September 2012




A new way to determine refractive operations efficacy

by A.I. Myagkikh, Ph.D., Ost-Optik K Co., Ltd., Vladivostok, Russia

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Source (all) : Alexander I. Myagkikh, Ph.D.

In the last 10 years, researchers and clinicians have made efforts to unify how the results of refractive operations are represented. The common goal has been to standardize output data to quickly evaluate the efficacy, safety, predictability, and stability of refractive surgery. One of the recommended graphical representations has been a histogram of Snellen's cumulative non-corrected visual acuity added with the cumulative corrected visual acuity before surgery.1 However, this kind of histogram is not completely successful for several reasons: 1. A cumulative representation does not consider what every operated eye contributes.

2. There is no descriptive presentation about the difference in pre- and post-op visual acuity in connection with the operation performed. This is particularly obvious in the event of a pre-op low visual acuity.

3. A mathematical analysis of cumulative representations is difficult. In particular, it is impossible to calculate common parameters such as the average and dispersion, both of which provide the most accurate characterization of the processes under consideration.

Pre- and post-op visual acuity comparisons can provide information on the efficiency of refractive operations.2 An ideal case would be a comparison under cycloplegia. However, this type of screening can be time consuming. This is why in most refractive clinics, it is necessary to use the pre-op value of the corrected distance visual acuity (CDVA) and the post-op value of the uncorrected distance visual acuity (UDVA). This comparison is performed as a calculation of UDVA to CDVA ratio for every operated eye and construction of a graph of relevant distribution (number of eyes versus value of calculated parameter) for all data sets. The ratio of the visual acuity purely expresses improvement achieved as a result of the operation, and construction of distributions considers the influence of every operation on the "big picture." Thus, by definition, Keff = UDVA post-op/CDVA pre-op, where Keff is the efficiency coefficient of the performed refractive operation for the given eye.

The mathematical ratio may be calculated both in decimal representation and directly as Snellen's fractions in accordance with the standard mathematical rules. Calculations may also be made in logMAR scale using subtraction instead of division. Coincidence of a post-op result with a result planned in usual scales will be characterized by the following values: Keff =1, and in the logMAR scale, Keff=0.

Figure 1 shows an example of data representation in the proposed format. For comparison, the same data are represented in a cumulative form in Figure 2.

Examining the new approach

In the theoretical ideal, the resulting distribution of efficiency coefficient should represent a delta function having a zero value according to all parameters and number of operations in point 1.0 (Figure 3). In other words, all operated eyes should have a visual acuity that corresponds exactly to the corrected pre-op acuity to the fullest degree. However, it does not usually work this way for many reasonsavailability of errors in the determination of a visual acuity and calculations of operation, individual peculiarities of post-op eyesight recovery, and various methodical approaches (e.g., incomplete correction according to age). Therefore, distribution of Keff in its most informative part (about 1.0) should be similar to Gaussian normal distribution, which enables the use of standard methods of mathematical analysis. Deviation of the obtained distribution from delta function immediately gives a general idea of the efficiency of a group of the operations performed. In addition, the algorithm's high sensitivity makes possible the analysis and comparison of specific data sets as applied to different degrees of initial myopia (Figure 4), different installations, and different physicians (Figure 5). It also makes it possible to analyze the results of refractive surgery to reveal and eliminate errors. For example, a shift of the average of distribution from 1.0 may point to the availability of a systematic error in calculations or measurements and high dispersion to low accuracy of measurements or uncertainty as a result of the used ablation algorithm. Points widely dropped out of a normal distribution picture are instantly identified and reveal reasons for any shifts. For example, values on the "tail end" on the left from maximum of distribution (provided that this is not the consequence of implementation of the method's monovision or blended vision) may characterize incomplete or inaccurate correction or complications that reduce visual acuity. Values that are on the far right from maximum most likely demonstrate improper technique of visual correction before operation. This procedure may be expediently used when comparing the results of various methods of refractive surgical performance or when performing expert evaluations of the quality of work at some medical centers.

The described method includes refractive operation results only. However, it may be easily applied to any other measurements that can be compared pre- and post-op. The only requirement is that the measurements should be made with proper discreteness and accuracy. This same approach could be used for data on the quality of night and twilight vision, contrast sensitivity, IOP value, and other areas.


1. Dupps WJ, Kohnen T, Mamalis, N, et al. Standardized graphs and terms for refractive surgery results. J Refractive Surg. 2011; 27:7-9.

2. Myagkikh A.I. Methods of determining the quality of refractive surgery. In Tahchidi JP, ed. Fyodorov reading 2002: A collection of scientific papers. Moscow, 2002: 246-248.

Editors' note: Dr. Myagkikh has no financial interests related to this article.

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