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Vector Analysis of Residual Cylinder
LEITERS
number of data points as has been more commonly done in previous studies. I agree that axial curvature maps do not reflect shape. They are not supposed to. They simply reflect the axial curvature solution. Local curvature maps (instantaneous or tangential) do not reflect shape either. Shape can only be derived from local curvature maps by making certain assumptions about corneal shape. These assumptions, while often appropriate for normal corneas, can lead to significant errors and erroneous clinical conclusions in abnormal corneas. Since the utility of topography is in analyzing abnormal corneas, I would urge extreme caution in evaluating "shape" maps derived solely from curvature data. While it is true that false ring patterns can arrive from sharp object transitions, this was clinically a problem for only the simulated hyperopic test object. All the systems were able to image the remaining objects without dropped or doubled rings. The paper's conclusions were independent of the single hyperopic test object. In reference to the authors' statement concerning their previous paper dealing with the accuracy of the Keratron and its clinical applicability, I find a number of potential shortcomings in their study. 1. The authors averaged 1024 to determine accuracy. All the points fell on the same rotational plane and had the same local curvature. By averaging over 1000 points, it is impossible to conclude anything specific about the point accuracy of the unit. Local curvature maps use second-order differentials and are inherently more noisy than axial maps. The averaging severely limits the clinical usefulness of the study. 2. The test objects utilized were rotationally symmetric aspheres. While it is true that the cornea is aspherical, it is not rotationally symmetric. A human cornea would not have the same local curvature values along an entire plane. Conclusions drawn in the paper are not readily applicable to human corneas. 3. The majority of the data reporting and accuracy values were derived outside the central 2 mm optical zone. This is, however, the area in our testing in which the Keratron performed poorly. The central 2 mm is an area of clinical concern and is critical for central island detection and for evaluating visual aberrations. Although the paper describes the advantages of the arc-step method, the Humphrey MasterVue, which also utilizes an arc-step reconstruction, performed differently and did not have the large errors in the central region that were exhibited by the Keratron . Dr. Cohen and Ms. Tripoli should be commended on their numerous papers, which have added significantly to the understanding of topography. Each study, however, has inherent limitations. I believe the value and limitations of my study were clearly outlined. Corneal topography is
872
continually evolving. It is not my intention to suggest that anyone study be solely relied on.-Michae/ W. Belin, MD
Vector Analysis of Residual Cylinder
I
n the paper on photo refractive keratectomy using an erodible mask, I it is disappointing to see the obviously satisfactory results of the technique described without reference to cylinder axis. It is quite apparent that reduction of astigmatism can only be fully analyzed if the axis of the preoperative cylinder is compared with the postoperative axis. If there is a reduction of cylinder power and a "shift" in axis of the residual cylinder by comparison with the preoperative axis, then, in topographical terms, one cannot express the residual cylinder power as a percentage of the original cylinder power. What has happened on the corneal surface is that all the preoperative cylinder at the preoperative axis has been removed and a new cylinder induced at the postoperative axis. Methods for this kind of analysis exist. 2,3 Vector analysis should now be the standard for reporting refractive, keratometric, and topographic outcome of all procedures aimed at altering astigmatism. MICHAEL G OGGIN, FRCSI, FRCOPHTH, DO
Dublin, Ireland References 1. Niles C, Culp B, Teal P. Excimer laser photorefractive keratectomy using an erodible mask to treat myopic astigmatism. J Cataract Refract Surg 1996; 22:436-440 2. Alpins NA. A new method of analyzing vectors for changes in astigmatism. J Cataract Refract Surg 1993; 19:524-533 3. Holladay JT, Cravy TV, Koch DO. Calculating the surgically induced refractive change following ocular surgery. J Cataract Refract Surg 1992; 18:429-443
Reply: We agree completely with Dr. Goggin that a vector analysis is necessary for meaningful interpretation of data. The concept of using a poly(methyl methacrylate) (PMMA) disc to correct astigmatism originated with Summit. At the time our article was prepared, the only means available was to do the correction with a handheld apparatus. The method was terribly cumbersome and technically difficult for the surgeon, as well as psychologically difficult for the patient. Only the most calm could maintain reasonable fixation during the duration. What we really wanted to determine was whether there appeared to be any merit to the concept of an ablatable mask for the correction of astigmatism.
