OPTOMETRY. An analysis of the astigmatic changes induced by accelerated o rt ho ke ratolog y I ORIGINALPAPER 1

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1 OPTOMETRY I ORIGINALPAPER 1 An analysis of the astigmatic changes induced by accelerated o rt ho ke ratolog y Clin Exp Optom ; 85: 5: John Mountford* DipAppSc FAAO FVCO FCLS Konrad Pesudovst PhD FAAO FVCO * Private Practice, Brisbane + Department of Optometry, Bradford University Submitted: 1 February Revised: 8 May Accepted for publication: 1 May Purpose: The change in corneal astigmatism induced by reverse geometry lenses for orthokeratology has not been described previously. This study examines the efficacy of accelerated orthokeratology for reducing astigmatism and whether this varies with the degree of preexisting astigmatism. Method: Twenty-three randomly chosen eyes exhibiting.5 D to 1.75 D pre-fitting with-the-rule astigmatism were retrospectively analysed. Astigmatism was measured by simulated keratometry and corneal topography before and at the completion of a course of orthokeratology. The change in astigmatism measured by keratometry was calculated by two vector analysis techniques: the Bailey-Carney method, which was designed for contact lens-induced corneal shape changes, and the Alpins method, which was designed for surgically-induced corneal shape changes. The change in astigmatism measured by corneal topography was calculated by the EyeSys Version 3. software. Results: Most patients (/3) had some reduction of astigmatism but orthokeratology is incapable of a total elimination of pre-fit astigmatism. Alpins vector analysis showed that an increased efficacy of 6 to 8 per cent would be required to eliminate astigmatism. All three methods found a 5 per cent mean reduction in astigmatism from the pre-fit level. Topographical analysis indicates that the reduction in astigmatism occurs mainly over the central. mm chord. There is a very poor correlation between the pre-and post-wear corneal astigmatism at the. mm chord (R =.11, p =.4) and the predictability of the final astigmatic axis is also poor (angle of error = 1. * 7.35). Conclusions: Accelerated orthokeratology seems more successful than conventional orthokeratology at reducing with-the-rule astigmatism. However, it reduces pre-existing astigmatism by an average of only 5 per cent and it does not do so reliably either for magnitude or direction. These results provide two useful patient selection criteria for orthokeratology. They are: assuming.5 D to.75 D of astigmatism is a satisfactory outcome, orthokeratology can be expected to be successful for pre-fitting astigmatism of up to 1. D to 1.5 D; and the greater the pre-existing astigmatism, the less likely orthokeratology is to be successful. Key words: astigmatism, contact lenses, corneal topography, orthokeratology, vector analysis This study was designed to examine the impact of reverse geometry lenses (lenses where the first peripheral curve is steeper than the back optic zone radius (BOZR)) on astigmatism in the process of accelerated orthokeratology. Specifically, this study examines the efficacy of accelerated orthokeratology for reducing astigmatism and whether this varies with the degree of Clinical and Experimental Optometry 85.5 September 4

2 Astigmatic changes in orthokeratology Mountjmd and Pesudovs preexisting astigmatism as a means of generating patient selection criteria for the procedure. Accelerated orthokeratology differs from the traditional techniques of May-Grant1 and Tabb techniques, both in the lens design and fitting philosophy as well as the corneal shape changes induced.s4-6 Orthokeratology outcome studies have mainly dealt with the changes in spherical equivalent refractive error with scant description of the astigmatic changes associated with the procedure. Kerns4 reported an unwanted increase in with-the-rule (WTR) astigmatism due primarily to the poor centration of the flat fitting lenses used in early orthokeratology. Although Coon did not report an increase in astigmatism using the Tabb designed lens, which tended to maintain centration better than the May-Grant design, reduction of preexisting astigmatism was poor. The level of astigmatic change found in the Berkeley study was also low. Ir Patterson studied the astigmatic changes induced by the Fontana method. The lens is best described as a recessed optic design wherein the central 6. mm BOZD had a curve cut 1.OO D flatter than the surrounding peripheral curves, which were fitted on-k with respect to the original corneal shape. He found a 6 per cent retention of the original astigmatism, with the general trend in astigmatic change to be: against-the-rule (ATR) to sphere or with-the-rule with-the-rule to sphere sphere to with-the-rule. The study group consisted of 8 subjects (54 eyes) and the general finding was that the reduction of astigmatism was about 4 per cent of the original value. Soni and Homer reported an approximate 6 per cent reduction in astigmatism in their studies of the OK-3 lens for orthokeratology. Although not specifically related to orthokeratology, Bailey and Carney s analysis of lens-induced astigmatic changesg indicates that where lenses are fitted flatter-than-k, the