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Abstract
The exposure and emission limits of ICNIRP, IEC 60825-1 and ANSI Z136.1 to protect the skin 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 400 nm to 20 µm and was validated by comparison with all applicable experimental threshold data (ED50) in the wavelength range from 488 nm to 10.6 µm and exposure durations between 8 µs and 630 s. The model predictions compare favorably with the in-vivo data with an average ratio of computer prediction to ED50 of 1.01 (standard deviation ± 46%) and a maximum deviation of 2.6. This computer model can be used to improve exposure limits or for a quantitative risk analysis of a given exposure of the skin.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laser radiation in the visible and infrared range is absorbed in the skin to such a degree so that thermally induced injuries constitute a health hazard. Exposure limits to protect the skin are promulgated on the international level by ICNIRP [1] and in the United States of America in ANSI Z136.1 [2], where they are referred to as the maximum permissible exposure (MPE). The international laser product safety standard IEC 60825-1 [3] also defined MPEs in the annex to protect the skin and to this end adopts the exposure limits as recommended by ICNIRP. Skin-related MPEs are historically based on injury thresholds obtained with porcine models or human volunteers. The discussion in this paper relates to thermally induced skin injury, which is to be distinguished from photochemically induced injury in the ultraviolet range (< 400 nm) [4] and from potential thermo-mechanical injury mechanisms (micro-cavitation around melanosomes) or other non-linear mechanisms for short pulse durations [5].
The injury thresholds, usually expressed as radiant exposure or irradiance, show a strong dependence on wavelength and pulse duration and, to a degree, on the diameter of the laser beam incident on the tissue. While the collection of experimental data covers the parameter range sufficiently to set MPEs, computer models can form the basis for a systematic comparison of injury thresholds with MPEs over a wide range of wavelengths, pulse durations and beam diameters of interest. Of particular interest for such a comparison is the interdependence of trends with wavelength and pulse duration. A number of computer models dedicated to thermal injury of the skin already exist but have been for instance limited to single wavelengths [6,7] or have not been validated against injury threshold levels [8]. However, to the best of our knowledge, none has been validated against in-vivo injury thresholds over a wide range of wavelengths and exposure durations.
The current paper describes in detail a computer model and demonstrates its validity on the basis of a comparison with experimental data in the relevant range of pulse durations longer than 8 µs and wavelengths above 488 nm. An earlier version of the model was presented in 2013 [9]; since then the model has been improved and the experimental database significantly extended. This paper focuses on the systematic review of experimental threshold data and the description and validation of a generalized computer model. An extensive comparison of multiple pulse thresholds against the respective MPE values is discussed in another publication [10]. A detailed comparison of computed thresholds with the exposure limits of ICNIRP and ANSI Z136.1 is the topic of another publication [11].
2. Review of bioeffects and experimental data
2.1 Anatomy and physiology
The human skin consists of three main layers. The outermost layer, the epidermis, is a stratified tissue made up to 95% of keratinocytes [12]. The underlying dermis is a heterogeneous assembly of connective tissues – composed among others of collagen and elastic fibers – and including sebaceous glands, hair bulbs and blood capillaries. The hypodermal tissue, referred to as hypodermis or subcutaneous tissue, is essentially made up of fat cells.
Pigmentation of the epidermis originates in the melanocytes, located in the basal part of the epidermis, which produce melanosomes that migrate within the keratinocytes. The thickness of the human epidermis varies amongst different body parts and interdigitates in the dermis (papillae) but it was reported to average between 65 µm and 68 µm on the face, neck and arms [13] and 75 µm on the forearm [14]. The dermis thickness varies between 1 mm and 2 mm depending on the body region [15,16]. Pig skin is a widely accepted model for the human skin with respect to anatomy [13] and response to thermal insult [17,18].
