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The shape and profile of the cornea after excimer photoablative refractive surgery: Implications for post-operative contact lens fitting
Journalofthe British ContactLensAssociation,Vol. 15, No. 4, pp 167-169, 1992
© 1992 British Contact LensAssociation
Printed in Great Britain
THE SHAPE AND PROFILE OFTHE CORNEA AFTER EXCIMER PHOTOABLATIVE REFRACTIVE SURGERY: IMPLICATIONS FOR POST-OPERATIVE CONTACT LENS FITTING Sudi Patel a
KEYWOROS:Corneal shape, refractive surgery, post-operative fitting.
Introduction Correction of ametropia by refractive means invariably involves the cornea. The refractive surgical technique which has gained the most publicity is radial keratotomy. Unfortunately, this particular surgical procedure is highly unpredictable and the complications which can arise from it are most unwelcome? New techniques are continuously being developed to reduce these complications and improve upon the final post-operative dioptral outcome. Obviously, the chief purpose of refractive surgery is to correct the refractive error present in the eye. Also, the technique must not: • Reduce the clarity of the ocular dioptric apparatus. • Produce irregular refracting surfaces. If a technique is developed which fulfils these two conditions, then it is reasonable to propose that the technique does not enhance the aberrations of the eye. The excimer laser and the intrastromal ring techniques of refractive surgery both have the potential to satisfy the conditions. Basically, the excimer laser removes surface layers of molecular proportions by photo-ablation. The technique, when applied to the cornea, is termed photorefractive keratectomy (PRIQ? The depth of tissue removal is a function of the incident energy and its duration. Under controlled conditions a slowly expanding diaphragm is used to control the diameter of the incident beam. This produces an effect whereby the removal of tissue commences at the corneal apex and gradually extends towards the limit of the beam diameter in the more peripheral regions of the cornea. If the extent of tissue removal gradually reduces from the corneal apex outwards toward the periphery, then plus power is, in effect, being removed from the cornea. The net result is a flattening of the corneal apex and, therefore, a reduction of myopia (see Figure 1). The intrastromal ring is a perspex ring which is passed through a previously cut circum-corneal channel) ,4As the ring is either expanded or contracted, it produces a change in the corneal curvature. Expanding the ring will flatten the cornea and reduce myopia, as depicted in Figure 2. The technique has the a
BSc (Hons), MPhil, MBCO.
Post-ablated_ corneal ~ contour
Pre-operative normalcorneal contour
Figure 1. The effect of photorefractive keratectomy on
the
corneal apex.
Normalcornealcontour Flattene ~ cornea w
_
\ Expanded intrastromal ring
The effect on the corneal apex of expanding the intrastromal ring.
Figure 2.
potential to reduce the refractive error in a controlled and precise manner, without invading the corneal optical zone. There is no obvious reason why this should reduce the clarity of the cornea. As we approach the twenty-first century, both the excimer laser and intrastromal ring have the potential to become the preferred techniques of refractive surgery. If they should become commonplace, the contact lens practitioner will need answers to two main questions: • The surgical procedures may reduce ametropia, but could they enhance the aberrations of the eye and hence reduce its optical performance? • If there is a residual refractive error, or a natural change in the refractive state of the eye, and the patient wishes to be fitted with contact lenses, what will be the likely topography of these corneas? The excimer laser, by the nature of its aperture control mechanism, could ablate aspheric surfaces of limitless topographies. However, the intrastromal ring cannot be so well-controlled because, ultimately, the
167
SUDIPATEL
technique is controlled by a surgeon's hand and his precision. What should be the ideal asphericity of the corneal contour after refractive surgery? Before attempting to answer this, we require a numerical description of asphericity and a suitable model eye for predictive purposes. The normal corneal contour is commonly described as a flattening ellipse, and it is well known that this tends to reduce the spherical aberration of the eye. Assuming that the corneal contour within the apical region can be approximated by a conic section, then corneal asphericity can be quantified using p, the shape factor, in Baker's equation s, as follows: Y/"2 = ( 2 x R x X )
-
( p x (X^2))
where R is the apical radius of the corneal contour, and X and Y are Cartesian co-ordinates. The apex of the conic section is centred at the origin of the X, Ygraph. In Figure 3, various conic sections are drawn. When p is less than 1, the conic section is a flattening ellipse. When p is greater than 1, the conic section is a steepening ellipse. Using a suitable model eye (which incorporates aspheric interfaces and gradient index optics), after refractive surgical correction the ideal corneal
Y
/
(SQR( ( (dY/ dX)^2)+ I) ) .dX Unfortunately, in the case of Baker's equation there is no obvious solution to the integration. However, for an initial intrastromal ring diameter of 8mm, the arc length of the corneal contour can be approximated by numerical integration. For a range of axial myopia from - 1D to - 10D, our computer models predict that, commencing with a corneal shape factor of 0.82 (a typical value for the normal cornea), the average post-operative corneal shape factor is 0.6. From Figure 2 it is clear that expanding the intrastromal ring to reduce myopia will also reduce the depth of the anterior chamber. In actual fact, the optical performance of the eye will be further degraded by the slight reduction in the anterior chamber depth, unless the original correcting algorithms take this into account.
