Ординатура / Офтальмология / Учебные материалы / Orthokeratology Principles and Practice 2004

202 ORTHOKERATOLOGY

In contrast, however, the most commonly reported problems occurred with the quality of unaided vision, in that the patients with the higher refractive errors more commonly reported poor distance or near vision, and poor-quality vision in dim illumination (Table 7.1). This is the first research into the patient satisfaction with orthokeratology, and should not be the last. It is vital that the level of satisfaction be determined, so that patients can be told the expected success rate before starting treatment.

SUMMARY

When a reverse geometry lens is applied to the cornea, things happen quickly. The central cornea flattens in curvature and the mid-periphery steepens. There is an associated reduction in refractive error and an improvement in unaided highand low-contrast VA, although the two factors are not mutually dependent. The time for

References

an effective reduction in myopia and improved acuity is dramatically faster than that required for traditional orthokeratology, and the changes are greater in magnitude. Also, the number of lenses required has now been theoretically lowered to one set, worn on an overnight basis, compared to an average of six sets of lenses worn on a dailywear basis with the older techniques.

The changes in corneal shape and refraction are associated with the change in corneal asphericity, and this can be used as an accurate predictor of the refractive change possible. The refractive change, however, occurs as a direct result of central epithelial thinning.

There is a lot of scope for further research in these areas, including confocal microscopy of the epithelium and stroma, investigations on the relevance of mid-peripheral corneal stromal thickening, the optical quality of the posttreatment corneal shape and its effect on vision and, finally, the differences that lens design and fitting philosophy have on the outcomes.

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John Mountford

CHAPTER CONTENTS

Introduction 205 Surface area 205

The constant lamellar length model 207 Sphere oroblate: does it really matter? 210 Lens design and fitting software 212

INTRODUCTION

One of the many criticisms that have been leveled at orthokeratology is the apparent lack of a model that will accurately predict the outcome. The following section attempts to answer the criticism by using three mathematical models of corneal shape change based on the surface area and constancy of lamellar length concepts, and a modification of Munnerlyn's original formula. The second section deals with the many computer programs available to practitioners that help in the design and fitting of the lenses.

SURFACE AREA

The surface area of the cornea is considered to be constant despite localized shape changes, with the exception of keratoglobus (Smolek & Klyce 1998). The model of constant surface area as a means of predicting refractive changes in orthokeratology was developed by Day (unpublished), and is commonly referred to as the Kappa function.

In effect, the model states that the corneal surface area is a constant, and will not be changed by the effects of reverse geometry lens (RGL) wear. The cornea is assumed to change from a prolate ellipse to a sphere, with the change in apical power being equivalent to the refractive change. The surface area of the prefit cornea is calculated using the apical radius (Ro), corneal asphericity (Q), horizontal visible iris diameter

(HVID), and the resultant sag (see Ch. 4). Once the surface area is known, the equivalent spherical radius for the same surface area is found, assuming a change in sag of 9 IJ-m/D of refractive change. Kappa function is the refractive change that occurs given an initial aspheric surface that becomes spherical following treatment.

When modeling corneal shape changes, Q (asphericity) is preferred to e (eccentricity) due to the former's ability to distinguish between prolate and oblate surfaces. For the majority of the rest of this section, the asphericity (Q) changes are related to eccentricity changes only when the cornea is assumed to change for a prolate ellipse to a sphere. If the assumption that a change towards an oblate surface occurs, only the Qvalue is used.

The range of refractive change for given apical radius and corneal eccentricity values assuming a HVID of 12 mm is shown in Figure 8.1. Note that the same refractive error correction exists for a number of Ro and eccentricity values. The trend and shape of the curve are similar to

that seen for the equivalency of corneal sags, as the whole process is dependent on the initial eccentricity.

The model assumes a symmetrically rotational aspheric surface. However, in cases of with-the- rule (WTR) corneal astigmatism, the vertical curvature and eccentricity as well as the corneal diameter differ from that of the horizontal. Kwok (1984) has shown that in cases of a nonrotationally symmetrical asphere (ellipsoid), the surface area of the cornea decreases for WTR astigmatism, and increases for against-the-rule astigmatism when compared to the rotationally symmetrical model. Over the mean range of astigmatism, the error is approximately 3%, so this must be included in the kappa function in order to arrive at the correct final apical radius value. The other method of resolving the error is to use the direct integration of the variables instead of the formula (J Day, personal communication).

In the case of a model cornea of Ro 7.80, e = 0.5, and HVID 12 mm, the surface area is 130 mm-. Assuming a sag change over the same chord of

20 urn, and resolving the formula to find Ro when eccentricity is zero and the surface area 130 mm-, the corrected final Rois 8.18 mm. This equates to a refractive change of 2.00 D.

The limit of astigmatic reduction can be calculated by resolving the changes for both the steep and flat meridian using the Ro, e, and HVID values in turn, and calculating surface area for both. The difference between the final apical radii gives the value for the residual astigmatism.

