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1 July 2010 Relationships of skin depths and temperatures when varying pulse repetition frequencies from 2.0-µm laser light incident on pig skin
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Human perception of 2.0-µm infrared laser irradiation has become significant in such disparate fields as law enforcement, neuroscience, and pain research. Several recent studies have found damage thresholds for single-pulse and continuous wave irradiations at this wavelength. However, the only publication using multiple-pulse irradiations was investigating the cornea rather than skin. Literature has claimed that the 2.0-µm light characteristic thermal diffusion time was as long as 300-ms. Irradiating the skin with 2.0-µm lasers to produce sensation should follow published recommendations to use pulses on the order of 10 to 100 ms, which approach the theoretical thermal diffusion time. Therefore, investigation of the heating of skin for a variety of laser pulse combinations was undertaken. Temperatures of ex vivo pig skin were measured at the surface and at three depths from pulse sequences of six different duty factors. Differences were found in temperature rise per unit exposure that did not follow a linear relation to duty factor. The differences can be explained by significant heat conduction during the pulses. Therefore, the common heat modeling assumption of thermal confinement during a pulse may need to be experimentally verified if the pulse approaches the theoretical thermal confinement time.



The irradiation of skin by laser light has been a subject of study since shortly after the ruby laser was introduced in 1960,1 with the first publication on rabbit and human skin in 1963.2 From very early in the history of lasers, skin irradiation safety limits have been based on both pulsed (0.1Jcm2) and CW (1.0Wcm2) operation.3 Current safety standards from the American National Standards Institute (ANSI) set the skin exposure limit in the infrared (IR) at 0.56×t0.25 , in units of Jcm2 , where t is the exposure time between 103 and 10s . (Ref. 4). The ANSI report is based on observed damage thresholds to the cornea of the eye, quantified in radiant exposure, H (Jcm2) (Ref. 5). From dermatology, skin damage is described in units of temperature. Accurate temperature prediction is important because the gap between skin tolerance and injury is as narrow as 3to6°C , depending on duration of heating.6, 7, 8

The skin temperature change due to IR laser irradiation has been measured in many studies with temperature and time as predictors of skin damage.6 Moncrief sets the threshold for irreversible damage to the basal cells of the epidermis at 44°C for extended time in minutes. For brief exposures, Moncrief gives 51°C as the limiting temperature.7 Leach had reported 47°C as the critical temperature for visible change to skin and 50to55°C as the threshold for permanent damage.8

Establishing injury thresholds from laser irradiation with very short durations often focuses on the energy and leaves temperature to calculation rather than measurement.9 The most frequent method of skin temperature measurement during laser irradiation has been the noncontact IR camera. This type of instrument was used for single pulses of 2.0-μm laser by Chen 5 Pulsed irradiation of skin with 2.94-μm laser was measured by a thermal imaging camera.10 IR pyrometers have also been used to measure surface temperatures during laser irradiation.11, 12 Leandri again demonstrated the difficulties in temperature measurement with a correlation of temperature to laser energy, but not to pulse duration.11 Temperatures deep within tissue during and following continuous wave (CW) laser irradiation have also been measured with thermocouples.13, 14

Tissue effects comparing different laser pulse conditions have been investigated for many purposes, including medical uses and injury investigation. Different results have been found when one or more of the following parameters have been varied: pulse repetition frequency (PRF), pulse width combinations of different widths, different spacing (i.e., not a repetitive frequency), or sequences with different power per pulse. Pulse sequence optimization of ErYAG lasers has been of particular interest to dermatologists to replace their CO2 lasers.

A summary of representative studies of pulse sequence effects is given in Table 1 . As seen in Table 1, pulse width can change the amount of radiant energy to produce damage in tissue or change the extent of damage. Pulse repetition frequency can change the observed temperature or type of tissue damage. Increasing the number of pulses can affect the depth of injury per pulse.

Table 1

Sampling of laser pulse sequence manipulation studies.

VariableChangeConstantResultWavelength (μm) Study
Pulse widthReduced tp Equal tissuedamageRequired H reduced1.5Ref. 15
0.532Ref. 16
0.577Ref. 17
Pulse widthIncrease tp Equal radiantenergyNo change indepth ofcoagulation2.94Ref. 18
Pulse widthIncrease tp Equal radiantenergyIncreaseddepth ofcoagulation2.94Ref. 19
2.94Ref. 20
PRFIncrease PRFEqual radiantenergyReducedtemperature2.09Ref. 21
PRFReduce PRFEqual radiantenergyChanged effectfrom ablationto coagulation2.94Ref. 22
PRFIncrease PRFEqual radiantenergyIncreasedablationto coagulation2.94Ref. 10
Numberof pulsesIncrease Np Equal radiantenergyIncreaseddepth of injury10.6Ref. 23

Many studies use ablation or coagulation depth as a metric for pulse sequence comparison.10, 20, 24 For those modeling the temperature from laser pulse irradiation, the energy deposition is assumed to be an instantaneous impulse confined within the volume of deposition.25, 26, 27, 28, 29 The conditions required for this assumption to be valid depend on the optical penetration in the tissue and the rate of heat flow or thermal diffusivity of the tissue.

