1.

Introduction

This study was initiated to provide relevant data, both experimental and modeling, for the effects of near-infrared laser pulses on the skin due to the growing application of high-energy lasers operating at wavelengths around $1315\mathrm{nm}$ . Near-infrared (NIR) lasers are becoming increasingly popular in various military, industrial, and medical applications. The development of high-power chemical oxygen iodine lasers (COIL) for use by the military has led to renewed interest in the safety of 1315-nm irradiation. Potential uses in new applications involve systems with nominal powers from the tens of kilowatts to the megawatt range. Though demonstrated to be one of the “safest” laser wavelengths with respect to human effects (requiring more energy than any other laser wavelength to cause injury), the types of injury associated with $1315\mathrm{nm}$ have been shown to be of particular concern.^{1, 2, 3}

The American National Standards Institute (ANSI) standard Z136.1, 2000 (Ref. 4) defines wavelengths in the range of 1200 to $1400\mathrm{nm}$ to be NIR and recommends a constant maximum permissible exposure (MPE). MPE levels for skin exposure, which are established by the ANSI Z136.1 bioeffects subcommittee through threshold studies and modeling, are based on little experimental data in this wavelength regime. There has been some work researching the ocular effects of this wavelength region,^{5, 6} but little for skin effects. Unlike most other laser wavelengths, 1315-nm irradiation has been shown to cause damage at corneal, lenticular, and retinal sites. At relatively short exposure durations (i.e., $350\mathrm{\mu }\sec$ ) and large beam profiles at the cornea $\left(5\text{-}\mathrm{mm}\mathrm{diam}\right)$ , Zuclich ³ found that threshold-level damage occurred at the back of the eye, involving the retina and the nerve fiber layers. On the other hand, Zuclich also found that for 1315- and 1318-nm laser beams smaller than $1\mathrm{mm}\mathrm{diam}$ , threshold-level injury occurred at the cornea for exposure durations from $350\mathrm{\mu }\sec$ to $10\sec$ . This unusual threshold injury site dependence as a function of exposure duration and corneal beam size was presumed to be related to a probable change in optical properties of the cornea, such as thermal lensing, as a function of prolonged exposure and subsequent thermal injury, thus interfering with transmission of irradiation to the retina for the longer $(>0.28\sec )$ exposures. Corneal threshold measurements have been reported by several researchers^{7, 8, 9} for wavelengths between 1315 and $1356\mathrm{nm}$ for various spot size diameters and pulse durations. The reported thresholds range between $42{\mathrm{Jcm}}^{-2}$ at $300\mathrm{\mu }\mathrm{s}$ to $1890{\mathrm{Jcm}}^{-2}$ for a 10-sec exposure of $1318\mathrm{nm}$ .

Several types of laser systems other than the COIL laser can produce wavelengths in the NIR region, with pulse durations ranging from Q-switched nanoseconds (ns) to continuous wave (cw). A commonly used laser that generates these wavelengths $\left(1314\mathrm{nm}\right)$ is the neodymium:ytterbium lithium fluoride $(\mathrm{Nd}:\mathrm{YLF})$ laser. This specific system can develop energies from millijoules to joules, and can wavelength shift many nanometers by gain pulling. Another laser system, the $\mathrm{Nd}:\mathrm{YAG}$ , can be operated at $1318\mathrm{nm}$ in the Q-switched mode to produce nanosecond pulses with many joules-per-pulse output. The data presented in this study are produced using a 1314-nm $\mathrm{Nd}:\mathrm{YLF}$ laser system in the long-pulse mode $\left(350\mathrm{\mu }\mathrm{s}\right)$ with 3-J/pulse output and a $\mathrm{Nd}:\mathrm{YAG}$ operating at $1318\mathrm{nm}$ in the short-pulse mode $\left(50\mathrm{ns}\right)$ with a 5-J/pulse output.

Lasers operating at the 1320-nm wavelength have also become very popular and widely used in repairing artery anastomosis using human albumin solder (HAS). Several laboratories^{10, 11, 12} have reported using the $\mathrm{Nd}:\mathrm{YAG}$ laser operating at 1320-nm wavelength for laser-tissue welding of carotid arteries. These lasers heat up the solder used to weld the arteries together with minimal thermal damage. Lauto ¹⁰ describe their welding of fresh canine arteries and report their results for various powers, energies, and temperature rises. For a 35-sec heating time, they reported energies used for soldering that ranged from 24 to $74\mathrm{J}$ and temperature increases of up to $25°\mathrm{C}$ .

