Refractive keratotomies are a remarkable group of procedures that have allowed surgeons to create subtle changes in refractive error without a detailed understanding of how these changes occur. Our current application of radial keratotomy for the correction of myopia is based on empirical measurement refined by the many procedures performed on patients over the last 10 to 15 years. These empirical investigations have concentrated predominately on safety,1-4 evaluation of the effect over time,4 and predictability,3 while tending to overlook the biomechanical mechanisms leading to flattening of the central cornea. Under and overcorrections have provided much of the impetus that is needed to better understand the mechanics of radial keratotomy.5"7
In an effort to understand under- and overcorrections, the concept of the tissue addition theory of radial keratotomy has been advanced.8 In this theory, the additional tissue introduced by means of spreading of the incisions and filling with scar tissue is associated with central corneal flattening in radial keratotomy. Undercorrections and overcorrections can be explained within this context. Overcorrections have been attributed to incomplete wound healing9-10 resulting in wide incisions. Increasing the tensile stress across the wound, thereby reducing wound gape, as seen with the circular suture or individual sutures, has been an effective means of reducing overcorrections. Undercorrections have been attributed to incisions of inadequate depth, resulting in incisions which do not spread adequately. Studies of secondary operations to deepen these incisions, thus increasing wound gape, have shown an increase in central corneal flattening.11,12 Additional radial incisions, which also add additional tissue, have also been shown to be effective in secondary operations to increase the effect of radial keratotomy.5"7,13,14 Thus incision width is seen within the context of this theory to be an important parameter in radial keratotomy. While incision spreading is a consistent morphologic indication of effect, it does not provide a mechanism for prediction of effect.
FIGURE 1 : Schematic diagram of experimental setup.
Topographic evaluation of the corneal surface has certainly given insight into the changes which occur after refractive keratotomy. Rowsey et al have shown that the cornea flattens over incisions and that radial incisions flatten the cornea in the meridian of the incision and 90° away.15"16 Both photokeratography and the more sophisticated videokeratography instruments17"18 clearly show flattening of the central cornea and midperipheral bulging associated with radial keratotomy incisions. These data suggest that weakening of the cornea, resulting in bulging, may play an important role in the effect of radial keratotomy. Unfortunately, topographic investigation of incisional procedures provides only tantahzing clues to the mechanism underpinning these changes since both the additional tissue theory and the corneal weakening theory give similar topological appearances.
Attempts to utilize elasticity theory to expose the mechanisms of radial keratotomy have provided evidence of the potential of this approach;19"22 however, most of these studies are based on theoretical analysis without new laboratory measurements. To fully evaluate these analyses, measurements must be performed and experiments must be constructed to test and improve our models of the cornea.
Most investigations of the constitutive properties of the human cornea have utilized a strip testing methodology.23"26 Strip testing provides a convenient geometric form to conduct stress/strain measurements, but in the case of the cornea, this methodology has distinct limitations. First, the water balance of the cornea, which is maintained by an intact Descemet's membrane and Bowman's layer, is compromised and the cornea has a tendency to swell if its hydration is maintained with exogenous fluids. Moreover, the cornea is a layered structure and the collagen fibrils, which run at roughly orthogonal angles in successive layers, are severed, thus compromising the essential structure of the test strip. An improved approach involves measurement of strain with an intact cornea, since this technique maintains the integrity of Descemet's membrane, Bowman's layer, and the collagen fibrils. This technique is a variant of the membrane inflation method, since the cornea forms a natural membrane. The analysis of membrane inflation measurements, particularly with the cornea, is complicated by the very low magnitude of corneal deformation across the physiologic range of pressure, as the cornea stretches only a few microns in this range. The other problems associated with this analysis are the varying thickness across the cornea, the significant inhomogeneity as regarding the layered internal structure of the cornea, and problems involving the thin membrane approximation for the relatively thick cornea.
Membrane inflation of the cornea for the measurement of the stress/strain relationship is reported in the literature;2729 however, the methodologies presented in these studies do not lend themselves to the measurement of strain across keratotomy incisions. To our knowledge, the spreading profile of radial keratotomy incisions has not been measured. In this article, we have measured the spreading of radial keratotomy wounds as a function of the distance from the optical center, thus providing a wound spreading profile over the length of the incisions. This work has been performed in human cadaver specimens. We have evaluated the spreading of the wound under physiologic conditions with increasing intraocular pressure.
