Ординатура / Офтальмология / Английские материалы / Orthokeratology Principles and Practice_Mountford, Ruston, Dave_2004

across the corneal surface initiates surface shape changes such that the cornea is altered until a state of equilibrium of force exists in the postlens tear layer. Areas of disparate force will always find equilibrium over the smallest possible surface area. The smallest surface area is a sphere (Kwok 1984).

In theory the central cornea will alter shape until a spherical surface exists over the diameter required for equalization to occur. Since the initial corneal shape is aspheric, the equalization will occur over discrete zones (Fig. 10.25).

The corneal shape change is associated with central epithelial thinning and mid-peripheral stromal thickening (Swarbrick et al 1998, Swarbrick & Alharbi 2001). There is little or no change in the extreme periphery (Mountford 1997, Lui & Edwards 2000).

Therefore, as the cornea changes shape, the apical clearance increases as the epithelium thins, and the depth of the tear layer at the BOZD decreases as the stroma thickens. This can be modeled using Noack's relationship between corneal radius change and asphericity. The modeled lens is placed on the initial cornea (Ro 7.80, 0.50 eccentricity), and then the baseline corneal data altered to include the Ro and eccen-

Figure 10.25 Bull's-eye postwear topography plot showing areas of isodioptric change and areas of equal sphericalization. The greatest change should always occur at the apex of the cornea.

tricity changes as the cornea alters from a prolate geometry to a sphere. The maximum central corneal thickness change is assumed to be 20 urn, so at the start the lens will have a calculated apical clearance of 5 J.1m, increasing to a

Figure 10.26 The equalization of force occurring under the lens as the cornea changes from a prolate ellipse to a sphere following the Noack model. Note the drop in central compression and the decrease in tension at the edge of the optic zone (back optic zone diameter). In theory, the final lineshould bevirtuallystraight. This graph can also explain whythe same lens works on the altered eye shape, and the effects of regression (see text).

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maximum of 25 urn by the stage sphericalization is reached.

The change in the force is shown in Figure 10.26. As the cornea alters shape, there is a decrease in central compression and also in tension at the edge of the BOZD, leading to virtual equalization at sphericalization. The limitation of the model in this instance is due to the inability to determine correctly the volume of the torus generated in the postwear cornea at the BOZD (red ring in Fig. 10.25). If this were possible, the postwear force line would theoretically be a straight line.

The graph answers an interesting question. A reverse geometry lens is designed and fitted to the prefit cornea, based on the rules of sag fitting. It then proceeds to alter the shape of the cornea dramatically. The question that follows is: why

does the same lens still work on the altered corneal shape?

For example, the changes occurring with the first overnight wear rarely cause a total reduction in myopia, and the lens needs to be worn every night until the full change is achieved. In Figure 10.26, the initial force exerted on the lens is the dark blue line. Assuming that the cornea changes shape such that the force becomes the light blue line after the first overnight wear period, then total refractive change has not occurred. The lens is not worn during the day, so the cornea regresses to the pink line. That night, on insertion, the instigating force is now the pink line and not the red. Once again, the cornea is altered in the quest for equalization of force, and progressively reaches the goal. When regression occurs, the force generated by the lens on the altered

corneal shape will fall somewhere between the initial and equalized states. This cascade of events is totally dependent on the lens being the correct fit in the first instance, and also that a bull's-eye postwear topography plot occurs.

FORCES CAUSING BULL'S-EYEPLOTS

The requirements for a bull's-eye response are simple: optimized redistribution of force and centration. Figure 10.27 shows the change in corneal topography for a 4.50 D myope, with initial corneal data of Ro 7.20 mm and eccentricity 0.75. The refractive change achieved was 4.90 D with a final Ro of 8.05 mm and an eccentricity of zero. It should be pointed out that the postwear eccentricity values in the top left-hand side of the lower left plot are totally erroneous. As has been shown by Lui & Edwards (2000), the elliptical model of corneal shape breaks down following reverse geometry lens wear. Also, Tang et al (2000) have shown the inability of corneal topographers to record bicurve and oblate surfaces accurately. An eccentricity value of 0.56 is given for the surface, whilst the axial map shows a spherical surface centrally. In an attempt to overcome the limitations of the torus, the postwear

topography data were used to create a "best-fit" asphere and the initial lens placed on the surface. The tear layer profile was then calculated followed by the force. The change in force for this eye is shown in Figure 10.28. Note that in the initial phase the force is centered on the cornea apex (point zero on the x-axis). Following lens wear, equalization of force occurs. The "red ring" that appears as an area of corneal steepening is aligned with the area of maximum tension under the lens.

