2.1.

Experimental Setup

Figure 2 shows a schematic overview of the setup for the irradiation of the samples, with the exception of minimal spot diameters. Two frequency-doubled Nd:YAG lasers (Omicron Laserage FK-LA 8000, Rodgau, Germany) provide continuous laser radiation at a wavelength of $532\mathrm{nm}$ and with a total output power of up to $18\mathrm{W}$ . These lasers have a beam propagation factor ${\mathrm{M}}^2$ of about 8. In front of each laser aperture, a computer-controlled acousto-optical modulator (AOM1 and AOM2) was placed. The AOMs control the laser power as function of time with a temporal resolution of $10\mu \mathrm{s}$ and a throughput resolution of 1024 steps between zero and maximum transmission, and thus allow control of both the pulse shape as well as the energy per pulse. For the experiments reported in this work, the temporal pulse shape was rectangular. After combining the two laser beams by a polarization crystal, the beam was coupled into either a $50\text{-}\mu \mathrm{m}$ (for spot sizes less than $1\mathrm{mm}$ ) or a $200\text{-}\mu \mathrm{m}$ fiber, (for spot sizes $1\mathrm{mm}$ or greater). A lens imaged the distal tip of the fiber onto the sample. The length of the fiber was $10\mathrm{m}$ . The beam finally enters a galvanometer-driven scan head (SCANLAB hurry SCAN™ 14, Puchheim, Germany), which produces a computer-controlled scan pattern on the sample. Concurrent control of the scanner and the AOMs was affected with a PC interface card (SCANLAB RTC® 4) and a self-developed computer program. With this computer program, it is possible to expose a sample with a grid of individual laser exposures in a short amount of time. For instance, for small laser spots $\left(23\mu \mathrm{m}\right)$ , it is possible to place 200 exposures with varying energy per pulse on a sample area of $5\times 5{\mathrm{mm}}^2$ within one minute. A calibrated laser power meter [Ophir 3A and Ophir L40(150)A, North Logan, Utah] was placed beneath the scanner before and immediately after the exposures to record the power incident on the sample for an “open” AOM, i.e., the maximum peak power level. The actual energy deposited on each irradiated location on the sample was calculated in Microsoft Excel, using pulse duration, power, and the AOM’s throughput setting, which was calibrated with the laser power meter. The experimental uncertainties related to the power incident on the sample are: laser power instability less than $\pm 3\%$ ; uncertainty of power radiometers $\pm 3\%$ ; and deviation of AOM throughput from calibration function $\pm 1\%$ resulting in a total power uncertainty of $\pm 4.4\%$ . Prior to the exposures, the spatial beam profile was recorded in the sample plane with a COHU charge-coupled device camera (model 7512) with $6.7\text{-}\mu \mathrm{m}\text{pixel}$ pitch, and the beam diameter defined at the 1/e level was calculated with a beam analyzer software (Spiricon LBA-700PC North Logan, Utah). The beam profile on the sample for all but the smallest laser spots was a nominal top hat, i.e., inconstant irradiance level (the difference of the threshold between a perfect top hat and the actual profile was calculated with the thermal model to be less than $\pm 2\%$ ). To achieve small spots ( $23\mu \mathrm{m}$ diam), a continuous frequency-doubled Nd:YAG ${\mathrm{TEM}}_{00}$ laser (CrystaLaser GCL-100-L, Reno, Nevada) with a wavelength of $532\mathrm{nm}$ and $100\text{-}\mathrm{mW}$ output power was used instead of the two Omicron lasers. This laser has a ${\mathrm{M}}^2$ value of close to 1 and the beam profile for the $23\text{-}\mu \mathrm{m}$ -diam spots (diameter specified at the 1/e level) was Gaussian. For the $23\text{-}\mu \mathrm{m}$ spots, no fiber was used. The uncertainty of the diameter measurement for the $23\text{-}\mu \mathrm{m}$ spots was estimated to be $\pm 14\%$ , for $73\text{-}\mu \mathrm{m}$ spot size $\pm 5\%$ , and for the larger spot sizes less than $\pm 3\%$ .

Fig. 2

Experimental setup for the ex vivo explant exposures.

2.2.

Sample Preparation and Analysis

The ex vivo (explant) samples were obtained from fresh bovine eyes that were received from a local slaughterhouse. After dissection of the surrounding connective tissue, the eye was opened approximately $7\mathrm{mm}$ beneath its equator and the vitreous body was removed. The black-pigmented parts of the fundus of the eye were cut into rectangular pieces and placed in phosphate-buffered solution. The sensory retina (the photoreceptor layer and attached nerve layers) was removed by cleaving the outer segments of the photoreceptors with Chondroitinase ABC (Sigma-Aldrich, Missouri), so that the uppermost layer was the retinal pigment epithelium (RPE), supported by the choroid and the sclera. Then, the tissue was stained with the viability marker Calcein AM ( $2.5\text{-}\mu \mathrm{M}∕\mathrm{ml}$ phosphate buffered saline, Sigma Aldrich, Missouri). Calcein is absorbed by the vital cells and reduced to a fluorescent dye by means of cellular esterases (excitation maximum at $490\mathrm{nm}$ , emission at $520\mathrm{nm}$ ). The incubation time before laser exposure was between $30\min$ and $2\mathrm{h}$ . The samples were examined before laser exposure with a Zeiss Axiovert (Jena, Germany) inverted microscope to ensure viability of the cells and quality of the sample. Subsequent to the examination, the samples were stored in Hank’s Balanced Salt Solution (Krackeler Scientific, Albany, New York). The RPE cells remained vital for a total duration of $8\text{to}10\mathrm{h}$ after slaughtering of the animals. The samples were also kept covered with Hank’s Solution during laser exposure to prevent dehydration. The temperature of the sample before laser exposure was $23\pm 1°\mathrm{C}$ . The examination of viability with the Zeiss Axiovert inverted microscope took place between $15\min$ and $1\mathrm{h}$ after exposure. For some samples, the development of lesions over time was observed, and it was found that the number of cells showing damage did not increase after the $15\text{-}\min$ postexposure evaluation. Vital cells show a bright green fluorescence, whereas the damaged cells appear dark due to loss of dye. The examination was performed by Husinsky only due to time constraints regarding the viability of the samples. A horizontal and vertical line with overexposed “shots” formed a cross in the exposure grid to aid the evaluation. Exposed sites where determined to be either damaged or not affected. It was noted that on occasion, the exposed area appeared distinctively brighter than the surrounding nonexposed area, or that highly fluorescent droplets formed at the edge of the region where cells were dark (see Fig. 3 ). For very small laser spots, occasionally only droplets could be seen and it was not possible to determine whether the cell behind the droplet appeared dark (i.e., dead) or fluorescent. The exact reason for this increased brightness and formation of droplets is not known but is expected to be related to leaking of Calcein out of compromised cells. These cases were also counted as damaged. The lesion dose-response data were evaluated by Probit analysis software (ProbitFit V1.0.2 by Brian Lund, Northrop Grumman, Los Angeles, California) to obtain ED50 and slope values (see for instance Sliney ¹⁰ for a discussion on these parameters). A light micrograph $(40\times \text{magnification})$ of a histological section showing the lesion confined to the RPE is shown in Fig. 4 .