The optical penetration depth, d , is a measure of how deep the energy fluence will travel before being absorbed. Optical penetration depth depends on the absorption and scatter of the light in the tissue and the beam width.30, 31 For absorption-dominated tissue, the optical penetration depth is d=1μa . For optically turbid material, the optical penetration depth is defined by Ritz 31 as

Eq. 1

where μa is the absorption coefficient, and μs is the reduced scattering coefficient [ μs=μs(1g) , with g being the anisotropy factor]. The optical zone, where the incident energy fluence has been reduced by 1e , in turbid media has an additional factor to account for backscattered reflections.30

The 2.0-μm TmYAG laser has yet to have optical absorption and scatter properties conclusively established. The diversity of published attenuation coefficients produces a wide range of optical penetration depths, as seen in Table 2 .

Table 2

Optical penetration depth (mm), using published constants and optical zone for a beam with a 1∕e2 radius of 3.28mm .

μa (cm−1) μs’ (cm−1) Optical penetrationdepth, δ Optical zone, d
21.7610.4600.4600.460Ref. 32
280.3570.3570.357Ref. 33
58.0220.1720.1720.172Ref. 32
1.7513.251.1272.2092.017Ref. 34
48100.1090.2140.214Ref. 35
82100.0660.1300.130Ref. 36

aAbsorption coefficient for epidermis;

babsorption coefficient for dermis.

The heating of tissue below the skin surface is complicated by the flow of heat into or out of the volume of interest during the irradiation. Therefore, models of tissue heating are simplified if they assume that the energy is deposited as an impulse with no heat flow until the pulse has terminated. The conventional criteria for neglecting heat transfer from the irradiated tissue is for the laser pulse to be significantly smaller than the thermal diffusion time,30 τdiff , also known as the thermal relaxation time, expressed by Eq. 2, where D is the thermal diffusivity of the tissue. The thermal relaxation time, τdiff , is considered to confine the heat transferred within the optical penetration depth:30

Eq. 2

Analytical thermal analysis of laser pulses assume no residual thermal influence of prior pulses if the pulse length is much less than the thermal relaxation time;37 however, these analyses do not address the pulse repetition frequency—that is, the time between “impulses” of energy deposited. This assumption has been applied to pulse durations up to 300ms . (Ref. 38). Some analytic functions have been reported to fit tissue temperature changes best for short (microsecond) pulses,39, 40 while others fit best for longer pulse widths (> 100ms) .41 However, both of these solutions were evaluated for a single laser pulse rather than for a series of pulses as a whole.40

The skin tissue is composed of three anatomical layers, which have different optical properties. The exterior skin layer is the stratum corneum, which ranges from 10μmto20μm thick, depending on anatomic site and study. Underneath is the epidermis, ranging from 30μmto150μm thick. Last, the dermis has been reported to be from 981μmto4000μm thick.42 This places the optical penetration depth of 2.0-μm laser light within the dermis if absorption is dominant in skin. If skin is a turbid medium with scatter dominant, then the penetration depth is deeper into or beyond the dermis. If skin is a mildly turbid medium with both absorption and scatter, then the optical zone is close to the border between the epidermis and dermis.

Considering pulses of 2.01μm infrared from Tm:YAG fiber lasers, the range of published values of thermal constants listed in Table 3 , combined with the range of optical zones, d , found earlier in Table 2, produce thermal diffusion times that would indicate that virtually any pulse widths are thermally confined. As shown in Table 4 , different combinations of constants can produce thermal diffusion times over a range of four orders of magnitude. The thermal diffusivity, D , depends on the tissue type and any vascular perfusion.

Table 3

Thermal constants of human and pig skin.

