Jack T. Holladay

Proper method for calculating average visual acuity.

C alculating the average visual acuity and standard deviation on a series of patients is not difficult , but has been done incorrectly in most studies. 1 The basic problem relates to the difference between the arithmetic and geometric mean for a set of numbers. For the correct average visual acuity, the geometric mean must be used, which gives significantly different values than the arithmetic mean. Modern visual acuity charts are designed so that the letter sizes on each line follow a geometric progression (ie, change in a uniform step on a logarithmic scale). 2-4 The accepted step size has been chosen to be 0.1 log unit steps, which is equivalent to letter sizes changing by a factor of 1.2589 between lines. This standard gave rise to the LogMAR (log of the minimum angle of resolution) notation, as shown in Table 1. A geometric progression of lines on the visual acuity chart was chosen because it parallels the way our visual system functions. If patient #1 has a visual acuity of 20/20 and patient #2 has a visual acuity of 20/40, we conclude that patient #1 has two times better visual acuity than patient #2 because he or she can recognize a letter twice as small. Once we have chosen to compare vision as a ratio using a reference visual angle (20/20), a geometric progression results and a geometric mean must be calculated for a meaningful result. Notice in Table 1 that the only values that increase linearly are the line numbers and the LogMar notation. The Snellen acuity, decimal acuity, and visual angle all increase by the geometric factor of 1.2589. Once we decide that equal steps in visual acuity measurement are geometric and not arithmetic , we must use the appropriate geometric mean to compute the correct average (Figure). In Table 1 and the Figure, we see that line 0 is the 20/20 Snellen acuity that corresponds to the LogMAR value zero, since 20/20 is the standard. We also see that line 10 is the 20/200 Snellen visual acuity that corresponds to a LogMAR value of +1.00 (ten times or 1 log unit worse than 20/20). Intuitively, it would appear that halfway between line 0 and line 10 would be line 5, or 20/63. This is the correct average, because geometrically it is halfway between 20/200 and 20/20. The two incorrect methods would be to take the arithmetic …

A three-part system for refining intraocular lens power calculations

ABSTRACT A three‐part system that determines the correct power for an intraocular lens (IOL) to achieve a desired postoperative refraction is presented. The three components are (1) data screening criteria to identify improbable axial length and keratometry measurements, (2) a new IOL calculation formula that exceeds the current accuracy of other formulas for short, medium, and long eyes, and (3) a personalized “surgeon factor” that adjusts for any consistent bias in the surgeons results, from any source, based on a reverse solution of the new formula; the reverse solution uses the postoperative stabilized refraction, the dioptric power of the implanted IOL, and the preoperative corneal and axial length measurements to calculate the personalized surgeon factor. The improved accuracy of the new formula was proven by performing IOL power calculations on 2,000 eyes from 12 surgeons and comparing the results to seven other currently used formulas.

A new intraocular lens design to reduce spherical aberration of pseudophakic eyes.

PURPOSE The aim of this study was to design and evaluate in the laboratory a new intraocular lens (IOL) intended to provide superior ocular optical quality by reducing spherical aberration. METHODS Corneal topography measurements were performed on 71 cataract patients using an Orbscan I. The measured corneal surface shapes were used to determine the wavefront aberration of each cornea. A model cornea was then designed to reproduce the measured average spherical aberration. This model cornea was used to design IOLs having a fixed amount of negative spherical aberration that partially compensates for the average positive spherical aberration of the cornea. Theoretical and physical eye models were used to assess the expected improvement in optical quality of an eye implanted with this lens. RESULTS Measurements of optical quality provided evidence that if this modified prolate IOL was centered within 0.4 mm and tilted less than 7 degrees, it would exceed the optical performance of a conventional spherical IOL. This improvement occurred without an apparent loss in depth of focus. CONCLUSION A new IOL with a prolate anterior surface, designed to partially compensate for the average spherical aberration of the cornea, is intended to improve the ocular optical quality of pseudophakic patients.

