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Refractive, keratometric, and topographic determination of astigmatic axis after penetrating keratoplasty
  1. Corneal and External Eye Disease Service, St Paul's Eye Unit, 8Z Link, Royal Liverpool University Hospital, Prescot Street, Liverpool L7 8XP, UK
  1. A R S SARHAN,
  2. H S DUA,
  3. M BEACH
  1. Division of Ophthalmology and Visual Sciences, University of Nottingham, University Hospital, Queen's Medical Centre, Nottingham NG7 2UH, UK

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Editor,—We read with interest the article by Sarhanet al 1 on the effect of disagreement between refractive, keratometric, and topographic determination of astigmatic axis on suture removal after penetrating keratoplasty.

The authors make some fundamental errors in their use of vectors for the calculation of mean astigmatism and have failed to refer to the dependence of astigmatism on the overall refractive power. As clearly discussed by several authors,2-4 it is inappropriate to analyse astigmatism without analysing the overall change in refractive power. The authors state that the two groups (agreement and disagreement) were comparable before suture removal in the preoperative vector of astigmatism but do not present the mean presuture removal vector. The authors appear to calculate a mean of the scalar component of astigmatism. Vectors have both direction and magnitude and cannot be averaged in this way; doing so leads to erroneous and incorrect conclusions. It is also of concern that no post-suture removal data or refractive data are presented.

The authors also calculate the change in astigmatism using a method5 that relies on obtaining a square root—although no mention is made of which root they have used.6 As with the presuture removal data, in the calculation of the mean change in the vector of astigmatism the directional component of the vector (for example, the ordinate axis of Fig 1) is disregarded with at test on the scalar. There are several published methods for analysing astigmatism,7 ,8 which the authors appear to have overlooked. The authors need to determine to what extent the degree and direction of change in astigmatism was in the direction of the sutures removed6 and how this differed between the two groups. The presence of pseudophakia is also relevant, since there may be an influence from non-corneal astigmatism. A table including details of each subject's refraction before and after suture removal would have been illuminating.

Changes in refraction, keratometry, and topography might occur even without suture removal as part of the natural evolution of the cornea after penetrating keratoplasty so a control group is required. For example, the two groups might not have been similarly stable over time; in particular, we need to know whether the astigmatism within each group had been changing at the same or different rates.

The management of post-keratoplasty astigmatism remains an important subject and further work is needed.



Editor,—Kaye and colleagues make some valid though theoretical comments regarding vector analysis in the evaluation of post-keratoplasty astigmatism. We did use a software program for vector analysis based on the Jaffe and Clayman method of analysis of the vectors. Several formulas have been adopted to determine surgically induced astigmatism by vector analysis and further modifications have been carried out. The fundamental advantage of the Jaffe formula is its inherent consistency between refractive and keratometric changes and its sound mathematical basis.

The authors of the letter make the valid comment that natural changes in refraction, keratometry, and topography might occur as part of the natural evolution of the cornea after penetrating keratoplasty. This is correct but again a very theoretical consideration. In practice, in the presence of significant post-keratoplasty astigmatism, most corneal surgeons will not wait and hope for natural progression to obviate the error. Intervention in the form of suture removal is undertaken between 4–6 months post-graft in order to influence the existing astigmatism. Such intervention does indeed influence the astigmatism, usually favourably. Rate of change of astigmatism, in the first 6 months does not influence the decision to remove sutures.

The simple observation reported in this paper was that, in patients who have undergone penetrating keratoplasty, the axis of astigmatism as determined by refraction, keratometry, and topography does not always coincide. This observation is undisputed. The simple message of the paper was that when these three measures do not coincide, removal of sutures as indicated by topography (which is the standard practice) does not always give the desired result as when the three measures do coincide. In the absence of conformity of the three measures, other clues such as inspection of the sutures and presence of striae and stress lines should also be considered before deciding which suture to remove.


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