This study uses the Yucatan mini-pig (Sus scrofa domestica) as the model to determine the estimated dose for 50% probability of laser-induced damage $\left({\mathrm{ED}}_{50}\right)$ to skin at wavelengths of $1314\mathrm{nm}$ $\left(0.35\mathrm{ms}\right)$ and $1318\mathrm{nm}$ $\left(50\mathrm{ns}\right)$ with single pulse exposures. The Yucatan mini-pig has higher anatomical similarity to human skin than the commonly used Yorkshire pig.¹³ The Yucatan mini-pig skin is melanated and, on the flank, is of similar thickness to that on the human arm, which has high probability of accidental exposure. By using this model, the properties of human skin can be more closely approximated to gain a better understanding of the human laser-tissue interaction for the wavelength of interest. The data on porcine skin damage obtained from this study will contribute to the further understanding of laser injury mechanisms and will add to the existing data on laser skin effects, on which safety standards are based and which affect employment of these laser systems.

1.1.

Thermal Modeling

The use of a mathematical model for predicting skin injury could be helpful in determining the key factors associated with these types of injury. Numerous models have been developed to predict laser energy absorption, source terms, temperature rise, and tissue damage. A schematic of such a combined model for ocular injury where light scattering is not significant is shown in Fig. 1 .

Fig. 1

Schematic of model for tissue injury from laser radiation.

In the early 1970’s, Mainster, White, and Allen¹⁴ solved the heat conduction equation of the form

Eq. 1

$$\rho c\frac{\partial T}{\partial t}=Q+\frac{k}{r}\frac{\partial T}{\partial r}+\frac{\partial }{\partial r}\left(k\frac{\partial T}{\partial r}\right)+\frac{\partial }{\partial z}\left(k\frac{\partial T}{\partial z}\right),$$

where cylindrical symmetry and thermally homogeneous media are assumed, and $T(r,z,t)$ =temperature rise (K), $t$ =time (s), $k$ is conductivity $(\mathrm{W}\bullet {\mathrm{m}}^{-1}\bullet {\mathrm{K}}^{-1})$ , $c$ is specific heat $(\mathrm{J}\bullet \mathrm{kg}\bullet \mathrm{K})$ , $\rho$ is density $(\mathrm{kg}\bullet {\mathrm{m}}^{-3})$ , and $Q(r,z,t)$ is the source strength $(\mathrm{W}\bullet {\mathrm{m}}^{-3})$ .

The source strength for the tissue layers are, respectively,

Eq. 2

$$Q_{PE}=h{H}_0{\mu }_{PE}\exp (-{\mu }_{PE}z)(0\le z\le d_{PE}),$$

and

3.

$$Q_{Ch}=h{H}_0{\mu }_{Ch}\exp (d_{Ch}{\mu }_{PE}-d_{PE}{\mu }_{PE}-{\mu }_{Ch}z)$$

$$(d_{PE}<z<d_{PE}+d_{Ch}),$$

where $h\left(r\right)$ =radial irradiance profile, $H_0$ =the irradiance at $H$ $(0,0,t)$ , for $H$ $(r,z,t)$ =irradiance at the first and second layers, respectively, $\mu$ =absorption coefficient at the first and second layers $\left({\mathrm{m}}^{-1}\right)$ , and $d$ =thickness of the tissue layers $\left({\mathrm{m}}^{-1}\right)$ .

Mainster, White, and Allen¹⁴ used a finite difference solution to Eq. 1, and Vassiliadis, Christian, and Dedrick¹⁵ developed a Green’s function solution for symmetrical noncoherent sources. They also applied a rate process damage model to their temperature model. Welch, ¹⁶ combined the rate process model with the finite difference model, and Takata ¹⁷ expanded and modified the model to include multiple absorbing layers, reflection, blood perfusion, damage, and steam formation. At the same time, Takata ¹⁷ also developed a skin and corneal model of thermal injury. The damage model is based on the work of Henriques¹⁸ in pig skin, and takes the form

Eq. 4

$$\Omega (r,z)=A{\int }_0^t\exp (-E∕RT)dt,$$

where $A$ =molecular collision frequency factor $\left({\mathrm{s}}^{-1}\right)$ , $E$ =deactivation energy (J/M), $R=8.3143$ =universal gas constant (J/MK), $T=T(r,z,t)$ =temperature (K), $\Omega (r,z)$ =damage integral, and $t$ =time at final recovery of temperature after exposure.