Tissue(depth or specifier)Conductivity κ Wm−1°C−1 Diffusivity D m2s−1 Density ρ gcm−3 Specific heat C Jkg−1°C−1 Year
Stratum corneum0.2351.536002008 (Ref. 43)
Epidermis0.2136002000 (Ref. 44)
Epidermis0.222442006 (Ref. 32)
Epidermis0.231.235902004 (Ref. 45)
Epidermis0.2351.19036002008 (Ref. 45)
Epidermis (forearm)0.5691977 (Ref. 46)
Epidermis (in vitro)0.2091977 (Ref. 47)
Dermis0.5338002000 (Ref. 44)
Dermis0.4936632006 (Ref. 32)
Dermis0.451.233002004 (Ref. 45)
Dermis0.4451.11636802008 (Ref. 43)
Dermis (forearm)0.8371977 (Ref. 46)
Dermis (in vitro)0.2931977 (Ref. 47)
Skin0.23–0.4141975 (Ref. 48)
Skin0.45 1.10×107 1998 (Ref. 49)
Skin0.542002002 (Ref. 50)
Skin0.391.11632002003 (Ref. 51)
Skin 1.30×107 1983 (Ref. 52)
Skin0.37141802000 (Ref. 53)
Skin0.532001 (Ref. 54)
Skin (0.26mm) 0.4×107 1975 (Ref. 48)
Skin (0.45mm) 0.6×107 1975 (Ref. 48)
Skin (0.90mm) 0.85×1071.20×107 1975 (Ref. 48)
Skin (02mm) 0.3761975 (Ref. 48)
Skin0.561.0734002006 (Ref. 55)
Skin (in vitro) 0.82×1071.2×107 2000 (Ref. 56)
Skin (in vitro)0.21–0.41 0.82×1071.2×107 1985 (Ref. 57)
Skin (in vitro)0.2931.233891954 (Ref. 58)
Skin (in vivo)0.5–2.8 0.4×1071.6×107 1987 (Ref. 59)
Tissue 1.20×107 1985 (Ref. 60)
Tissue0.441.07035001986 (Ref. 61)
pig epidermis (in vitro)0.2091977 (Ref. 47)
pig skin (opaque)0.414 0.82×1070.86×107 1975 (Ref. 48)

Table 4

Thermal relaxation times, τdiff , for 2.0μm light in both depth and radial direction using published constants (s).

μa (cm−1) μs’ (cm−1) Slow thermal diffusivity1Fast thermal diffusivity1Study
21.7625.285.281.321.32Ref. 33 30
58.0230.740.740.190.19Ref. 33
1.7513.25121.90101.7030.525.4Ref. 32
48101. 40
82100.420.420.110.11Ref. 39

aFast D=4×10−4cm2s−1 from Bowman (Ref. 48) slow D=1.6×10−3cm2s−1 from Chato (Ref. 57);



This work explores the relationship of computed and measured temperatures of 2-μm laser light incident on pig skin with varying pulse repetition frequencies and skin depths. The objective of this work is to investigate the validity of the common assumption of isolated, thermally confined pulses used in analytical temperature modeling. The variable of interest is the duty cycle of pulsed irradiations. Measurements of temperature at the surface and internal temperature at three depths beyond the optical penetration depth were evaluated for differences of heating between sequences of varying PRF, while total energy is held constant. Temperatures predicted by models that rely on the assumption of thermal confinement within a thermal relaxation time were found to have varying agreement depending on pulse cycle duty factor. Temperature rise per unit exposure was found to be different between pulse sequence duty factors at all four depths.


Materials and Methods


Temperature Measurements

Temperature measurements of six distinct pulse sequences were taken at four ex vivo skin depths, nominally at the surface, at 300μm , at 400μm , and at 650μm . The entire skin sample and holder with thermocouple in place was centered in the beam of a 2.0-μm laser by scanning the probe through the beam on a 2-D optical stage with a micrometer (Model TXS, Melles-Griot, Albuquerque, New Mexico) in 500-μm increments first in the N–S direction and then in the E–W direction. The measurements at central axis (CAX) of the IR beam were repeated four times for each pulse sequence on each sample of pig skin. The first sequence was also repeated another four times in order to show that the skin conditions had not changed during the measurements. Three different samples of pig skin were used at each depth for a total of nine skin samples. (Surface measurements were performed concurrently.)

Temperatures were measured with two instrument systems: an infrared camera with microbolometer array for skin surface measurements and with a type T (Copper-Constantan) microthermocouple for below-surface depths. The model S65HSV thermal imaging camera (FLIR Systems, Weisbaden, Germany) detector was composed of a 320×240 array of uncooled microbolometer detectors. The sensitivity is calibrated at 0.05°C with an accuracy specification of +2°C . Image sequences were collected and sent to a PC (XPS, Dell, Round Rock, Texas) at a rate of 60Hz , giving a temporal resolution of 17ms per data point. The images were read and analyzed using Reasercher Pro version 2.8 (FLIR Systems, Weisbaden, Germany), which offers region of interest and line profile extraction. The camera is sensitive in the spectral range of 7.5to13μm . The lens has a minimum focusing distance of 0.3m , with a quoted spatial resolution of 1.1mrad of divergence. The thermal camera was positioned in the same location for all exposures at one meter from the skin surface, approximately 30deg from normal to the skin in the E–W direction in order to not interfere with the beam delivery arm. The camera was calibrated by the manufacturer using NIST traceable blackbody sources.

