The amount of tissue ablation by means of an excimer laser for corneal refractive surgery depends on the applied laser pulse energy per area (radiant exposure) of each laser pulse. Therefore, a precise calibration of the laser energy or the radiant exposure before treatment is critical to achieve a predictable refractive outcome. In clinical routine, the radiant exposure can be measured by photoablation of polymethylmethacrylate (PMMA) with a predetermined refractive correction. The central ablation depth of these PMMA plates is measured after photoablation and the laser energy may be readjusted to achieve a predetermined central ablation depth. Polymethylmethacrylate is strong, has excellent optical properties, and offers high consistency of ablation depth under controlled environmental conditions during laser calibration.1,2
The influence of environmental factors on the ablation depth has been investigated.3 Humidity and temperature within the surgery4 are known to affect the photoablation process and suggestions have been made to control them.5 Many studies have analyzed temperature increases in the cornea and PMMA during treatment in general6–9 or independent of scanning algorithms,10 wavelength,11 or radiant exposure.12 However, there is little knowledge available about the influence of initial material temperature on ablation depth in general.13 In refractive surgery, the initial material temperature has practical relevance because no standard exists for storage conditions of PMMA plates used for laser calibration. Therefore, a potential temperature shift of PMMA plates due to time of day or other environmental changes may influence the laser energy adjustment during calibration and this may be critical for the subsequent surgery and needs to be studied.
The purpose of this study is to investigate the relevance of the initial temperature of PMMA plates used as a target for photoablation during calibration of excimer lasers performed in daily clinical routine.
Materials and Methods
The experimental setup used to determine the dependence of the ablation depth on the initial temperature of PMMA plates is shown in Figure 1.
Figure 1. Experimental setup for polymethylmethacrylate (PMMA) ablation measurements.
The prototype laser system corresponds to the clinically used ALLEGRETTO Wave laser platform (Wave-Light Laser Technologie AG, Erlangen, Germany) as reported in earlier publications.10,14,15
The optical system of the laser platform includes a beam homogenizer that transfers the initial beam profile emitted from the argon fluoride excimer laser into a Gaussian-shaped intensity distribution within the treatment plane. The beam profile was measured within the treatment plane by a beam profiling camera prior to each treatment (reference beam-profile camera) to assure accurate alignment of the optical setup of the laser system. The PMMA plates were positioned by two aiming beams that overlap at the treatment plane and in the center of the treatment zone. In all experiments, a myopic ablation profile of −9.00 diopters (D) was applied with a predicted ablation depth of 120 μm with an optical zone diameter of 6.5 mm. The excimer laser with a wavelength of 193 nm was working at a repetition rate of 1050 Hz.
The pulse energy was set to 2.10 mJ for all experiments corresponding to a central peak radiant exposure of 500 and 250 mJ/cm2 averaged over the Gaussian-beam profile. Pulse energy was measured by means of an energy detector (J25LP-3-0A0; Coherent Inc, Dieburg, Germany). After the energy value was set to its attempted value, the internal energy sensor was preset to control the excimer laser to maintain the pulse energy values during a complete myopic treatment.
The system was working with a pulse duration of 8 ns during the experiments and was measured by means of a ultraviolet-sensitive photodiode (UPD-200-UD; Alphalas GmbH, Goettingen, Germany) and a fast oscilloscope (RDS3032B; Tektronix, Beaverton, Oregon). The single pulse duration was derived from the temporal beam profile (full width at half maximum).
As in the clinical system, the experiments were performed with an air aspiration system mounted 70 mm above the ablation zone. The laminar air flow of 5±0.5 m/s was controlled with an impeller anemometer (RS 180-7111; RS Components GmbH, Mörfelden-Walldorf, Germany). The relevance of such a laminar air flow for PMMA ablation measurements has been reported previously.2
The plane surfaces of 20 PMMA plates with a size of 30×50×3 mm were ablated at different initial material temperatures ranging from 10.1°C to 75.7°C. Therefore, the previously cooled or heated plates underwent different warm-up or cool-down phases until the attempted initial temperatures were achieved. All temperature measurements were performed by an infrared camera (VarioTHERM; Jenoptik AG, Jena, Germany) that was mounted in front of the PMMA plates under an angle of 40° with respect to the optical axis of the laser system. The initial temperature was defined as the measured mean temperature within the optical zone before the first laser pulse.
