051个，共建立单元数为5154。建立SOLID185单元4032个，其中角膜部分为2304个，巩膜部分为1728个；建立SURF154单元共1152个。
2、LASIK手术中各手术参数变化对手术效果的影响模拟
LASIK手术中，切削30％角膜厚度及以下时，同一光学切削区直径、同一眼压条件下，角膜的应力有随切削深度增加而增加的趋势，但是应变在同一水平上。眼压不变条件下，光学切削区直径增加，角膜的应力增加，应变则维持不变。光学切削区直径不变条件下，不同的眼压作用下引起的角膜变形量是不同的，当眼压值达20mmHg时，应变增加了32.0％左右，当眼压增至25mmHg时，应变增加了65.0％左右；而当眼压升高到30mmHg，角膜应变增加98.0％左右，6.0mm的光学切削区直径，在不同的眼压条件下引起的角膜变形最小，在光学切削区直径6.5mm时，在不同的眼压条件下，导致的角膜的变形量最大。
结论
1、LASIK手术中，当30％整体角膜厚度的基质激光消融时，角膜仍维持其粘弹性材料特征。
2、应用有限元方法能够成功建立角膜的三维仿真实体模型；应用手工分网及单元拆分技术能够成功模拟LASIK手术过程。
3、20mmHg的眼内压引起的角膜变形在33％左右，是保持角膜弹性变形的临界眼压值。
4、6.0mm的光学切削区直径，在不同的眼压条件下引起的角膜变形最小，是LASIK手术的首选光学切削区。
Preface
Biomechanics is the science which concerns about the mechanical aspects of organism, that is, the response of a certain organ or tissue to force or locomotion. Biomechanics had been widely used in medical field, and formed a new branch-clinical biomechanics. Biomechanics had its effects in dealing with the problems as following: (1) in understanding the physiological and pathological process of life-form in the level of molecule, cell, and organ. (2) in promoting the development of clinical diagnosis and treatment. (3) in the design of rectify and manufacture of substitute, (4) in the exaltation of effectiveness of human activity in different circumstances. Biomechanics had also been used in Ophthalmology. The basal researches can help to improve the prediction and clinical effect of refractive surgery. The important characteristics of cornea are the transparency and with no blood vessels, and its major function is to refract light. The deep understand of material properties of cornea is of great importance for evaluation of results of modern refractive surgery.
Surgery, disease and injury can cause biomechanical changes in cornea, and the major factors on this changes are the material property and thin shell property of cornea. These two important factors must be descriptive in biomechanical studies for prediction of surgery, disease and injury in cornea in macro level.
There are a kind of methods applied in research of biomechanics of cornea, including ultrasound elastic microscope, monoaxial extension, confocal microscope, laser scanning track system, dynamic mechanical spectroscope, holographic interferometer.
Material property are described with structural equation, it is generally a stress-strain equation. The structural equation of a certain material can only be determined by experiment. The most simple experiment for solid tissue material is the monoaxial extension. Professor Feng yuanzheng had put forward the concept of sub-linear visco-elasticity by plane-extension text of soft tissue.
At present, there are two methods in describing material properties of cornea in biomechanical researches; inflate test (button test), and strip extension test. Inflate test can only provide plane data though it is close to the physiological status of cornea; whereas strip extension test can reflect the property of ani-sotropy of cornea, though it is affected by original status of material. Both methods can prove the non-linear elastic material behavior. It is clinically important to understand deeply the biomechanical response of cornea to disease, injury and surgery by finding out the material property of cornea which is the basic factor in constitution of imitate model based on finite element technology with the application of engineering, mathematical and digital techniques.
For the past decade, Finite element method (FEM) had been widely used in the field of biomechanics in our country. The international status has been concerned in the aspects of study methods of mechanism, evaluation of medical equipment, clinical simulation, and so on. Imitate modeling and relative studies had been performed.
Finite element method is a mathematical-physical technique, which is used to simulate and solve problems in engineering mechanics, calorifics, electromagnetics and etc. FEM had shown huge advantages when used in the study of biomechanics of human body which is a perfect mechanical structure. FEM will also be a effective method in the study of mechanical behavior, for common methods can not be used directly in human body.
Up to now, refractive correction with excimer laser has been proved to be effective and safe. Laser in situ keratomileusis (LASIK) has been ratified and applied worldwide in an increasing population with satisfied postoperative result. But we still face with problems such as operation-induced keratoconus, decrease of corneal tensility. However, there are still a few correlative basic researches, especially in the field of biomechanics.