The model HYP-0 thermocouple (Omega Engineering, Inc., Stamford, Connecticut) consisted of the thermocouple junction imbedded in the tip of a stainless steel 33-gauge hypodermic needle. The outer diameter of the needle was 200μm . The thermocouple response was recorded using iNet software (Omega Engineering, Inc.). The iNET settings were 150 readings per second, with the noise filter set to exclude signals over 200Hz , signal integration time set to 0.001s , with 4000 readings collected for 26s of monitoring. The iNet system recording was initiated by the same pulse triggering the laser via connection to the output of the HP model 33120A wave form generator (Hewlett Packard, Palo Alto, California) with a coaxial T connector. The IPG model TLR-50-2010 Tm:YAG laser (IPG Photonics, Oxford, Massachusetts) fired as the transistor-transistor Logic (TTL) signal reached its maximum of 5V , while the iNet was set to begin collecting data at a TTL signal of 0.5V in order to measure the initial temperature of the tissue prior to the laser pulse. Prior to each exposure session, the thermocouple–iNet system was self-tested for connectivity, with results stored to disk. The thermocouple relative accuracy and constancy was verified three times during the study by immersion into a water bath at four different temperatures, ranging from boiling to ice water. The water temperature was determined by the average reading of four Barnstead Ever-Safe N16B organic liquid filled thermometers (Thermo Scientific, Waltham, Massachusetts). The thermocouple probe was inserted in the pig skin in the N–S direction.

Direct heating of the thermocouple probe by the 2.0-μm beam rather than the surrounding tissue, considered a significant impact in several laser studies,62, 63, 64 was judged to be negligible in this experiment for three reasons. First, the thermocouple used was considerably smaller than the one used in the Manns study. The 33-gauge needle presents a 0.21-mm diameter as opposed to their 23-gauge needle’s 0.61mm to intercept the direct beam fluence. Second, the 2.01-μm wavelength IR of the Tm:YAG laser does not penetrate to the depth of the needle, as did the 1.06-μm beam of Manns’s Nd:YAG laser.62 For example, consider the difference 1μm of wavelength makes in the two beams’ attenuation coefficient in water. From Hale and Querry, the coefficients are 69.12cm1 at 2000nm but only 0.12cm1 at 1060-nm wavelength.65 Using these attenuation coefficients, weighted by the water content of skin,30, 32 the 2.0-μm beam is reduced to 19% of original intensity by Beer’s law at the 0.3-mm depth of the probe. In contrast, the Nd:YAG beam in the Manns study would still be at 95% at the 5-mm distance to their closest thermocouple. Last, the graphs of skin temperature rise during the laser pulse recorded with this thermocouple did not exhibit the instantaneous temperature jump that has been claimed to be the indication of direct thermocouple absorption of laser beam energy.63, 64


Skin Samples

Pig skin (Sus Scrofa Domestica) was obtained via an agreement with the professional veterinary program at Colorado State University. Approval to utilize tissue samples from these pigs was obtained from the University Institutional Animal Care and Use Committee. Tissue sample disposal procedures were approved by the Institutional Biosafety Committee (IBC) of the Research Integrity and Compliance Office.

Skin samples were excised from the rear flank of pigs within 24h of animal euthanasia. Skin excision was performed in the Veterinary Medicine Anatomy Lab. After identifying a suitable area of skin free of injury or scars, with uniform pigmentation, the hair was removed with electric clippers set to the closest setting that would not scratch the skin. This left hair of approximately 1.5-mm length on the skin. Skin samples of approximately 100cm2 were taken with approximately 0.5cm of fatty tissue thickness. The samples were maintained at 5°C in airtight containers with 1ml saline solution to maintain moisture. Skin samples were handled from the sides and edges to avoid any abrasion or tearing of the surfaces to be irradiated.

Under optical magnification, a 25-gauge , 58-in , hypodermic needle (Becton Dickenson, Franklin Lakes, New Jersey) was used to pierce the surface of the skin and was directed parallel to the skin surface. The HYP-0 thermocouple needle was immediately inserted through the 25-g needle until it extended 10mm past the tip. This method proved to be the most reliable to insert the probe, as the 33-g needle construction of the thermocouple was too fragile to penetrate the skin by itself. The thermocouple insertion is shown in Fig. 1 .

Fig. 1

Needle insertion into pig skin: (a) successful placement of probe; (b) needle has resurfaced.


Insertion attempts were balanced between the goal of positioning the probe at shallow depth and the tendency to penetrate the delicate epidermal tissue from the inside [see Fig. 1]. When this occurred, the needle was withdrawn from the hole and the process begun again 5mm lateral to the ruptured hole site. The sample with the thermocouple inserted was then mounted on the optical translation stage using screws and rubber washers to clamp down a Petri dish containing the skin sample.


Laser and Optics

The pig skin was irradiated with a commercial 50-W Tm:YAG fiber laser (IPG Photonics, Oxford, Massachusetts), producing a 2.01-μm wavelength beam. The laser pulse sequences were created by two model 33120A 15-MHz digital wave form generators (Hewlett Packard, Englewood, Colorado) connected in series to control the duration and number of laser pulses, respectively. A single 10-ms laser pulse was created by setting the first wave form generator to deliver a single 50-Hz square-wave pulse, and offsetting the voltage by half the amplitude, thereby generating a TTL signal that served as a trigger for the laser control. The six pulse sequences were repetitions of the 10-ms single pulses as triggered by the second wave form generator, which was set to the desired PRF (see Fig. 2 for illustration of the multipulse sequence timing). In all sequences, individual 10-ms pulses were fired within a 250-ms period. The 50-W laser was adjusted in power to produce approximately equal total radiant exposures for each sequence.