trends for changes from the initial astigmatism were for: against-the-rule: weak trend towards reduction spherical: trend towards increased withthe-rule mild with-the-rule: no change substantial with-the-rule: trend towards reduction. The literature abounds with anecdotal reports of the effect of various fitting philosophies on the reduction of astigmatism but most reports of the impact of orthokeratology on refractive error ignore astigmatism entirely. Moreover, there have been no reports on the effect of accelerated orthokeratology techniques on the reduction of corneal astigmatism. In this paper, three techniques are used to assess the corneal changes induced by lens fitting. The first uses the Bailey-Carney vector analysis approach, the second uses the vector analysis method described by Alpins, while the third is an analysis of the topographical changes measured by videokeratoscopy. The Bailey-Carney method was chosen as it demonstrates the empirics ofvector analysis and can be readily understood by those unfamiliar with the technique. It is also the technique used in the only other comprehensive study into the astigmatic changes induced by contact lens wear that makes for easy compari- S O ~. The ~ J ~ Alpins methodi4 has been designed and mainly used for refractive surgery and is able to give reliable data on the relative efficiency of a procedure. It is used here to facilitate an assessment of the efficacy of orthokeratology with respect to astigmatic outcomes. Corneal topographical analysis is used as it provides a means of analysing the corneal shape changes at specific corneal locations and meridians. METHODS Patients This paper uses the same cohort of sub jects as a previous paper that reported on the spherical topographical changes occurring in the cornea as a result of the accelerated orthokeratology procedure.6 The lens design, fitting philosophy and aftercare procedures have been described in that paper. The entire group consisted of 6 subjects, but only 5 had astigmatism of greater than or equal to.5 D and only 15 had astigmatism of greater than or equal to.75 D. Although statistics allow us to evaluate changes in astigmatism for those patients with less than.5 D, this is clearly not clinically relevant. Therefore, we have confined our analysis to those subjects with at least.5 D of astigmatism. This left a group of 3 subjects in the analysis (Table l), all of whom had WTR astigmatism of between.5 D and 1.75 D. Also, the analysis was restricted to with-the-rule astigmatism with the major axis within 3 degrees of horizontal. Some patient selection also occurred prior to the initial trial of 6 patients. This was based on the clinical experience of one of the authors (JM; see Appendix 1). For topographical analysis, the accuracy of any instrument involves a degree of noise (standard deviations too much affected by instrument margin of error).15 To assess the impact of such errors, six repeated measurements on six subjects exhibiting.5 D corneal astigmatism were made using the EyeSys instrument and the standard deviations in axial corneal power at.5 mm half chord intervals along the flat and steep meridians were calculated (Table ). The standard deviations indicated that the analysis could be more representative ifa range of.75 D or greater astigmatism was used. Although this leaves a group of only 15 subjects for the topographical analysis, it is a sufficiently large group to detect significant changes in astigmatism. This probably provides more useful information than a larger group where the real changes are partially obscured by noise. In all cases, the degree of corneal astigmatism was equal to the refractive astigmatism, so changes to the corneal astigmatism were, in effect, equal to the changes in refractive astigmatism. Bailey-Carney vector analysis Bailey and CarneyIs described a system in which the pre-fit lens-to-cornea relationship is defined as an x-y co-ordinate with a further co-ordinate describing the postwear lens-tocornea relationship plotted on the same graph. The vectorjoining the two mode-of-fit co-ordinates describes the change in corneal shape as a result of lens Clinical and Experimental Optometry 85.5 September 85

3 Astigmatic changes in orthokeratology Mmntjimd and Pesudovs Subject lnlt Rx Final Rx 1.oo oo oo Delta Rx lnit ACP Final ACP OO Orlg cyl Axis Final cyl.38 1.oo Axis Table 1. Pre- and post-treatment data Half chord (mm).5 1.oo SD (dloptres) f.1 f.14 f.15 f.4 f.37 f.36 f.45 f.35 Table. Standard deviations of repeated (6) axial radius of astigmatism (the difference between the steep and flat meridian) in six subjects with.5 D corneal astigmatism at the nominated half-chords wear. This is common to all vector analysis of astigmatism techniques. The polar coordinates for each point are made by subtracting the horizontal and vertical keratometry readings from the BOZR of the lens fitted, both pre- and post-lens wear. Figure 1 shows the graphical system used, where the x-axis is BOZR - Kh and the Y-axis BOZR - Kv. A point Po represents the mode of fit pre-wear, while point PI represents the mode of fit post-wear found by subtracting the altered horizontal and vertical keratometer values from the BOZR. Where spherical