After partial ablation by LASIK, what status on distortion the cornea is in, what rule it will obey, what force the cornea will endure,what impact on the outcome each parameter will have, and what change on stress-strain the cornea will meet, all these are necessarily concerned. we put up a pilot study on biomechanical behavior of cornea after LASIK with Finite Element Method, analyze post-operative biomechanical changes quantificationally, and setup a mathematical model in an attempt to obtain a safety-threshold of laser ablation.
Material and Method
一、Experiment on biomechanics
1、Constitutive models of ablated porcine cornea
Usual LASIK was performed on 92 fresh porcine eyes (42 for stress-strain test, 42 for strain relaxation test respectively) with stable intraocular pressure (IOP) maintained through optic nerve irrigation. The ablation depth on stromal side is 30%、50%、70% respectively(10 eyes each depth). 10 eyes had only flap-cutting procedure, anther 6 eyes without management for control. Then the dumbbell-shaped corneal strip segments were cut and stored in 20% Human Albumin solution for use (about 12 hr).
2、Stress-strain test and stress relaxation test
Corneal specimens were mounted onto a specially designed bracket attached on to Tytron250 machine equipped with a 50 N capacity load cell. For stressstrain test, the loading speed was 10mm/min; and for stress relaxation test, the loading speed was 385mm/min, with elongation rate of 1. 5 and relaxation time of 1000s. The data were collected electronically.
二、computer simulation
(一)、imitate 3-dimension LASIK model
1、modeling of corneal trans-section
1.1 geometric model of cornea
Corneal geometric parameters are based on recognized data, as shown in table 1.
table 1 corneal geometric parameter (mm)
axial length 26.50 Horizontal diameter 11.20
corneal main thickness 0.67 Vertical diameter 11.0
Central thickness (Φ3.0) 0.55 Pericentral thickness (3.0～7.0) 0.72
Peripheral thickness (Φ7.0-12.0) 1.0 Corneal anterior radius 7.80
Corneal posterior radius 6. 80
NURBS (Non-Uniform Rational B-Splines) mathematical method was used to protract the ideal corneal trans-section profile curve by denotation of subarea thickness.
1. 2 definition of geometric shape with NURBS.
C2 criterion was taken in continuity of two NURBS curves of corneal transsection. because the corneal geometric parameters are regional, subarea method was chosen, some points were selected as assistance in construction of corneal medel. AutoCAD software was used in the protract of corneal section plane.
1.3 model of reverse calculation of NURBS curve with AutoCAD.
With given values in point {pi} i =0, 1,…, n, reverse calculating the apical points {dj}, j =0, 1,…, n + k-1, then construct the NURBS draft curve by {pi} passing through {dj}; because the series vector of node were U = [ u0, u1,…, un +2k], so accumulated increment of srings method was adopted. Triple NURBS curve was renewed with number of k-1=2 boundary conditions, under this circumstances, tangent vector procedure was selected in AutoCAD. With default wj = 1 for AutoCAD, SPLINEDIT\REFINE\WEIGHT instruction was chosen to refine the original curve.
2、building of actual LASIK model
In LASIK procedure, a corneal flap was firstly made with the diameter of 9mm and the depth of 130μm, then stromal ablation was performed with excimer laser, recover the flap finally. The construction of model is similar to the operation, a intact corneal model was built first with the trans-section curves described above, in order to apply Bull-calculation and modification. Then simulate the operation, beginning with the corneal flap cutting, and succedent ablation, recovery of flap.
3、definition of material
The calculation was based on recognized data. The cornea was deemed to be non-compressable. The Poisson' s ratio was 0.49 determined by Dr. Woo and recognized widely.
The constant used in this study were: Ex = 1. 8MPa Ey = 1. 8MPaμ= 0.49 for cornea;,Ex =3.08MPa Ey =3.08MPaμ=0.49 for sclera.
Normal body temperature(37℃.) was selected for working temperature.
4、select of calculation unit
There are different kinds of calculation unit for selection in ANSYS software database. Because of the regularity of cornea, SOLID18 and SURF154 unit were chosen.
(二)、construction of finite element model
In this study, we only built a corneo-scleral portrait trans-section, it is better for corneal modeling with NURBS data, and for subsequent manual net topology. After the corneal section modeling with AutoCAD, the section of flap was modeled with corneal data.