Fig. 2

TTL signal laser pulse sequences, with duty factors (DFs) and pulse repetition frequencies (PRFs) listed.


The IR laser pulses were aligned to be colinear with a commercial HeNe laser (Model 05-LLR-811, Melles-Griot, Carlsbad, California) using a dual-axis adjustable gold mirror (Model PF20-03-M01, ThorLabs, Newton, New Jersey) with average reflectivity greater than 98% from 1μmto5μm . This HeNe was selected in part for the low divergence of its beam at 1.7mrad in the far field. The HeNe beam was essential to the laser operator for aiming the beam. The colinear beams were then directed into a custom optical articulating arm assembly (Oxid Corp., Farmington Hills, Michigan). This arm used seven articulating joints with gold mirrors to allow both the visible and IR beams to be directed to the measurement site safely. The laser and optics are diagrammed in Fig. 3 .

Fig. 3

Optics path: IR beam is dashed, red positioning beam is gray.


The 2% of the IR beam reflected by the HeNe alignment mirror was measured and recorded for each exposure of the pig skin. The IR laser output from the articulating arm was calibrated to the split beam sample prior to each exposure session. A total of 21 exposures were simultaneously measured by both the sampling probe and another probe placed on the optical stage in place of the skin sample. The beam probes were PM10 air-cooled thermopile sensors (Coherent, Santa Clara, California) calibrated by the manufacturer with an uncertainty of ±1% . The sensors were read by an EPM2000 model meter (Coherent). The meter was also calibrated by the manufacturer with a stated resolution of ±0.03% of full-scale reading. The beam output and sampling data points covered laser settings from 30% to 100% power output and were fit to a straight line with correlation coefficient greater than 0.98 without forcing the intercept to zero. This provided a high confidence in the calculated beam energy for each exposure.

The IR beam incident on the pig skin had a Gaussian shape with a 3.28mm 1e2 radius using a pinhole technique66 in both directions. Beam diameter was measured in both directions on five occasions throughout the study, with a standard deviation of 0.33mm between all results. Beam shape was confirmed to be uniform, circular in the lowest order mode, and aligned with the HeNe beam using Zap-It thermal paper (Kentek, Pittsfield, New Hampshire) prior to each measurement session. Exposures were made on the thermal paper prior to the beam entering the armature and after the beam exiting the arm at the level of the skin sample. The thermal paper impressions were then visually compared to previous sessions’ marks to identify any changes. The thermal paper exposures were performed using a four-pulse sequence with the laser set to 50% power to produce reasonable beam patterns both entering and exiting the articulating arm with the same laser settings.



After the laser exposures were completed, the surface of the pig skin was marked with black ink parallel to the needle from the insertion point to the end of the probe. The HYP-O probe was then withdrawn from the sample and from the 25-g needle. Before the 25-g needle was withdrawn, a 3-cc syringe containing yellow tissue marking dye (Cancer Diagnostics, Inc., Birmingham, Michigan) was connected to the Leur-lock of the needle. As the 25-g needle was withdrawn from the skin, gentle pressure on the syringe injected the dye into the cavity evacuated by the needle. This prevented the cavity from collapsing on itself and rendered it clearly distinguishable under a microscope. The pressure on the syringe plunger was minimal, to prevent the dye from being forced into the surrounding tissue and expanding or rupturing the cavity. The sample was then cut down with 2-mm margins around the ink marks and submerged in the freezing solution, Tissue-Tek OCT (Sakura Fintek, Torrance, California), as shown in Fig. 4 .

Fig. 4

Pig skin after exposure during preparation for freezing: (a) needle insertion marked with ink on left and sample cut out on right; (b) inked and cut sample in OCT solution in labeled freezing cup on right, and OCT for unexposed skin on left.


In order to freeze the sample in a known orientation, the skin was held in place with cotton thread sutured to the edges deep in the muscle layer of the sample. This was necessary to prevent sectioning geometry uncertainty. The sample container was marked with the needle direction and sample number. It was then frozen for 24h at 80°C . The frozen sample was affixed to a ball joint holder with (OCT) solution and mounted in the microtome (Bright Instruments, Huntington UK), as shown in Fig. 5 . The sample was aligned perpendicular to the knife edge and trimmed down until the black ink markings on the surface, indicating the needle insertion, were visible. As soon as the black ink was identified, sections of 15-μm thickness were cut and mounted on slides. Digital images were taken of the slides at 4× magnification on a BH2 microscope (Olympus, Center Valley, Pennsylvania), as shown in Fig. 6 . Depths were measured on the images to the center of the dye-stained hole using Spot software version 4.09 (Digital Instruments, Inc., Sterling Heights, Michigan). Measurements from the four distal images showing the probe cavity were averaged with a maximum standard deviation of a sample being 0.065mm at the 0.650-mm depth. The distance measurement function of the Spot software was calibrated for the 4× lens with a digital test pattern, Model USAF1951 (Edmund Optics, Barrington, New Jersey).