corneas are fitted with spherical lenses such that BOZR - Kh = BOZR - Kv, the mode of fit then lies along a sphericity locus that intersects the origin at an angle of 45 degrees. When the x and y coordinates are positive values, the fit of the lens is flat along the meridian concerned and if negative, the fit of the lens is steep along that meridian. In cases of WTR astigmatism, Kh is greater than Kv and the mode-of-fit point lies above the sphericity locus. Conversely, if Kv is greater than Kh, ATR astigmatism exists and the mode-of-fit point will lie below the sphericity locus. A line joining Po to PI is termed the vector and represents the change in corneal curvature induced by the lens. As with all vector analysis of astigmatism methods, the length of the vector is the index of magnitude of the refractive change and the vector direction indicates the type of change ind~ced. ~J~ The angular direction and length of the vector were determined by standard trigonometry techniques. A more detailed analysis of astigmatic changes induced by contact lens wear requires a further expansion of the technique. If the vector is parallel to the sphericity locus, Clinical and Experimental Optometry 85.5 September 86

4 Astigmatic changes in orthokeratology Mountfod and Pesudovs Figure 1. Derivation of vector direction. The relationship between pre-fit (Po) and post wear (P,) is described by the vector Po-P,. The length of the vector and its direction indicate the effect of contact lens wear on corneal shape change and refraction. Figure. Astigmatic changes are represented by the direction of the vector with respect to the sphericity locus. P,+P,: change in astigmatism, Po-P,: increase in with-the-rule astigmatism, P,+P,: total reduction in astigmatism, P,+P,: the actual change in astigmatism. the induced changes are equal in both meridians and the initial and final amounts of astigmatism remain the same. Ifthe vector direction is not parallel to the sphericity locus, then there has been a change in the astigmatism between the pre- and post-wear states. There are four possible outcomes to describe astigmatic changes assessed by vector analysis: 1. The vector direction remains parallel to the sphericity locus (that is, zero change in astigmatism).. The vector direction moves away from the sphericity locus, indicating an increase in WTR astigmatism or a decrease in ATR astigmatism. 3. The vector direction intersects the sphericity locus, indicating a total reduction of the astigmatism. 4. The vector moves in a direction somewhere between the zero change situation and the sphericity locus, indicating a reduction in but not an elimination of the astigmatism. These are shown in Figure. The line Po+P, is a vector parallel to the sphericity locus (45 to 5 degrees), whereas line Po+P, runs away from the sphericity locus, indicating an increase in WTR astigmatism. Lines Po+P, and Po+P, show the other two possibilities. In the case of Po+P,, the post-wear end-point of the vector lies on the sphericity locus, indicating that the final corneal shape is spherical and that all the pre-fit astigmatism has been eradicated. The vector Po+P, represents a condition whereby the astigmatism has been reduced from the original pre-fit level. The analysis of the differences between these vector directions is used to determine the overall effect of orthokeratology on the degree of change in corneal astigmatism. This is the main advantage of this method, as it distinctively deals with the type of astigmatism, with- and against-the-rule, so that the way each type is altered can be described. In Figure, it is obvious that the length of the vector is partly determined by the degree of astigmatic change induced. For example, in the case of Po to P,, there is a total reduction of astigmatism and the vector length is greater than for Po to P, or P,. Therefore, for the purpose of this analysis, three possible vector lengths were calculated for each individual case. The calculated vector (V,) was determined by assuming that there had been no change in the astigmatism pre- and post-lens wear in that the post-wear coordinate values were: x = BOZR- Kh,,, and y = BOZR - ( Khfina,- (Khiniea,- Kvinitidt). The actual vector (V) was that determined by the Bailey-Carney technique, whereby the post-wear coordinates were: x = BOZR - Kh (final) and y = BOZR - Kv (final). Finally, the zero astigmatism (V,) vector was determined by assuming that the post-wear coordinates lay on the sphericity locus, where x = BOZR - Kh (final) and y = BOZR - Kh (final), where Kh and Kv were equal. The vector lengths were converted to dioptric equivalents using the same relationship used by Bailey and CarneyIs (. mm equals 1. D). The proportional difference between the calculated Clinical and Experimental Optometry 85.5 September 87