Henriques¹⁸ used rate coefficients for Eq. 4 such that complete necrosis of the skin was associated with $\Omega =1$ , and determined that $A=3.1\times {10}^{98}$ $\left({\mathrm{s}}^{-1}\right)$ and $E=6.28\times {10}^5(\mathrm{J}∕\mathrm{M})$ .

Cain and Welch¹⁹ tested the model temperature predictions for visible laser irradiation in the rabbit eye and determined it to be quite accurate for pulse durations exceeding approximately $10\mathrm{msec}$ . Welch²⁰ and Welch and van Gemert²¹ have looked extensively at numerous factors affecting the model and its predictive power. Unfortunately, very little data on biological effects exist for the near-infrared wavelength of $1315\mathrm{nm}$ , and work is needed to evaluate the behavior of these models in this regime.

The skin model developed by Takata ¹⁷ is similar in structure to the retinal model, though it uses skin geometries as well as optical and thermal properties of the skin. It also allows for appropriate alteration of the beam profile as the irradiation traverses the various layers of skin.

Takata ¹⁷ pointed out the importance of the use of reliable parameters in the model, and particularly the selection of absorption coefficients for the ocular media or skin. The values for these critical parameters as used by Takata were derived primarily from the work of Coogan, Hughes, and Mollsen,²² Boettner,²³ and Geeraets ^{24, 25, 26} One of the most challenging issues in the use of these models for the near-infrared region is the paucity of key parameters beyond $1200\mathrm{nm}$ (i.e., absorption coefficients and scattering).

2.

Methods

An array of laser exposures (with varying pulse energy) was placed on the flanks of Yucatan mini-pigs, and Probit analysis was used to determine the ${\mathrm{ED}}_{50}\mathrm{s}$ for thermal injury. Two laser systems were employed to deliver either 1314-nm light at $0.35\mathrm{ms}$ or 1318-nm light at $50\mathrm{ns}$ . Laser exposures were accomplished with a laser system (Positive Light, Los Gatos, California) using a $\mathrm{Nd}:\mathrm{YLF}$ rod, delivering 1314-nm light at 0.350-ms exposure time, and at various pulse energies. The laser produced a top-hat profile, and two experimental spot sizes (700 and $1300\mathrm{\mu }\mathrm{m}$ ) were used in this study. Spot sizes were measured using an Electrophysics IR camera (Electrophysics Corporation, Fairfield, New Jersy) with a Spiricon LBA 500 Laser Beam analyzer (Spiricon, Incorporated, Logan, Utah) and beam grabber card. The pulse duration is measured by an ET-3000 $\mathrm{InGaAs}$ (Electro-Optics Technology, Incorporated, Traverse City, Michigan) photodiode connected to a Tektronix TDS 220 oscilloscope (Tektronix, Incorporated, Beaverton, Oregon). Energy measurements are made with a Coherent-Molectron EPM2000 energy meter (Coherent Incorporated, Santa Clara, California) and JD25 and JD50 energy probes, which were placed after a 90/10 beamsplitter to collect 10% of the beam energy, and thus determine the actual energy delivered to the skin. An articulating arm laser beam delivery system from Laser Mechanisms, Incorporated (Farmington Hills, Michigan) was used to deliver the beam without having to move the subject. A metal “aiming ring” was attached to the end of the articulating arm, which maintained a constant distance between the arm’s aperture and the subject. This allowed for precise positioning and distance control necessary to deliver exposures of known spot size, more accurate beam delivery, and a higher number of exposures per subject, resulting in a reduction of the total number of subjects required. The laser system setup is depicted in Fig. 2 .

Fig. 2

Experimental setup for thermal dynamics imaging experiment.

2.1.