p>l
Corneal Shape p=l
p
X
Figure 3. The shapefactor. asphericity is predicted to average at 0.8 in order to minimise the lateral spherical aberration of the eye. Therefore, the corneal contour after excimer photoablative refractive surgery should produce a flattening elliptical corneal contour. This figure is similar to the mean corneal shape factors present within the normal population. 6-8 What about for the intrastromal ring? What will happen to the shape factor of the corneal contour as the ring is expanded? The cornea is resistant to stretching 9,1°, and therefore the arc length of the corneal contour can be assumed to remain constant. If
168
we calculate the arc length of the corneal contour before expansion of the ring and accept that this remains constant, then using computer reiterative procedures we can calculate the shape factor of the corneal contour after ring expansion, incorporating the desired final apical radius of the corneal contour that will correct the ametropia of the eye. The arc length of a curve can be calculated by integration of the following expression 11over the desired limits of X:
Initial clinical trials of the excimer laser have been favourable, except for the reports of subepithelial haze and a thickened post-operative corneal epithelium. 1~-14 The haze may, in some cases, be responsible for any reduced visual performance. Prior to the operation, the corneal epithelium is removed and the bare stromal surface is ablated. During the healing stage, the epithelium regenerates. The re-modelled epithelium is regarded as being responsible for the reports of postoperative regression in refraction. 14 The patient may eventually require a contact lens after the eye has setfled at its new ametropic level. It is possible during the healing phase, while the epithelium is regenerating, for the cornea to develop an abnormal surface shape within the limits of the corneal apical zone. We need to assess the corneal shape of the post-operated eye before making any other conclusions. To measure the corneal shape within this zone, a photokeratoscope was developed which consisted of a Placido disc that projected 18 tings within the pupil. The corneas of subjects who received excimer PRK were examined. (The intrastromal ring technique could not be assessed because at the time of investigation no subjects had received this operation in the UK) The corneas of 50 eyes were examined at least 1 month post-operatively. The average corneal shape was found to lie within the limits of age-matched norms. A significant number of corneas were found to have topographies akin to a steepening ellipse. Even if these eyes were fitted with spectacles to correct any residual refractive error, the optical performance would be poor
CORNEAAFTEREXCIMERPHOTOABLAT1VESURGERY
because of the high levels of spherical aberration. Such corneas would present the contact lens practitioner with major fitting problems. Referring to Figure 1, the postablated cornea may have an apical radius of 8.2ram; the cornea gradually steepens from the apex up to the limit of the ablated zone, where it resorts back to its original curvature and has a typical shape factor of, say, 0.82. Traditionally, the back surface of a contact lens flattens off towards the periphery. Perhaps this corneal profile is best fitted with a lens in which the central optic zone is spherical with a steepening towards the periphery or even a steepening ellipse. The front surface of the lens should be aspherical to further opfimise the optical performance of the lens-eye complex. If this form of refractive surgery does become commonplace, the contact lens industry will have to produce new lens designs to cater for this new type of cornea.
Acknowledgements Thanks go to Dr David Gartry and Mr Malcolm Kerr Muir for allowing me access to their patients, and to Dr Chris Lohman for organising the laboratory sessions.
Address for Correspondence Sudi Patel, Senior Lecturer, Department of Optometry and Vision Science, Glasgow Polytechnic, Cowcaddens Road, Glasgow G4 0BA, Scotland.