Calculating the surgically induced refractive change following ocular surgery

ABSTRACT Calculating the surgically induced refractive change following ocular surgery is important for evaluating the results of keratorefractive procedures, smaller incisions and various wound closures for cataract surgery, and the effect of suturing techniques and suture removal following corneal transplant surgery. We present a ten‐step method of calculating the spherical‐ and cylindrical‐induced refractive change in a manner suitable for a programmable calculator or personal computer. Several applications are given including (1) adding the overrefraction to the spectacle correction, (2) determining the surgically induced refractive change from the preoperative and postoperative refractions, (3) determining the surgically induced refractive change from the K‐readings, (4) rotating axes, (5) determining the power at meridians oblique to the principal meridians of a spherocylinder, (6) determining the coupling ratio, and (7) averaging axes. Standard methods for calculating and reporting aggregate results are also given.

Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing, and corneal topography

PURPOSE To demonstrate the functional vision and corneal changes following laser in situ keratomileusis (LASIK) determined by contrast sensitivity, glare testing, and corneal topography. SETTING University of Texas Medical School, Houston, Texas, USA. METHODS Seven patients ranging in age from 20 to 61 years who had bilateral LASIK were evaluated preoperatively and 1 day, 1 week, and 1 and 6 months postoperatively. Visual acuity, using letters on the Baylor Visual Acuity Testor (BVAT) at 98% (standard acuity) and 13% contrast, and the contrast threshold were determined at 3 light levels (darkness, medium brightness acuity testor [BAT], high BAT). Pupil sizes were measured at each level, and corneal topography was performed at each visit. RESULTS The greatest changes were found 1 day postoperatively: The contrast threshold worsened by a mean of 0.6 lines +/- 1.0 (SD) (P = .05) in darkness, 0.4 +/- 0.7 lines (P = .05) at medium BAT, and 0.8 +/- 0.7 lines (P = .002) at high BAT. The 98% contrast acuity decreased a mean of 1.4 +/- 1.6 lines (P = .01) in darkness, 1.0 +/- 2.0 lines (P = .09) at medium BAT, and 0.8 +/- 2.3 lines (P = .22) at high BAT. The 13% contrast acuity decreased a mean of 2.2 +/- 2.6 lines (P = .01) in darkness, 1.3 +/- 1.9 lines (P = .02) at medium BAT, and 1.4 +/- 2.5 lines (P = .07) at high BAT. The predicted corneal acuity (PCA) obtained from corneal topography decreased by a mean of 3.3 +/- 3.1 lines (P = .002), and the asphericity (Q-value) increased by an average of +0.35 +/- 0.67 (P = .07). All values returned to the preoperative levels by 1 week except PCA, asphericity, visual acuity at 13%, and contrast threshold in darkness, which improved slightly but had not returned to baseline by 6 months. The 98% contrast acuity at medium BAT improved by 0.2 +/- 1.0 lines (P = .34) and 0.3 +/- 0.8 lines (P = .16) at high BAT at 1 month. The 98% contrast acuity values remained 0.3 lines over baseline through 6 months. Corneal topography showed that all corneas became oblate after LASIK to a mean Q-value of +0.47 +/- 0.40 (P = .0001) and PCA was decreased by 1.6 +/- 1.1 lines (P = .0002) at 6 months. CONCLUSIONS Functional vision changes do occur after LASIK. The optical quality of the cornea is reduced and the asphericity becomes oblate. Changes in functional vision worsen as the target contrast diminishes and the pupil size increases. These findings indicate that the oblate shape of the cornea following LASIK is the predominant factor in the functional vision decrease.

Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations

Purpose: To provide a method and values that facilitate standardization of constants for ultrasonic biometry, keratometry, and intraocular lens (IOL) power calculations. Setting: University of Texas Medical School, Houston, Texas, USA. Methods: Keratometry and ultrasonic biometry provide the two measured input variables for the six variable vergence equations used to calculate the appropriate IOL power for a specific patient with a cataract. A review of the literature reflecting the past 156 years of research and development reveals the appropriate index of refraction to be used with the keratometer for net optical corneal power, the location of the principal planes of the cornea, the nominal value for retinal thickness, and the appropriate velocities for ultrasonic measurement of the axial length. The relationship of the thick IOL to the thin IOL is derived along with the physical location of the thick lens. Two methods are described that provide the best IOL constant to be used by a manufacturer to minimize the prediction error for a surgeon using the lens for the first time. The formulas for phakic IOLs and secondary piggyback IOLs are also derived and applied to methods described above for standard IOLs. Results: Using a standardized net index of refraction of 4/3 for the cornea eliminates a variability of 0.56 diopter (D) in the predicted refraction. Using a standardized 1532 m/s velocity for axial length measurements and adding a value of 0.28 mm reduces the tolerance of axial length measurements to ±0.03 mm for any length eye. The physical location of the thick IOL’s secondary principal plane must be anterior to the thin lens equivalent by approximately the separation of the principal planes of the thick lens. For biconvex poly(methyl methacrylate) IOLs, the separation in the principal planes is approximately 0.10 mm. Using these relationships, the physical position of the thick lens within the eye can be used to confirm the lens constant for any IOL style. Conclusions: Standardizing the constants for keratometry, ultrasonic biometry, and IOL power calculations can significantly improve the predictability of refractive outcomes. Back‐calculating and physically measuring the position of the lens within the eye can provide surgeons with an initial lens constant known to have a standard error of the mean of ±0.05 mm (±0.10 D). Other parameters such as the cardinal points of a lens, the shape factor, the lens‐haptic plane, and the center lens thickness would allow further refinement of IOL power calculations.

Analysis of aggregate surgically induced refractive change, prediction error, and intraocular astigmatism

Purpose: To demonstrate analytical methods for evaluating the results of keratorefractive surgical procedures and emphasize the importance of intraocular astigmatism. Setting: University of Texas Medical School, Houston, Texas, USA. Methods: A standard data set, provided by an editor of this journal, comprising the preoperative and postoperative keratometric and refractive measurements of 100 eyes that had keratorefractive surgery was evaluated by 2 methods, vector and spheroequivalent (SEQ) analysis. The individual and aggregate surgically induced refractive changes (SIRCs) and prediction errors were determined from the refractive and keratometric measurements using both methods and then compared. The refraction vertex distance, keratometric index of refraction, and corneal asphericity were used to make the results calculated from refractive data directly comparable to those derived from keratometric data. Doubled‐angle and equivalency plots as well as frequency and cumulative histograms were used to display the data. Standard descriptive statistics were used to determine the mean and standard deviation of the aggregate induced astigmatism after converting the polar values (cylinder and axis) to Cartesian (x and y) values. Results: The preoperative SEQ refractive errors were undercorrected by at least 0.25 diopter (D) in most cases (78%). Six percent were corrected within ± 0.24 D, and 16% were overcorrected by at least 0.25 D SEQ. The mean SEQ was −6.68 D ± 2.49 (SD) before and −0.61 ± 0.82 D after surgery, reflecting a SIRC SEQ of −6.07 ± 2.40 D. The defocus equivalent (DEQ) was 7.41 ± 2.53 D before and 0.96 ± 0.74 D after surgery; for a nominal 3.0 mm pupil, this corresponded to an estimated improvement in uncorrected visual acuity (UCVA) from worse than 20/200 to better than 20/25, respectively. The predictability of the treatment decreased as the attempted refractive correction increased. The average magnitude of the refractive astigmatism was 1.46 ± 0.61 D before and 0.40 ± 0.38 D after surgery. The centroid of the refractive astigmatism was +0.96 × 87.9 ± 0.85 D, &rgr; = 0.43 before and +0.11 × 83.1 ± 0.37, &rgr; = 0.49 after surgery. The decrease in the square root of the centroid standard deviation shape factor (&rgr;1/2) indicated an 8% increase in the amount of oblique astigmatism in the population. The prevalence of preoperative keratometric irregular astigmatism in excess of 0.5 D in this group of patients was 13%. The correlation between keratometric and refractive astigmatism was extremely poor before (r2 = 0.26) and especially after surgery (r2 = 0.02), demonstrating the presence of intraocular astigmatism and the limitations of manual keratometry. The centroid of intraocular astigmatism at the corneal plane was +0.48 × 178 ± 0.49 D, &rgr; = 0.59, and was compensatory. Conclusions: The 2 analytical methods are complimentary and permit thorough and quantitative evaluation of SIRCs and allow valid statistical comparisons within and between data sets. The DEQ allows comparison of refractive and visual results. The decrease in refractive predictability with higher corrections is well demonstrated by the SEQ and doubled‐angle plots of the SIRC. Doubled‐angle plots were particularly useful in interpreting errors of cylinder treatment amount and errors in alignment. The correlation between refractive and keratometric astigmatism was poor for preoperative, postoperative, and SIRC data, indicating the presence of astigmatic elements beyond the corneal surface (ie, intraocular astigmatism). Sources of error in refractive outcome statistics include the use of multiple lens systems in the phoropter, errors in vertex calculations, difficulty in accurately defining the axis of astigmatism, and failure to consider measurement errors when working with keratometric data. The analysis of this particular data set demonstrates the significant clinical benefits of refractive surgery: an 8‐fold increase in UCVA, an 11‐fold decrease in SEQ refractive error, as well as a 9‐fold and nearly a 2 1/2‐fold decrease in the magnitude and distribution of astigmatism, respectively.