Q-Switched Nanosecond Pulses

A custom-built Q-switched $\mathrm{Nd}:\mathrm{YAG}$ laser manufactured by Continuum Lasers was used to deliver 50-ns exposures to animal subjects. The laser was designed to yield high-power 50-ns pulses at $1318\mathrm{nm}$ . The maximum pulse energy of the laser was rated at $5\mathrm{J}$ , but in practice the output was limited to $\sim 4\mathrm{J}$ per pulse because of the alignment required daily. A general schematic of the experimental setup is shown in Fig. 3 . Two series of experiments were taken, one set for the smaller spot sizes $(\sim 2\mathrm{mm}\mathrm{diam})$ utilized the delivery arm as shown in Fig. 3, and the other set $\left(5\mathrm{mm}\mathrm{diam}\right)$ sent the beam directly to the animal skin.

Fig. 3

Experimental setup for nanosecond experiment.

3.

Results

Visible lesion threshold measurements for two pulse durations with two spot sizes for each pulse duration are being reported, and enough data points were taken to provide the ${\mathrm{ED}}_{50}\mathrm{s}$ and their fiducial limits at the 95% confidence level using Probit analysis. Results for the ${\mathrm{ED}}_{50}\mathrm{s}$ using the long pulse $\left(350\mathrm{\mu }\mathrm{s}\right)$ are reported for both the 1- and 24-h postexposure readings in Table 5 , along with their fiducial limits and slopes of the Probit curves ( $\mathrm{slope}=\delta p∕\delta d$ , where $\delta p$ =delta probability and $\delta d$ =delta dose). Fiducial limits as shown in the table for the 1.3-mm-diam spot size produces only $a\pm 4\%$ spread around the ${\mathrm{ED}}_{50}$ , and this low value is due to the large number of data points recorded. Many of the laser exposures, especially for the smaller spot size, produced laser-induced breakdown (LIB) at the surface of the skin and we also heard a pop. However, no attempts were made to correlate the LIB with the damage thresholds. We do know that plasma shielding did affect the higher energy exposures, and that some very-high-energy pulses did not create lesions after $24\mathrm{h}$ that were observable at the 1-h reading.

Table 5

Visible lesion thresholds on Yucatan mini-pig skin at 1314nm (for a 1.3-mm-diam, spot, E for 83Jcm−2=1.1J , FD limits= +∕−4% ).

Most lesions initially appeared as a blotched red coloring (erthema) near the center of the exposure site where the laser beam penetrated the skin. These red spots appeared almost immediately and many disappeared before the 1-h reading. Exposures sites were observed visually after $1\mathrm{h}$ , and most of the immediate lesions were no longer red splotches but very small discolorations in the skin. At the 24-h postexposure reading, more lesions could be clearly observed than were visible at 1-h postexposure for either spot size.

For the Q-switched 50-ns pulse exposures, attempts were made to utilize the smaller beam diameters at the skin, but this was not possible because of the LIB occurring in the air before reaching the skin. The irradiances in $\mathrm{W}∕{\mathrm{cm}}^2$ for the nanosecond pulses were so large that the air broke down and shielded the skin from the laser pulses. Results for the two spot sizes used, 2 and $5\mathrm{mm}$ diameters, are listed in Table 6 for the same parameters at listed in Table 5. For the 5-mm spot size, fiducial limits calculated give a spread of only $\pm 5\%$ around the ${\mathrm{ED}}_{50}$ value. Most all of the visible lesion produced with the 2-mm-diam laser beam had LIB at the skin surface and a flash of light was visible. Since the mathematical models do not predict a spot-size dependency for pulse durations below one $\mathrm{\mu }\sec$ , there should be no difference between the two spot sizes. Shielding by the plasma at the skin surface increased the minimum visible lesion (MVL) threshold by almost a factor of 4. The Q-switched pulses for the 5-mm-diam spots were not sent through the manipulating arm as all previous exposures to have enough energy at the skin for this large diameter of exposure. Even with the higher energy pulses, no LIB occurred nor was any flash visible. Profiles of the laser pulse at the skin surfaces were taken before and after each exposure session for all conditions, and these were used to measure the area of the exposure on the skin. Most of the pulses for the 2-mm-diam pulses produced LIB at the skin surface, and these are discussed later, but none of the 5-mm-diam exposures created plasma at the skin surface.

Table 6

Visible lesion thresholds on Yucatan mini-pig skin at 1318nm (for a spot of 5mmdiam E of 2.1J for 10.5Jcm−2 , FD limits= +∕−5% ).

