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A. Fernandes, G.M. Silva, A.G. Rosal, D.D. Almeida, R.C. Lima; Numerical Study of the Temperature Field and Damage Function of the Cornea During Laser Refractive Surgery . Invest. Ophthalmol. Vis. Sci. 2003;44(13):2574.
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Purpose: To create a numerical model to calculate the values of temperature and damage function for the cornea and surrounding tissues during laser application for refractive surgery. Methods: The method used considered the eye as a sphere and the cornea as a smaller sphere where the laser beams are applied. The profile of the temperature in the transient state was obtained from the Pennes' Bioheat Transfer Equation. The numerical method used was the finite volumes in a structured mesh with spherical coordinates. In our simulation we used a geometric pattern of laser delivery system identical of that employed for the Laser Thermal Keratoplasty (LTK) for the treatment of hyperopia. The numerical three-dimensional model used 25 selected points on the corneal surface and 36 inner radial points. Because of the symmetry of the problem only one corneal quadrant was used in the model. We also calculated the damage function in an attempt to quantify it for all nodes of the mesh. The damage function was calculated by an empirical equation derived from the Arrhenius equation, which is employed for the speed of a chemical reaction. The model also took into account tear film evaporation by the use of an appropriate convection heat transfer coefficient. Individual coefficients of laser light absorption were considered for the cornea, the aqueous humor, and the lens. We used Fortran90 language in our analysis. Results: Our results were calculated for a pulsed Ho: YAG laser for 5 s application, with a frequency of 5 Hz, pulse length of 250ms, and fluency of 19mJ/pulse. In all laser application sites the calculated temperatures were bellow 57.5 °C. For the highest temperature site, the damage function reached a value of 0.065 after 5 s. The highest temperature for the endothelium was 55.2°C with a damage function value of 0.028. All mesh nodes that were located bellow the corneal surface revealed lower temperatures than 57.5°C. All damage function values for the mesh nodes were bellow 0.53, a limit value after which irreversible damage can occur in vivo tissues. Conclusions: Our model demonstrates that the obtained values of temperature and damage function present no risk of heat damage to the corneal endothelium with the use of Ho:YAG laser for LTK surgery.
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