Fig. 5

Pig skin sample frozen in OCT mounted in the microtome. Notice the black ink marks visible on the surface (horizontal arrows) and the large yellow dye spot (vertical arrow) from excessive pressure on the syringe during needle withdrawal. (Yellow dye from successful injection yields inadequate contrast to identify in photographs.) (Color online only.)


Fig. 6

Histology image of pigskin showing the dye-marked thermocouple probe hole (arrow) and the ink marked surface. (Ink appears brown in the two valleys on either side of the hole.) (Color online only.)



Data Analysis

Temperature for each exposure was measured simultaneously both at depth and on the surface. The relative temperature rise per exposure in °CmJ1mm2 was calculated. In the case of the thermocouple temperature, baseline was taken as the first data point. The thermal camera was set to take 20 data points prior to the exposure for background subtraction.

The maximum temperature rise per exposure (Δ°CmJ1mm2) for each pulse sequence was examined with an analysis of variance (ANOVA) to determine whether any differences existed between the pulse sequences. The data were then compared with Fisher’s least significant difference (LSD) procedure to find which sequences produced a different temperature rise at the 95% confidence level.

The measured temperatures were then compared to expected temperatures calculated with an adaptation of the Green’s function solution to the tissue bioheat differential equation from Vyas and Rustgi [Eq. 3].40 As there was no blood flow in the pigskin samples, the first exponential term from the published solution is one and is dropped. The second exponential term from Vyas and Rustgi is also one for these central axis (r=0) temperatures, and is therefore omitted. For the multiple-pulse exposures, the calculated temperatures from the individual pulses were summed at the end of the pulse sequence. The Vyas solution was chosen over the Grossweiner 39 or the Roider 26 solutions, as it describes the temperature in both the depth and radial directions with time:

Eq. 3

In Eq. 3, μa is the optical absorption coefficient for the tissue, Eo is the energy deposited, ρ is the tissue density, C is the specific heat capacity, a is the laser beam 1e2 radius, D is the tissue thermal diffusivity, z is the depth in tissue, and t is the time. The literature provides a wide range of values for the thermal constants for skin tissue, as listed in Table 2. The constants used in this study were as follows: μa=2.176mm1 (Ref. 32); ρ=0.00107gmm3 (Refs. 55, 61); C=3.4Jg1°C1 (Ref. 55); D=0.12mm2s1 (Refs. 40, 60); and the beam radius a=3.2mm . These values were chosen because they fall near the middle of the range of published values and the diffusivity value was also used by Vyas and Rustgi.



The temperature of pig skin was measured simultaneously on the surface and at depth during six different pulsing sequences of 2.0-μm laser exposure. Four measurements of each sequence on three different skin samples produced at least 12 data points for each sequence at depths of 300μm , 400μm , and 650μm . The IR camera provided surface temperature readings during each irradiation. The measurements produced repeatable temperature increases per incident exposure with the maximum variance of a data group at 0.013°CmJ1mm2 for the single-pulse (duty factor 0.04) surface data. The depth of measurement was determined by histological examination of the irradiated skin with a maximum variance of 0.004mm , attributed to the irregular surface of skin within a sample. The measurements were compared to expected temperatures calculated with an analytical expression.


Temperature Rise per Exposure—Measured

The temperature rise per H in °CmJ1mm2 was measured at four depths in pig skin using six different laser pulse patterns. The measured results, shown in Fig. 7 , reveal a different pattern on the surface at low duty factor compared to the measurements below the optical penetration depth. As the duty factor increases, the temperature rise per exposure levels off.

Fig. 7

Graph of measured temperature rise per exposure at four depths in pig skin versus duty factor of the pulse sequence.



Temperature Rise per Exposure—Calculated

The difference between the temperatures calculated using the Vyas equation for the pulse sequences under consideration and the corresponding measured temperatures are shown in Fig. 8 . Here, the surface temperature calculated was dramatically less than the measured temperature for all but the single-pulse sequence. Below the surface, the temperatures calculated from the model were higher than the measured results. The calculated temperatures at 0.4-mm depth were 5to10degrees higher than measured. This corresponds to the measurements at 0.4mm , being equivalent to the temperatures at 0.65mm seen in Fig. 7. Calculated temperatures at 0.65-mm depth matched the measured temperatures reasonably well for all duty factors. The model results gave maximum temperatures at depths between 90μm and 170μm , as shown in Fig. 9 .