5 ~~ Astigmatic changes in orthokeratology Mounlford and Pesudous vector (V,), the zero astigmatism vector (V,) and the actual vector (V) and the zero astigmatism vector represent the percentage of achieved astigmatic reduction: that is, V,- Vc = Maximum astigmatic change (Amax) and V - Vc = Actual astigmatic change (AAC). Therefore, the percentage change in astigmatism due to orthokeratology can be expressed as: Astigmatic change ( per cent) =,4AC x loq Amax Alpins vector analysis The analysis of corneal shape change induced by orthokeratology is analogous to the analysis of corneal shape change induced by surgery. Orthokeratology is often described as a non-permanent alternative to refractive surgery, so if the effectiveness of the two is to be compared, a common protocol for comparison should be employed. Alpinsl4.l6 has described a tech- nique of vector analysis that not only describes the astigmatic changes that occur as a result of surgical intervention but also applies a method of rating the success or failure of the surgery in correcting astigmatism. This is important as it facilitates the modification of the procedure by applying greater or lesser treatment to improve accuracy. The underlying principles and mathematics are fundamentally the same as those of Bailey and CarneyIs in that vector lengths represent power and angles represent axes with the change being rep resented by difference vectors, which are calculated in the same way. However, the nomenclature assumes surgery is involved and the method is extended for evaluation of the success of the treatment. For the ease of comparison to surgical procedures, the same nomenclature will be used. The term surgical induced astigmatism (SIA) is used for lens or treatment induced astigmatism, even though no surgery is involved. The analysis of the SIA where the intention is to reduce cylinder power requires the setting of a target and analysis of how well the SIA fits with the targeted induced astigmatism (TIA).I4 This allows for measurements of degrees of success and modification of subsequent treatment to improve the final result. This subsequent modification is facilitated by the proportion of the astigmatic target achieved (Alpins correction index [SIA/TIA] or its inverse, the coefficient of adjustment).l4*l6 Accurate or efficacious treatments will achieve a coefficient of adjustment close to 1.. The obvious target for any treatment is zero astigmatism, but less than.5 D is probably not clinically significant and is thus a reasonable target. Moreover, if treating large amounts of astigmatism (for example, relaxing incisions for astigmatism remaining after penetrating keratoplasty), there is insufficient predictability to aim for zero astigmatism; indeed, four dioptres is an achievable and reasonable optical result. 7 Similarly, clinical experience with orthokeratology seems to demonstrate that the procedure fails to precisely neutralise existing corneal astigrnati~m.~ For treatments that do not reduce astigmatism entirely, this method provides an elegant way of describing the efficacy of the treatment. As far as the analysis of directional changes in astigmatism is concerned, the comparison of SIA to TIA allows for an assessment of the accuracy of axis placement of treatment (Alpins angle of error ).I4 Most treatments of astigmatism aim to reduce the magnitude and not alter the axis. However, if the axis is altered, it is important to be able to specify the result with reference to the initial axis. This requires a sign convention which is plus for anti-clockwise and minus for clockwise. It is important to note that this annotation is opposite to that used in the Bailey-Carney method, where rotations away from the sphericity locus (anticlockwise) are negative. According to alp in^,'^.'^ well-placed or successful treatments will have an angle of error close to zero, with small deviations on the mean. In line with recent attempts to standardise the reporting of surgicallyinduced astigmati~m,l** ~ the data will be presented in the form of mean SIA, mean TIA, co-efficient of adjustment and angle of error. Corneal topography analysis The final group of 15 eyes with corneal astigmatism of.75 D or greater was ana- lysed by measuring the axial radius of curvature at.5 mm steps along the flat and steep corneal meridians both pre- and post-lens wear. The changes in corneal curvature and astigmatism were then measured by subtracting the pre- and post; lens wear values for each corneal position. In all cases, the topographical data were collected using the EyeSys videokeratoscope (Version 3. aspheric algorithm), which was routinely calibrated according to the manufacturer s instructions. The main purpose of using this method was to apply a technique with which a majority of contact lens practitioners were familiar. Additionally, topography allows us to examine the differential impact of orthokeratology at various distances from the corneal apex and in each hemimeridian. RESULTS Bailey-Carney vector analysis The vector directions and powers for the 3 subjects are shown in Figure 3. Of the 3 subjects, one showed no change in astigmatism (vector direction parallel to the sphericity locus 5 degrees). Two subjects exhibited vector directions moving away from the sphericity locus, indicating an increase in with-the-rule astigmatism. The rest of the group showed varying degrees of movement towards the sphericity locus, indicating a reduction in WTR astigmatism. The relationship between the deviation from the sphericity locus and the reduction in astigmatism is shown in Figure 4. Note that the vector direction is given as a negative (counter-clockwise rotation) value. The greater the deviation from the sphericity locus, the greater the reduction in astigmatism induced by the lens. However, the maximum deviation was only 13 degrees with an associated approximate reduction of 1. D astigmatism. The mean vector lengths plus standard deviations for the three possible outcomes were: Vc =.6 f.9 D V, = 3.98 f.95 D V=.96 f 1.19 D. Therefore, the actual astigmatic Clinical and Experimental Optometry 85.5 September 88