Optical performance of multifocal intraocular lenses

ABSTRACT The optical performance of one monofocal and five multifocal lenses was evaluated in the laboratory and photographically. The laboratory testing included determination of the modulation transfer function (INITF), through focus response (TFR), resolution efficiency, and Strehl ratio of each lens. The photographic testing included photographs of the Regan high contrast acuity chart at ten feet with clearest focus and 18 additional photographs in which the image was defocused using minus trial lenses in 0.25 diopter increments. A color photograph of the Kodak color chart was also taken using each lens. All testing was conducted using a 3 mm artificial pupil under ideal implant conditions with no decentration or tilt. The laboratory and photographic results demonstrate that all the multifocal lenses had a two‐ to three‐fold increase in the depth of field with at least a 50% lower contrast in the retinal image. The photographic testing revealed aone to two line better resolution limit with the monofocal lens, which corresponded to the 12% to 41% better MTF cut‐off value with the monofocal lens by laboratory testing. The measured resolution efficiencies of all six lenses were comparable. The color photographs revealed color mixing of adjacent colors vvith the multifocal lenses, whereas the colors appeared unchanged from the original with the monofocal lens.

The FDA Report on Intraocular Lenses

Clinical studies of intraocular lenses (IOLs) as investigational devices have been regulated in the United States by the Food and Drug Administration (FDA) since 9 February 1978. As of August 1982, data have been collected on more than one million IOLs implanted. During the last 12 months of the study, 409 000 IOLs were implanted. Visual acuity of 20/40 or better at one year after surgery was present in 85% of over 45 000 cases reviewed. Increasing patient age, surgical problems, postoperative complications, and adverse reactions were factors that reduced the visual acuity. The current trend in the USA is for implantation of posterior chamber and anterior chamber IOLs.

Evaluating and reporting astigmatism for individual and aggregate data

Purpose: To demonstrate the proper method for evaluating and reporting astigmatism for individual and aggregate data. Setting: University of Texas Medical School and Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA. Methods: The surgically induced refractive change (SIRC) was determined for three data sets of patients who have had keratorefractive (photorefractive keratectomy) or cataract surgery. To make changes in refraction comparable, vertex distances for the refractions and keratometric index of refraction were considered. Doubledangle plots and single‐angle plots were then used to display the data. Polar values (cylinder and axis) were converted to a Cartesian (x and y) coordinate system to determine the mean value of the induced astigmatism for each data set. Results: Doubled‐angle plots clearly demonstrated the trends of induced astigmatism for each data set, and the mean value for induced astigmatism agreed exactly with the intuitive appearance of the plot. Conclusions: Converting astigmatism data to a Cartesian coordinate system allowed the correct computation of descriptive statistics such as mean values, standard deviations, and correlation coefficients. Using doubled‐angle plots to display the data provides the investigator with the best method of recognizing trends in the data.