Update on Astigmatism Analysis

The June issue of JCRS includes two articles by a working group initiated by the journal’s editors to update and establish astigmatic reporting guidelines. The first paper provides an overview of astigmatism, covering definitions, measurement technologies, and sources of error. The second paper offers recommendations for the statistical analysis of astigmatic outcomes.

The authors note astigmatism as the difference between the orthogonal principal planes of minimal and maximal powers of a toric surface or lens. Corneal astigmatism is a common condition, and studies indicate 60–78% of individuals have more than 0.5 D of astigmatism, and 20% have more than 1.5 D.

As the magnitude of astigmatism increases, the incidence of against-the-rule (ATR) astigmatism is nearly constant, varying from 26% to 31%. By contrast, the incidence of with-the-rule (WTR) astigmatism increases as magnitude increases, from 26% to 64%, corresponding to a decreased incidence of oblique astigmatism. Corneal astigmatism also changes with age. Most population studies show an age-related shift in anterior corneal astigmatism from a vertical steepness (WTR) to a horizontal steepness (ATR).

Total corneal astigmatism is calculated through raytracing, using anterior and posterior curvature measurements and corneal thickness. Various imaging technologies and algorithms help perform these measurements, including reflection (rings or single-point mires), Scheimpflug imaging, and optical coherence tomography. However, measurements from different devices are generally not interchangeable because distance differences from the centre can result in both magnitude and axis variations. Zonal keratometry (topography/tomography) over the patient’s mesopic entrance pupil samples a larger region of the central cornea, with the zone size customisable to each specific patient.

Astigmatism can be represented as a vector since it has both magnitude and direction. The magnitude is the absolute power difference between principal meridians, and the direction is defined by the meridian of greatest positive (or least negative) power. Since meridians extend in two directions from the centre, the angle must be doubled for Euclidean vector calculations. Using double-angle plots allows for vector algebra and statistical analyses, after which the angle is halved for single-angle results. JCRS will use double-angle plots to report astigmatic outcomes.

The vector prediction error (PE) is the key expression for evaluating surgically induced astigmatic change—defined as the vector difference between the postoperatively observed and refractive astigmatism predicted from preoperative measurements. Vector calculations can be performed independent of or relative to a reference meridian or axis. Double-angle plots with convex polygons and statistical analysis for astigmatism data can be easily obtained with the wrap-up functions from the Wilcox-Holladay-Wang-Koch Statistical Software using the free R Project for Statistical Computing software or with Eyetemis software, also available online.

T Kohnen, et al. “Review/Update: Standards for Analyzing Astigmatic Outcomes: Part I,” 51(6): ahead of print.

D Koch, et al. “Review/Update: Standards for Analyzing Astigmatic Outcomes: Part II,” 51(6): ahead of print.