In Table 7 , we compare the MPE values calculated from the ANSI standard to our MVL- ${\mathrm{ED}}_{50}$ threshold values measured for the larger spot sizes at the 24-h reading for both pulse durations. In the last column, we show the safety margin as the ratio of the ${\mathrm{ED}}_{50}$ to the MPE values, or how many times larger the ${\mathrm{ED}}_{50}$ is. We show that for both pulse durations it is 2 orders of magnitude larger than the MPE.

Table 7

ANSI-MPE for skin compared to measured MVL- ED50 .

Measured temperature rises as a function of pulse energies are shown in Fig. 4 for the 1314-nm laser and with a spot size of 1.3-mm diameter (top-hat profile). Also shown are the Monte-Carlo FD model calculations for the temperature rise versus exposure energy at the center of the laser beam and just below the skin surface. The distribution of temperature rises at the end of the laser pulse is shown in Fig. 5 for both radial and axial directions. For the parameters used in the model, this graph shows that the model temperatures that were calculated based on a laser pulse with a top-hat profile are moderately higher that those actually measured (Fig. 4). Also, there was a delay between the end of the laser pulse and the thermal imaging of up to $10\mathrm{ms}$ because the thermal camera was not synchronized with the laser pulse. Thus, hot spots in the laser profile and the uncertainty in the spot size contributed to the differences between the model and measurements.

Fig. 4

Measured skin surface-temperature increases for varying pulse energies and Monte-Carlo FD model calculations using measured parameters.

Fig. 5

Computed in-depth temperature distribution in both radial and axial directions at the end of laser pulse $\left(350\mathrm{\mu }\mathrm{s}\right)$ : a pulse energy $1.1\mathrm{J}$ ; wavelength $1314\mathrm{nm}$ ; spot diameter $1.3\mathrm{mm}$ .

The temperature-time decay on the surface of the skin was calculated for the 1.3-mm-diam spot, and these values compared to the actual temperature measurements as plotted in Fig. 6 . This figure shows both the temperature measured with the infrared camera and calculated decay out to $4\sec$ for temperature rises above ambient, not actual temperatures as plotted in Fig. 4. The camera was free running at a hundred frames per second.

Fig. 6

Comparison between computed (upper-faced solid triangle) and measured (circle) time-dependent temperature relaxations (wavelength of $1314\mathrm{nm}$ , at the center of the beam, $h=500\mathrm{W}∕{\mathrm{m}}^2\mathrm{K}$ , $D=1.3\mathrm{mm}$ ).

The model also calculated the damage integral output [Henriques’ Eq. 4] at each time step, giving values throughout the volume as a function of time. Assuming an Omega=1 as burn threshold, the model calculated that the maximum radius for burn was $1.6\mathrm{mm}$ and the axial depth of burn was calculated to be $2.1\mathrm{mm}$ for the parameters stated.

Values of ${\mu }_a$ and ${\mu }_s^{\prime }$ for specific wavelengths used in our model calculations are given in Table 4. Our in-vitro optical property measurements from Yucatan mini-pig skin are consistent with published values for the visible spectrum. Our spectrophotometer measurements from 1.0 to $1.6\mathrm{\mu }\mathrm{m}$ indicated that the reduced scattering coefficient is much larger than the absorption coefficient below a wavelength of $1.35\mathrm{\mu }\mathrm{m}$ . Thus it is necessary to include the effects of light scattering at $\lambda =1.314\mathrm{\mu }\mathrm{m}$ in a Monte-Carlo simulation of light propagation to determine the heat source term for the heat conduction equation. We kept our samples in a water bath until measurements were made, and water absorption by the samples and evaporation in the spectrophotometer may have contaminated our measurements for wavelengths above $1.4\mathrm{\mu }\mathrm{m}$ .