The section was transferred into SAT format which can be recognized by ANSYS analysis software, and then transmit to ANSYS through SAT meet.
Manual net topology was decided to artificially control the precision., and to decrease the analysis coast. Net plot and imitation were performed and refined with the combination of AutoCA and ANSYS.
several models should be made with different value of parameters such as ablation depth, to evaluate the effect on the result of surgery. These parameters were; ablation depth of 30%、50%、70%; the optic diameter of 5. 0mm, 5. 5mm,6. 0mm,6. 5mm; the marginal area of 3mm; the IOP of 15, 20, 25, 30mmHg(2000, 2670, 3330, 4000 Pa respectively). Corneal parameter were as in table 1, and corneal arch is 3.100mm.
Because of the non-penetrating cutting, the cornea is a 3-dimension structure, and should be built by multi-steps.
Bull-calculation was used in combined spherical unit and other kind of unit applied in this study, to create a partially ablated model.
Result
一、Biomechanical properties of porcine cornea after LASIK
1, As ablation depth increased, the Break-Stress decreased, and Stress-at-Yield also decreased. When the ablation depth was 30%, the corneal elastic modulus was similar to that of a single flap-cutting cornea as well as a normal cornea, with no statistical significance (P＞0. 05). When the ablation reached to 50% and 70%, the corneal elastic modulus decreased obviously, and it is easy to break the strip with a minimal load. The critical strain-at-yield of cornea was about 30%. The corneal material had not a relaxed phase. When the ablation depth was more than 50%, the corneal load-at-yield in vertical meridian was lower than that in horizontal direction (P＜0. 01).
2, In LASIK procedure, though a single flap-cutting can cause a little reduction of corneal stress relaxation, P＜0. 05, the cornea may still remain its property of visco-elasticity. When ablation depth was 30% or more, corneal stress relaxation decreased to almost one half, P＜0.01.
Corneal stress relaxation in vertical meridian was lower than that in horizontal direction, especially when ablation depth was 70%, and it' s statistically significant P＜0.001).
二、computer simulation of LASIK with Finite Element Method
1、construction of 3-dimension imitate LASIK model
Based on the integration function of software, the corneo-scleral model was constructed, and then, was the LASIK model. There were certainly differences in finite element modeling because of the geometric shape. For example, in the case with the ablation depth of 30% (0.165mm) and diameter of 5.0mm, 6051 nodes had been built, within these, 4032 units for SOLID185, 2304 for cornea, 1728 for sclera, and 1152 units for SURF154.
2、simulation of effects of varied parameters on LASIK
When the ablation depth was under 30% of corneal thickness, corneal stress had the trend to increase with the depth, and the strain was in the same level. When the IOP was stable, corneal stress increased with ablation diameter, the strain remained unchanged. When the ablation diameter was fixed, corneal deformation was different with different IOP, the strain increased 32. 0% under IOP of 20mmHg; when IOP was 25mmHg, the strain increased 65.0%; when IOP was 30mmHg, the strain increased 98.0%. Under different IOP With ablation diameter of 6. 0mm, corneal deformity is the least. The corneal deformation was most serious with ablation diameter of 6.5mm under different IOP.
Conclusion
1. Cornea will still maintain its visco-elastic property even if 30% of its total thickness was ablated by LASIK.
2. 3-dimension imitate true model can be built with finite element method; LASIK procedure can be simulated with manual net topology and unit split technique.
3. 20mmHg of IOP can cause corneal deformation of 33% percent, it is the critical IOP.
4. Under different IOP With ablation diameter of 6.0mm, corneal deformity is the least, it is the preferred diameter.
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22．甘为人体肌骨软组织动力响应的混合有限元解法[J]湘潭大学自然科学学报，2000，22(2)：115-118
23．刘一，徐莘香 股骨干骨折钢板固定的三维有限元模型[J]白求恩医科大学学报，1995，22(2)：147-149
24．张美超，黄文华，王柏川，等应用有限方法评价颈前路蝶形钢板的力学性能[J]第一军医大学学报，2001，21(10)：740-742
25．帅玉妹，曹清气压膝关节机构强度的三维有限元分析[J]江汉石油学院学报，2000，22(2)：40-41
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28. Pinsky PM, et al. A microstructurally-based finite element model of the incised human cornea. J Biomech,1991;24(10):907-922.
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