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Fig. 12.15. Thermal damage inside the cornea during minute coagulation of continuous-wave laser radiation.

minute coagulation. This smaller size is surprising given that the increase in corneal temperature during the 10-s coagulation is higher than during the minute coagulation. Similarly, larger thermal damage is predicted for the pulsed laser radiation than for the continuous-wave laser radiation, since temperature increases during pulsed laser treatment are greater than during the continuous-wave laser.

From Fig. 12.14, it is established that the 10-s coagulation produces irreversible thermal damage inside the cornea. The irreversible thermal damage occurs only at depths up to 200 µm from the corneal surface, however. In the minute coagulation, complete necrosis is found at depths of 0 ≤ z ≤ 300 µm.

12.8. Discussion

The numerical results obtained from the present study are validated with the experimental and numerical data obtained that can be found in literature provided by other researchers. Generally, the temperature profiles of the cornea during pulsed laser radiation shown in Figs. 12.4 and 12.6 agree with those predicted by Manns et al.12 Comparisons of the transient variations of the maximum (at z = 0) and minimum temperatures (z = 588 µm) in Fig. 12.4 with the experimental results presented by Papaioannou et al.2

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also show good qualitative agreement. The corneal temperatures measured by Papaioannou et al.2 however, are smaller than the predictions obtained from the present study.

In continuous-wave laser radiation, the temperature distributions in Figs. 12.11 and 12.12 show isotherms that agree with the predictions obtained by Brinkmann et al.10 The magnitudes of temperature, however, are different. In the present study, the largest corneal temperatures during the 10-s and minute coagulations are found to be 75.6 and 70.1◦C, respectively, while Brinkmann et al.10 predict values of 110 and 90◦C, respectively. Discrepancies may be due to the absence of intra-corneal focusing in the present study, which was taken into account by Brinkmann et al.10 The use of the simplified model approach may also be a contributing factor.

One of the differences between the model in the present study and those found in the literature is the geometry of the cornea. In earlier studies, the assumption that the cornea can be modeled as a cylinder or a tissue slab with finite thickness has been highly idealized. In the present study, the model is anatomically and physiologically more complete and realistic where various components of the human eye have been taken into consideration. The use of a complete model provides a more accurate anatomical representation of the human cornea. At the same time, boundary conditions can be specified based on the physical observation of the actual human eye. In maintaining the axisymmetrical feature of the human eye model, we have assumed that only one laser spot is applied to the center of the corneal surface. While this single spot does not represent the actual treatment of LTKP, the assumption is not expected to introduce significant errors to our analysis, since the corneal temperature changes are localized to the area where heating takes place. The thermal response of the cornea in each laser spot is not affected by the temperature changes in the other parts of the cornea where the other laser spots are applied.

From the numerical results presented in Sec. 12.5, the pulsed laser has been found to cause a greater increase in the corneal temperature than the continuous-wave laser causes. In particular, the temperature at the corneal epithelium has been predicted to be as high as 111◦C, which may imply a total destruction of the epithelial layer. Based on the corneal temperature alone, one may be inclined to deduce that the pulsed laser produces greater thermal damage on the cornea than the continuous-wave laser. On the

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contrary, the assessment of thermal damage carried out using the Arrhenius integral appears to suggest otherwise. In Sec. 12.6, the amount of thermal damage suffered by the cornea during continuous-wave laser radiation is estimated to be greater than the pulsed laser radiation. This observation may be partially due to the duration of heating.

From Eq. (12.16), we find that the degree of thermal damage inside the cornea depends on both the temperature and the duration of heating. In the treatment of LTKP using pulsed laser, the duration when heating actually takes place is only a few milliseconds. Consequently, while the cornea is subjected to intense heat during each laser pulse, the period when heating actually takes place is short. On the other hand, the continuous exposure of the cornea toward heat makes it more susceptible to thermal damage. This explanation is further supported by the results presented in Figs. 12.14 and 12.15, where the minute coagulation that has a prolonged heating duration, causes a more severe thermal damage than the 10-s coagulation despite the smaller increase in corneal temperature during the minute coagulation. Results from the thermal damage assessment suggest that the duration of heating plays a more important role than the magnitude of temperature increase in determining the degree of thermal damage inside the cornea during LTKP.

According to Jean et al.16 continuous-wave lasers are better suited to treat LTKP than pulsed lasers are. This suitability has been attributed to the smaller corneal temperature, which helps to avoid overheating and corneal relaxation. The ability of continuous-wave lasers to produce various coagulation depths (due to the tunability of the laser wavelength) and the consumption of less energy loss than pulsed laser also makes the continuous-wave laser a preferred choice. If the temperature profile of the cornea is used for determining the type of laser that is best suited for LTKP, the results obtained from the present study would then support the conclusion drawn by Jean et al.16 However, if one considers the degree of thermal damage to be a more important criterion, the results from the thermal damage assessment would suggest that the pulsed laser is a better choice, since the thermal damage induced onto the cornea is less severe.

It may be premature, in this study, to draw a conclusion on the type of laser that is best suited for the treatment LTKP, since the degree of corneal shrinkages has not been taken into consideration. Additionally, the

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accuracy of the thermal damage estimated in the present study depends on how well the Arrhenius damage integral models the thermal damage inside the human cornea. While the thermal damage of the human skin may be accurately described,32 the same may not be said of the cornea. In the present study, the severity of the thermal damage inside the cornea has been categorized based on the classification for the human skin. More studies have to be carried out in the future to determine if such a classification can accurately represent the severity of the thermal damage inside the cornea.

The model in the present study can be further improved by taking into account the effects of intracorneal focusing, such as in the work carried out by Brinkmann and et al.8−10 Some issues that we have presented in this study, which regard the eye model, should be addressed in future studies. During LTKP, shrinkages alter the dimension and shape of the cornea. This aspect has not been considered in the present study. Inclusion of this feature, which involves a moving boundary problem, may produce results that are different from those presented in Sec. 12.5.

The absorption coefficient of the cornea has been taken to be the same as the absorption coefficient of water, which we assume to be constant. Previous studies, however, have shown this assumption to be misleading.35 According to Ith et al.35 the absorption coefficient of water is subjected to dynamic changes during laser–tissue interaction. Some studies have found the accuracy of simulated results to be severely affected by the assumption of constant optical properties.36,37 The variation of the thermal conductivity of the cornea with temperature has also been reported. According to Bhattacharya and Mahajan,38 the thermal conductivity of the cornea increases linearly with temperature. This linear increase in temperature has not been considered in the present study, since the relationship was obtained using sheep cornea and is only valid for heating temperatures up to 55◦C. More research has to be carried out in future studies to examine the effects of these factors on the thermal response of the cornea during LTKP.

12.9. Concluding Remarks

A model of the human eye has been successfully developed for simulating temperature changes inside the cornea during LTKP. Its accuracy is demonstrated by the good qualitative agreement between the numerical

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