Fig. 8

Difference between calculated and measured temperature rise for exposures used in study. Calculation maximum temperature and calculated zero depth temperatures are compared to IR camera measurements, while temperatures at depth relate to thermocouple measurements. The depths of the calculated maximum temperatures are given in Fig. 9.


Fig. 9

Calculated skin depth of maximum temperature from exposure to TmYAG laser.



Statistical Analysis

Comparing the measured temperatures per exposure between the different pulse sequences, the ANOVA showed that there were significant differences between pulse sequences at each depth at the 95% confidence level. A summary of the p -values and variance within each group are given in Table 5 .

Table 5

ANOVA results.

Depth p -value Sw2
Surface 1.47×1023 0.00874
300μm 0.0009140.00875
400μm 0.0008520.00290
650μm 8.07×1010 0.00073

The LSD procedure performed for each depth showed that the differences were between the low duty factor sequences and the high duty factor sequences. The relations between sequences are given in Tables 6, 7, 8, 9 for depths from surface to 650μm . Within each depth’s table, the italicized results indicate that the two sequences produced insignificantly different temperature rise per unit exposure to 2.0-μm laser irradiation. The bold values were found to be statistically different from each other.

Table 6

Significant difference in temperature per exposure at surface (significant differences in bold; differences less than Fisher’s LSD, 0.031, in italics).

Pulse sequence1 pulse2 pulse3 pulse4 pulse9 pulse25 (CW)
1 pulse 0.16 0.14 0.13 0.07 0.04
2 pulse0.
3 pulse0.14 0.02
4 pulse0.13 0.02 0.01 0.070.17
9 pulse0.07 0.09 0.07 0.07 0.10
25 (CW) 0.04 0.19 0.18 0.17 0.10

Table 7

Significant difference in temperature per exposure at 0.30mm (significant differences in bold; differences less than Fisher’s LSD, 0.054, in italics).

Pulse sequence1 pulse2 pulse3 pulse4 pulse9 pulse25 (CW)
1 pulse0.
2 pulse 0.03
3 pulse 0.06 0.03
4 pulse 0.07 0.05 0.01 0.050.08
9 pulse 0.12 0.09 0.06 0.05 0.03
25 (CW) 0.15 0.12 0.09 0.08 0.03

Table 8

Significant difference in temperature per exposure at 0.40mm (significant differences in bold; differences less than Fisher’s LSD, 0.031, in italics).

Pulse squence1 pulse2 pulse3 pulse4 pulse9 pulse25 (CW)
1 pulse0.
2 pulse 0.01
3 pulse 0.03 0.02
4 pulse 0.04 0.03 0.01 0.020.05
9 pulse 0.05 0.05 0.02 0.02 0.03
25 (CW) 0.09 0.08 0.06 0.05 0.03

Table 9

Significant difference in temperature per exposure at 0.65mm (significant differences in bold; differences less than Fisher’s LSD, 0.015, in italics).

Pulse sequence1 pulse2 pulse3 pulse4 pulse9 pulse25 (CW)
1 pulse0.
2 pulse 0.03
3 pulse 0.04
4 pulse 0.04 0.01
9 pulse 0.06 0.03 0.03 0.02 0.02
25 (CW) 0.09 0.05 0.05 0.04 0.02

The different pulse sequences were found to produce statistically different temperature rise per total exposure at all four depths, with p -values less than 0.001 from ANOVA results. At all depths, the two-pulse, three-pulse, and four-pulse sequences were equivalent. The 300-μm and 400-μm depths produced temperatures that were not significantly different from the temperature rise produced between adjoining sequences.



The temperature rise per exposure on the surface was found to follow a different trend at low duty factor (single pulse) than the temperatures measured at depths below the surface. The measurements below the surface represent direct heating as well as heat flow from tissue above. The increase in temperature appears to rise as the duty factor increases for depths below the surface. In contrast, from the IR camera measurements, this trend does not hold for the single-pulse (low duty factor) sequence on the surface.

However, as seen in Fig. 8, the calculated temperatures using the Vyas model demonstrate that the model was very good at predicting temperature for 650-μm depth for all duty factors from one pulse up to CW. The model’s predicted temperatures were 5°to10°C high for the 400-μm depth for all duty factors, with the largest difference at the medium duty factor of 0.16. The linear superposition of multiple pulses exaggerated the model’s difference from measured temperature. At a 300-μm depth in skin, the calculations were within 1° for duty factors of 0.16 and higher, but increasingly diverged to 7°C from measurements at lower duty factors. This was unexpected from this model, which was originally validated with microsecond pulse widths.