A sequence of the measured IR images is given in Fig. 7 for times out to almost $3\sec$ . Clearly there is a hot spot in the first frame at $T=0+$ , and this could be due to either a hot spot in the laser beam profile, higher absorption properties on the skin, or both. The third and fifth frames are offset from the other frames, and we know that this is due to respiration artifacts, because the IR camera was fixed in space and the animal flank did move up and down with its breathing. A box is inserted to mark the selected area of maximum temperature. At $t=0^{+}$ [Fig. 7a], the first frame after laser pulse occurs is shown. At $t=80\mathrm{ms}$ [Fig. 7b], the hot spot begins to cool. At $t=630\mathrm{ms}$ [Fig. 7c], respiration artifacts produce a noticeable upward shift of the temperature field with respect to the camera field of view. The hot spot is no longer visible, but the area temperature relaxation occurs from the radial center of the area. At $t=1710\mathrm{ms}$ [Fig. 7d], the target area shifted back downward after breathing and continuing to cool. At $t=2630\mathrm{ms}$ [Fig. 7e], the area is almost completely cooled, and the target shifts back upward due to breathing again.

Fig. 7

Sequence of IR images with a 1.3-mm beam diameter (measured), and energy of $1.29\mathrm{J}$ .

4.

Discussion

We have performed measurements on live pig skin and compare these thresholds with mathematical modeling to determine the thresholds for visible lesions, and then compare these trends with the ANSI safe exposure limits. Since the ANSI safe exposure limits for skin are based on both laser wavelength and exposure time, we have measured thresholds for two different pulse durations on two different laser spot sizes on the skin, as given in Tables 5, 6. Only preliminary data have been reported²⁹ in the past, and that was for a spot size of only $0.25\mathrm{mm}$ in diameter due to laser pulse energy limitations. We had a higher energy laser and were therefore able to use much larger spot diameters of 0.7 and $1.3\mathrm{mm}$ . For the 0.7-mm spot, we measured an $\mathrm{MVL}\text{-}{\mathrm{ED}}_{50}$ threshold of $111{\mathrm{Jcm}}^{-2}$ at the 1-h reading, and $99{\mathrm{Jcm}}^{-2}$ at the 24-h reading, which indicates that a few more lesions were observable after $24\mathrm{h}$ . It was observed but not recorded that during the higher energy exposures, a visible flash was seen and a loud pop was heard due to LIB occurring at the skin surface. This LIB could have had some affect on the thresholds and was not noticeable during the larger spot $\left(1.3\mathrm{mm}\right)$ exposures. The occurrence of LIB is frequently seen for the large fluences in these exposures.³⁰ The $\mathrm{MVL}\text{-}{\mathrm{ED}}_{50}$ thresholds for this larger spot size were somewhat lower ( $95{\mathrm{Jcm}}^{-2}$ at $1\mathrm{h}$ and $83{\mathrm{Jcm}}^{-2}$ at $24\mathrm{h}$ ), and the differences could be due to a spot-size dependency, as predicted by the model for spot sizes smaller than about $1\mathrm{mm}$ in diameter. It could also have been due to the LIB at the surface for the smaller spot size. The slope of the Probit line was 33 for the 1.3-mm-diam spot, while only 3.3 for the 0.7-mm spot, which indicates more scatter in the data for the smaller spot. The ANSI exposure limit as given in Table 7 for this pulse duration $\left(350\mathrm{\mu }\mathrm{s}\right)$ is only $0.75{\mathrm{Jcm}}^{-2}$ or slightly more than two orders of magnitude below our $83{\mathrm{Jcm}}^{-2}$ for the ${\mathrm{ED}}_{50}$ measurement.

The skin surface-temperature measurements during and after the laser pulse for the 1.3-mm spot size is shown in Fig. 6 for pulse energies out to $1.4\mathrm{J}∕\mathrm{pulse}$ . For a comparison, the pulse energy at the ${\mathrm{ED}}_{50}$ value was $1.1\mathrm{J}$ , and this value indicates a temperature increase of $16°\mathrm{C}$ rise over the $28°\mathrm{C}$ skin surface ambient. The Monte-Carlo FD model predicted a $30°\mathrm{C}$ rise due to the laser pulse using the parameters listed in Tables 1, 2, 4.