2.2 Nature of the injury
This work is exclusively dedicated to thermally-induced threshold injury of the skin; other interaction mechanisms such as photomechanical damage in the nanosecond regime [19,20] or photochemically induced damage arising from exposure to ultraviolet radiation are not considered. In the thermal regime, absorbed laser energy translates into heat and an injury can occur when critical temperatures are exceeded in the tissue. The mildest reaction to be observed in-vivo by the naked eye is an erythema – often referred to as first-degree burn. On lightly pigmented skin this at-threshold reaction appears as a superficial reddening, while for heavily pigmented skin, skin darkening is observed [21].
In the nanosecond pulse range, several studies report injury thresholds (ED50) for white pig or guinea pig skin significantly lower than in the micro- and millisecond range. At the wavelength of 1314 nm, a ns-pulse ED50 of 10.5 J·cm-2 was reported, a level up to 8 times lower than ED50s obtained with 600 µs pulses [22]. At 1064 nm, a ns-pulse ED50 of 0.7 J·cm-2 was reported [20], similar to melanosome thresholds for micro-cavitation [19] and over an order of magnitude lower than ED50s obtained in the µs regime (see Fig. 2(b)), thus suggestive of a photomechanical damage mechanism mediated by the skin pigmentation. At wavelengths approximately longer than 1400 nm, the difference in threshold levels for pulses shorter or longer than 1 µs is less striking, with 3.5 J·cm-2 vs. 6.5 J·cm-2 at 1540 nm [23], 6.1 J·cm-2 vs. 7.4 J·cm-2 at 1540 nm [24] or 0.51 J·cm-2 vs. 0.97 J·cm-2 at 10.6 µm [25] for pulse durations shorter than 1 µs vs. longer than 1 µs, respectively. The latter observations, along with the fact that the role of melanin decreases with increasing wavelength, raise the question whether or not nanosecond-pulse ED50s at wavelengths above approximately 1400 nm are purely thermal in nature, so that a bulk thermal model would also apply. However, injury thresholds obtained with ns-pulses were not further considered in this paper.
2.3 Endpoint for threshold studies
Studies conducted to support the setting of exposure limits need to be based on the determination of the exposure level that just results in a minimum erythemal reaction (or minimum visible lesion, MVL), referred to as threshold lesion. The common endpoint for such studies is the detection of a MVL by direct visual observation at a defined delay after the exposure, such as 1 hour or 24 hours after exposure. Skin thresholds as used for this validation are exclusively based on visual observation by the un-aided eye to determine if a lesion is formed; other types of assessment such as the examination of biopsies, were not considered, and are also extremely rare when it comes to determination of thresholds.
A threshold is usually defined as the dose having a 50% probability of resulting in a visible lesion and is referred to as the ED50. An in-depth discussion on the meaning of the ED50 level and in laser injury experiments can be found in Ref. [26]. The ED50 can be obtained by probit analysis of the yes/no injury data [27]. Alternatively to a probit analysis, an injury threshold level can be obtained by bracketing responsive and non-responsive exposure levels, i.e. by consecutively decreasing the exposure from the side where a lesion is detected and increasing the exposure from the side where no lesion is detected – a technique which, however, lends itself only for short delays for the lesion detection [26]. There is no evidence that the results obtained with these two methods differ significantly when applied to skin threshold injuries. However, probit analysis offers some advantages, such as the possibility to quantify the steepness of the tissue response expressed by the ratio of ED84 to ED50, commonly referred to as slope of the dose-response curve. For the identified experimental data that were obtained by probit analysis, the median slope was 1.19 (150 samples, maximum slope 2.23), which corresponds to a standard deviation of ±17%, thus indicating a rather steep dose-response curve as compared to other bioeffects or tissues. Noticeably, the average ratio of lowest exposure level leading to an observable lesion to the ED50 level was 0.74 (13 samples, minimum ratio 0.30). In the remainder of the paper, the symbol ED50 is used even for the case that the threshold was determined by bracketing and not by probit analysis.
