**Purpose.**:
To evaluate ablation algorithms and temperature changes in laser refractive surgery.

**Methods.**:
The model (virtual laser system [VLS]) simulates different physical effects of an entire surgical process, simulating the shot-by-shot ablation process based on a modeled beam profile. The model is comprehensive and directly considers applied correction; corneal geometry, including astigmatism; laser beam characteristics; and ablative spot properties.

**Results.**:
Pulse lists collected from actual treatments were used to simulate the temperature increase during the ablation process. Ablation efficiency reduction in the periphery resulted in a lower peripheral temperature increase. Steep corneas had lesser temperature increases than flat ones. The maximum rise in temperature depends on the spatial density of the ablation pulses. For the same number of ablative pulses, myopic corrections showed the highest temperature increase, followed by myopic astigmatism, mixed astigmatism, phototherapeutic keratectomy (PTK), hyperopic astigmatism, and hyperopic treatments.

**Conclusions.**:
The proposed model can be used, at relatively low cost, for calibration, verification, and validation of the laser systems used for ablation processes and would directly improve the quality of the results.

^{ 1 }Using a flying laser beam, the surgeon has better control over laser energy delivery at each corneal position and therefore a greater demand to reproduce details accurately is put on the laser systems.

^{ 2 }To implement wavefront-based customized ablation, a surgical laser system must be capable of reproducing the details of complex wavefront-driven ablations while reducing the incidence of high-order aberrations after surgery.

^{ 3,4 }It is well known that a successful surgery depends on the correct design of an ablation profile, precise delivery of laser energy to the corneal position, and reliable understanding of the corneal tissue response.

^{ 5 –10 }as well as in the laboratory.

^{ 11,12 }The rise in corneal temperature and its associated consequences are not yet fully understood.

^{ 13 }hyperopia,

^{ 14 }and astigmatism.

^{ 15 }Achieving accurate clinical outcomes and reducing the likelihood of a retreatment procedure are major goals of refractive surgery. For that, accurately calibrated lasers are essential.

^{ 16,17 }ablation decentration and registration,

^{ 18,19 }eye tracking,

^{ 20,21 }flap,

^{ 22 }physical characteristics of ablation,

^{ 23 –29 }wound-healing, and biomechanics of the cornea

^{ 30 –33 }have been explored to predict or explain the clinically observed discrepancy between intended and actual outcomes. The quantification of influence of these factors is important for providing the optimal outcome in refractive surgeries.

^{ 34 }The temperature-cooling model used is an immediate effect model, because the thermal absorption time is very short and the local heat propagation can be regarded as infinity velocity propagation, as when using the Fourier models.

^{ 35 }

*c*= 2.93 J/(g K), the ablation threshold at

*I*

_{Th}= 44 mJ/cm

^{2}, and the absorption coefficient of the cornea at 193 nm α = 3.57 × 10

^{6}m

^{−1}(Fig. 1).

^{ 38 }With the flying-spot laser system, the corneal ablation behavior is mainly governed by the relationship between the per-pulse tissue ablation depth and the radiant exposure (energy per illuminated area) to the incident laser radiation.

^{ 39,40 }

^{ 41 }The temperature-cooling model used is a simple diffusion model that can be obtained from simple propagation models by assuming that the environment is much bigger than the tissue where the diffusion mainly occurs.

^{ 42 }

^{ 43 }This form of heat loss principle, however, is not very precise; a more accurate formulation requires an analysis of heat flow based on the heat equation in an inhomogeneous medium. This simplification can be applied so long as it is permitted by the Biot number.

*T*

_{env}is the asymptotic temperature (temperature of the environment), and τ

_{r}is the so-called thermal relaxation time. The thermal relaxation time depends on the geometry of the heated volume and is different for objects embedded in heat-conducting material, with a surface in air. It is a material-specific quantity depending on the absorption coefficient, the thermal conductivity, the density, and the heat capacity (τ

_{r}= ρ

*c*/4α

^{2}κ).

^{ 36 }

_{r}= 0.14 seconds (Fig. 2).

^{ 44 }this equation is: where

*T*is temperature as a function of space and time and

*k*is the thermal diffusivity, a material-specific quantity depending on the thermal conductivity, the density, and the heat capacity (

*k*= κ/ρ

*c*).

^{ 45 }

^{ 46 }

^{ 47 }

*T*by using the Taylor formula, we get We consider, for any single point at the temperature matrix, the influence coming from its eight primary neighbors. We should then consider a specific case whenever we are at a corner or edge of the matrix.

*t*is “short enough” to ensure gradual smoothing of the initial temperature distribution by the flow of heat from warmer to colder areas of an object.

^{ 8 }Considering that normal ocular surface temperature lies at approximately 33°C, the thermal load of the treatments should be limited to approximately 7°C.

^{2}to approximately 500 mJ/cm

^{2}, corresponding to thermal loads of approximately 0.1 K and approximately 0.6 K, respectively.

*F*(

*z*) as a function of depth

*z*for values

*F*<

*F*th. However, we did not consider the energy dissipation that results from the ablation.

^{2}and 1-mm diameter spot size, ablating onto a spherical cornea of a 7.77-mm radius, the thermal load decreases from 0.33 K centrally to 0.20 K at a 5-mm radial distance. The thermal load for peripheral locations decreases as well with steeper corneal curvatures. In our example, at 3 mm radially from the central cornea, the thermal load of a single pulse reduces from 0.30 K for a spherical cornea with a 9.80-mm radius to 0.26 K for a spherical cornea with a 6.44-mm radius.

^{2}peak radiant exposure, the thermal load of a single pulse is 0.4 K. If the system fires at 400 Hz without local frequency controls, the thermal load of the treatment may exceed 25 K. If the same system includes local frequency controls of 40 Hz, the thermal load of a treatment will be confined to 3 K.

^{ 48 –50 }

^{ 12 }Using our model with their specifications, we have obtained 19 K at a 1050-Hz repetition rate (i.e., 210 Hz local frequency control), 11 K at 500 Hz (i.e., a 100-Hz local frequency control), 9 K at 400 Hz (i.e., a 80-Hz local frequency control), and 5 K at 200 Hz (i.e., a 40-Hz local frequency control).

^{ 51 }featuring a high-speed repetition rate, as well as constant frequency per area delivery. The latter ensures a constant, effective ablation rate; by varying the delivered pulse rate to remain constant per area (at 5 Hz/mm

^{2}), the entire ablation retains consistent delivery of energy. Using our model with their (iVIS iRES; iVIS Technologies, Taranto, Italy) specifications, we have obtained 11 K at a 2 × 500-Hz repetition rate with a 5-Hz/mm

^{2}local frequency control).

^{ 52,53 }similar ablation thresholds for 193- and 213-nm laser radiation, but much lower absorption coefficients for 213 nm (ablation threshold

*I*

_{Th}= 44 mJ/cm

^{2}at 193 nm vs. ∼50 mJ/cm

^{2}at 213 nm and the absorption coefficients of the cornea α = 3.57 × 10

^{6}m

^{−1}at 193 nm vs. ∼2.1 × 10

^{6}m

^{−1}at 213 nm). Taking this into account, for laser application with the same radiant exposure at 193 or 213 nm, the temperature rise of a single pulse is approximately 60% at 213 nm of the value at 193 nm. On the other hand, the thermal relaxation time is almost three times longer at 213 nm than at 193 nm. This means that only for very short applications (<1 s) or very slow repetition rates (<4 Hz) is the cumulative thermal load at 213 nm lower than that of its 193-nm equivalent. Above these values the cumulative thermal load at 213 nm is ∼60% higher than its 193-nm equivalent.