J CATARACf REFRACf SURG- VOL 22, SEPTEMBER 1996
number of data points as has been more commonly done in previous studies. I agree that axial curvature maps do not reflect shape. They are not supposed to. They simply reflect the axial curvature solution. Local curvature maps (instantaneous or tangential) do not reflect shape either. Shape can only be derived from local curvature maps by making certain assumptions about corneal shape. These assumptions, while often appropriate for normal corneas, can lead to significant errors and erroneous clinical conclusions in abnormal corneas. Since the utility of topography is in analyzing abnormal corneas, I would urge extreme caution in evaluating "shape" maps derived solely from curvature data. While it is true that false ring patterns can arrive from sharp object transitions, this was clinically a problem for only the simulated hyperopic test object. All the systems were able to image the remaining objects without dropped or doubled rings. The paper's conclusions were independent of the single hyperopic test object. In reference to the authors' statement concerning their previous paper dealing with the accuracy of the Keratron and its clinical applicability, I find a number of potential shortcomings in their study. 1. The authors averaged 1024 to determine accuracy. All the points fell on the same rotational plane and had the same local curvature. By averaging over 1000 points, it is impossible to conclude anything specific about the point accuracy of the unit. Local curvature maps use second-order differentials and are inherently more noisy than axial maps. The averaging severely limits the clinical usefulness of the study. 2. The test objects utilized were rotationally symmetric aspheres. While it is true that the cornea is aspherical, it is not rotationally symmetric. A human cornea would not have the same local curvature values along an entire plane. Conclusions drawn in the paper are not readily applicable to human corneas. 3. The majority of the data reporting and accuracy values were derived outside the central 2 mm optical zone. This is, however, the area in our testing in which the Keratron performed poorly. The central 2 mm is an area of clinical concern and is critical for central island detection and for evaluating visual aberrations. Although the paper describes the advantages of the arc-step method, the Humphrey MasterVue, which also utilizes an arc-step reconstruction, performed differently and did not have the large errors in the central region that were exhibited by the Keratron . Dr. Cohen and Ms. Tripoli should be commended on their numerous papers, which have added significantly to the understanding of topography. Each study, however, has inherent limitations. I believe the value and limitations of my study were clearly outlined. Corneal topography is
872
continually evolving. It is not my intention to suggest that anyone study be solely relied on.-Michae/ W. Belin, MD
Vector Analysis of Residual Cylinder
I
n the paper on photo refractive keratectomy using an erodible mask, I it is disappointing to see the obviously satisfactory results of the technique described without reference to cylinder axis. It is quite apparent that reduction of astigmatism can only be fully analyzed if the axis of the preoperative cylinder is compared with the postoperative axis. If there is a reduction of cylinder power and a "shift" in axis of the residual cylinder by comparison with the preoperative axis, then, in topographical terms, one cannot express the residual cylinder power as a percentage of the original cylinder power. What has happened on the corneal surface is that all the preoperative cylinder at the preoperative axis has been removed and a new cylinder induced at the postoperative axis. Methods for this kind of analysis exist. 2,3 Vector analysis should now be the standard for reporting refractive, keratometric, and topographic outcome of all procedures aimed at altering astigmatism. MICHAEL G OGGIN, FRCSI, FRCOPHTH, DO
Dublin, Ireland References 1. Niles C, Culp B, Teal P. Excimer laser photorefractive keratectomy using an erodible mask to treat myopic astigmatism. J Cataract Refract Surg 1996; 22:436-440 2. Alpins NA. A new method of analyzing vectors for changes in astigmatism. J Cataract Refract Surg 1993; 19:524-533 3. Holladay JT, Cravy TV, Koch DO. Calculating the surgically induced refractive change following ocular surgery. J Cataract Refract Surg 1992; 18:429-443
Reply: We agree completely with Dr. Goggin that a vector analysis is necessary for meaningful interpretation of data. The concept of using a poly(methyl methacrylate) (PMMA) disc to correct astigmatism originated with Summit. At the time our article was prepared, the only means available was to do the correction with a handheld apparatus. The method was terribly cumbersome and technically difficult for the surgeon, as well as psychologically difficult for the patient. Only the most calm could maintain reasonable fixation during the duration. What we really wanted to determine was whether there appeared to be any merit to the concept of an ablatable mask for the correction of astigmatism.
J CATARACf REFRACf SURG- VOL 22, SEPTEMBER 1996