Near-threshold lesions evolve in the course of 48 hours. A near-threshold lesion typically appears within few minutes and tends to resolve within a few days [28]. Endpoints are typically 1 h and 24 h, a time course over which one could expect the ED50 to change the least. An analysis of experimental studies where the ED50s were reported at different endpoints shows that the 1 h to 24 h ED50 ratio on average is close to 1 (see Fig. 1). However, subgroups of the data show the ED50s at 1 h 30% to 65% higher than the ED50s at 24 h [24,29] as well as 30% to 33% lower [23,30], respectively. The different ratios could not be related to either pigmentation, exposure duration, wavelength, spot size or optical penetration depth.
Fig. 1. Ratio of experimental ED50s taken at different endpoints (for references, see section 2.4 and Table S1 in Document 1); endpoints between 1 min and 15 min after exposures were pooled together (labelled as 5 min), endpoints at 24 h and 48 h were pooled together (labelled as 24 h).
On average, the difference between ED50s at 5 minutes and 24 h was significant (p < 0.005) but not a large difference relative to the typical standard deviation of experimental threshold levels; the average ED50 for the 24 hours endpoint was a factor 0.83 of the average ED50 for the 5 minute endpoint. The difference between 5 minutes and 1 h ED50 was not significant, and neither was the difference between 1 h and 24 h (p > 0.1). From this analysis it was concluded that the ED50 for all endpoints could be pooled to be jointly used for the validation of the computer model. In other words, it was not necessary to develop different Arrhenius parameters for the different endpoints, nor to base the computer model just on 1 h and 24 h data.
2.4 Experimental thresholds
A literature review was conducted in order to identify all relevant experimental studies that report laser induced injury thresholds in-vivo for the skin. A total of 293 experimental injury thresholds were identified; 42 of them conducted with human volunteers and 251 with a porcine model of various breeds (Yorkshire, Sinclair, Hanford, Hampshire, Duroc, Chester, white pig and Yucatan mini-pig). The range of relevant experimental data reached from 488 nm to 10.6 µm in terms of wavelength and from 8 µs to 630 seconds in terms of exposure duration. In order to use a consistent term when referring to a wide temporal regime, such as in plots, “exposure duration” is preferred to “pulse duration” even when that regime includes microsecond pulses. Pulses shorter than 1 µs were not considered due to non-purely thermal damage mechanisms. Pulses shorter than 100 µs were only considered for wavelengths above 1600 nm where the contribution of melanin is marginal, as demonstrated in a study with Yucatan mini-pigs at a wavelength of 2000 nm [31]. The irradiance profile of the laser beam incident on the skin was either Gaussian or “top hat”. For the specification of the “diameter” of a Gaussian beam profile, the 1/e irradiance level is consistently used throughout this paper, so that dividing the total power by the area defined by the 1/e diameter results in the peak irradiance of the Gaussian beam profile. The beam diameter incident on the skin ranged from 169 µm to 67 mm. Multiple pulse data with up to 3000 pulses were also identified and included.
The relevant injury thresholds [6,7,8,18,21,23–25,28–53] are listed in Table S1 in Supplement 1 along with the predictions of the computer model in the form of a ratio referred to as RED50, defined as the ratio of the computer model injury threshold to the experimental ED50. The predicted lesion depth is also given (zero being set as the skin surface). Besides wavelength, exposure duration and beam diameter, the skin type and the presence of hair follicles were distinguished for the purpose of modelling. In Table S1 in Supplement 1, the skin color was divided into three groups: “light” for studies reporting “light”, “white” or “pigment free” skin types (e.g. “Caucasian” subjects, Yorkshire or Chester white pigs), “medium” for studies reporting “light to dark”, “skin type I to type IV” or “lightly pigmented” skin types (e.g. “Chinese” or “light Negro” subjects or Hanford pigs) and “dark” for studies reporting “pigmented” or “dark” skins (e.g. “dark Negro” subjects, Duroc pigs or Yucatan mini-pigs). In cases where the pigmentation was not explicitly reported, photographs or best judgment were used to determine the category. Hairiness was also classified in two categories: “hairless” for studies reporting either hairless (e.g. anterior forearm) or waxed skin sites and “hairy” otherwise. From a total number of 293 thresholds, 5 were not included in the comparison with the predictions of the computer model, for the following reasons.
