Sir,

where:

SIA= corneal surgically induced astigmatism (in D),

Af= final corneal astigmatism (in D),

αf= final angle of cornea steepest meridian,

A0= initial corneal astigmatism (in D),

α0= initial angle of cornea steepest meridian.

The evolution and perfecting of cataract surgery technique poses an increasing relevance on refractive success. Astigmatism management is hence key. The knowledge and application of one’s surgically induced astigmatism (SIA) is essential for toric IOL implantation and an important step for any phaco surgeon striving for cataract surgery proficiency.

This formula enables single case quantitative calculation of the change in corneal astigmatism after cataract phacoemulsification surgery. It can also be applied in any other surgery or situation when astigmatism is regular. It works for with the rule and against the rule astigmatism. It has been obtained by means of basic trigonometry calculations (Figure 1) and to the knowledge of the author and after extensive research it has not been published before in this or an equivalent form. It is based on vector calculations but obviates the need of drawing while providing more exact results.

Figure 1
figure 1

Initial and final astigmatism can be represented as vectors A0 and Af. Parallel lines to the axis are drawn with resulting right-angle triangles. By the trigonometric functions of sine and cosine:

SIA, b and d form another right-angle triangle where SIA is the hypotenuse. Applying Pythagoras’ theorem:

Angle determination of the SIA can be obtained by the tangent function:

where αSIA is the angle of the meridian where more steepening occurs, the most flattened meridian will be perpendicular to it, at ±90°.

Full size image

Excellent applications that allow multi-patient analysis of SIA are available for download1 (https://sia-calculator.com) and surgeons are encouraged to use them. There may be circumstances, however, when a quick case calculation is needed or such resources are simply not available. In such cases this formula enables anyone with a scientific calculator, online or else, to quickly determine the SIA. The only required data are initial corneal astigmatism magnitude and axis and final corneal astigmatism magnitude and axis, determined by optic biometry or corneal topography.