Investigative Ophthalmology & Visual Science Cover Image for Volume 59, Issue 9
July 2018
Volume 59, Issue 9
Open Access
ARVO Annual Meeting Abstract  |   July 2018
Final Astigmatism Formula: An easy way to predict astigmatism after cataract surgery
Sara Sanchez Tabernero
Author Affiliations & Notes
  • Sara Sanchez Tabernero
    Cornea, Ashford and St Peter's Hospital, London, London, United Kingdom
    Hospital Clínico Universitario de Valladolid, Valladolid, Spain
  • Footnotes
    Commercial Relationships   Sara Sanchez Tabernero, None
  • Footnotes
    Support  None
Investigative Ophthalmology & Visual Science July 2018, Vol.59, 2228. doi:
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      Sara Sanchez Tabernero; Final Astigmatism Formula: An easy way to predict astigmatism after cataract surgery. Invest. Ophthalmol. Vis. Sci. 2018;59(9):2228.

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Abstract

Purpose : The evolution and perfecting of cataract surgery technique poses an increasing relevance on refractive success. Astigmatism management is hence key. With this purely theoretical work we aim to provide a quick tool to predict resulting corneal postoperative astigmatism.

Methods : This formula has been obtained by means of basic trigonometry calculations. It is based on vector calculations (Figure 1) but obviates the need of drawing while providing more exact results.

Results : Figure 2
This tool can be used for single case quantitative calculation of the resulting corneal astigmatism after cataract phacoemulsification surgery. It also applies in any other surgery or situation when astigmatism is regular. It works for with the rule and against the rule astigmatism.

Conclusions : This formula enables anyone with a scientific calculator, online or else, to quickly determine final corneal astigmatism. The only required data are initial corneal astigmatism magnitude and axis and SIA magnitude and axis. A derived formula can also be used to calculate SIA, if initial and final astigmatism are known.

This is an abstract that was submitted for the 2018 ARVO Annual Meeting, held in Honolulu, Hawaii, April 29 - May 3, 2018.

 

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: cos α0=α/A0 → a=A0cos α0 cos αSIA=b/SIA → b=SIAcos αSIA sin α0=c/A0 → c=A0sin α0 sin αSIA=d/SIA → d=SIAsin αSIA Af, a+b and c+d form another right-angle triangle where Af is the hypotenuse. By Pythagoras’ Theorem: Af2= (a+b)2+(c+d)2 Af=√(a+b)2+(c+d)2 Af=√(A0cos α0+SIAcos αSIA)2+(A0sin α0+SIAsin αSIA)2
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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:

cos α0=α/A0 → a=A0cos α0
cos αSIA=b/SIA → b=SIAcos αSIA
sin α0=c/A0 → c=A0sin α0
sin αSIA=d/SIA → d=SIAsin αSIA

Af, a+b and c+d form another right-angle triangle where Af is the hypotenuse.
By Pythagoras’ Theorem:

Af2= (a+b)2+(c+d)2
Af=√(a+b)2+(c+d)2
Af=√(A0cos α0+SIAcos αSIA)2+(A0sin α0+SIAsin αSIA)2

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:

cos α0=α/A0 → a=A0cos α0
cos αSIA=b/SIA → b=SIAcos αSIA
sin α0=c/A0 → c=A0sin α0
sin αSIA=d/SIA → d=SIAsin αSIA

Af, a+b and c+d form another right-angle triangle where Af is the hypotenuse.
By Pythagoras’ Theorem:

Af2= (a+b)2+(c+d)2
Af=√(a+b)2+(c+d)2
Af=√(A0cos α0+SIAcos αSIA)2+(A0sin α0+SIAsin αSIA)2

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: cos α0=α/A0 → a=A0cos α0 cos αSIA=b/SIA → b=SIAcos αSIA sin α0=c/A0 → c=A0sin α0 sin αSIA=d/SIA → d=SIAsin αSIA Af, a+b and c+d form another right-angle triangle where Af is the hypotenuse. By Pythagoras’ Theorem: Af2= (a+b)2+(c+d)2 Af=√(a+b)2+(c+d)2 Af=√(A0cos α0+SIAcos αSIA)2+(A0sin α0+SIAsin αSIA)2
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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 SIA= corneal Surgically Induced Astigmatism (in D) aSIA= angle of cornea meridian where more steepening occurs
View OriginalDownload Slide

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
SIA= corneal Surgically Induced Astigmatism (in D)
aSIA= angle of cornea meridian where more steepening occurs

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
SIA= corneal Surgically Induced Astigmatism (in D)
aSIA= angle of cornea meridian where more steepening occurs

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 SIA= corneal Surgically Induced Astigmatism (in D) aSIA= angle of cornea meridian where more steepening occurs
View OriginalDownload Slide

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Copyright © 2025 Association for Research in Vision and Ophthalmology.
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