Analysis of customized corneal ablations: theoretical limitations of increasing negative asphericity

To determine the ablation depths of customized myopic excimer laser photoablations performed to change corneal asphericity after laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK).

A mathematical model of aspheric myopic corneal laser surgery was generated. The initial corneal surface was modeled as a conic section of apical radius R(1) and asphericity Q(1). The final corneal surface was modeled as a conic section of apical R(2) and asphericity Q(2), where R(2) was calculated from the paraxial optical formula for a given treatment magnitude (D), and Q(2) was the intended final asphericity. The aspheric profile of ablation was defined as the difference between the initial and final corneal profiles for a given optical zone diameter (S), and the maximal depth of ablation was calculated from these equations. Using the Taylor series expansion, an equation was derived that allowed the approximation of the central depth of ablation (t(0)) for various magnitudes of treatment, optical zone diameters, and asphericity. In addition to the Munnerlyn term (M), incorporating Munnerlyn's approximation (-D small middle dot S(2)/3), the equation included an asphericity term (A) and a change of asphericity term (Delta). This formula (t(0) = M + A + Delta) was used to predict the maximal depth of ablation and the limits of customized asphericity treatments in several theoretical situations.

When the initial and final asphericities were identical (no intended change in asphericity; Q(1) = Q(2); Delta = 0), the maximal depth of ablation (t(0) = M + A) increased linearly with the asphericity Q(1). To achieve a more prolate final asphericity (Q(2) < Q(1); dQ < 0; Delta > 0), the maximal depth of ablation (M + A + Delta) was increased. For treatments in which Q(2) was intended to be more oblate than Q(1) (Q(2) > Q(1); dQ > 0; Delta < 0), the maximal depth of ablation was reduced. These effects sharply increased with increasing diameters of the optical zone(s). Similarly, in the case of PRK, the differential increase in epithelial thickness in the center of the cornea compared with the periphery resulted in increased oblateness.

Aspheric profiles of ablation result in varying central depths of ablation. Oblateness of the initial corneal surface, intentional increase in negative asphericity, and enlargement of the optical zone diameter result in deeper central ablations. This may be of clinical importance in planning aspheric profiles of ablation in LASIK procedures to correct spherical aberration without compromising the mechanical integrity of the cornea.