MATERIALS AND METHODS
Five human cadaver eyes were utilized in this study which were prepared by placing them under high pressure in SK solution as described by Swinger and Kornmehl.30 The cornea was removed with approximately a 2.00- to 3.00-millimeter rim of sclera and placed in an artificial anterior chamber designed to attach to the Baribeau Micronscope® (Fig 1). This artificial anterior chamber was then connected to a mercury manometer through IV tubing filled with BSS so that the cornea could be maintained at a specified pressure. Corneal curvature was measured on each cornea with a Humphrey automated keratometer and found to be an average of 7.70 ± 0.30 mm. Central corneal pachometry was performed on each cornea and an average of 0.73 ± .030 mm was obtained. A 3. 00-millimeter optical zone was marked using an optical zone marker and gentian violet. A four-zone radial keratotomy marker was used to mark the position of the incisions so that two of the incisions were along the axis of one of the micrometers of the micronscope used to move the stage laterally. Using a 10-0 nylon suture on a TG- 140 needle, two suture fragments were inserted very superficially and parallel to the incision to be measured approximately 0.10 mm apart. The distance between the sutures at the optical zone was measured and this was repeated in 1.00millimeter increments to 4.00 mm beyond the optical zone or 5.50 mm from the optical center (Fig 2).
FIGURE 2: Schematic representation of sutures and incisions placed in corneal specimen.
These distances were measured at 25 and 100 mm Hg as measured with the mercury manometer. Since strain is defined as the change in length divided by the resting length, we may plot our results in terms of strain which is a dimensionless quantity rather than actual separation between sutures. Moreover, by utilizing the governing equation for transverse stress in a thin-walled spherical membrane:31
transverse stress = pressure × radius/2 × thickness
we can calculate the stress at a given internal pressure shown in Table 1. Although this equation is correct for thin-walled spheres and independent of material properties, the cornea, with its complex layered structure and peripheral scleral support, is not in reality described as a thin spherical membrane and should be more accurately described by a finite element model. Nevertheless, equation 1 provides an adequate first approximation for the transverse stress induced by internal pressure in this experiment using the measured keratometry and pachometry.
The radial incision was then created using a diamond knife from the limbus toward the optical zone set at 100% of the paracentral thickness as measured with a DGH pachometer. The distance between sutures was then remeasured at the optical zone and at 1.00-millimeter increments extending to 4.00 mm from the optical zone or 5.50 mm from the optical center at both 25 and 100 mm Hg. Finally, three additional incisions were created using the technique noted above forming a four-incision radial keratotomy. The incisions were remeasured at the optical zone and at 1.00-millimeter increments extending to 4.00 mm from the optical zone or 5.50 mm from the optical center at both 25 and 100 mm Hg. Each measurement was repeated three times and an average value was taken for the distance between sutures at that point. Furthermore, to avoid measurement bias, the readings were taken from the micrometer by a separate observer so that the measurement was blind from the viewpoint of the person actually taking the measurement.
Sample Calculations Utilizing Equation 1 to Calculate Change in Transverse Stress
In the first part of the experiment, we measured the increase in separation between sutures as the pressure was raised from 25 to 100 mm Hg before any incisions were made. In Figure 3, the strain induced due to a pressure increase from 25 to 100 mm Hg is plotted as a function of distance from the optical center. Also plotted is the average strain with a solid line. The average strain for the entire experiment is 6.95 × IO^sup -3^. There seems to be no discernible pattern of strain as a function of distance from optical center which is consistent with our general assumption that the cornea is relatively homogeneous as we progress outwards from the optical center. By utilizing equation 1 for a thin-walled sphere using our average values for corneal thickness (0.73 mm) and radius (7.70 mm), we can calculate the stress over this interval and the elastic modulus. This calculation yields an average value of 7.58 × 106 N/mp 2 and is slightly higher than the value measured by Hoeltzel et al23 with strip testing of human cornea in this range of intraocular pressure (Table 2).32"34 It should be noted that this approximation has limitations since we are aware of the nonlinear relationship that exists between stress and strain in the cornea, and this measurement represents only a first order linear approximation (secant modulus in this experiment versus tangent modulus with the strip testing).23 It should also be noted that most of the previous measurements of elastic modulus for the cornea and sclera were performed with strip extensiometry and this method utilized a whole cornea which may induce a difference. Finally, a finite element model, such as that performed by Woo et al27 should really be used instead of equation 1 to calculate elastic modulus.
FIGURE 3: Strain induced by increasing pressure from 25 to 100 mm Hg with average strain represented by solid line.