Ablation Depth Measurements
The ablation depth measurements were carried out with a surface profiling system (Mahr Perthometer PCV with software Perthometer Concept 6.3; Mahr GmbH, Goettingen, Germany). A contact force of 10 mN and a measurement speed for the tactile measurement head of 0.6 mm/s were used to measure the contour of the ablated optical zone after laser treatment. The maximum depth of the measured central line (length: 11.00 mm) within the treatment zone with respect to the plane surface of the untreated material was defined as ablation depth (Fig 2).
Figure 2. Scheme of the ablation depth measurement on polymethylmethacrylate (PMMA) plates.
Measurement data were evaluated using Microcal Origin version 6.0 (OriginLab Corp, Northampton, Massachusetts). Twenty different initial temperatures were used and corresponding ablation depths were determined from surface profile measurements. A linear regression between achieved ablation depth and initial temperature was performed. Additionally, the coefficient of determination, significance level of the correlation (P value), and confidence interval were determined.
Figure 3 shows the measured ablation depth of the 20 PMMA plates as a function of different initial temperatures. The ablation depth increases from 73.9 to 96.3 μm within a temperature increase from 10.1°C to 75.7°C. This yields to an increase rate of 0.3192 μm/K. The correlation for the linear fit was found to be significant (P<.05) with a coefficient of determination of R2=0.95.
Figure 3. Ablation depth as a function of initial temperature of polymethylmethacrylate plates.
Determing Refractive Correction
A more analytical approach to determine the refractive correction in a patient’s eye can be deduced from the relationship of the radiant exposure (energy per area) f with the central ablation depth of a myopic correction.16–18
= central ablation depth, N
= number of laser pulses in the central area of the treatment, α = effective absorption coefficient, f
= applied fluence, and fth
= ablation threshold fluence. The change in laser pulse fluence Δf
originating from a certain temperature deviation of PMMA plates ΔTPMMA
during laser calibration can be calculated with Eq.() and the resulting change in ablation depth ΔDCornea
on the cornea. Based on the literature, the following parameters were used: αPMMA
= 52 000 cm−1
= 67 mJ/cm2
= 29 000 cm−1
, and fth,Cornea
= 50 mJ/cm2
, respectively. The number of laser pulses N
within the central area of the ablation zone can be estimated from Eq.() by dividing the central ablation depth of a −9.00-D profile of 120 μm by the single-pulse ablation on the cornea of 0.79 μm, which yields N
A given relative change of ablation depth on the cornea ΔdCornea can be translated directly into the relative change of optical correction Δ(ΔDCornea) because of the relation19:
= 1.376 the refractive index of the cornea and r0
= radius of the optical zone.
The purpose of the experiments was to analyze how the initial temperature of PMMA plates used during clinical excimer laser calibration influences the outcome of corneal refractive surgery. The experimental results have shown a linear dependence of ablation depth on initial surface temperature of PMMA plates. Consequently, laser calibration with PMMA plates of different temperatures affects the calibration setting of the laser system in clinical routine. By using PMMA plates with higher initial temperature than standard room temperature (20°C), the resulting ablation depth is too high. In this case, the laser energy will be reduced during clinical calibration and the ablation of the corneal tissue will be performed with a lower energy. As a consequence, the outcome of the refractive surgery procedure on the cornea will be an undercorrection.
The erroneous calibration with PMMA plates having a temperature of 30°C instead of standard room temperature of 20°C leads to an undercorrection of 0.25 D in an attempted optical correction >6.75 D. At higher refractive corrections of 9.00 D, an undercorrection of 0.25 D may occur at an initial temperature of 27.5°C. Figure 4 shows the complete dependence of allowed temperature bias to remain within an error of 0.25 D on the attempted refractive correction.
Figure 4. Range of allowed temperature bias of polymethylmethacrylate (PMMA) plates for calibration to achieve refractive surgery outcomes within 0.25 D of desired values (the Y axis is the allowed deviation from the assumed standard room temperature of 20°). (Assumption: Calibration done at 20°.)
Overall, our theoretical analysis indicates that only an extreme temperature bias of the PMMA plate has a relevant effect on the refractive outcome, and would most likely not occur in a typical climate-controlled clinical environment. It is important to note that a potential constant temperature bias in a specific clinical environment will not impact the surgical outcome if the nomogram adjustment is done under the same conditions. In this case, the temperature bias is reflected and compensated in the nomogram.
