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Fig. 12.5. The corneal temperature along the pupillary axis (against z at r = 0) at the end of each laser pulse.

maximum temperature achieved by the corneal endothelium is smaller than 65◦C; implying an absence of endothelial cell deaths.

The spatial temperature profiles over a small cross-section of the cornea and the anterior chamber on the rz plane are shown in Fig. 12.6. The crosssection is selected in such a way that significant variation in the temperature can be observed. For a clearer visualization, the temperature plots in Fig. 12.6 are given with the mirror images about the z-axis.

There appears to be a large temperature gradient at approximately z = 0.5 mm. This may be attributed to the penetration depth of the laser inside the cornea, which according to Eq. (12.4) and based on the properties of the pulsed laser given in Table 12.3, is calculated to be 0.5 mm. Temperature increase at regions defined by z < 0.5 mm is, thus, caused by the absorption of laser energy, while temperature increase at z > 0.5 mm is due to the diffusion of heat from the regions at z < 0.5 mm.

12.7.2. Continuous-Wave Laser

The transient temperature changes inside the eye during the treatment of LTKP using a continuous-wave laser are examined in this section. Both the 10-s coagulation and the minute coagulation (see Sec. 12.2) are investigated. Parameters of the continuous-wave laser used in a typical treatment of LTKP are tabulated in Table 12.4, which are obtained from Brinkmann et al.10 Wavelengths of the lasers used to treat LTKP using continuous-wave lasers

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Fig. 12.6. Spatial temperature profiles over a selected cross-section of the eye subject to pulsed laser irradiation.

Table 12.4. Typical laser parameters chosen for the continuous-wave laser.

may vary between 1.85 and 1.87 µm. However, in the present study, only the laser that is emitted at a wavelength of 1.87 µm is considered.10 Values of peak irradiance, Eo, are obtained using the expression:

P

Eo = πw2 ,

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where P is laser power. The expressions of ψ(t) for the 10-s and minute coagulations are given by:

respectively. When executing the time stepping scheme, a value of t = 0.1 s is chosen for the 10-s coagulation while for the minute coagulation, a value of t = 0.5 is selected.

Figures 12.7 and 12.8 illustrate the transient temperature profiles along the pupillary axis (r = 0) at various depths of the cornea during the treatment of LTKP for the 10-s and minute coagulations, respectively. Both approaches show uniform increases in the corneal temperature, which are unlike the temperature profiles observed in Fig. 12.4 during pulsed laser radiation. At the end of the laser treatment, a sharp decrease in temperature is found because of the rapid dissipation of heat to the environment and adjacent regions inside the human eye.

The largest temperature reached inside the cornea during the 10-s and minute coagulations are 75.6◦C and 70.1◦C, respectively. The higher

Fig. 12.7. Transient temperature profiles at various depths of the cornea in the 10-s coagulation.

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Fig. 12.8. Transient temperature profiles at various depths of the cornea in the minute coagulation.

temperature observed in the 10-s coagulation may be attributed to laser power, which is higher than the laser power used in minute coagulation (0.125 vs. 0.10 W). A large portion of the corneal stroma, defined by depths between 50 and 550 µm, are heated beyond the threshold for corneal shrinkages. This heating is true for both the 10-s and minute coagulations. In both coagulations, no corneal relaxation occurs, since the largest temperatures achieved are not greater than 90◦C.

Figures 12.9 and 12.10 correspondingly show the temperature profiles along the pupillary axis (r = 0) of the cornea at various time levels for both the 10-s and minute coagulations. During the course of radiation, temperatures at the endothelium (z > 550 µm) are found to be less than 55◦C for both the 10-s and minute coagulations. These observations imply that no endothelial cell deaths occur during continuous-wave laser radiation.

The spatial temperature distribution over a small cross-section of the cornea and anterior chamber at t = 2, 4, 6, 8, and 10-s for the 10-s coagulation and at t = 12, 24, 36, 48, and 60 s for the minute coagulation are illustrated in Figs. 10.11 and 10.12, respectively. The temperature plots in Figs. 10.11 and 10.12 have been presented with the mirror images throughout the z-axis. The isotherms observed in Figs. 12.11 and 12.12 appear to

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Fig. 12.9. Temperature distribution inside the cornea at various time levels in the 10-s coagulation.

Fig. 12.10. Temperature distribution inside the cornea at various time levels in the minute coagulation.

be more uniformly distributed when compared to the isotherms observed during pulsed laser radiation. A large thermal gradient is observed at about z = 0.52 mm, which is approximately the point defined by the penetration depth of the continuous-wave laser.

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Fig. 12.11. Spatial temperature profiles over a selected cross-section of the eye subject to 10-s coagulation radiation.

Fig. 12.12. Spatial temperature profiles over a selected cross-section of the eye subject to minute coagulation radiation.

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