MVL threshold measurements at the short pulse duration of $50\mathrm{ns}$ required special considerations to prevent LIB occurring in air, even before the laser pulse reached the pig skin. Pulse energies of $0.4\mathrm{J}∕\mathrm{pulse}$ when focused to spot sizes less than $1\mathrm{mm}\mathrm{diam}$ produce an irradiance of more than ${10}^9{\mathrm{Wcm}}^{-2}$ . Because we were able to expose the skin with energies up to $3.2\mathrm{J}∕\mathrm{pulse}$ at $50\mathrm{ns}$ , we had to utilize spot diameters of at least $2\mathrm{mm}$ to prevent LIB in the air and shielding of the pulses for the skin exposures. Even for the 2-mm spot diameter, most of the recorded lesions indicated that the observers either saw a flash of light or heard a pop. At a spot diameter of $5\mathrm{mm}$ and with the $3.2\mathrm{J}∕\mathrm{pulse}$ maximum pulse energy available, the irradiances only reached a value of $3\times {10}^8{\mathrm{Wcm}}^{-2}$ or well below the breakdown value for air or on the skin surface. The occurrence of LIB at the skin surface for thresholds lower than in free air is expected as free electrons are created at the skin surface by the large fluences from these exposures. The threshold for these phenomena is also reduced by significant linear absorption, up to a factor of 1000 reduction for very absorbing wavelengths in the far infrared.³⁰ We believe that LIB at the skin surface was the reason that the $\mathrm{MVL}\text{-}{\mathrm{ED}}_{50}$ threshold for the 2-mm-diam spot ( $39{\mathrm{Jcm}}^{-2}$ , Table 6) was almost four times the value for the 5-mm-diam spot ( $10.5{\mathrm{Jcm}}^{-2}$ , Table 6). Also, no thermal model indicates that there will be a spot-size dependency of the thresholds for pulse durations of less that a microsecond. It is interesting to note that the $\mathrm{MVL}\text{-}{\mathrm{ED}}_{50}$ thresholds at the 1-h reading were almost identical for both spot sizes.

Temperature calculation by the model for the 50-ns pulse had a computed temperature rise of a couple of degrees for no scattering and $8°\mathrm{C}$ rise with scattering for the 5-mm, 2.2-J laser pulse. Thus we believe that the damage should be mechanical and not thermal. Certainly, we could have had LIB and acoustic shock waves without the indicators described before producing this visible skin damage.

5.

Conclusions

We measure the minimum visible lesion thresholds in porcine skin for two different pulse durations and spot sizes and compare these values with a thermal damage model and the ANSI standards for the maximum permissible exposures at this wavelength. We use the standard finite element thermal model of heat conduction coupled with the Monte-Carlo light propagation simulation and feed the results into Henriques’ rate process model of thermal damage. With this model, we can determine the maximum temperature reached during and after the laser pulse, temperature distribution throughout the tissue, and the damage levels reached within tissue. Absorption and scattering parameters were measured in vitro from freshly harvested skin from the same animal used for the high-speed temperature measurements, and these parameters were used in the model for all temperature calculations. The major difference between the parameters measured here and those measured many years ago during the first skin modeling attempts (Takata ³¹) is that in the past, light scattering within the skin was not understood well, and that internal scattered light was considered to be reflected back to the surface and be included in calculations by the reflection coefficient. The Takata model predicts the temperature rises adequately for large spot sizes but breaks down for very small spot sizes. We now know that light is scattered within the tissue and the light transport can be calculated using a scattering coefficient or reduced scattering coefficient²¹ within the Monte-Carlo FE Model. Other researchers have reported porcine skin measurements that are similar to our measurements. The main difference between the our measurements and those reported by Du ³² is that our measurements are from a porcine skin containing melanin granules and the theirs came from a domestic pig with white skin and no melanin.

We calculate the maximum permissible exposures from ANSI standards for this wavelength and these exposure times and find them to be two orders of magnitude lower than the ${\mathrm{ED}}_{50}$ thresholds measured. We cannot say for certain that there is a spot-size dependency for the long pulse durations $(>1\mathrm{\mu }\mathrm{s})$ because of the very large field intensities for spot sizes below $1\mathrm{mm}$ and LIB occurring. However, we can now postulate that the MPE for skin at this wavelength of $1315\mathrm{nm}$ could be increased by an order of magnitude, i.e., from $0.75{\mathrm{Jcm}}^{-2}$ to $7.5{\mathrm{Jcm}}^{-2}$ at $0.35\mathrm{ms}$ , and for a pulse duration of $50\mathrm{ns}$ , it could be increased from $0.1{\mathrm{Jcm}}^{-2}$ to $1{\mathrm{Jcm}}^{-2}$ without jeopardizing the safety of exposures to the skin for this wavelength.