The model shows that, for a bull's eye to occur, the force must be well-centered, meaning that the lens fit is optimal. In order for this to occur, the data on which the lens is calculated must be accurate, and this is dependent on the accuracy of the topography data and the refinements made following the overnight trial.

However, the fit is less than optimal in some cases, resulting in either a smiley-face or central island postwear plot.

FORCES CAUSING SMILEY FACES

Clinical experience indicates that a smiley-face topographic response is caused by a flat lens that decenters, usually superiorly. This is a commonly accepted fact by all orthokeratology lens designers and fitters. The remedial action required to correct a smiley face is the same for all lens designs: steepen the fit. Placed in the context of

Figure 10.28 The prefit and postwear topographical data from the eye in Figure 10.27 were used to generate the difference in squeeze film force. The final force is equalized across the surface. Complex surface shape analysis of the final corneal curves was used to generate the "final" tear layer profile on which the force was calculated. Bull's-eyeplotsoccur due to ideal lens fit and distribution of force.

Figure 10.29 The ideal tear layer profile of a BE lens and one that is fitted 10IJ.m too flat. The flat lens shows central touch, and clearance at the tangent zone. This usually causes superior decentration.

Figure 10.30 The tear layer profile of the vertical meridian of a lens fitted 10um too flat. The lens has decentered 1.00 mm superiorly until anapical clearance of approximately 5.00 ILm exists. Note that the tear layer thickness is deeper superiorly than inferiorly.

Figure 10.31 The squeeze forcegenerated by the flat lens shows greater tension inferiorly. The compression zone is superior to the corneal apex.

sag philosophy, this simply means that the sag of the lens was initially less than that of the cornea, and is rectified by increasing the sag of the lens by alterations to either the alignment curves or reverse curve. An "ideal" tear layer profile (blue line) and one due to a lens fitted 10 J.Lm too "flat" is shown in Figure 10.29. Note that the flat lens touches at the apex and has clearance at the normal point of contact in the periphery. Under these conditions, a squeeze film force does not exist, so the lid moves the lens until a tear layer that forms a squeeze film is produced (Hayashi

1977).

The tear layer of the lens with 1 mm superior decentration is shown in Figure 10.30. A small (5 J.Lm) clearance is present, with the superior area showing a deeper tear layer at the edge of the BOZO than the inferior. The force generated is

shown in Figure 10.31. Note that the area of compression is decentered superiorly and that the tension force is greater in the inferior section. The superior area shows less tension than the inferior, which is contrary to what would normally be expected, as the tear layer is deeper superiorly than inferiorly. This is due to the boundary conditions placed on the <X factor, in that there is an upper limit of TLTthat will occur before the force decreases. In this instance, the maximum tension developed at 4.2 mm superiorly is -26 x 10-7 Nm2, compared to -134 x 10-7 Nm2 at 2.00 mm inferiorly. A smiley-face postwear plot is shown in Figure 10.32.

It is interesting to note that the superior area of flattening on the map is in the same position as the compression zone in the force graph. Also, the red "smile" of steepening occurs at a point

2.00 mm inferiorly, which corresponds to the area of greatest tension on the force graph. The model therefore indicates that smiley faces are caused by an inequality of the squeeze film forces between the superior and inferior cornea that is produced when a lens of insufficient apical clearance is decentered by the lid.

