Laser-induced corneal injury: validation of a computer model to predict thresholds

Abstract

The exposure and emission limits of ICNIRP, IEC 60825-1 and ANSI Z136.1 to protect the cornea are based on a limited number of in-vivo studies. To broaden the database, a computer model was developed to predict injury thresholds in the wavelength range from 1050 nm to 10.6 µm and was validated by comparison with all applicable experimental threshold data (ED₅₀) with exposure duration between 1.7 ns and 100 s. The model predictions compare favorably with the in-vivo data with an average ratio of computer prediction to ED₅₀ of 0.94 (standard deviation ± 30%) and a maximum deviation of less than 2. This computer model can be used to improve exposure limits or for a quantitative risk analysis of a given exposure of the cornea.

Fig. 1.

Appearance of a corneal lesion produced by a CO2 laser (10.6 µm) in a non-human primate at a radiant exposure level three times above the injury threshold (photograph taken at 15 minutes post exposure; courtesy of B.E. Stuck).

Fig. 2.

Absorption coefficient and penetration depth for the cornea (solid line, Ref. [26]) and for water (broken line, Ref. [27]).

Fig. 3.

Experimental data (dots; data not included in the computer model validation are red open diamonds) and computer model predictions (solid line) with ± 2 standard deviations (dashed lines) for 1.54 µm (a) and for 10.6 µm (b). The injury thresholds were computed for a 1 mm beam diameter, and for exposure durations longer than 100 ms, experimental data points were selected to have approximate beam diameters of 1 mm in order to avoid deviations resulting from a beam-diameter dependence.

Fig. 4.

Distribution of R_ED50 ratios for the non-human primate and rabbit models (bars), split into bins of constant size on log scale; also shown is a normal distribution with identical average and standard deviation (solid line).

Fig. 5.

Distribution of individual R_ED50 ratios as a function of (a) exposure duration, (b) wavelength and (c) beam diameter; to provide further information, the data in each diagram is split in (a) wavelengths shorter or longer than 3 µm, (b) exposure durations shorter or longer than 100 µs and (c) assessment delays shorter or longer than 1 h after exposure.

Fig. 6.

Experimental (squares; open square for the threshold reported by Archibald and Taboada for 1410 nm) and computer model (dashed curve) injury thresholds, and MPEs (solid black line) as function of wavelength in the thermal confinement regime

Fig. 7.

Prediction of the depth (a) and associated highest temperature (b) of a corneal threshold injury as a function of exposure duration for 1 mm (dashed line), 3 mm (solid line) and 7 mm (dotted line) top hat corneal irradiance profiles.

Fig. 8.

Per experimental study, the lowest injury threshold is plotted (as a relative value to the ED₅₀, circles) as a function of the probit slope that was reported for the respective study. Additionally, the reduction relative to the ED₅₀ necessary to achieve a certain probability for injury is shown as lines; for the example of a probit slope equal to 1.1, the ED₁ (1% probability of injury) is found at an exposure level 20% below the ED₅₀.