Fig. 3

Fluorescent micrograph of exposures with a beam diameter of $23\mu \mathrm{m}$ and a pulse duration of $100\mathrm{ms}$ . The energy per pulse was varied. Individual RPE cells are visible.

Fig. 4

Light micrograph of a histological section showing a damaged RPE layer in the center and normal RPE to both sides.

2.3.

Computer Model

Laser-induced retinal thermal injury thresholds were calculated with a computer model based on the concept published by Thompson, ⁸ usually referred to as the Thompson-Gerstman model. However, the basic model was extended to also model the choroid as an absorbing layer, which is necessary for accurate calculations in the thermal damage regime. The absorbing spheres in the model were regarded as means to couple radiant energy into the system and were not intended to model actual distributions of melanosomes. In the pulse duration regime of interest to thermal damage, the absorbing layers of the RPE and choroid can be treated as homogeneous absorbers; the localized absorption by melanosomes only plays a role for pulse durations in the microsecond regime and shorter (where, however, microbubble formation is the dominating damage mechanism, which cannot be modeled with the Thompson-Gerstman model). A comparison with a finite difference model (also often referred to as the Takata’ model⁷) showed that for an equivalent percentage of absorption in the retina, the Thompson-Gerstman model for pulse durations above $10\mu \mathrm{s}$ yields threshold damage values identical to those calculated with the finite difference model. This equivalence is due to the homogenization of the temperature field by heat flow, which after some time averages out the hotspots around the melanosome spheres. The Thompson-Gerstman model was used for the temperature calculations presented here. The advantage of this extended Thompson-Gerstman model is that it is, in many cases, much faster than, for instance, a model based on finite differences or finite elements. To avoid variabilities due to the placement of the laser spot on the computational grid, a regular distribution of melanosomes was chosen. No shadowing was assumed in the RPE, i.e., the irradiance level as a function of depth was constant. The RPE thickness (or rather, the thickness of the high-pigment-density layer in the RPE) was set to $5\mu \mathrm{m}$ . The melanosome diameter was $0.8\mu \mathrm{m}$ , melanosome spacing (center to center) was $1\mu \mathrm{m}$ , and the absorption coefficient of the melanosome was set to $4609{\mathrm{cm}}^{-1}$ , which resulted in an absorptance of 67% in the RPE and an equivalent homogeneous bulk absorption coefficient of $1340{\mathrm{cm}}^{-1}$ . The absorption coefficient of the RPE was varied to find the value that would provide an optimum fit to the explant ex vivo damage threshold data for the complete range of pulse durations $\left(0.1\mathrm{ms}\text{to}2\mathrm{s}\right)$ and spot diameters $\left(23\mu \mathrm{m}\text{to}2\mathrm{mm}\right)$ . The choroid was populated with melanosomes with $1\mu \mathrm{m}$ diam, placed next to each other, with an absorption coefficient of $36{\mathrm{cm}}^{-1}$ and an exponentially decreasing irradiance level with an effective absorption coefficient of $150{\mathrm{cm}}^{-1}$ . This value is specified for Negro by Takata .⁷ The choroid was assumed to be thick enough so that the thickness would not influence the calculated thresholds, i.e., the choroid is assumed to be semi-infinite. Thermal properties of water at $65°\mathrm{C}$ were used for all media,¹¹ i.e., a density of $1\mathrm{g}{\mathrm{cm}}^{-3}$ , specific heat of $4.185\mathrm{J}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ , and thermal conductivity of $0.00629\mathrm{W}{\mathrm{cm}}^{-1}{\mathrm{K}}^{-1}$ . It is necessary for the Thompson-Gerstman model to assume that all media within the model have the same thermal properties and that these are constant with time. Consequently, varying thermal properties in different layers or temperature dependent values cannot be modeled. The Arrhenius integral was used to calculate damage thresholds, and the rate and energy parameters were chosen as given by Welch and Polhamus,¹² i.e., $\mathrm{A}=1.3$ ${10}^{99}{\mathrm{s}}^{-1}$ and $\mathrm{E}∕\mathrm{R}=75519\mathrm{K}$ . The minimum retinal area, which had to reach an Arrhenius integral value of at least 1 to be recorded as damaged, was set to a diameter of $20\mu \mathrm{m}$ . The model parameters described in this section were used without adjustment or variation to model the complete range of experimental threshold parameters of pulse durations from $10\mu \mathrm{s}\text{to}2\mathrm{s}$ and spot sizes between $23\mu \mathrm{m}$ and $3\mathrm{mm}$ , including both Gaussian as well as top-hat irradiance profiles.