Comparison of Measured Results for Elastic Modulus IOP Modulus
In Figure 4, we present the spreading of a single incision of an eight-incision radial keratotomy performed with a 3.00-millimeter optical zone as a function of distance from the optical center for each of the five eyes at 25 mm Hg. The solid line represents the average of the five measurements (one for each eye) at each position. Although the data is quite variable, we can appreciate the following general trends. The incisions spread least at the ends and most in the middle. The maximum average spreading of the incision occurs at the 7.00-millimeter optical zone (3.50 mm from the optical center) and is approximately 50 µ or 0.05 mm.
In Figure 5, we examine the additional (original spreading at 25 mm Hg subtracted) spreading of one radial incision as the intraocular pressure is raised from 25 to 100 mm Hg. Although the data are somewhat variable, we can appreciate a definite additional spreading of the incision at 100 mm Hg compared to that measured at 25 mm Hg of approximately an additional 20 µ. This additional spreading appears to be smallest at the ends of the incisions and greatest at the 7.00-millimeter diameter zone, 3.50 mm from the optical center. This increased spreading with increases in intraocular pressure gives an experimental rationale to the use of pressure lowering medications to reduce the refractive effect of radial keratotomy. Moreover, this supports the use of suturing at a 7-millimeter diameter zone (where wound spreading is measured to be the greatest) to further reduce overcorrections.
FIGURE 4: Spreading profile of radial incision as a function of distance from optical center measured in microns with error bars showing standard error of the mean at each measurement location.
FIGURE 5: Additional spreading of radial incision caused by raising pressure from 25 to 100 mm Hg calculated as the difference between the spreading profile at 25 and 100 mm Hg.
We have examined the coupling effect of radial incisions by measuring the spreading profile of our original radial incision after adding the three additional radial incisions necessary to complete a fourincision radial keratotomy. In Figure 6, we show the additional spreading (original spreading at 25 mm Hg subtracted out) profile of the radial incision after the completion of a four-incision radial keratotomy at 25 mm Hg. Very little additional spreading is seen at 25 mm Hg; however, in Figure 7, we show the additional spreading (original spreading at 100 mm Hg subtracted) at 100 mm Hg with the addition of the complete four-incision radial keratotomy. The changes are quite small, but there appears to be a definite additional spreading induced by coupling from the other radial incisions at 100 mm Hg.
FIGURE 6: Additional spreading of radial incision with the completion of a fourincision radial keratotomy calculated as the difference between the spreading profile of a single radial incision and four radial incisions at 25 mm Hg.
FIGURE 7: Additional spreading of radial incision from 25 to 100 mm Hg with a four-incision radial keratotomy calculated as the difference between the wound spreading profile with a single radial incision at 100 mm Hg and four radial incisions at 100 mm Hg.
We present a method for the precise measurement of strain in the intact cornea. The advantage of this method lies in the ability of the micrometers used in the Baribeau Micronscope to achieve 1.00micron precision and the ability to measure corneal changes with an intact cornea. This technique should yield more accurate measurements than strip extensiometry which requires cutting the cornea (and the transverse corneal collagen fibers) into square strips.
The measurement of the spreading of radial incisions as used in radial keratotomy is an important parameter which in quantitative form can be used to test the reliability of finite element modeling of the cornea. To our knowledge, no quantitative measurements of this spreading have been published. The finding that the incisions spread most in the midcornea is not surprising given the midcorneal bulging seen on topological studies of the postradial keratotomy cornea. The maximum spreading at the 7.00millimeter diameter zone is an interesting result which supports the use of circular and interrupted sutures at this optical zone to correct overcorrections.35
Equally interesting is the observation that the spreading of incisions is increased when the intraocular pressure is increased and that this additional spreading of the incisions is largest in the midcornea at the 7.00-millimeter diameter zone. Finally, the measurement of incision spreading when additional radial incisions are added to create a four-incision radial keratotomy shows the effect of coupling in radial keratotomy. Although these measurements are difficult with the precision available in this experiment, there seems to be definite evidence of increased spreading or coupling particularly in the wound spreading profile at 100 mm Hg (Fig 7).
The variability seen in this experiment indicates incomplete stabilization of relevant variables. Certainly, the lengths to be measured are so small that very subtle issues, such as shifting of the sutures in the tissue, can have profound effects on the data. Despite these shortcomings, we believe that this work illustrates a new and practical experimental environment to study quantitative surface strain in the cornea after refractive surgery.
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Sample Calculations Utilizing Equation 1 to Calculate Change in Transverse Stress