6 Astigmatic changes in orthokeratology Mountford and Pesudovs change (AAC) = V - Vc = =.338 and the maximum astigmatic change (Amax) = V,- Vc = =.676. The mean reduction in astigmatism from the initial pre-wear state expressed as a percentage is 1 x.338/.676 = 5. per cent. Alpins vector analysis Aiming for total astigmatism reduction in the 3 subjects with astigmatism of.5 D and greater (mean.87 f.36 D, range.5 to 1.75 D); mean SIA =.47D k.5 D, mean TIA =.75 f.36 D, co-efficient of correction (SIA/TIA) = 1.6 and angle of error = - 1. f 7.35 degrees. This indicates that for orthokeratology to totally correct.5 D or greater of astigmatism, the procedure would need to be 6 per cent more effective. Clearly, total elimination of astigmatism is unrealistic. A more realistic target would be a 5 per cent reduction in astigmatism. Aiming for a 5 per cent reduction in astigmatism in the 3 subjects with astigmatism of.5 D and greater; mean SIA = D, mean TIA =.43 f.18 D, co-efficient of adjustment (SIA/TIA) =.93 and angle of error = - 1. f 7.35 degrees. Therefore, a 5 per cent reduction of astigmatism for.5 D or greater is achieved with treatment effect to spare. For the purposes of comparison, the Alpins vector analysis results for the 16 subjects with astigmatism of.75 D and greater (mean = 1.3 f.36 D, range.75 to 1.75 D), areincluded. Aimingfora 1 per cent reduction of pre-existing astigmatism, the results according to Alpins method are: mean SIA =.91 *.36 D, mean TIA =.51k.8 D, co-efficient of adjustment (TIA/SIA) = 1.8, angle of error = degrees. Therefore, for orthokeratology to cause a total reduction of astigmatism in this group, it would need to be 8 per cent more effective. Notably, three subjects who began with more than.75 D astigmatism remained above.75 D after orthokeratology, whereas only one subject who began with between.5 D and.75 D astigmatism remained above.5 D after orthokeratology. Aiming for a 5 per cent reduction in H lo $ 8 v) 8 4 Subject Vector direction (degrees) Figure 3. Vector lengths and directions for 3 subjects with.5 D astigmatism or greater, o y ~ I A. I I 4 * - R a- \ -.-. Deviation from sphericity locus (degrees) Figure 4. The relationship between deviation from sphericity locus to astigmatic change the original astigmatism, the results are: mean SIA.51 f.8 D, mean TIA.5 f.18 D, co-efficient of adjustment (TIA/ SIA) = 1., angle of error = 1.49 f 31.7 degrees. Thus, for a pre-existing astigmatism of.75 D or greater, a 5 per cent reduction after orthokeratology can be expected. Four of the 16 subjects still had astigmatism of greater than.75 D after orthokeratology. Topographical analysis The pre-and post-orthokeratology astigmatism for the.75 D or greater group (n = 16) is shown in Figure 5. Paired student t- tests were performed on the pre- and postorthokeratology values at.5 mm half chords from centre. These showed a statistically significant difference over the central 1.5 mm halfchord:.5 mm, p =.4; 1.OO mm, p =.; 1.5 mm, p =.1. From. mm to 4. mm half chords, the differences were not statistically significant. The change in astigmatism is shown in Figure 6. The major reduction in corneal astigmatism occurs within the central 1.5 mm chord. The reduction at the 1. mm chord is approximately twice that observed n LI Clinical and Experimental Optometry 85.5 September 89

7 I." Astigmatic changes in orthokeratology Mountford and Pesudovs -.5 I I I I I I I Oh ) h Q 1. I A E o! '. '.!.!.!>-z I t l s t k I\ 35 "'I I I Distam from centre (mm) Figure 5. b and post-orthokeratology astigmatism for subjects with astigmatism from.75 D to. D Figure 6. The change in astigmatism caused by orthokeratology for subjects with astigmatism from.75 D to. D. y =.34x R..11 p =.M s l-. E.8 - E f :4-4.. _. I PreOK astigmatlm (D) Figure 7. The relationship between pre- and post-orthokeratology astigmatism. Although statistically significant, the agreement is poor. at the 3. mm (keratometer measurement position) chord. The relationship between the pre- and post-orthokeratology astigmatism over the 1. mm chord is shown in Figure 7. There is a very poor correlation between the two ( r =.1 1, p =.4). Figure 8 shows a subtractive topography plot of the change in astigmatism over the central area. The percentage reduction in astigmatism for the different half chord lengths are:.5 mm, 54.6 per cent; 1. mm, 49. per cent; 1.5 mm, 9.7 per cent;. mm, 1. per cent. This indicates that the major change in astigmatism occurs over the central. mm chord, the values of which agree with the results observed with the other two techniques used. DISCUSSION Vector analysis is a sensible and simple method for exploring changes in corneal shape or refractive error. It is the current standard method used for analysis of changes in astigmati~m.