Amongst eight injury thresholds obtained with pulsed ruby lasers for various skin types, two data using white porcine models appear to be significantly higher (2.5 x to 3.4 x) than other comparable data, as shown in Fig. 2(a). It is noted that the injury threshold does not depend upon the beam diameter for the respective pulse width regime. The data plotted as “light skin” come from human volunteers and white pigs. While it cannot be excluded that the specimen used to derive the highest thresholds (Chester white pig [44] and white pig [51]) were actually pigment-deficient or far less pigmented than other “light skin” subjects (Caucasian volunteers [21,44]), it is argued that such inconsistency is detrimental for the purpose of model validation. Furthermore, the two highest ED50s are 24 times higher than ED50s obtained with dark skins (Hampshire/Duroc pigs [44] and heavily pigmented volunteers [21]). Such ratios across skin types have never been reported in any other study nor seen across the database available from the literature. Consequently, the two highest ED50s were discarded.
Fig. 2. In-vivo ED50s obtained with (a) pulsed ruby laser for various skin types and highlighting the inconsistency of two data (b) Nd:YAG laser for various skin types along with the respective model predictions and highlighting the inconsistency of a datum at 200 µs and (c) 1940 nm laser radiation on light-skinned porcine models along with the respective model predictions and highlighting the inconsistency of a 70 ms datum.
The injury threshold for pulsed Nd:YAG (200 µs, 1060 nm) on Chinese volunteers reported by Qingshen [39] was 2.6 times lower than the ED50 reported in a similar study [40] (9.9 J cm-2 vs 26.0 J cm-2). Since laser wavelength, pulse duration, beam diameter, skin type and endpoint (5 minutes) were identical, it is argued that one of the two thresholds must be considered as inconsistent with the overall collection of thresholds. The in-vivo ED50s plotted in Fig. 2(b) (endpoint within 5 minutes, 1060 nm, 5 mm beam diameter, Chinese test subjects) together with the proposed model tend to support the view that the data by Qingshen (9.9 J cm-2) is inconsistent and shall be consequently ignored. Furthermore, the above mentioned article also reports an even lower preliminary ED50 obtained with a white pig model (Shanghai white pig, 4.6 J cm-2). That a light skin ED50 lies a factor of 2 below that of a pigmented skin is not consistent with biophysical principles, further justifying the rejection of this 1060-nm study for the purpose of model validation.
Finally, the Oliver study of 2010 with a wavelength of 1940 nm [7] contains one inconsistent threshold as shown in Fig.2c. The ED50 obtained for a 70 ms exposure and 4.8 mm beam (1/e2) is 3.1 times higher than other data at comparable exposure durations. It is noted that the injury threshold does not depend on the beam diameter for such relatively short exposures at 1940 nm. Since these data all originate from the same study, it can be argued that no uncontrolled parameter (or unreported parameter) could justify such deviation. Consequently, the 1-h and 24-h ED50s (4.8 mm, 70 ms) were not considered in the process of model validation.
3. Description of the computer model
3.1 Optical properties
The skin is a turbid media, for which reflectance is dominated by backscattering in the visible and IR-A (700 nm to 1400 nm) range and specular reflection at longer wavelengths. It has been demonstrated that the melanin content is the dominating parameter when quantifying the diffuse reflectance [21,54] as shown in Fig. 3. Rockwell’s data obtained for “Caucasian” and “light Negro” skin types were used in our model for “light” and “medium/dark” skins, respectively.
Fig. 3. Diffuse reflectance of various skin types as a function of wavelength found in the literature for human and pig skin.