3.1.

Ex Vivo Bovine and Computer Model

The explant ex vivo damage thresholds (ED50) of this study are summarized in Table 1 and are shown in Fig. 5 together with results of the extended Thompson-Gerstman computer model. The overall variability and uncertainty for the ED50 values is estimated to be about $\pm 20\%$ . The explant ex vivo thresholds cover a pulse duration range of $100\mu \mathrm{s}\text{to}2\mathrm{s}$ and a spot diameter range of $23\mu \mathrm{m}\text{to}2\mathrm{mm}$ . The computer model data were extended to include also values for $10\text{-}\mu \mathrm{s}$ pulse duration and spot sizes of up to $3\mathrm{mm}$ . The slope $S$ (ED84/ED50) that results from Probit analysis of the experimental data is close to 1 (typically less than 1.1, but never larger than 1.2), indicating both little variability within different eyes as well as a small uncertainty.¹⁰ When the slope is listed as $<1.01$ , the probit analysis software indicated that the value of the slope was so close to 1 that the calculated slope (less than 1.01) was somewhat uncertain. To derive the 31 threshold injury values, a total number of 4911 exposures were placed on 166 retinal samples. These numbers underpin why it is not realistic to obtain a full set of threshold data in terms of pulse duration and spot size dependence with in vivo models.

Fig. 5

Damage threshold values for bovine explant ex vivo samples plotted as retinal radial exposure as a function of retinal spot diameter. Square symbols indicate a Gaussian beam profile (small spots), and star symbols represent top-hat profiles. The lines are the result of an extended Thompson-Gerstman model, full lines indicate top hat, and dotted lines Gaussian profiles.

Table 1

Probit threshold data for the range of pulse durations between 100μs and 2s and retinal spot diameters, where relevant, from 23μm to 2mm for the bovine ex vivo explant model for 532-nm laser radiation. The Slope S is defined as ED84/ED16, and FL stands for fiducial limits. The profile for 23-μm -diam retinal spots was Gaussian (1/e diameter criteria): all larger spots were constant-irradiance profile (top hat). The ED50 given as retinal radiant exposure was determined from the ED50 given in terms of total energy (TIE) by division with the area calculated from the spot diameter.

Two regions can be clearly distinguished in Fig. 5, one where the logarithmic slopes of the threshold curves (threshold as function of diameter $D$ ) are close to $-1$ , i.e., a $1∕D$ dependence, and another where the thresholds do not depend on the diameter $D$ , i.e., a logarithmic slope of 0. These two regions are separated by an inflection point in the curve. The position of the inflection point depends on the pulse duration: the longer the pulse duration, the larger the spot size value where the inflection occurs. The computer model data fit the experimental data over the full range of retinal spot diameters and pulse duration to within a factor of better than 1.2. For retinal spot diameters less than about $30\mu \mathrm{m}$ , both the computer model and the experimental threshold data exhibit a spot size dependence that is steeper than $-1$ .

The threshold data can also be plotted as function of pulse duration for a given spot size (Fig. 6 ). The pulse duration dependence data shown in Fig. 6 can be envisaged as a vertical section through the spot diameter dependence data of Fig. 5: for small spots, in Fig. 5, the lines for given pulse durations are spaced a farther apart than for large spot diameters. This represents a different pulse duration dependence of the thresholds for small and large spot diameters, which can be seen in Fig. 6. For pulse durations below about $0.1\mathrm{ms}$ , the family of curves merge (except for the curve for $23\text{-}\mu \mathrm{m}$ spot size, which is due to the Gaussian profile), and for pulse durations below about $10\mu \mathrm{s}$ , the computer model data show no pulse duration dependence, as is expected for the condition of thermal confinement. For pulse durations longer than about $0.1\mathrm{ms}$ , the family of curves separate: the curves for small spot diameters separate for shorter pulse durations, and the curves for larger spots separate only at longer pulse durations. Those curves that are separated, i.e., the small spot diameter curves, approach a pulse duration dependence with a slope of ${\mathrm{t}}^{0.9}$ . The large spot diameter threshold data follows a pulse duration dependence of ${\mathrm{t}}^{0.41}$ .

Fig. 6

Ex vivo and computer model threshold data shown in Fig. 5 plotted as a function of pulse duration for a range of retinal spot size diameters.

3.2.

Comparison with $100\text{-}\mathrm{ms}$ Nonhuman Primate Threshold Data

Recently, in vivo laser-induced retinal injury thresholds were determined in the Rhesus monkey for exposure to a $514\text{-}\mathrm{nm}$ argon laser with a pulse duration of $100\mathrm{ms}$ for a range of retinal spot diameters,⁹ as shown in Fig. 7 . In Fig. 7, the nominal retinal spot diameter is not the actual diameter at the monkey retina (which is not known), but rather a theoretical value that would apply for a perfect optical system. The value of the nominal retinal laser spot diameter is derived from the measured far-field divergence of the laser beam equal to the angular subtense of the retinal image for an eye accommodated to infinity. This nominal value is to be differentiated from the actual retinal spot diameter, which might be larger due to scattering, for instance. The laser beam diameter at the cornea was $2.5\text{to}3\mathrm{mm}$ to minimize the influence of aberrations of the eye. The in vivo data ( $1\text{-}\mathrm{h}$ and $24\text{-}\mathrm{h}$ endpoint, macula and extramacula) are shown in Fig. 7 together with injury threshold data resulting from laser exposure of the bovine ex vivo explant and results from the computer model. In the range of spot diameters between 100 and $600\mu \mathrm{m}$ , the computer results and ex plant data fit very well with the NHP data, with the difference being less than a factor of 1.3. When plotted as TIE (Fig. 7), the computer and ex vivo data continue to decrease for spot diameters less than $100\mu \mathrm{m}$ , while the NHP data remains constant.