~~j~j~j~ The clinical sensitivity of vector analysis is illustrated in Figure 9, which shows a near perfect correlation between vector length (in dioptres) and refractive change (r' =.95, p <.1). This vindication of the use of vector analysis was included for the benefit of clinicians who may not be familiar with vector analysis. The mean length of the vectors (that is, corneal flattening,.96 D) induced by orthokeratology with reverse geometry lenses is significantly greater than that found by Bailey and Carney, where only 5 per cent of their 'flatter than K sample showed changes of approximately 1. D. The good correlations between vector length and refractive change and also vector deviation and the difference in astigmatic change justifies the use of this method as a technique for evaluating the corneal and refractive changes induced by contact lens wear. However, the Bailey-Carney method gives little predictive information on the axis direction changes that can be expected from orthokeratology. In this area, the Alpins technique has a distinct advantage. In this sample, orthokeratology did reduce WTR astigmatism but not consistently or reliably. Most patients exhibit a reduction in WTR astigmatism, however, of the 3 cases, two had an increase in WTR astigmatism, one stayed the same and the, remainder had varying degrees of improvement. Orthokeratology does not totally elimi- Clinical and Experimental Optometry 85.5 September 9

8 Astigmatic changes in orthokeratology Mountfwd and Pesudovs y = x.89 R =.95 p c o.ooo1 ~ s Change in refraction (D) Figure 9. The relationship between vector length and refractive change. There is a high correlation between the two (rp=.95, p <.1). Figure 8. The subtractive or difference plot of a subject exhibiting WTR astigmatism. Note that the vertical meridian has flattened to a greater extent than the horizontal, but mainly within the central. mm chord. nate pre-existing astigmatism. All three techniques for measuring change in astigmatism induced by orthokeratology demonstrate that a 5 per cent reduction of preexisting astigmatism occurs. The two vector analysis methods show good concordance, which is expected as they have a common basis. The Alpins vector analysis method has the advantage of quantifylng the increase or decrease in treatment effect required to reach the outcome target, the coefficient of adjustment. The results gave coefficients of adjustment of 1.6 for the greater than.5 D group and 1.8for the greater than.75 D group. Thus, the procedure would have to be between 6 per cent and 8 per cent more effective to totally correct astigmatism. The coefficient of adjustment is a more clinically sensible term when applied to laser refractive surgery because the ablation could be modified to be 6 per cent more effective. This is not possible for orthokeratology but the coefficient of adjustment is a useful description of the inadequacy of orthokeratology in eliminating astigmatism. Figure 1a. Pre- and post-wear topographyplot of a case of limbus to limbus astigmatism. Note the flattened superior cornea compared to the inferior cornea. Figure lob. Central astigmatism appears to be more evenly affected by the lens, leading to a reduction in astigmatism Clinical and Experimental Optometry 85.5 September 91

9 Astigmatic changes in orthokeratology Mountjiid and Pesudous Zero astigmatism is not a clinically necessary outcome. Certainly.5 D astigmatism has minimal negative impact on distance vision and a putative benefit for near vision in the presbyopic condition. Arguably, the same could be said for.75 D of astigmatism. Thus, orthokeratology should aim to reduce astigmatism to these levels rather than to zero. The Alpins vector analysis was repeated for a target of a 5 per cent reduction in astigmatism. For the.5 D group, this was achieved with seven per cent of treatment effect to spare. For the.75 D group, two per cent more effect was required. Thus, orthokeratology is very effective at reducing preexisting astigmatism by half. This leads us to a helpful guideline for patient selection for orthokeratology. If the realistic goal is either.5 D or.75 D of post-treatment astigmatis, these results show that orthokeratology will produce clinically acceptable results, provided that the initial astigmatism is between 1. D and 1.5 D, depending on the level of acceptable posttreatment astigmatism. Comparing the Alpins vector analysis results for the.5 D and.75 D groups demonstrates that orthokeratology is less effective at reducing higher levels of astigmatism. This is illustrated by the coefficient of adjustment. When aiming for zero astigmatism, 6 per cent more treatment effect was required to get the.5 D group to zero and 8 per cent more treatment effect was required to get the.75 D group to zero. Similarly, for 5 per cent reduction in astigmatism, the.5 D group did it with seven per cent effect to spare but the.75 D group required two per cent more effect. The other evidence for this is that four subjects who began with over.75 D still had over.75 D after orthokeratology, but only one subject with between.5 D and.75 D still had more than.5 D after orthokeratology. This may be a sample