Scattering in skin tissue has been identified as predominant over absorption in the visible and near infrared [55,56] and certain computer models have implemented light propagation models using Monte Carlo techniques (e.g. [43]). The proposed model considers attenuation within the different skin layers to be exclusively governed by linear absorption. The attenuation of irradiance E as a function of depth z due to absorption was modelled according to the Beer-Lambert’s law:
where R represents the reflectance and the depth z equals zero at the outer surface of the skin. A combination of four absorbers (melanin, water, blood and fat) at different concentrations in three skin layers (epidermis, dermis and subcutaneous fat) were considered in this model. All pigments are assumed to be homogeneously distributed in their respective layers. The data are summarized in Fig. 4 and Table 1 listing absorption coefficients. In spectral regions where no data are available, the coefficients were set to 0 (blood above 1250 nm and fat above 2600 nm). The layer properties are summarized in Table 2. Epidermis thickness and the volume fraction of the different absorbers were adjusted in the course of an optimization process in order to improve the computer model predictions compared to experimental injury thresholds.Fig. 4. Absorption coefficient of melanin [57], blood [58], water [59] (data available until 10.6 µm and beyond) and fat [60,61] (data available up to 2600 nm).
Table 1. Bulk absorption coefficients of skin constituents (wavelength λ in nm); see Fig. 4 for water and fat
Table 2. Optical properties of the skin layers; concentrations are volume fractions (“l” for light, “m” for medium and “d” for dark skin)
3.2 Transient increase in temperature
A time-dependent thermal model was developed using a finite-element Multiphysics package (COMSOL 3.5a, Comsol AB, Stockholm, Sweden, 2008), with three contiguous flat slabs representing the epidermis, dermis, subcutis. All layers exhibit homogeneous and isotropic properties. Axial symmetry of the laser beam (either Gaussian or Top Hat) and the irradiated local skin area reduces the problem to a 2D case. The extent of the finite-element domains, both radially and in depth, was set to allow sufficient heat diffusion, i.e. varying with exposure duration and penetration depth. The boundary conditions were adiabatic, except at the air-skin interface where heat losses were accounted for by non-linear boundary conditions. The equation to be solved can be written in the form of the Penne’s bio-heat equation:
where T(t,r,z) is the increase in temperature, Q(t,r,z) represents the heat source (laser radiation) and Saq the heat sink in the tissue. The parameters k, ρ and C are conductivity, density and heat capacity, respectively. The time, radial and axial variables are noted t, r and z, respectively. Heat losses occurring in the dermis via blood flow were taken into account in the bio-heat equation as a negative heat source (heat sink). Besides heat conduction, convection was considered in the dermis via a negative heat source (heat sink) representing the blood flow. Such heat loss can be inserted in the bio-heat equation as a perfusion term ρ·C·ω·(Tb-T), ω being the perfusion rate and Tb the body temperature. The boundary conditions were as follows:Table 3. List of parameters used in the thermal model
3.3 Damage model
A thermally-induced threshold injury can be conceptualized as an accumulation of microscopic sub-lethal damage [64], which eventually leads to cell death by apoptosis or necrosis [65]. Such pathway can be modelled by using the Arrhenius equation which describes the temperature-dependent rate of reaction κ and when integrated over time results in a measure of macroscopic damage:
Table 4. List of parameters associated used in the damage model
4. Model validation
The computer model described in section 3 was used to reproduce injury thresholds for those wavelengths, exposure durations and laser beam diameters for which relevant experimental threshold data is available, according to section 2 (288 data). The main figure of merit used to evaluate the validity of the computer model was the ratio RED50, defined as the ratio of computer model injury threshold to experimental ED50 (see Table S1 in Supplement 1). Thus for RED50 > 1, the predictions of the computer model can be interpreted as potentially to err on the unsafe side. Further figures of merit such as the trend of RED50 with different laser parameters, animal models or assessment delays were also investigated to confirm the general validity of the computer model. Figure 5 shows the distribution of ratios RED50 with a mean value of 1.01 and the standard deviation of 46%, as listed in Table 5, together with other relevant descriptive statistics. The distribution of RED50s is close to a normal distribution with a coefficient of determination of 0.92.
