Biomechanical Properties Of Cornea After LASIK And Relative Studies

PrefaceBiomechanics 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 biomechanics1,Constitutive models of ablated porcine corneaUsual 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 testCorneal 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 model1,modeling of corneal trans-section1.1 geometric model of corneaCorneal geometric parameters are based on recognized data, as shown in table 1. table 1 corneal geometric parameter (mm)axial length 26.50 Horizontal diameter 11.20corneal main thickness 0.67 Vertical diameter 11.0Central thickness (Φ3.0) 0.55 Pericentral thickness (3.0～7.0) 0.72Peripheral thickness (Φ7.0-12.0) 1.0 Corneal anterior radius 7.80Corneal posterior radius 6. 80NURBS (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 modelIn 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 materialThe 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 unitThere 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 modelIn 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 LASIK1, 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 Method1,construction of 3-dimension imitate LASIK modelBased 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.Conclusion1. 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.