THE CONSTANT LAMELLAR LENGTH MODEL

This iterative model was developed by O'Leary (Mountford & Noack 1998). It is based on the fact that, under normal physiological loads, stromal lamellae can be neither stretched nor compressed. In other words, it doesn't matter what happens to the shape of the cornea, the lamellar length will remain constant. The other constant in this argument is that the corneal diameter is fixed, and is approximately 1.25 mm greater than HVID. The question therefore becomes: if the initial Ro, asphericity (Q), and fiber length are known over a specific chord, what is the relationship between Ro and Q as the shape changes from a prolate ellipsoidal shape to a sphere and on to an oblate ellipse? The difference between the initial and "final" Ro is equivalent to the refractive change. The calculations are iterative, and require a custom program to complete.

For the model cornea of Ro 7.80 mm, Q 0.25, and HVID 12 mm, the lamellar length is 14.474 mm. The relationship between apical radius change and change in asphericity is shown in Figure 8.2. Note that the hypothetical relationship is virtually linear, with a high correlation (r 2 = 1.00). The same linear relationship exists between all combinations of Ro and Q, with only the slope of the intercept changing.

The expected refractive change is shown in Figure 8.3. The expected refractive change that occurs for a change from a prolate ellipsoidal geometry of Q 0.25 to a sphere is 2.25 D, which is indeed similar to that predicted by the kappa function. For greater refractive change, the cornea

Relationship between apical radius and asphericity (Q)

Figure 8.2 The relationship between corneal curvature change and asphericity assuming a constant lamellar length. The initial Q is 0.25 with an Ro of 7.80 mm. As Ro flattens to 8.176 mm, the Qvalue approaches zero. If the

flattening of R continues, the Q becomes negative or o

oblate.

Relationship between aspherlclty andrefractive change

Figure 8.3 The relationship between asphericity and refractive change for a model cornea of Ro7.80 and

Q= 0.25. The refractive change when Qis zero is 2.25D. If Q becomes oblate to -0.25, the maximum refractive change is approximately 4.50 D.

is assumed to become oblate, with the apical radius and asphericity changing in the same linear fashion.

Therefore, a cornea with the initial shape data as set out above has an initial limit of 2.00 D refractive change if the "final" corneal shape is a sphere (Q = 0). If, however, the assumption is made that the cornea can become oblate with

208 ORTHOKERATOLOGY

Refractive change and apical radius for Q 0.25

Change inasphericity (0)

Figure 8.4 The effect that the initial apical radius has on refractive change. Starting from a Qof zero, the refractive change increases as the Q value increases. For

steeper values of R (given the same Qvalue) the o

refractive change is greater than that of flatter Rovalues.

Relationship between asphericlty (Q). HVID and refractive change

Figure 8.5 The effect that horizontal visible iris diameter (HVID) has on refractive change. Assuming an

initial R of 7.80mm, the refractive change achieved as o

Q increases in value is greater for higher HVID values.

Predicted Vsactual refractive change

orthokeratology, the maximum refractive change becomes approximately 4.00 0, when Q = -0.2. For smaller refractive changes, between 2.25 and 4.500, the cornea is assumed to "come to rest" at an oblate shape of intermediate Ro and Qvalues.

The other variables analyzed were the effect of HVID and the initial Ro value. In the past orthokeratology studies have always noted that steep corneas change to a greater extent than flat corneas, so it is interesting to note that the model supports these observations (Fig. 8.4). However, the difference, according to the model, is not that significant, with only a 0.75 0 difference between the steepest and flattest Ro values.

The model also predicts that the greater the HVID, the greater the possible refractive change, with a variance of approximately 0.750 for an apical radius of 7.80 rom (Fig. 8.5). Unfortunately, the ideal situation of a steep cornea and a large HVIO does not occur: steep corneas are generally associated with smaller HVIOs and flat corneas with larger HVIDs (Mandell 1978).

Noack extended the program to find the intercept between the prefit aspheric surface and the final spherical surface, assuming a maximal corneal thickness change of 20 urn at the apex. The result is an approximation of the treatment zone (TxZ) diameter (see later).

Figure 8.6 The relationship between predicted (modeled) and actual refractive change. The correlation appears to be good, with the predicted refractive change being 0.15 D greater than the measured refractive change.

The accuracy of the concept was assessed by comparing the results of the predicted outcome based on the initial corneal data to the measured changes in apical corneal power using the EyeSys version 3.2 software and Contex 704T lenses on 65 randomly chosen eyes. The regression between predicted and actual changes appears quite good (Fig. 8.6), with a form of y = 1.00x + 0.15 (r2 = 0.83). This equates to a refractive change of 1.150 for 1.000 predicted change, or 2.150 for 2.000 predicted change, and so on. This would therefore indicate that the

Figure 8.7 More recent analysis shows the scatter of results, indicating that the predictions are within ± 0.40 D of the actual change at the 95% confidence level.

model tends to underestimate slightly the possible refractive change.