Fig. 5. Distribution of RED50 ratios for the human and pig 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).
Table 5. Descriptive statistics of the RED50 ratios.
The individual RED50s can also be illustrated as function of exposure duration, wavelength and beam diameter (Fig. 6). No trend indicative of a systematic deviation of the model predictions with a laser parameter was found. It can be seen that the ratios RED50 are approximately evenly distributed around a value of 1 regardless of the laser parameter under consideration. However, it is noted that the computer model overestimates experimental ED50s at the wavelength of 1540 nm, for which the RED50s on average were found to be significantly different from RED50s at any other wavelength (p < 0.01). These data originate from three studies [23,24,45] and have the pig model and the laser source (pulsed Er:glass laser) in common and encompass a wide range of beam diameters (400 µm to 10 mm) and multiple-pulse exposures with up to 64 pulses, but no single parameter was found that could explain the discrepancy at 1540 nm.
Fig. 6. Distribution of individual RED50 ratios as a function of (a) exposure duration, (b) wavelength and (c) beam diameter (1/e definition); to provide further information, the data in each diagram is split in (a) endpoint at 15 min or less, 1h/2h, 24h/48h after exposure, (b) skin types “light”, “medium” or “dark” (c) wavelength below 780 nm, between 780 nm and 1400 nm (IR-A) or above 1400 nm (IR-B or C).
Finally, a number of discrete variables were identified to further analyze the performance of the computer model: the endpoint (categorized as “5 min” for endpoints within 15 minutes after exposure, “1 h” for endpoints at 1 h or 2 h and “24 h” for endpoints at 24 h or 48 h), the species (pig or human), the pigmentation (“light”, “medium” or “dark”, more details in section 2.4), the method used to derive a threshold level (“probit” for probit analysis or “other”), the exposure type (“single pulse” or “multiple pulses”), the lesion depth predicted by the computer model (“epidermis” or “dermis”) and the presence of hair follicles (“hairless, depilated” or not). A two-tailed unpaired t-test was used to evaluate the geometric mean of RED50s between groups, the results of which are summarized in Table 6. The t-test was performed for unequal variances whenever the ratio of variances between groups was smaller than 0.5 or greater than 2.
Table 6. Statistical comparison for various variables of interest divided into two groups (threshold for statistical significance: 0.05 level, N.S. means non-significant, the number of samples for each group is given in parentheses; XAB represents the variance of group A over the variance of group B)
5. Discussion
Over the entire range of laser parameters for which laser-induced threshold injuries of the skin are available in the thermal regime, the largest deviation of our computer model predictions to the “unsafe” side, i.e. where model predictions are higher than experimental results, was RED50 = 2.62. The maximum deviation to the other side, i.e. where the model threshold predictions are lower than the experimental data, was similar with RED50 = 0.41.
Although the endpoints at 5 min and 24h/48h in experimental ED50s were significantly different (see Fig. 1), the average ratio was only 0.83 and therefore negligible as compared to the overall spread of RED50s. Moreover, the statistics of Table 6 suggests that it is not necessary to differentiate between endpoints. As mentioned in section 2.3, this further demonstrates that the wide range of ratios observed between different endpoints in experimental studies is not reproducible, i.e. cannot be accounted for in simulations, and result in an irreducible deviation of the computer predictions from the in-vivo data.