The Vyas model did not predict surface temperatures well. At shallow depths, either exact skin surface (z=0μm) or at the depths of calculated maximum temperatures, the model underestimated temperature rise. The Vyas model was best at predicting temperatures for the smallest duty factor (0.04). The predicted temperatures fell significantly below measured temperatures by approximately 5to7°C for the middle duty factors (0.08 to 0.16). As the duty factor increased to 0.36 and above, the model underestimated the temperatures by 10°C . At the calculated air–skin interface (z=0μm) , the predicted temperatures were 6°C lower, while following the same pattern with duty factor. The agreement of measurements to calculated temperatures near, but not at, the air–skin interface indicated that the IR camera’s microbolometer is responding to IR emitted by a region below the skin surface. The Vyas model produced maximum temperatures at increasing depths between 90μm and 170μm , as seen in Fig. 9. The disagreement between the model and the measurements becomes larger as the maximum temperature occurs deeper in the skin. This discrepancy is most significant because it occurs in the region of the basal layer of the epidermis in human skin.

The analysis of measured temperature rise per exposure between pulse sequences of different duty factors showed a significant difference between some of the sequences, but not the same ones at different depths. For the surface and 650-μm depths of Tables 4, 7, the measured rise per exposure was found to be statistically different between any combination two sequences, including one with a duty factor of 0.04 or above 0.36. The single-pulse, the nine-pulse, and the CW irradiations were different from any other sequence. At 300-μm and 400-μm depths in Tables 5, 6, the single-pulse sequence was equivalent to the double-pulse sequence, but different from all higher duty factors. The 300-μm and 400-μm depths were unique in the temperature rise per exposure relations between sequences of higher duty factor. At 300-μm depth, a sequence with duty factor of 0.36 was equivalent to both a CW irradiation and a pulse sequence with duty factor of 0.16. At 400-μm depth, a sequence with duty factor of 0.36 was different from the CW irradiation but equivalent to both a 0.16 and 0.12 duty factor sequence. Therefore, while there were several combinations of pulse sequence, duty factors producing equivalent temperature rise per radiant energy, only the nine-pulse sequence with duty factor 0.36 heated the tissue the same as a CW beam at 300μm . At all depths then, the pulsed beams produced lower temperatures per radiant exposure than did the CW beam for equivalent energy input.

The maximum temperatures measured at the 400-μm and 650-μm depths were virtually the same for all duty factors, all within one standard deviation. By a simple Beer’s law calculation, there is at least an order of magnitude difference in incident beam energy at these two depths. Chen’s attenuation coefficient of 21.76cm1 gives the closest beam intensities at depths of 400μm and 650μm from among the various attenuation coefficient values from Table 1. This attenuation coefficient used in Vyas’s model also predicted temperatures closest to the measurements. Therefore, there appears to be rapid heat transfer in the axial direction to bring the deeper measurements to the same maximum temperature. However, the significant differences between pulse sequences of 0.36 duty factor at 650μm that are not found at 400μm indicate that the heat flows fast enough to distinguish each separate pulse at duty factors between 0.04 and 0.36. The differences in temperature normalized to radiant energy indicate that the assumption of linear superposition of successive pulses does not represent the thermal dynamics of pulsed irradiation of skin for pulse sequences with duty factors between 0.04 and 0.36 at depths from the surface to 650μm , roughly the middle of the dermis. The ANSI Z136.1 limit of radiant exposure for 250-ms pulse sequences of 2.0-μm IR is MPE=0.56×0.25000.25=0.396Jcm2 , which is roughly 10 times less than the maximum exposure of 3.17Jcm2 delivered in this study. It is worth noting that while the exposures delivered in this study were very close to the ED50 levels of Chen 5 for in vivo pig skin ( 3.6Jcm2 and 2.9Jcm2 for beams of radii of 2.4mm and 4.8mm , respectively), no reddening of the ex vivo skin was observed. Furthermore, the maximum absolute temperature increase recorded was 36.2°C from the IR camera surface measurement of an exposure sequence with 0.16 duty factor. The maximum temperature increase for any one exposure beneath the surface was 20.7°C above background for a 0.16 duty factor sequence at 300-μm depth. This increase is over twice Moncrief’s “brief” temperature tolerated by skin, yet even with no vascular heat removal, no damage was observed visually or on the histology slides. Therefore, the ANSI Z136.1 limitations for skin exposure are shown to be inherently conservative, as they do not apply the Rule 3 correction factor based on number of pulses to skin. However, a correction factor based on pulse sequence duty factor may be appropriate in this region of the far infrared.

The differences in temperature rise per unit exposure between the pulse sequences can be explained by significant heat conduction during the pulses. Therefore, the common assumption of thermal confinement may need to be experimentally verified.


The views expressed in this article are those of the authors and do not reflect the official policy or position of the U. S. Air Force, The Department of Defense, or the U.S. Government. We want to acknowledge and thank Dr. Robert E. Lee, Antonio Serpa, and Aimee Oke for their generous support and expertise.



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©(2010) Society of Photo-Optical Instrumentation Engineers (SPIE)
David N. Schaaf Jr. and Thomas E. Johnson "Relationships of skin depths and temperatures when varying pulse repetition frequencies from 2.0-µm laser light incident on pig skin," Journal of Biomedical Optics 15(4), 045007 (1 July 2010).
Published: 1 July 2010

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