CENTRAL ISLANDS

Central islands are caused by steep lenses that exhibit excessive apical clearance, or alternatively, lenses that have a tight alignment curve that causes "peripheral compression." However, as has been shown before, if the apical clearance is excessive, the squeeze film force differential under the lens is minimal, and there is little change in corneal shape. Central islands cause marked changes in corneal shape but with an accompanying decrease in corrected vision due to the central distortion (Fig. 10.33). Note the excellent centration and the steeper central zone surrounded by a "moat" of increased corneal flattening followed by the red ring of steepening. What type of squeeze film force could create this?

Modeling central islands requires some rethinking of the tear layer distribution under the lens. The Conway model assumes an axissymmetrical surface, with a slight difference between the meridians to act as an escape mechanism for the fluid. In clinical terms, the escape channel becomes either a small degree of with- the-rule astigmatism or, in purely aspheric surfaces, the difference in eccentricity between the flat and steep meridian, and the difference between the horizontal and vertical corneal diameter. The model is based on the assumption that the minimum TLT occurs at the corneal apex, and that greater degrees of clearance at the lens periphery do not affect the u function. In cases where the apical clearance is excessive, the alignment curve is tight, resulting in "seal-off" in the flat meridian. In these cases, the minimum TLT occurs at the periphery of the lens, and not centrally. In effect, the squeeze film force is reversed. The maximum TLT is still present at the edge of the BOZD, but the minimum occurs at a point along the alignment curve in the steep meridian or vertical corneal diameter. The u function is

Figure 10.34 The squeeze force of an ideal fit compared to that which causes a central island response. Note the drop in central compression, and the marked increase in tension at the back opticzone diameter.

then determined by these two values, with the apical clearance becoming just another area of force.

The force distribution of an ideal-fitting lens and a lens fitted 20 um too steep on a cornea with a difference of 0.05 between the horizontal and vertical eccentricity is shown in Figure 10.34. Note that the central zone over an approximate chord of 2.00 mm shows a marked drop in central compression, and is surrounded by a zone of marked tension. The peripheral compression does not differ from that of the ideal-fitting lens. Another point of interest is the slight sudden change in force at the 2.00 mm central zone. This is a complex system. The immediate assumption would be that, since the squeeze forces are "reversed," the stress acts towards the center instead of away from it, thereby causing the steepened island. In the case of a bull's eye and a smiley face the area of paracentral steepening coincides with the point of maximum tension under the lens. This is also the case with the central island, but the exact mechanism that causes the steep central area is difficult to understand. The effect could simply be due to the relative drop in central compression combined with the marked increase in tension near the edge of the BOZD resolving to a tangential stress that tends to act towards the center.

The major problem with both central islands and smiley faces is that the model currently only

gives the force distribution at the initial phase of the fitting, and not the postwear picture following any equilibrium that may occur. This is primarily due to the difficulties in properly and accurately measuring the postwear corneal curvature changes. Hopefully, further study and development will resolve some of the outstanding issues.

ASTIGMATISM

As shown in Chapter 7, astigmatism presents some interesting complications to orthokeratology treatment. The results are not only dependent on the initial degree of astigmatism, but also on the type of astigmatism with respect to the topography. If central bowtie astigmatism exists, the likely reduction is approximately 50% (Mountford & Pesudovs 2002). Limbus-to-limbus astigmatism, however, appears to be worsened by reverse geometry lens wear due to an inability to "push" the astigmatism out past the pupil zone. The enigma of larger degrees of against-the-rule astigmatism remains just that: an enigma.

The following section shows the squeeze film force model that occurs in both central bowtie and limbus-to-limbus astigmatism.

Figure 10.35 is a simple case of 0.75 D with-the- rule astigmatism with an initial refraction of -2.00/-0.75 x 180. The apical radius is 7.40 mm with eccentricities of 0.56 horizontally and 0.65 vertically (Q values appear on the maps). The forces along the steep and flat meridian generated

Figure 10.36 The squeeze force for the horizontal meridian and the vertical meridian. The lower eccentricity of the flat meridian means that the lens will be relatively steep in the vertical, leading to compression, but no tension force. The force required to correct the refractive error of the vertical meridian isalso shown. This would require a novel lens design.

