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Assessing anterior corneal surface changes with age
LETTERS
Assessing anterior corneal surface changes with age
Q 2010 ASCRS and ESCRS Published by Elsevier Inc.
46 44
Radius (Diopters)
The recent article by Scholz et al.1 describes the change in curvature of the anterior corneal surface with age. Still remaining is the basis of our understanding of how we mathematically model the human cornea. The Q asphericity coefficient mathematically describes the rate of curvature change of the cornea from its center to the periphery and specifies the type of conicoid that best describes that cornea. Traditionally, the Q value calculated at axis 90 ignores the other axes and thus assumes that the other axes reflect rotational symmetry about axis 90. The slope measurement is customarily defined as the derivative of the function whose graph is a given curve evaluated at a designated point. The PAR Corneal Topography System (PAR Vision Systems Corp.) uses rasterphotogrammetry and, when combined with surface modeling, a proprietary technique, electronically recreates the anterior corneal surface without relying on any mathematical assumptions, such as underlying surface sphericity, and allows the placement of splines on the surface, thereby determining the arc radii along the spline at a given axis (D. Lieberman, MD, ‘‘Corneal Depth and Spline Length Measurement in Keratoconus,’’ presented at the ASCRS Symposium on Cataract, IOL and Refractive Surgery, San Diego, California, USA, April 2007). Figure 1 is an example of an uncorrected distance visual acuity of 20/15 and includes the 4 principal meridians. The spline at a given axis/diameter is calculated by 3 points: one edge point is at the corneal apex, the second edge point is at the diameter of regard, and the center point is one half the top-down 2-diameter in 3-dimensional space distance between the 2 edge points. As can be seen, the curve overall shape at the 4 axes is quite disparate. The slope measurement at axis 0 is 0.86798; at axis 90, 0.34942; at axis 180, 1.3766; and at axis 270, 0.32934. This corneal surface is clearly not rotationally symmetrical around the 4 principal meridians. Beware of the power of an average, which is what we commonly do in trying to simplify the mathematics of a complex shape, for the average of the slopes of the 4 axes is 0.26932. The authors also considered the concept(s) of fitting the mean (an average of a very large population) of the flattest/steepest arc to a generalized shape. The angle of the generalized best-fit arc changes with diameter and thus, mathematically, does not validly fit the individual cornea. Any rotationally symmetrical intraocular lens (IOL) will modify incoming light across the 4 meridians equally. A prolate aspheric IOL will make the axes that are oblate optically worse. Is this the reason
OD_Curvature Measurement at Principle Meridians 48
42
Axis 0
40
Axis 90 Axis 180
38
Axis 270
36 34 32 30
3
3.5
4
4.5
5
5.5
6
6.5
7
Diameter
Figure 1. Curvature measurement at principal meridians in a right eye.
some people are not pleased with the optical results? Mathematically, if one were to fit this cornea with an IOL that is of a sphere, the 4 meridians would be modified in power only and not in the overall profile shape. Is this the reason most IOL patients fit with a spherical IOL have very few complaints? We need to reconsider our oversimplification of corneal curvature modeling if we are to truly understand optical quality and patient satisfaction. We congratulate the authors on an excellent study and ask them to consider our concerns about currently standard assumptions of corneal symmetry. David Lieberman, MD Jonathan Grierson Brooklyn, New York, USA REFERENCE 1. Scholz K, Messner A, Eppig T, Bruenner H, Langenbucher A. Topography-based assessment of anterior corneal curvature and asphericity as a function of age, sex, and refractive status. J Cataract Refract Surg 2009; 35:1046–1054
REPLY: We are glad to address the comments of Lieberman and Grierson. First, it must be pointed out that the measurement of the asphericity coefficient Q was not limited to the vertical meridian (axis 90). To our knowledge of the instrument used and the manufacturer’s data, the measurement of the videokeratoscope involved several meridians of the cornea to calculate an average value of Q. The simplification of the shape of the human cornea to a conic section constitutes a quite rough approximation, but one that seems reasonable bearing in mind that today’s main focus in cataract surgery is to improve the contrast vision by correcting the rotational symmetric 3rd-order spherical aberration, which can be modeled by this simplification. The degradation of image quality caused by the disparity in different meridians of the cornea and the lens 0886-3350/10/$dsee front matter doi:10.1016/j.jcrs.2009.07.018
181
Assessing anterior corneal surface changes with age
Q 2010 ASCRS and ESCRS Published by Elsevier Inc.