effect; the.75 D group had only 16 subjects so a couple of poor results would skew the findings. Nevertheless, the results do suggest that orthokeratology is less effective at higher levels of astigmatism. However, further study of the impact of orthokeratology on astigmatism using higher levels of astigmatism would be required to prove this point. The Alpins vector analysis method also quantifies the angular accuracy of placement of the treatment: the angle of error. For both greater than.5 D and greater than.75 D groups, the angle of error is very small (close to zero), indicating that the treatment is on axis, but the standard deviation of the angle of error is very large (greater than.5 D, 7.35 degrees; greater than.75 D, 31.7 degrees) This indicates that the direction of treatment, although on average accurate, is highly unpredictable. This unpredictability is also seen in corneal topography comparison of pre- and post-orthokeratology astigmatism, which are very poorly correlated (Figure 7). Although orthokeratology reduces preexisting astigmatism by 5 per cent, the magnitude and direction of the post-orthokeratology astigmatism cannot be predicted from pre-orthokeratology values. It is interesting to speculate on the reasons for the angle of error being so variable. There seem to be two main possibilities. First, the interaction of the lens with the cornea may be random. Whether it is random loss of centration or some other mechanism, the lens induces a highly variable, directional shape change. Alternatively, the lens is designed and fitted with respect to the flat meridian of the cornea, based on the eccentricity value of that meridian. Theoretically, a difference in the eccentricity of the steeper meridian could effect a difference in change in that meridian, which would result in a variation in the resultant vector direction. Perhaps the variability in results reflects the inadequacy of spherocylindrical refraction or keratometry in reflecting asymmetric changes. Further evidence for this is that the topography results show that substantial corneal shape changes are found outside the area measured by the keratometer. Corneal topography finds a 5 per cent reduction but only for the central. mm chord. This implies that refractive findings are greatly influenced by the central cornea. Moreover, orthokeratology has a greater influence on astigmatism reduction in the central cornea compared to the peripheral cornea. The topography results demonstrate that orthokeratology does not reduce astigmatism in the peripheral cornea (outside the central 4. mm). This confirms the clinical observation of Mountford6 that limbus-to-limbus astigmatism is difficult to treat compared to central astigmatism and justifies the selection criteria of including central astigmatism but excluding limbus-to-limbus astigmatism (Appendix 1). The major changes occur inside the area measured by traditional keratometry, namely in the central. mm chord, whereas the keratometer measures the mean meridional changes over a 3. mm chord. Topographical analysis indicates that the change in astigmatism as measured by keratometry would account for only approximately 5 per cent of the change seen. These findings reinforce the importance of corneal topography in orthokeratology. The magnitude of the reduction in astigmatism seen here with accelerated orthokeratology seems superior to previous studies of conventional orthokeratology. The directional findings of previous studies are not reproduced here, reflected by the angle of error being close to zero. The trend toward increased WTR astigmatism seems to have been eliminated by the bettercentring reverse geometry lenses. This study has several limitations. Most importantly, the patient group was selected to not include large amounts of astigmatism, limbus-to-limbus astigmatism or ATR astigmatism, as clinical experience indicates that these patients are less likely to succeed. The results presented above do suggest that patients with greater than two dioptres of astigmatism are unlikely to get sufficient benefit from orthokeratology. The majority of astigmatism reduction occurs in the central cornea, so limbus-tolimbus astigmatism is less likely than central astigmatism to be successfully treated. However, it should be stressed that these are just theories that would require additional investigation before they could be proven. A more extensive study of the impact of orthokeratology on larger amounts of astigmatism where directions and extent are compared would be ideal. The effect, if any, of a variance in corneal Clinical and Experimental Optometry 85.5 September 9