Figure 10.35 A case of simple central bowtie astigmatism of 0.75 D. Note that the horizontal eccentricity is0.32, whilst the vertical is 0.43.

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by the lens are shown in Figure 10.36. Note that the difference in the vertical meridian results in no relative tension at the edge of the BOZD of the lens. Equalization of force will result in this case, but there will be less of an effect vertically than horizontally, The force required to sphericalize the vertical meridian is also shown in Figure 10.36. This would require a novel lens construction, with the parameters based on the need for force differentiation in the two meridians. It will not be a toric lens, as the limitations are based on the apical clearance required in the vertical meridian, with the horizontal meridian parameters requiring modification due to the force differentials in apical clearance.

Figure 10.37 shows the effect of a spherical lens on a cornea with simple central astigmatism.

Note that there has been a reduction in the astigmatism, but only over the central 2.00 mm chord. There is no change in astigmatism at the keratometer chord. A lens designed on the force model would, in theory, create greater flattening in the vertical meridian, with a resultant oval treatment zone.

Limbus-to-limbus astigmatism presents an entirely different scenario. A topography map of this complex type of astigmatism is shown in Figure 10.38. Note that, in contrast to the simple central bowtie astigmatism, the astigmatism appears to extend to the peripheral cornea. The apical radius is 7.72 mm, with an eccentricity of 0.68 horizontally, and only 0.15 vertically. The refraction is -2.00/-2.50 x 10. When a spherical lens is fitted to this type of eye, there is an

increase in the postwear astigmatism (Fig. 10.39). The reason appears to be an inability to "push" the astigmatism out past the pupil zone. The force produced by a spherical lens on the cornea is shown in Figure 10.40.

If the Conway model is used, the force generated in the vertical meridian is zero, due to the absence of apical clearance resulting in an a value of 1. However, this type of astigmatism fulfills the requirements of the parabolic two-dimensional model of Allaire & Flack (1980), which would once again result in zero force along the vertical meridian, but approximately double the force of the Conway model in the horizontal meridian. This would cause an increased flattening of the horizontal meridian past that required, leading to a hypermetropic horizontal meridian, with an increased astigmatism vertically. The postwear refraction of the patient shown in Figure 10.39 was +1.00/ -3.50 x 180.

The model shows that, for astigmatism to be effectively reduced, novel reverse geometry lens designs are required. Mountford & Pesudovs (2002) have shown that, for orthokeratology to reduce totally astigmatism of up to 2.000, the "effectiveness" of the lenses would need to be

Figure 10.38 Complex limbus-to-limbus astigmatism. Notethe differences between the eccentricities in the horizontal (0.68) and vertical (0.15) meridians.

increased by approximately 80% using Alpins analysis. The lack of efficacy of spherical lenses on astigmatic corneas could be due to the relative lack of a tension force in the steep meridian, which could only be rectified by the use of novel designs. Experiments with the Fargo and BE lenses are currently under way in order to develop these novel astigmatic designs. However, work to date seems to indicate that the level of accuracy that is currently possible for lens manufacture is less than that required to produce lenses that are effective for limbus-to-limbus astigmatism. It would therefore be prudent to exclude those presenting with noncentral astigmatism from orthokeratology for the foreseeable future.

To summarize, the quasistatic model combines the effects of lid forces and the squeeze film forces under the lens. The lids are assumed to be closed, thereby avoiding the effects of surface tension forces. In order for the model to work, some degree of apical clearance must be present, with the lens resting on the peripheral cornea. The escape channel for the squeeze force is the presence of mild with-the-rule astigmatism, or simply the difference between the horizontal and vertical

Figure 10.40 Squeeze force of limbus-to-limbus astigmatism. There is noforce generated in the vertical meridian. The force generated by the Conway and Allaire & Flack models are shown (see text].

Figure 10.41 The lens-eye relationship where the lens is fitted with greater than zero apical clearance. The squeeze film forcecauses corneal sphericalization, with an increase in apical clearance due to epithelial thinning, and decreased clearance at the back optic zone diameter, leading to an "equalization" of the tear layer thickness under the lens.