Fig. 7

$100\text{-}\mathrm{ms}$ NHP threshold data (small symbols), bovine ex vivo threshold data (large crossed circles), model data (full red line), and the current MPE values (dotted blue line). The data are plotted in terms of TIE (corneal space) (not corrected for transmission losses for the case of the NHP model). (Color online only.)

3.3.

Comparison with Nanosecond and Microsecond Data

The current spot size dependence of the MPEs has been in doubt for some time, especially for pulse durations in the microsecond range and for shorter pulses. In the condition of thermal confinement for a homogeneous absorbing layer (i.e., when the pulse duration is shorter than the time it takes for heat flow to have an effect on the threshold), it would not be expected that the threshold in terms of retinal radiant exposure would depend on the diameter of the retinal spot, but should depend only on the local radiant exposure value. This concern was supported by a study published¹³ in 2000 for nanosecond and microsecond pulse durations (data shown in Fig. 8 .). The NHP in vivo laser-induced retinal injury thresholds of that study exhibit a $D^2$ dependence when plotted as TIE (i.e., no spot size dependence when plotted as retinal radiant exposure) for spot sizes above about $80\mu \mathrm{m}$ , as would be predicted by thermal models. The threshold data, as calculated with the extended Thompson-Gerstman model used in this work for pulse durations less than $20\mu \mathrm{s}$ and for spot diameters above $100\mu \mathrm{m}$ , compare quite well with the in vivo injury thresholds determined for $3\text{-}\mu \mathrm{s}$ -duration exposures, but is a factor of about 10 too high compared to injury thresholds determined for $5\text{-}\mathrm{ns}$ -duration exposures. Schüle ¹⁴ as well as Lee, Alt ¹⁵ showed in an explant ex vivo model that for pulse durations less than about $10\mu \mathrm{s}$ , cell death induced by bubble formation around the melanosomes (microcavitation) has a lower threshold than thermally induced cell death. Thus, bubble-induced cell damage appears to be the reason for the difference between the $5\text{-}\mathrm{ns}$ and $3\text{-}\mu \mathrm{s}$ pulse duration thresholds.

Fig. 8

Experimental $24\text{-}\mathrm{h}$ retinal injury threshold values (TIE) for $3\text{-}\mu \mathrm{s}$ -duration exposures $\left(590\mathrm{nm}\right)$ and $5\text{-}\mathrm{ns}$ duration exposures $\left(532\mathrm{nm}\right)$ from Zuclich ¹³ The computer model data for pulse durations less than $20\mu \mathrm{s}$ are also shown as a full line. Also shown are the current MPE values.

The injury thresholds, when plotted as TIE as shown in Fig. 8, for spot sizes smaller than about $80\mu \mathrm{m}$ (for the $3\text{-}\mu \mathrm{s}$ exposures at a less well-defined breakpoint than for the $5\text{-}\mathrm{ns}$ data) do not follow this expected $D^2$ dependence. The $5\text{-}\mathrm{ns}$ data do not exhibit any spot size dependence, and the $3\text{-}\mu \mathrm{s}$ data show a distinctively shallower spot size dependence than the expected $D^2$ dependence. This “small spot—spot size behavior” has presented a challenge for interpretation and understanding since the publication of the data. A similar small spot threshold behavior is also found for millisecond-duration exposures (Fig. 7) as well as for ultrashort and seconds-duration exposures, as reviewed by Lund ⁹ The discussion is also relevant for the problem that the damage threshold for $5\text{-}\mathrm{ns}$ pulse duration and $77\text{-}\mu \mathrm{m}$ retinal spot diameter is basically at the current MPE value, i.e., there is a need that the respective MPEs are reduced.

3.4.

Other Threshold Data

In published in vivo laser-induced retinal injury threshold studies, no NHP threshold data are available where the spot size dependence in terms of the inflection point between $D^{-1}$ threshold dependence and $D^0$ dependence for the retinal radiant exposure can be evaluated. In the microsecond and nanosecond pulse duration regime, the spot size dependence is already $D^0$ for all spot sizes greater than about $80\mu \mathrm{m}$ . The only available NHP threshold data for longer laser exposures is for^{16, 17} $250\mathrm{ms}$ and $1\mathrm{s}$ , but these threshold data do not include data for sufficiently large spot sizes, so that the data only shows the $D^{-1}$ dependence. The only NHP retinal injury threshold data that cover a large enough spot size range in the millisecond range was obtained for xenon arc lamp exposure,¹⁸ and these data do show the predicted breakpoint with $D^{-1}$ dependence of the retinal radiant exposure thresholds to the left of the breakpoint and $D^0$ dependence for spot sizes larger than the breakpoint (Fig. 9 ).

Fig. 9

NHP threshold data¹⁸ for exposure to a xenon lamp obtained $5\min$ after exposure (symbols) and computer model threshold data (lines, this work) for four different pulse durations, as a function of retinal spot size. The NHP threshold data, expressed as retinal radiant exposure, are not corrected for preretinal transmission losses, i.e., the values are derived by dividing the TIE threshold value with the area of retinal exposure.

All published NHP threshold data in the visible wavelength range that included at least three different spot sizes for pulse durations between $1\mathrm{ms}$ and $1\mathrm{s}$ are collected in Table 2 . For each set of experimental threshold values, a multiplication factor was chosen to approximately minimize the difference between the experimental values and the computer model data. This multiplication factor for the computer model data also covers the influence of differences in retinal absorption for different wavelengths, as well as differences in tissue baseline temperature. The optical transmission was corrected for the NHP data to calculate energy incident on the retina by using the ocular transmission data of Maher.¹⁹

Table 2

Comparison of available experimental threshold data with calculated thresholds. The criteria for selection of the experimental data were: wavelength range between 400 to 700nm , pulse duration between 1ms and 1s , Rhesus monkey eyes, and minimum of three data points for different spot sizes.