However, it was important to distinguish between different pigment concentrations. The choice of accounting for three skin types in the computer model arose from the wide variety of skin types used in in-vivo studies. As shown in Fig. 7, the predicted injury threshold can vary by as much as 3.6 depending on the skin pigmentation. The difference relates primarily to the reflectance (see wavelength dependence in Fig. 3) and to a lesser degree to the relative contribution of melanin in terms of absorption. This data also demonstrates the challenge for the development of computer models on the basis of in-vivo ED50s, since the categorization of skin types and degree of pigmentation in most published works could be qualified as rough. In the absence of a more meaningful classification scheme quantifying the pigmentation such as the Fitzpatrick’s scale, the model must assume a certain pigmentation and its respective properties for each ED50 to be reproduced. It is hypothesized that a large part of the RED50 spread is related to the coarse skin types. The computer model was best in line with the experimental ED50s for melanin concentrations in the epidermis of 7%, 9.5% and 12% for light, medium and dark skin, respectively. Volume fractions reported in the literature vary fairly, with 1% in pale skin to 5% in darker skin [67], 2.5% to 20% for skin type II and skin type IV respectively [68] or an average of 3.8% in light-skinned adults to 30.5% for darkly pigmented skin [69].
Fig. 7. Change in injury threshold for various skin types according to the computer model, as a function of wavelength and for selected exposure durations.
Similarly to the skin type, the presence or absence of hair follicles was determined to be an important parameter in determining injury thresholds, as shown by DeLisi [30] where lightly pigmented waxed pigs required up to 2.5 times higher irradiance levels to induce a visible lesion than shaved pigs (10 ms, 1070 nm). The difference becomes less important for longer exposure durations and becomes negligible for exposures above 1 s. It was chosen to increase the melanin concentration in the epidermis in this model by 25% to account for the presence of hair follicles. The individual RED50s are plotted as a function of predicted lesion depth according to the proposed model in Fig. 8. It appears that the computer model overestimates experimental ED50s in the presence of hair follicles for deeply penetrating wavelengths (see RED50s Fig. 8(a) for lesion depths beyond 120 µm). It also appears that the highest deviations and a majority of RED50s larger than 2 actually relate to the single wavelength of 1540 nm (see Fig. 8(b)). Although hair takes root in the dermis, attempts to increase the pigmentation in this layer to simulate hair follicles have resulted in a larger spread of the RED50 ratios (data not shown). Any attempted modification of the content of the dermis (e.g. volume fraction of water) or the epidermis thickness also failed to improve the overall deviation. The question remains as to whether the discrepancy is due to the presence of hair follicles, to an optical property of the skin specific to wavelengths around 1540 nm that is not accounted for in the model, or to the properties of the Er:glass lasers used in these studies (e.g. pulse shape or beam profile).
Fig. 8. Predicted lesion depth according to the model, distinguishing (a) between the presence or absence of hair follicles and (b) between four wavelength ranges.
Overall, considering the range of wavelengths, pulse durations, beam diameters, skin types and endpoints, it is argued that the computer model predicts cutaneous injury thresholds relatively well. A significant part of the RED50 spread has been shown to relate to the coarse categorization of skin pigmentation, divided into three types whereas skin colors of the porcine model and human volunteers cover a continuous spectrum from the lightest to the darkest hues. The spread of RED50s can be assumed to arise to a significant degree from experimental uncertainties. Besides the inherent difficulty to visually infer a threshold lesion appearing as a slight contrast on the skin surface (this being even more difficult on dark skins [21]), experimental work providing ED50s for different beam diameters provide a good example of the uncertainty inherent to the in-vivo study of laser-tissue interactions, since for sufficiently short exposure durations, thermal confinement dictates that the injury thresholds do not depend on the beam diameter. The ED50s shown in Fig. 9 for two exposure durations from the same study [29] suggest an experimental uncertainty of a factor 1.5 to 2. The authors of this particular study mention that the short exposures (10 ms) with beams smaller than 10 mm may have been multifocal and lesions at thresholds showed signs of desiccation.
Fig. 9. Comparison of ED50s obtained for lightly-pigmented porcine models [29] (symbols) and model predictions (solid lines) as a function of beam diameter at a wavelength of 1070 nm highlighting the variability of experimental data in a pulse duration range where no spot-size dependence is to be expected.
The results also permit the conclusion that a homogenous bulk model is appropriate and it is not necessary to consider the granular aspect of the skin pigmentation for pulse durations above 100 µs, and even shorter durations at wavelengths at which melanin is transparent (above approximately 2000 nm).