As the storage of PMMA plates for laser calibration is not regulated, there are still potential scenarios in a clinical environment that could be critical. If a PMMA plate is exposed to sunlight or stored in a differently climated room, its initial calibration temperature could be altered significantly. Although a clinical environment should be temperature-controlled, temperature biases in extreme climate zones cannot be ruled out. According to our results, this could have a serious impact on the calibrated laser energy. This scenario is not likely to increase the error range of the refractive outcome, but still shifts the outcome average in the nomogram. This may lead to a reduction of eyes within ±0.50 D of the attempted correction, which cannot be tolerated. We believe that a recommendation for storage and temperature of PMMA plates used for excimer laser calibration should be defined as a standard in a clinical environment. Assuming a standard room temperature of 20°C, we recommend keeping the PMMA plate temperature between 18°C and 22°C to ensure the resulting refractive error is below 0.25 D even for higher refractive corrections up to ⩾10.00 D.
A physical explanation of the measured dependence of the ablation depth on the initial temperature of PMMA can be that both the highest temperature rise ΔTmax and the initial temperature of the substrate Tsub (PMMA) contribute to the ablation threshold Tth temperature as described in13:
As ΔTmax increases with laser pulse energy and Tth is constant, higher pulse energy enables the same ablation depth per pulse already at lower material temperature. Consequently, the same laser pulse energy will result in more ablated material if the initial temperature of the substrate is elevated. Although the characteristics of our study may be phenomenologically identical to the study of Gordon et al,13 a quantitative comparison is impossible because of the different laser parameters of a wavelength of 355 nm, a pulse duration of 20 to 35 ns, and a maximum pulse energy of 300 μJ.
In the theoretical analysis of our study, we correlate the central ablation depth with the dioptric power. It is important to note the limitation of this simplified approach. We assume a constant ablation depth per unit pulse across the ablation surface. The intensity profile of the laser beam across the ablation zone has a Gaussian shape that leads to a variation in ablation properties. Therefore, the ablation profile can deviate from its intended spherical shape. The resulting alteration in curvature should be characterized in further studies. With this limitation, our analysis can still provide a first estimation of the influence of different temperature deviations during PMMA calibration on different refractive corrections (see Fig 4).
Aside from initial temperature other factors can influence the ablation depth. Based on the findings in our study, a relationship of temperature increase during ablation6–9 and ablation depth is likely. Compared to the initial temperature, it may be a dominant factor contributing to an increased ablation depth. Therefore, the extrapolation of our results as significant to other laser systems is limited.
A further limitation of the theoretical analysis presented is the unknown dependence of the effective absorption coefficient α and the ablation threshold fluence fth on temperature that may be of relevance and of further interest for future experimental work.
Another aspect that could limit our study is the temperature profile per unit depth in PMMA plates prior to ablation. As the initial temperatures were measured at the surface only at some transient state, a thermal gradient inside the plate could influence the results. In a theoretical analysis of the thermodynamic behavior, the Biot number was calculated. Which is defined20 as
= heat transfer coefficient, LC
= characteristic length of the body, and kb
= thermal conductivity of the body. With h
≈ 5 W/m2
= 0.0015 m (because of the symmetry of the problem involving the PMMA plates with a thickness of 3 mm), and kPMMA
≈ 0.19 W/mK22
a Biot number of Bi ≈ 0.04 was calculated. Values of the Biot number smaller than ∼0.1 imply that the heat conduction inside the body is faster than the heat convection away from its surface, and temperature gradients are negligible inside of it.20
Therefore, we assume that the temperatures throughout the PMMA plates are well represented by the measured surface temperature at every time.
Throughout the theoretical interpretation of the experimental results in this study the temperature of the cornea was assumed to be constant. However, this may not be the case in reality as some surgeons cool down the cornea before surgery. By flushing the cornea with cold saline solution or applying cooled metal instruments, postoperative pain or haze may be reduced.23,24 Therefore, the examination of ablation depth dependent on initial corneal temperature is essential and should be realized going forward. However, in an appropriate experimental setup, the stromal hydration needs to be considered as its variation can influence the measurements significantly.25 Further experimental work is required to clarify the dependence of the corneal ablation on the initial tissue temperature.
Our experimental results have shown that increased initial temperature of PMMA plates for excimer laser calibration leads to a linear increase of the ablation depth. The calculated outcome of refractive surgery indicates that a temperature bias of PMMA during calibration is more critical with higher refractive corrections. As a consequence, the temperature of PMMA plates for clinical laser calibration should be controlled. Further experiments are required to determine the influence of different initial corneal temperatures on the refractive outcome.