In the interpretation of the value of the multiplication factor as “goodness of fit” of the calculated data, it needs to be considered that the experimental data are influenced by a number of factors,¹⁰ such as the region of the retina, the time of determination of the ophthalmoscopically visible lesion, and differences in ocular transmission and retinal absorption depending on wavelength. The macula is more highly pigmented, and thus macular thresholds are lower than thresholds determined in the extramacula. Some studies used a $5\text{-}\min$ endpoint such as for the xenon arc lamp data, while others use a 1- or $24\text{-}\mathrm{h}$ endpoint. The $24\text{-}\mathrm{h}$ thresholds are typically lower than the $5\text{-}\min$ or $1\text{-}\mathrm{h}$ thresholds. Also it is noted that the temporal pulse profile will have an influence on the threshold; for the ex vivo explant data presented in this work, rectangular temporal pulse shapes were used, which should be representative of those studied that used cw sources and shutters to define the pulse duration. Also the retinal profile in experimental studies is often Gaussian and not top hat, as assumed in the calculations, which gives rise to a difference, depending on the pulse duration, of up to a factor of 1.4 (ongoing modeling work, to be published).

Considering the range of pulse durations (3 orders of magnitude) and the range of spot sizes from $50\text{to}1300\mu \mathrm{m}$ (i.e., per study, usually over a range of a factor of 10 from the smallest to the largest spot), the general trend in terms of spot size dependence for different pulse durations, as predicted by the thermal model, fits very well with the available experimental data. Once a corresponding multiplication factor is chosen for a given experimental study, the difference between the model and the experimental data is generally less than $\pm 30\%$ . The spot size dependence is particularly well predicted for the $514\text{-}\mathrm{nm}$ , $1\text{-}\mathrm{s}$ in vivo data of Beatrice and Frisch,¹⁶ where the difference is less than $\pm 4\%$ for three spot sizes between 50 and $600\mu \mathrm{m}$ , as well as for the data of Allen ¹⁸ for $694\text{-}\mathrm{nm}$ , $2\mathrm{ms}$ -duration exposures at four spot sizes between $135\text{to}1350\mu \mathrm{m}$ , where the relative difference is less than $\pm 9\%$ . Also most of the xenon arc lamp data of Allen is very well described by the model calculations, with relative differences of less than $\pm 10\%$ for $100\text{-}\mathrm{ms}$ duration exposures at spot sizes between $220\text{to}1300\mu \mathrm{m}$ . The multiplication factor values reported in Table 2 fall well within the range, which can be expected for listed variabilities and experimental uncertainties.

4.1.

Comparison with Nonhuman Primate $100\text{-}\mathrm{ms}$ Data

Figure 7 shows that for retinal spot sizes larger than about $80\text{to}100\mu \mathrm{m}$ , the ex vivo bovine thresholds agree to within a factor of 1.3 with the $24\text{-}\mathrm{h}$ in vivo NHP threshold data (the small spot data are discussed in Sec. 4.2). It is noted that in vivo 1- and $24\text{-}\mathrm{h}$ threshold data for extramacula and macula exposures are also very similar with each other and only differ noticeably for spot sizes less than $80\text{to}100\mu \mathrm{m}$ . The in vivo threshold for a diameter of $1080\mu \mathrm{m}$ is lower than the interpolated bovine ex vivo explant threshold, as seen in Fig. 7. The reason for this difference is not entirely clear but could be due to the nonperfect top-hat profile of the monkey threshold. An inner region of higher retinal irradiance could lead to a smaller effective thermal diameter, so that this threshold in terms of TIE would have to be plotted at a smaller nominal retinal diameter—for instance, if this effective thermal diameter were $750\mu \mathrm{m}$ , it would lie on the curve predicted by the computer and bovine model. The spot size dependence in the spot diameter range between 100 and $500\mu \mathrm{m}$ when plotted as retinal radiant exposure is almost exactly $D^{-1}$ , i.e., the logarithmical slope of the threshold curve is, within the experimental uncertainly, identical to $-1$ . Unfortunately, the monkey data currently do not include large enough spot sizes to reach up to the inflection point of the spot size dependence, as seen in the ex vivo bovine and computer models.

The closeness of the thresholds for the different models for spot sizes larger than $80\mu \mathrm{m}$ might be surprising due to the difference of the in vivo NHP and the ex vivo bovine models and endpoints. For the ex vivo bovine samples, the RPE cell layer is exposed directly, i.e., there is no optical loss (reflection or absorption) due to preretinal media as in the NHP eye, as well as there is no pre-RPE influence on the laser profile (such as scattering). The transmittance associated to the rhesus monkey preretinal media for $532\mathrm{nm}$ equals¹⁹ 0.57. The inverse of 0.57 equals 1.7, and by this factor, the in vivo NHP TIE threshold should be higher than the ex vivo bovine threshold. However, the ex vivo bovine sample is at room temperature $(23\pm 1°\mathrm{C})$ and the monkey body temperature is about $38°\mathrm{C}$ , resulting in a lower threshold for the monkey. The computer model predicts a difference in thresholds by a factor of 1.5 for these two different background temperatures, compensating to a large degree for the difference in optical transmissivity.