However, more recent analysis of the data reveals a slightly different story. In order for the "true" picture to be shown, the difference between the "gold standard" (the refraction) and

Figure 8.8 The kappa function and Noack model are highlycorrelated due to the fact that theyboth take the initial eccentricity into account. The very high refractive changes shown here are due to a combination of very

steep (7.00 mm) R values and high (0.90) eccentricity o

values. Such pre-existing corneal shapes do not occur. The "real world" changes are within 1 standard deviation of

the norm, which is an R of 7.80 and a Qvalue of 0.25. In o

the majority of cases, the refractive change range is approxi mately 2.50 ± 1.00 D.

Figure 8.9 A postwear topography plot showing areas of isodioptric change. This can be viewed asrepresenting areas of distinct spherical surfaces.

with high eccentricities will show larger changes in refractive error as the cornea is more sphericalized by orthokeratology treatment than small, flat corneas with low eccentricity. This seems to accord with clinical experience.

SPHERE OR OBLATE: DOES IT REALLY MATTER?

A controversy exists in orthokeratology circles with respect to the final corneal shape: is it a spherical, or an oblate ellipse? The argument stems from the difference in refractive change possible with RGLs compared to the traditional orthokeratology techniques. The mean refractive change possible with the May-Grant or Tabb techniques is approximately 1.00 0, and was associated with corneal sphericalization, or a final eccentricity of zero. Since RGLs produce more than twice the refractive change associated with conventional designs, it has been proposed that the final corneal shape

the model must be calculated. This is then plotted against the mean of the two results (Bland & Altman 1986). In the above example, the mean difference is 0.18 0 with a standard deviation of 0.22 O. The graphical representation is shown in Figure 8.7. This shows that, at the 95% confidence level (limits of agreement), the majority of patients will achieve an outcome that is within ± 0.50 0 of that predicted by the model. The difference in outcomes could also be partly dependent on the lens design used, and this is discussed in a later section.

How well do the two theories correspond with each other? The relationship between the kappa function and Noack's model is shown in Figure 8.8. In effect, the two are identical, as both are based on the initial Ro, asphericity, and HVlD, but used different methodologies to arrive at the same answer. The calculated changes for a range of corneal shapes at a HVIO of 11.5 are shown in Table 8.1.

We can summarize the clinical consequences from these models as follows: large, steep corneas

Figure 8.10 The "final" corneal shape assuming a spherical surface over differentzones. Note that as the "final" spherical curve becomes flatter, the treatment zone (TxZ) diameter is decreased. The diagram shows three zones of increasing spherical curves from the center to the edge of the TxZ. Compare this with Figure 8.9.

Figure 8.11 The new postorthokeratology corneal profile isshown in yellow, illustrating an oblate surface. A topographer would reconstruct this surface as zones of equal dioptricchanges, as in Figure 8.9.

Refractive change: sphere and oblate

Figure 8.12 The difference in outcomes depending on whether an oblate or sphere is the model. The differences are not clinicallysignificantly different.

becomes oblate. This would explain a greater change than that which is possible when sphericalization occurs. This is supported by the appearance of the postwear topography maps that show the central cornea to be flatter than the midperipheral cornea (Fig. 8.9).

The "spherical shape" assumption is based on the results of the earlier studies into orthokeratology. Also, statistical analysis of the postwear corneal shape shows that the radii of curvature of the centralS.OO mm chord are not statistically different from each other, indicating a spherical surface (Mountford 1997).

If a greater refractive change is required over and above that which is possible with corneal sphericalization, the following model applies. Assuming a maximum change of central epithelial

Figure 8.14 The WAVE screen output. The tear layer profile, fluorescein pattern, andallied data areshown. "Topo demand" refers to the liquid lens power of the tear layer.

thickness of 20 urn, a greater refractive change would require a flatter spherical curve over a smaller diameter, resulting in a smaller TxZ diameter (Munnerlyn et aI1988). This is shown diagrammatically in Figure 8.10.

212 ORTHOKERATOlOGY

The postwear corneal topography plot shown in Figure 8.9 indicates that there are differing zones of isodioptric change. This is similar to the different radius zones in Figure 8.10. However, an oblate surface, as shown in Figure 8.11, would also show the same gradations of power change over the surface. The whole question then becomes: which model best describes the refractive changes achieved?

. T~e refractive change in excess of sphericalization for a cornea of Ro 7.80, eccentricity 0.50 when calculated using both models is shown in Figure 8.12. The oblate model underestimates the change by a mean of 0.21 ± 0.100 when compared to the spherical model. These differences are not really clinically significant, so in effect, both models are an acceptable method of representing the final corneal shape.

LENS DESIGN AND FITTING SOFTWARE

The following section deals with the currently available computer software that can be used as a means of fitting orthokeratology lenses. It does not cover the total number of programs that are currently in development, as these were not available for inclusion at the time of writing. The most important fact that the reader has to keep in mind when reviewing these software packages is this: they are all based on the assumption that the topography data input into the program are valid and accurate. This is generally not the case, as has been shown in Chapters 2 and 9. The practitioner still needs to be able to interpret the results of the trial wear period in order to come to the correct decisions as to the remedial steps required in order to optimize the fitting.