10 Astigmatic changes in orthokeratology Mountfmd and Pesudovs eccentricity between the major meridians and its effect on refractive change have not been addressed in this study due to the inability of the instrument used to calculate an eccentricity value for the steep meridian. CONCLUSIONS Although accelerated orthokeratology seems more successful at reducing WTR astigmatism than conventional orthokeratology, it still reduces pre-existing astigmatism by only an average of 5 per cent with currently available reverse geometry lenses. All currently available reverse geometry lenses have the same construction, with minor differences in the fitting philosophy, so the reductions in astigmatism achieved with the design used in this study could be expected to be reproduced with other similar designs. Moreover, it does not reduce the magnitude of the astigmatism reliably nor the direction predictably. However, these results provide several useful patient selection criteria for orthokeratology : Assuming.5 D to.75 D of astigmatism is a satisfactory outcome, orthokeratology can be expected to be successful for pre-fitting astigmatism up to 1. D to 1.5 D. The greater the pre-existing astigmatism, the less likely orthokeratology is to be successful. The topography results show that the astigmatism is reduced only centrally, which suggests that patients with central astigmatism are probably more likely to be successfully treated than those with limbus-telimbus astigmatism. ACKNOWLEDGEMENTS JM wishes to acknowledge the kind assistance of Professor Leo Carney and Associate Professor Michael Collins, School of Optometry, Queensland University of Technology in the preparation of this paper. KF would also like to acknowledge the editorial advice of Wendy Laffer from the Department of Ophthalmology at Flinders Medical Centre. REFERENCES 1. Grant SG, May CH. Orthokeratology-a therapeutic approach to contact lens procedures. Contacto 197; 14: Coon LJ. Orthokeratology. Part 1: Historical perspective.jam Optom Assoc 198; 53: Mountford JA. Orthokeratology. In: Phillips AJ, Speedwell L, eds: Contact Lenses: A Textbook for Students and Practitioner, 4th ed. London: Butterworths, 1997: Kerns R. Research in orthokeratology. Part 3.JAm Optom Assoc 1976; Poke KA, Brand RJ, Schwalbe JS. The Berkeley orthokeratology study. Part : Efficacy and duration. Am J Optom Physiol Opt 1983; 6: Mountford JA. An analysis of the changes in corneal shape and refractive error induced by accelerated orthokeratology. ZCLC 1997; 4: Patterson TC. Orthokeratology: changes to the corneal curvature and the effect on refractive power due to the sagittal length change. JAm OptomAssoc1975; Soni PS, Horner DG. Clinical Contact Lens Practice. Philadelphia: JB Lippincott, 1993, Bailey IL, Carney LG. A survey of corneal curvature changes from corneal lens wear. Contact Lens J1977; 6: Wlodyga RJ, Bryla C. Corneal molding: the easy way. Contact Lens Spect 1989; Paige N. The use of transverse axial oscillatory ocular movements to prevent or reduce corneal astigmatism during orthokeratological processing. Contacto 1981; : Potts AV. Orthokeratological reduction of astigmatism. Contact Lens Spect 1997; 1: Bailey IL, Carney LG. Analyzing contact lens induced changes of the corneal curvature. Am J Optom Arch Am Acud Optom 197; 47: Alpins NA. A new method of analysing vectors for changes in astigmatism. J Cat Refract Surg 1993; 19: Dave T, Ruston D, Fowler C. Evaluation of the EyeSys Model Computerized Videokeratoscope. Part : The repeatability and accuracy in measuring convex aspheric surfaces. Opt Vis Sci 1998; 75: Alpins NA. A new method of targeting vectors to treat astigmatism. J Cat Refract Surg 1997; 3: Lim L, Pesudovs K, Goggin M, Coster DJ. Surgical management of post penetrating keratoplasty due to recurrent keratoconus in the host cornea. Cwneu. In press. 18. Goggin M, Pesudovs K. Assessment of surgically induced astigmatism: toward an international standard. JCut Refruct Su7g1998; 4: Goggin M, Pesudovs K. Assessment of surgically induced astigmatism: toward an international standard 11. J Cat Rejract Surg 1998; 4: Sanders DR, Koch DD. An Atlas of Corneal Topography, 1st ed. New Jersey: Slack Incorporated, 1993: Author s address: John Mountford Suite 7, 1th Floor 141 Queen St Brisbane QLD 4 AUSTRALIA Appendix 1 The description of astigmatism using topographical maps divides regular corneal astigmatism into two main types when axial maps are used either limbus to limbus or central. Limbus-to-limbus astigmatism exists when the typical bow-tie pattern extends out to the limbal area. Conversely, central astigmatism exists when the bow tie is restricted to the central area of the cornea, the more peripheral corneal curves becoming almost spherical again. Clinical experience has shown that in cases of limbus-to-limbus astigmatism, the effect of reverse geometry lenses is to cause flattening of the superior half of the bow tie and steepening of the inferior half, resulting in a marked increase in corneal distortion and poor unaided visual acuity. This effect appears to be due mainly to an inability to control centration of the lenses in these cases, however, central astigmatism appears to be more evenly affected by the lens and leads to a more regular corneal surface and improved unaided vision. The topography plots of the two types of astigmatism and the effects of reverse geometry lenses on each are shown in Figures 1a and lob. All cases presenting for orthokeratology exhibiting limbus-to-limbus astigmatism were advised against proceeding with lens fitting due to the uncontrollable degree of induced corneal distortion seen in previous cases. It may be appropriate to test this hypothesis experimentally but this will be reserved for future work. Clinical and Experimental Optometry 85.5 September 93