More importantly for the validation of the ex vivo bovine model are the different endpoints. The ex vivo explant bovine thresholds are determined at about $15\min$ after exposure and they are based on RPE cell viability. In vivo NHP thresholds on the other hand are determined ophthalmoscopically (i.e., optical appearance change of the fundus) 1 and $24\mathrm{h}$ after exposure. From the similarity of the threshold data for spot sizes larger than $80\mu \mathrm{m}$ , it appears that the underlying mechanism is in both cases immediate RPE cell damage. Since the sensory retina is very weakly absorbing in the visible wavelength range (approximately 5%), for comparable pigmentation of the RPE in the two models, the temperature rise would be equivalent for the same retinal radiant exposure. It stands to reason that the RPE in the NHP model would be damaged at exposure levels similar to those that lead to RPE damage in the ex vivo explant model. For the case of the in vivo NHP threshold experiments, however, the viability of RPE cells cannot be determined, and detection of a lesion is based on a change of visual appearance, i.e., change of color or reflectance of the retina. The uppermost layer that is imaged is the sensory retina, not the RPE (outside of the fovea, the sensory retina has a thickness of about $200\text{to}300\mu \mathrm{m}$ ). It appears that the change of appearance of the sensory retina for the NHP 1- and $24\text{-}\mathrm{h}$ thresholds is caused by the physiological reaction of the system to the injured RPE cells. This reaction takes some time to develop, and after that time becomes noticeable as a visible change of appearance. It also follows that it is unlikely that the change of appearance at the 1- or $24\text{-}\mathrm{h}$ threshold is thermally induced coagulation of the sensory retina. Thermally induced coagulation of the sensory retina should be visible almost immediately after exposure, which is the case, for instance, in medical photocoagulation treatment of the retina. It is important to distinguish these acutely induced (immediately visible) lesions from changes of retinal appearance at threshold levels determined 1 and $24\text{-}\mathrm{h}$ after exposure. Only in the former case is the induced effect immediate thermal coagulation of the RPE as well as of the sensory retina, which requires higher temperatures and higher retinal radiant exposures than the 1- and $24\text{-}\mathrm{h}$ injury thresholds which are, however, the more appropriate endpoints for setting safety exposure limits. Also, thresholds that are determined $5\min$ after exposure are above the thresholds detected at 1 or $24\mathrm{h}$ after exposure, i.e., a higher exposure level is needed to induce thermal damage that is already visible $5\min$ after exposure as compared to lesions that become visible at 1 or $24\mathrm{h}$ after exposure.

4.2.

Small Spot/Spot Size Behavior

In the previous section we concluded that the underlying damage mechanism for both the in vivo NHP 1- and $24\text{-}\mathrm{h}$ ophthalmoscopically visible thresholds as well as the ex vivo bovine model is likely to be immediate thermal damage of RPE cells. For spot sizes above $80\mu \mathrm{m}$ , both models yield almost identical threshold levels. However, for spot diameters less than $80\mu \mathrm{m}$ , there is striking deviation of both the computer model and the ex vivo bovine model thresholds from the in vivo NHP thresholds. In terms of TIE, the NHP thresholds remain almost constant for smaller laser spots, while both the ex vivo bovine as well as the computer model continue to decrease with basically a linear spot diameter dependence. At a nominal laser spot diameter of $25\mu \mathrm{m}$ , the ex vivo bovine and computer model thresholds are a factor of about 3.5 lower than the interpolated NHP threshold. Very similar small spot—spot size behavior is also noted for $532\text{-}\mathrm{nm}$ ns-duration thresholds¹³ (Fig. 8). As shown by Lund, ⁹ equivalent small spot/spot size dependence can also be observed for millisecond-duration exposures and ultrashort exposures. The existence of this peculiar small spot behavior for exposure durations that clearly encompass different damage mechanisms (for instance, including bubble formation around melanosomes as seen in nanosecond threshold data, see discussion in Sec. 3.3) leads to the conclusion that the underlying effect is more generic and does not depend on the damage mechanism. Two explanations can be envisaged. (1) The laser spot that is incident on the RPE is enlarged, for instance by scattering, up to about $80\text{to}100\mu \mathrm{m}$ diam, even though the nominal (theoretical) laser spot diameter at the RPE is smaller than that (2) The laser beam at the retina and RPE is not enlarged, but there are factors for the NHP experiments related to the nonvisibility of small lesions. Assuming the retinal spot at the in vivo NHP RPE is not enlarged, the lower bovine and computer model thresholds suggest that in the NHP retina, RPE cells should also be damaged at exposure levels lower than those determined experimentally in vivo, shown in Fig. 7. In that case, at the small-spot threshold levels determined by the bovine and computer model, the NHP RPE cells would also be damaged. The observed NHP thresholds can be explained when, for some reason, these small diameter RPE lesions in the NHP eye do not produce the necessary change of optical appearance that is necessary to be detected as ophthalmoscopically visible lesions, and “superthreshold” exposure levels are needed to produce lesions that are ophthalmoscopically visible. This could be due to two reasons.