REFERENCES 1 Rashid, E. R. and Waring, G. O. Complications of radial and transverse keratotomy. Surv. Ophthal., 34, 73-106 (1989). 2 Marshall, J., Trokel, S., and Kreuger, R. Photoablafive reprofiling of the cornea using an excimer laser: photorefracfive keratectomy. Lasers in Opthal., 1, 21-48 (1986). 3 Fleming, J. F., Reynolds, A. E., and Kilmer, L. The intra-stromal corneal ring: two cases in rabbits. ]. Refract. Surg., 3, 227-232 (1987). 4 Fleming, J. F., Lee Wan, W., and Shanzlin, D. J. The theory of corneal curvature changes with the intra-stromal corneal ring. CLAOJ., 15, 146-150 (1989). Baker, T. Y. Ray tracing through non-spherical surfaces. Proe. Roy. Soc., 55, 361-354 (1943). 6 Guillon, M., Lydon, D. P. M., and Wilson, C. Corneal topography: a clinical model. Ophthal. Physiol. Opt., 6, 47-57 (1986). 7 Douthewaite, W. A. and Sheridan, M. Corneal asphericity and refractive error. Opthal. Physiol. Optics., 9, 235-238 (1989). s Lam, C. S. Y. and Loran, D. F. C. Designing contact lenses for the oriental eye.]. Br. Contaet Lens Assoc., 14, 109-114 (1991). 9 Brubaker, R. F., Ezekiel, S., Chin, L. et al. Stress and strain behaviour of the corneo-scleral envelope of the eye: development of a system for making in vivo measurements. Exp. Eye. Res, 21, 37-46 (1975). 19Edmund, C. Corneal elasticity and the ocular rigidity in normal and keratoconic eyes. Acta Ophthahnologica, 66, 134-140 (1988). ~1Porter, R. I. Further Elementary Analysis, 3rd edn, G. Bell and Sons, London (1965). ~2Taylor, D. M., L'Esperance, F. A., Del Pero, R. A., et al. Human excimer laser keratectomy: a clinical study. Ophthalmology, 96, 654-664 (1989). ~3Wu, W. C. S., Stark, W. J., and Green W. 1~ Corneal wound healing after 193nm laser keratectomy. Arehio. Ophthal., 109, 1426-1432 (1991). 14Gartry, D. S., Kerr Muir, M. G., and Marshall, J. Photorefracfive keratectomy with the argon fluoride excimer laser: a clinical study. Refrac. Corneal Surg., 7, 420-435 (1991).
169
© 1992 British Contact LensAssociation
Printed in Great Britain
THE SHAPE AND PROFILE OFTHE CORNEA AFTER EXCIMER PHOTOABLATIVE REFRACTIVE SURGERY: IMPLICATIONS FOR POST-OPERATIVE CONTACT LENS FITTING Sudi Patel a
KEYWOROS:Corneal shape, refractive surgery, post-operative fitting.
Introduction Correction of ametropia by refractive means invariably involves the cornea. The refractive surgical technique which has gained the most publicity is radial keratotomy. Unfortunately, this particular surgical procedure is highly unpredictable and the complications which can arise from it are most unwelcome? New techniques are continuously being developed to reduce these complications and improve upon the final post-operative dioptral outcome. Obviously, the chief purpose of refractive surgery is to correct the refractive error present in the eye. Also, the technique must not: • Reduce the clarity of the ocular dioptric apparatus. • Produce irregular refracting surfaces. If a technique is developed which fulfils these two conditions, then it is reasonable to propose that the technique does not enhance the aberrations of the eye. The excimer laser and the intrastromal ring techniques of refractive surgery both have the potential to satisfy the conditions. Basically, the excimer laser removes surface layers of molecular proportions by photo-ablation. The technique, when applied to the cornea, is termed photorefractive keratectomy (PRIQ? The depth of tissue removal is a function of the incident energy and its duration. Under controlled conditions a slowly expanding diaphragm is used to control the diameter of the incident beam. This produces an effect whereby the removal of tissue commences at the corneal apex and gradually extends towards the limit of the beam diameter in the more peripheral regions of the cornea. If the extent of tissue removal gradually reduces from the corneal apex outwards toward the periphery, then plus power is, in effect, being removed from the cornea. The net result is a flattening of the corneal apex and, therefore, a reduction of myopia (see Figure 1). The intrastromal ring is a perspex ring which is passed through a previously cut circum-corneal channel) ,4As the ring is either expanded or contracted, it produces a change in the corneal curvature. Expanding the ring will flatten the cornea and reduce myopia, as depicted in Figure 2. The technique has the a
BSc (Hons), MPhil, MBCO.