46 44
Radius (Diopters)
The recent article by Scholz et al.1 describes the change in curvature of the anterior corneal surface with age. Still remaining is the basis of our understanding of how we mathematically model the human cornea. The Q asphericity coefficient mathematically describes the rate of curvature change of the cornea from its center to the periphery and specifies the type of conicoid that best describes that cornea. Traditionally, the Q value calculated at axis 90 ignores the other axes and thus assumes that the other axes reflect rotational symmetry about axis 90. The slope measurement is customarily defined as the derivative of the function whose graph is a given curve evaluated at a designated point. The PAR Corneal Topography System (PAR Vision Systems Corp.) uses rasterphotogrammetry and, when combined with surface modeling, a proprietary technique, electronically recreates the anterior corneal surface without relying on any mathematical assumptions, such as underlying surface sphericity, and allows the placement of splines on the surface, thereby determining the arc radii along the spline at a given axis (D. Lieberman, MD, ‘‘Corneal Depth and Spline Length Measurement in Keratoconus,’’ presented at the ASCRS Symposium on Cataract, IOL and Refractive Surgery, San Diego, California, USA, April 2007). Figure 1 is an example of an uncorrected distance visual acuity of 20/15 and includes the 4 principal meridians. The spline at a given axis/diameter is calculated by 3 points: one edge point is at the corneal apex, the second edge point is at the diameter of regard, and the center point is one half the top-down 2-diameter in 3-dimensional space distance between the 2 edge points. As can be seen, the curve overall shape at the 4 axes is quite disparate. The slope measurement at axis 0 is 0.86798; at axis 90, 0.34942; at axis 180, 1.3766; and at axis 270, 0.32934. This corneal surface is clearly not rotationally symmetrical around the 4 principal meridians. Beware of the power of an average, which is what we commonly do in trying to simplify the mathematics of a complex shape, for the average of the slopes of the 4 axes is 0.26932. The authors also considered the concept(s) of fitting the mean (an average of a very large population) of the flattest/steepest arc to a generalized shape. The angle of the generalized best-fit arc changes with diameter and thus, mathematically, does not validly fit the individual cornea. Any rotationally symmetrical intraocular lens (IOL) will modify incoming light across the 4 meridians equally. A prolate aspheric IOL will make the axes that are oblate optically worse. Is this the reason
OD_Curvature Measurement at Principle Meridians 48
42
Axis 0
40
Axis 90 Axis 180
38
Axis 270
36 34 32 30
3
3.5
4
4.5
5
5.5
6
6.5
7
Diameter
Figure 1. Curvature measurement at principal meridians in a right eye.
some people are not pleased with the optical results? Mathematically, if one were to fit this cornea with an IOL that is of a sphere, the 4 meridians would be modified in power only and not in the overall profile shape. Is this the reason most IOL patients fit with a spherical IOL have very few complaints? We need to reconsider our oversimplification of corneal curvature modeling if we are to truly understand optical quality and patient satisfaction. We congratulate the authors on an excellent study and ask them to consider our concerns about currently standard assumptions of corneal symmetry. David Lieberman, MD Jonathan Grierson Brooklyn, New York, USA REFERENCE 1. Scholz K, Messner A, Eppig T, Bruenner H, Langenbucher A. Topography-based assessment of anterior corneal curvature and asphericity as a function of age, sex, and refractive status. J Cataract Refract Surg 2009; 35:1046–1054
REPLY: We are glad to address the comments of Lieberman and Grierson. First, it must be pointed out that the measurement of the asphericity coefficient Q was not limited to the vertical meridian (axis 90). To our knowledge of the instrument used and the manufacturer’s data, the measurement of the videokeratoscope involved several meridians of the cornea to calculate an average value of Q. The simplification of the shape of the human cornea to a conic section constitutes a quite rough approximation, but one that seems reasonable bearing in mind that today’s main focus in cataract surgery is to improve the contrast vision by correcting the rotational symmetric 3rd-order spherical aberration, which can be modeled by this simplification. The degradation of image quality caused by the disparity in different meridians of the cornea and the lens 0886-3350/10/$dsee front matter doi:10.1016/j.jcrs.2009.07.018
181