In both bulleted cases in (2), the laser energy per pulse needs to be correspondingly higher to produce a “superthreshold” RPE lesion that produces a systemic response that is ophthalmoscopically visible. For thermally induced lesions, it is tempting to envisage this superthreshold condition as thermal bleeding, i.e., thermal conduction leading to a lesion that is larger than the laser spot on the RPE. However, this can be ruled out by thermal modeling: one can compare the predicted damage threshold for a laser spot with a diameter of $100\mu \mathrm{m}$ to cases where the laser spot diameter is smaller than $100\mu \mathrm{m}$ but the minimal lesion diameter is set to $100\mu \mathrm{m}$ . For pulse durations of about $100\mathrm{ms}$ , the predicted thresholds for smaller laser beams in terms of energy (TIE) would be equal to the threshold for a $100\text{-}\mu \mathrm{m}$ laser spot diameter, in line with the experimental observations. However, the shorter the pulse duration gets, the more energy is needed for a smaller laser spot diameter to induce a $100\text{-}\mu \mathrm{m}$ lesion, as compared to the threshold for a $100\text{-}\mu \mathrm{m}$ laser spot, which contradicts the experimental observation that the threshold in the small spot regime is a constant energy value. Also, the calculated temperatures in the center of the laser spot would reach unrealistic values; for instance, to induce a $100\text{-}\mu \mathrm{m}$ lesion for a $25\text{-}\mu \mathrm{m}$ laser spot and a pulse duration of $1\mathrm{ms}$ , the temperature in the center of the laser spot would reach almost $4000°\mathrm{C}$ . Further, this spot size behavior is also seen for $5\text{-}\mathrm{ns}$ exposure durations where the damage mechanism at threshold appears to be bubble formation around the melanosomes in the RPE. For this damage mechanism, it is physically impossible to create the temperature rise necessary for bubble induction in an RPE region significantly larger than the actual region that is exposed to laser radiation, and at the same time exhibit thresholds for smaller diameters that are not higher than the threshold for an $80\text{-}\mu \mathrm{m}$ spot. The same arguments also lead to falsification of the hypothesis that superthreshold levels are needed to induce thermal damage of the sensory retina by conduction from the heated RPE. When thermal superthreshold effects can be ruled out, since they cannot explain the small spot/spot size thresholds for short pulses, it is still possible that the superthreshold exposures somehow lead to a nonthermally induced amplification of the response of the system as compared to exposure at RPE damage threshold levels. However, the effect would have to produce the observed constant energy thresholds in the NHP model (i.e., equal energy thresholds independent of the spot size for spot sizes less than about $80\text{to}100\mu \mathrm{m}$ ) for pulse durations between femtoseconds and seconds. While this possibility cannot be ruled out, it appears somewhat unlikely that such a nonthermal superthreshold effect could produce a constant energy threshold for such a wide range of pulse durations encompassing different damage mechanisms.

In summary, these arguments indicate that explanation number (2) is somewhat unlikely. Consequently, explanation number (1), an increase of the laser beam diameter on its path to the RPE, is further discussed. The obvious reasons for an increase of the laser beam profile are scattering and/or ocular aberration, i.e., wavefront distortion. Aberration is small for small laser beam diameters at the cornea. Forward scattering in the preretinal media has been given as a reason for the current value of the minimal angular subtense for the apparent source in laser safety²¹ of $1.5\mathrm{mrad}$ , which is equivalent to a retinal image diameter of $25\mu \mathrm{m}$ , while the diffraction-limited laser spot diameter for a perfect optical system would rather be in the range of $6\mu \mathrm{m}$ . However, if preretinal scatter can induce an increase of the retinal image of up to $80\text{to}100\mu \mathrm{m}$ , it should hamper vision, which is not the experience we have as humans. It should be noted that the eye of an anesthetized NHP is held open for exposure, which leads to the possibility of corneal dehydration and an increase in scatter. As an alternative to preretinal scattering, we offer intraretinal scatter as a new explanation of the small spot/spot size behavior in the visible wavelength range. Layers in the sensory retina—particularly the uppermost layer, the nerve fiber layer (NFL)—could induce scattering of optical radiation, which increases the diameter of a minimal laser beam incident on the NFL to a diameter of $80\text{to}100\mu \mathrm{m}$ at the RPE, at least in the parafoveal region where the distance between the NFL and the RPE is about $200\text{to}300\mu \mathrm{m}$ . This possibility is supported by images obtained in optical coherence tomography (OCT), where the back-reflection signal of the NFL is relatively strong, even for the usual OCT wavelength of $800\mathrm{nm}$ . Unterhuber, Považay, and Bizheva²² compared a number of wavelengths and noted that no signal from the RPE could be detected for the blue $475\text{-}\mathrm{nm}$ wavelength, and only a very weak signal for the red $605\text{-}\mathrm{nm}$ wavelength. For setting exposure limits, however, it is important to note that the NFL is pushed aside in the foveal pit to increase visual acuity there. The OCT backscatter signal from the sensory retina is minimal in the foveal region, which also ties together with our experience that we have high visual acuity in the fovea only and low acuity vision outside of the foveal region. Therefore, if the explanation of intraretinal scatter holds true, it is to be expected that in the foveal region, a minimal laser beam ( $25\mu \mathrm{m}$ diam for instance) is not significantly increased in diameter due to scattering, and it might well be that for direct exposure of the fovea, the damage thresholds are lower than the ones determined experimentally for the NHP outside of the fovea.

We note that for spot diameters less than $20\mu \mathrm{m}$ , the computer model data shown in Fig. 5 as retinal radiant exposure predict a small spot dependence that is steeper than the dependence for spots larger than $20\mu \mathrm{m}$ . This is due to the setting of the “minimal visible lesion” in the computer model to a value of $20\mu \mathrm{m}$ and the finite grid size of the model. The effect can best be seen for short pulse durations of, for instance, $10\mu \mathrm{s}$ where there should be no spot size dependence, i.e., the curve should be horizontal for all spot sizes. However, for the smallest spot size, the threshold is higher. This is not only seen in the computer model data, but can also be discerned for the $23\text{-}\mu \mathrm{m}$ bovine data, which is well fitted by the computer model data (Fig. 5). For the experimental data, the effect is related to the finite size of an RPE cell, which would be the smallest unit that can be determined to be damaged based on our endpoint, as well as to some likelihood that the $23\text{-}\mu \mathrm{m}$ laser spot is incident not only on one cell (which is of the order of this minimal spot diameter) but on, for instance, three cells, which increases the injury threshold.

4.3.