Post-ablated_ corneal ~ contour
Pre-operative normalcorneal contour
Figure 1. The effect of photorefractive keratectomy on
the
corneal apex.
Normalcornealcontour Flattene ~ cornea w
_
\ Expanded intrastromal ring
The effect on the corneal apex of expanding the intrastromal ring.
Figure 2.
potential to reduce the refractive error in a controlled and precise manner, without invading the corneal optical zone. There is no obvious reason why this should reduce the clarity of the cornea. As we approach the twenty-first century, both the excimer laser and intrastromal ring have the potential to become the preferred techniques of refractive surgery. If they should become commonplace, the contact lens practitioner will need answers to two main questions: • The surgical procedures may reduce ametropia, but could they enhance the aberrations of the eye and hence reduce its optical performance? • If there is a residual refractive error, or a natural change in the refractive state of the eye, and the patient wishes to be fitted with contact lenses, what will be the likely topography of these corneas? The excimer laser, by the nature of its aperture control mechanism, could ablate aspheric surfaces of limitless topographies. However, the intrastromal ring cannot be so well-controlled because, ultimately, the
167
SUDIPATEL
technique is controlled by a surgeon's hand and his precision. What should be the ideal asphericity of the corneal contour after refractive surgery? Before attempting to answer this, we require a numerical description of asphericity and a suitable model eye for predictive purposes. The normal corneal contour is commonly described as a flattening ellipse, and it is well known that this tends to reduce the spherical aberration of the eye. Assuming that the corneal contour within the apical region can be approximated by a conic section, then corneal asphericity can be quantified using p, the shape factor, in Baker's equation s, as follows: Y/"2 = ( 2 x R x X )
-
( p x (X^2))
where R is the apical radius of the corneal contour, and X and Y are Cartesian co-ordinates. The apex of the conic section is centred at the origin of the X, Ygraph. In Figure 3, various conic sections are drawn. When p is less than 1, the conic section is a flattening ellipse. When p is greater than 1, the conic section is a steepening ellipse. Using a suitable model eye (which incorporates aspheric interfaces and gradient index optics), after refractive surgical correction the ideal corneal
Y
/
(SQR( ( (dY/ dX)^2)+ I) ) .dX Unfortunately, in the case of Baker's equation there is no obvious solution to the integration. However, for an initial intrastromal ring diameter of 8mm, the arc length of the corneal contour can be approximated by numerical integration. For a range of axial myopia from - 1D to - 10D, our computer models predict that, commencing with a corneal shape factor of 0.82 (a typical value for the normal cornea), the average post-operative corneal shape factor is 0.6. From Figure 2 it is clear that expanding the intrastromal ring to reduce myopia will also reduce the depth of the anterior chamber. In actual fact, the optical performance of the eye will be further degraded by the slight reduction in the anterior chamber depth, unless the original correcting algorithms take this into account.
p>l
Corneal Shape p=l
p
X
Figure 3. The shapefactor. asphericity is predicted to average at 0.8 in order to minimise the lateral spherical aberration of the eye. Therefore, the corneal contour after excimer photoablative refractive surgery should produce a flattening elliptical corneal contour. This figure is similar to the mean corneal shape factors present within the normal population. 6-8 What about for the intrastromal ring? What will happen to the shape factor of the corneal contour as the ring is expanded? The cornea is resistant to stretching 9,1°, and therefore the arc length of the corneal contour can be assumed to remain constant. If
168
we calculate the arc length of the corneal contour before expansion of the ring and accept that this remains constant, then using computer reiterative procedures we can calculate the shape factor of the corneal contour after ring expansion, incorporating the desired final apical radius of the corneal contour that will correct the ametropia of the eye. The arc length of a curve can be calculated by integration of the following expression 11over the desired limits of X:
Initial clinical trials of the excimer laser have been favourable, except for the reports of subepithelial haze and a thickened post-operative corneal epithelium. 1~-14 The haze may, in some cases, be responsible for any reduced visual performance. Prior to the operation, the corneal epithelium is removed and the bare stromal surface is ablated. During the healing stage, the epithelium regenerates. The re-modelled epithelium is regarded as being responsible for the reports of postoperative regression in refraction. 14 The patient may eventually require a contact lens after the eye has setfled at its new ametropic level. It is possible during the healing phase, while the epithelium is regenerating, for the cornea to develop an abnormal surface shape within the limits of the corneal apical zone. We need to assess the corneal shape of the post-operated eye before making any other conclusions. To measure the corneal shape within this zone, a photokeratoscope was developed which consisted of a Placido disc that projected 18 tings within the pupil. The corneas of subjects who received excimer PRK were examined. (The intrastromal ring technique could not be assessed because at the time of investigation no subjects had received this operation in the UK) The corneas of 50 eyes were examined at least 1 month post-operatively. The average corneal shape was found to lie within the limits of age-matched norms. A significant number of corneas were found to have topographies akin to a steepening ellipse. Even if these eyes were fitted with spectacles to correct any residual refractive error, the optical performance would be poor
CORNEAAFTEREXCIMERPHOTOABLAT1VESURGERY
because of the high levels of spherical aberration. Such corneas would present the contact lens practitioner with major fitting problems. Referring to Figure 1, the postablated cornea may have an apical radius of 8.2ram; the cornea gradually steepens from the apex up to the limit of the ablated zone, where it resorts back to its original curvature and has a typical shape factor of, say, 0.82. Traditionally, the back surface of a contact lens flattens off towards the periphery. Perhaps this corneal profile is best fitted with a lens in which the central optic zone is spherical with a steepening towards the periphery or even a steepening ellipse. The front surface of the lens should be aspherical to further opfimise the optical performance of the lens-eye complex. If this form of refractive surgery does become commonplace, the contact lens industry will have to produce new lens designs to cater for this new type of cornea.
Acknowledgements Thanks go to Dr David Gartry and Mr Malcolm Kerr Muir for allowing me access to their patients, and to Dr Chris Lohman for organising the laboratory sessions.
Address for Correspondence Sudi Patel, Senior Lecturer, Department of Optometry and Vision Science, Glasgow Polytechnic, Cowcaddens Road, Glasgow G4 0BA, Scotland.
REFERENCES 1 Rashid, E. R. and Waring, G. O. Complications of radial and transverse keratotomy. Surv. Ophthal., 34, 73-106 (1989). 2 Marshall, J., Trokel, S., and Kreuger, R. Photoablafive reprofiling of the cornea using an excimer laser: photorefracfive keratectomy. Lasers in Opthal., 1, 21-48 (1986). 3 Fleming, J. F., Reynolds, A. E., and Kilmer, L. The intra-stromal corneal ring: two cases in rabbits. ]. Refract. Surg., 3, 227-232 (1987). 4 Fleming, J. F., Lee Wan, W., and Shanzlin, D. J. The theory of corneal curvature changes with the intra-stromal corneal ring. CLAOJ., 15, 146-150 (1989). Baker, T. Y. Ray tracing through non-spherical surfaces. Proe. Roy. Soc., 55, 361-354 (1943). 6 Guillon, M., Lydon, D. P. M., and Wilson, C. Corneal topography: a clinical model. Ophthal. Physiol. Opt., 6, 47-57 (1986). 7 Douthewaite, W. A. and Sheridan, M. Corneal asphericity and refractive error. Opthal. Physiol. Optics., 9, 235-238 (1989). s Lam, C. S. Y. and Loran, D. F. C. Designing contact lenses for the oriental eye.]. Br. Contaet Lens Assoc., 14, 109-114 (1991). 9 Brubaker, R. F., Ezekiel, S., Chin, L. et al. Stress and strain behaviour of the corneo-scleral envelope of the eye: development of a system for making in vivo measurements. Exp. Eye. Res, 21, 37-46 (1975). 19Edmund, C. Corneal elasticity and the ocular rigidity in normal and keratoconic eyes. Acta Ophthahnologica, 66, 134-140 (1988). ~1Porter, R. I. Further Elementary Analysis, 3rd edn, G. Bell and Sons, London (1965). ~2Taylor, D. M., L'Esperance, F. A., Del Pero, R. A., et al. Human excimer laser keratectomy: a clinical study. Ophthalmology, 96, 654-664 (1989). ~3Wu, W. C. S., Stark, W. J., and Green W. 1~ Corneal wound healing after 193nm laser keratectomy. Arehio. Ophthal., 109, 1426-1432 (1991). 14Gartry, D. S., Kerr Muir, M. G., and Marshall, J. Photorefracfive keratectomy with the argon fluoride excimer laser: a clinical study. Refrac. Corneal Surg., 7, 420-435 (1991).
169