Additionally, the use of light propagation models in turbid media to accurately simulate the scattering does not appear to be essential for the purpose of predicting injury thresholds in the thermal regime. Although scattering in the skin has been consistently reported in the literature to play a much bigger role in the laser attenuation than the linear absorption, the lack of discernable trend in the performance of this computer model over a wide range of beam diameters – namely 0.8 mm to 67 mm at the 1/e irradiance point – shows that injury thresholds can be predicted well by using the incident beam diameter as the diameter of the heat source within the tissue. Only for beam diameters smaller than 800 µm the heat source in the model was set to a diameter of 800 µm throughout the tissue. This adjustment, in combination with the MVL parameter, was necessary to fit the respective ED50s and can be seen as accounting for scattering in the model for small laser beam diameters. Transmittance measurements have shown that the impact of scattering is significantly greater for small beams than large beams [70]. If it were necessary to account for scattering for beam diameters above 800 µm, a systematic bias of the RED50s would be seen in the results shown in Fig. 6(c). It is hypothesized that the enlargement of the laser beam within the tissue due to scattering is not significant enough to impact the injury thresholds and that for beam diameters above about 800 µm, the incident beam diameter provides a sufficiently good measure of the radial extent of the heat source.
Additionally to the Arrhenius integral evaluated at the edge of a thin disk referred to as MVL area, a threshold criterion was based on the peak temperature in the beam axis reaching 100 °C. This alternate injury threshold criterion is relevant to exposures associated with small beams (typically less than 1 mm in diameter) and short exposures (typically less than a few milliseconds) where the Arrhenius integral would calculate a peak temperature in the order of 340 K at the MVL radius, while the peak temperature in the beam axis would reach around 400 K. It is argued that such a temperature, even for short times, may result in injuries of a different nature than a superficial erythema (supra-thresholds), especially in the presence of hair follicles. Thermal camera images showed that hair follicles heat over 100°C at exposure levels near ED50 while the surrounding skin tissue is associated to temperatures in the order of 40°C [29]. Predicted injury thresholds based on the 100°C criterion were best in line with the experimental ED50s for small beams and short exposures. Without the temperature limitation to 100 °C, additionally to the Arrhenius damage model, these predicted injury thresholds were approximately 40% higher.
Finally, it is noted that the optical properties as discussed in section 3.1 are defined in the wavelength range between 400 nm to 20 µm. Provided that the damage mechanism in the cell is of thermal nature, the predictions of the model can be assumed to be also applicable in the wavelength range of 400 nm to 488 nm and above 10.6 µm where no experimental ED50 data is available. In terms of exposure duration, it is suggested not to apply this model to pulses shorter than 100 µs for wavelengths shorter than approximately 1600 nm and shorter than 1 µs for wavelengths above 1600 nm, where bulk thermal models are not suitable.
6. Conclusion
Compared to the wide parameter range of wavelength, pulse duration, number of pulses, repetition frequency and beam diameter, the collection of experimentally determined skin injury thresholds is somewhat limited. The proposed model was validated to predict thresholds in good agreement with their experimental counterparts, with an overall deviation of 1% and a standard deviation of 46% over a wide range of wavelengths (488 nm to 10.6 µm), exposure durations (8µs to 630 s), beam diameters (0.17 mm to 63 mm) and skin types (light to dark). A validated computer model provides a mean to obtain thresholds in order to cover all combinations of laser parameters relevant to thermal laser-induced injuries and it can be a valuable tool to investigate the suitability of the current laser safety exposure limits and propose potential improvements. An exhaustive comparison of injury thresholds with the current MPEs is the subject of another publication by the authors [11].
Disclosures
The computer model described in this article is used – besides supporting the improvement of international safety limits – to predict skin injury thresholds as part of risk analysis studies for laser applications and products, offered by Seibersdorf Labor GmbH as commercial service.
Supplemental document
See Supplement 1 for supporting content.
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