General Spot Size Dependence

The thermal model and the ex vivo bovine threshold data show a previously unknown variation of the spot size dependence for different pulse duration. When expressed as retinal radiant exposure values, the breakpoint between the $D^{-1}$ threshold dependence and the constant threshold region for larger spots is not constant—as currently implied by the MPEs—but shifts to smaller diameters for shorter pulses. The breakpoint is in the region of $100\mathrm{mrad}$ $\left(1.7\mathrm{mm}\right)$ only for pulse durations longer than $1\mathrm{s}$ . For pulse durations of less than approximately $100\mu \mathrm{s}$ , there is no detectable spot size dependence, i.e., the damage threshold is a constant retinal radiant exposure value, independent of the actual laser spot size (with the exception of spot sizes of the order of the minimal visible lesion). This apparent dependence of the breakpoint on pulse duration can be explained based on thermal diffusion. Thermal diffusivity is a characteristic parameter that can be understood as the speed at which heat diffuses through a medium, or by which a temperature difference travels. The thermal diffusivity $D_{\mathrm{th}}$ is defined as the ratio of thermal conductivity over the specific heat and the density of the material, and thus has the units of ${\mathrm{cm}}^2∕\mathrm{s}$ . Within a time $t$ , a “heat wave” travels approximately a distance of about $2\surd \left(t{D}_{\mathrm{th}}\right)$ . This speed is also relevant for the radial cooling of the laser spot. As the heat wave travels in radial direction away from the rim of the disk that is heated by the laser spot, it heats the surrounding nonirradiated region. Due to this heat flow, the irradiated area is cooled, so that the zone that is affected by this cooling action (a negative heat wave, i.e., a cooling wave) travels inward from the rim of the laser spot toward the center of the laser spot. As long as the cooling front does not reach the center of the laser beam, the center of the laser spot remains unaffected by the radial cooling action, and therefore the temperature of the center is independent of the size of the laser spot. Although the Arrhenius damage integral adds up over the full duration where the tissue temperature is elevated, due to the strong nonlinearity of the Arrhenius integral with temperature, the main contribution to the damage integral comes from the higher temperatures during the exposure. Thus, for exposure duration ranges from ms to s, the characteristic time for thermally induced damage is, in first approximation, the laser pulse duration. It follows that the breakpoint characterizes the retinal spot radius (approximately) equal to the thermal diffusion distance for the respective pulse duration. If the spot is larger than this characteristic diameter, the center is not affected by radial cooling and is just given by the local retinal radiant exposure or irradiance, independent of the actual diameter of the spot. If the spot is smaller than this characteristic diameter, the center is affected by cooling, which leads to a lower temperature and to an increase of the threshold in relation to the case where there is no cooling. The smaller the spot, the earlier during the pulse duration the center is affected (cooled) radially, which results in the $D^{-1}$ dependence. (Note, however, that we did not find a simple line of reasoning based on the time-temperature history that would explain or predict the strict $D^{-1}$ dependence, as the Arrhenius integral is highly nonlinear with temperature). We do not believe that axial heat conduction plays a role in the $D^{-1}$ dependence, since axial heat conduction is independent of the laser spot size. The calculated maximum temperature rise for the case of a pulse duration of $100\mathrm{ms}$ is depicted as radial profiles in Fig. 10 for a range of spot diameters between 100 and $1600\mu \mathrm{m}$ for a radiant exposure value equal to the threshold for the $1600\text{-}\mu \mathrm{m}$ spot. For spot sizes above about $800\mu \mathrm{m}$ , the central temperature is independent of the spot diameter. This is also approximately the diameter where the horizontal part of the threshold curve for a pulse duration of $100\mathrm{ms}$ plotted in Fig. 5 commences.

Fig. 10

Calculated radial temperature increase profiles for a range of spot diameters in $200\text{-}\mu \mathrm{m}$ steps starting at $200\mu \mathrm{m}$ , plus the curve for a diameter of $100\mu \mathrm{m}$ .

4.4.

Time Dependence

The threshold data can also be plotted as a function of exposure duration for the range of retinal spot sizes to study their time dependence. The time dependence of the spot size dependence breakpoint also results in a variation of time dependence for the different retinal spot sizes currently not reflected in the MPEs. For a diameter of $23\mu \mathrm{m}$ , the slope in a log-log scaled time dependence is somewhat steeper than the value of 0.75 currently defined by the MPEs; it equals 0.9 for pulse durations longer than about $1\mathrm{ms}$ . For shorter exposure durations, the time dependence becomes shallower and, according to the thermal model, becomes zero (i.e., no time dependence) for pulse durations of less than about $10\mu \mathrm{s}$ , also referred to as the thermal confinement region. The larger the spot size becomes, the more the region of shallower time dependence extends to longer times, so that for a spot size diameter of $2\mathrm{mm}$ , according to the model, the time dependence slope in log-log scale becomes 0.4. For exposure durations of less than about $0.1\mathrm{ms}$ , all the curves (except the one for $23\mu \mathrm{m}$ , which is for Gaussian profile and close to the minimal visible lesion dimension) for the different spot sizes merge as they approach the thermal confinement region. Regarding the shallower time dependence for large spots, it can be noted that this is somewhat reminiscent of the time dependence of the MPEs for thermal corneal and skin damage, which is $t^{0.25}$ . After all, these corneal and skin MPEs are based on threshold studies that used image diameters in the order of millimeters, which would also exhibit a shallower time dependence than image sizes of less than $1\mathrm{mm}$ , relevant for retinal laser exposure. The thermal damage model predicts that under thermal confinement conditions of a homogeneous medium, the thresholds in terms of energy per pulse (or radiant exposure per pulse) would no longer depend on the exposure duration. However, as shown in Sec. 3.3, for exposure durations of less than about $10\mu \mathrm{s}$ , bubble-induced damage thresholds become lower than thermal damage thresholds, and the thermal damage model is no longer applicable.

4.5.

Limitation of the Models

For longer exposure durations in the seconds time regime, the bovine and computer models are limited by heat flow issues, because they do not include blood flow. They also do not model photochemically induced damage at wavelengths in the blue and green region, which for exposure durations in the multisecond range might have lower thresholds than thermally induced injuries. For pulse durations shorter than about $10\mu \mathrm{s}$ , the application of the computer model to model thermal damage is limited, since bubble formation and effects of ultrashort pulse exposure cannot be modeled.