A New Calculator For Averaging Multiple Keratometry Measurements That Incorporates In-Built Quality Checks For Spherical And Astigmatic Prediction Error

The current method of averaging multiple readings of astigmatism includes averaging orthogonal power co-ordinates. However, this produces magnitudes and angles that are skewed depending on the orientations of the meridians. For example: 1.00 D @ 0° and 1.20 D @ 10° produces an “average” of 1.08 D @ 5.45°. The purpose of this study was to investigate the aetiology of this mathematical result, develop an alternate averaging method that is more appropriate for corneal shape, and devise a clinically relevant way of detecting outlier keratometry inputs.

Ophthalmology clinic in Queensland, Australia

A series of computational examples were analysed to demonstrate the inherent flaws of averaging double angle power co-ordinates and back-calculating the “average”. Fundamental astigmatism theory was reviewed to identify the cause of this issue. Biometer exports and published data from the IOLMaster 700 (Carl Zeiss Meditec), and Eyestar 900 (Haag-Streit) were analysed to determine the averaging methods used by these flagship devices. A calculator was built that accurately averages keratometry readings and calculates the potential spherical and astigmatic prediction errors associated with each keratometry measurement.

Averaging double angle power components was found to be flawed because it involves a power-vs-meridian resolute that skews the output power and angle of repeated measurements. Biometer exports and documentation from Carl Zeiss Meditech and Haag-Streit revealed that both companies average keratometry power and angle separately. The “fan width minimisation method” was developed to correctly average any number of astigmatic meridians without computational error. The Euclidean distance between measurements was used to calculate the potential astigmatic prediction error, reported as the magnitude of an obliquely crossed cylinder.

Averaging orthogonal power co-ordinates is equivalent to averaging two power-vs-meridian curves. This is flawed because it causes a crossed-cylinder resolute. For non-negligible magnitudes of regular astigmatism, the average power and angle should be equidistant. This is because keratometry readings fundamentally reflect the geographic topography of the corneal surface. We present the PrecisionK calculator: a new tool that accurately averages keratometry readings and calculates the potential spherical and astigmatic prediction errors associated with the inputted measurements. This is freely available at: www.precisionkcalculator.com