University of Ljubljana

Faculty of mathematics and physics

Department of physics

MODELLING AND MEASUREMENTS OF

LASER-SKIN THERMAL INTERACTION

GRADUATE SEMINAR

Martin Gorjan

ADVISER: prof. dr. Martin Copic∗†

CO-ADVISER: dr. Marko Marincek§†

26th February 2008

Abstract

Thermal laser-skin interaction has principal role in laser dermatology, and it can besuccessfully modelled and measured. For modelling, the seminar covers all the steps in-volved, which range from determination of laser beam and skin optical properties, treat-ment of light propagation in the tissue, thermal diffusion of heat to thermal effects pre-diction. As a simple and efficient mean for measuring the thermal interaction, thermalimaging is introduced. The seminar concludes with some recent results and comparisonbetween modelling and measurements obtained at Fotona.

∗Faculty of mathematics and physics†Jozef Stefan Institute§Fotona d.d.

Contents

1 Introduction 3

2 Laser 42.1 Laser beam characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Skin 53.1 Skin optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Modelling light propagation 74.1 Photon transport theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1.1 Monte-Carlo simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 74.1.2 Calculated absorbed light distributions . . . . . . . . . . . . . . . . . . 8

5 Modelling thermal interaction 105.1 Estimation of thermal interaction effects . . . . . . . . . . . . . . . . . . . . . 105.2 Thermokinetic selectivity theory . . . . . . . . . . . . . . . . . . . . . . . . . 11

5.2.1 Calculated TRTs and temperature evolutions . . . . . . . . . . . . . . 12

6 Measurements of skin temperature 126.1 Measured temperature distributions . . . . . . . . . . . . . . . . . . . . . . . 13

7 Conclusion 15

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1 Introduction

Soon after the first laser was conceived in early 1960s, its great potential for certain medicalapplications was recognized. The qualities of laser light make it possible to deliver big amountsof optical energy to small targets on the surface or below the surface. The energy that isabsorbed by the tissue can change its properties in a way that was found to be beneficial inmany fields of medicine. Today, the use of lasers is already an established practice, amongothers, in ophthalmology, dentistry and dermatology.

The exact details of all the effects a laser beam can have on the tissue and their causingmechanisms are still being elusive. The complexity of living tissue structure and workings[1] reflects in the intricacy of laser-tissue interactions. Nevertheless, much progress has beenmade in both directions: many physiological effects were observed and catalogued [2], whilefive major interaction mechanisms were identified and explained [3], some have even beensuccessfully modelled [4]. Overview of the thermal interaction, for its pivotal role in laserdermatology, which is an important part of Fotona’s market share, is the topic of the presentseminar.

Thermal effects of a laser beam incident upon the skin can be predicted knowing full timedependence of temperature distribution within the skin. Calculating it requires modellingof the two processes: light propagation through the tissue, as the absorbed light producesheat, and thermal diffusion of the heat from exposed to surrounding tissue. Presuming thatthe skin’s optical parameters don’t change during laser pulse duration, both processes can betreated separately. [5, 6] The first is effectively done with the so called photon transport theory[7], which is covered in fourth chapter. The latter is described by the heat equation. Its specialapplication, a theory known as thermokinetic selectivity [8], commonly used to account forthermal effects on skin small structures like vascular lesions, hair papilla [9], pigment clusters[10, 11], tattoo particles [12], and others [13], is covered in the fifth chapter. In order toaccount for the photon propagation in the skin, both laser beam and skin optical propertieshave to be known [14], so these are covered in the previous two chapters. Finally, thermalimaging as an effective technique for measurements of skin temperature [15, 16] and also forestimation of optical and thermal parameters [17, 18], is presented in the last chapter.

Figure 1: A map of laser-skin thermal interaction study.

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2 Laser

LASER1 light is produced in a laser device via selective amplification of light by stimulatedemission of radiation. The nature of light generation along with the presence of laser resonatorgives the laserlight some unique properties: it has very well defined frequency (monochromac-ity), high spatial coherence and low divergence, meaning it can propagate in a well definedbeam. Consequently, its exceeding power per area per solid angle and per wavelength or spec-tral radiance dJ

dλ = d3PdS dΩ dλ makes it capable of delivering great amounts of energy to small

spots and small parts of light spectra, which is very convenient for a range of medical andmany other applications. [19]

2.1 Laser beam characterization

Laser beams can be adequately characterized by a few parameters [19], which influence thebeam propagation in the tissue and also determine the type of interaction taking place (moreon interactions follows in Sec. 5) [3].

Beam wavelength λ is determined by the laser media, which usually also gives commonnames for lasers. The most important medical lasers are solid-state: neodymium yttrium-aluminium-garnet (Nd:YAG) operating at λ = 1064 nm, frequency doubled Nd:YAG withλ = 532 nm, erbium YAG (Er:YAG) with λ = 2940 nm, alexandrite at λ = 755 nm andruby at λ = 694 nm. Other important examples are gas CO2 operating at λ = 10.6 µm andvarious diode lasers operating between λ = 800− 1000 nm. [8]

The spatial character of the laser beam is usually described by the transverse electromag-netic (or TEM) family of modes, with Gaussian beam (or TEM00, see Fig. 2a) being thediffraction limit for given wavelength. [19] However, because of heavy scattering in the tissue(more on it in Sec. 3.1), the beam angular characteristics are effectively randomized immedi-ately upon entering. Only the spatial energy distribution of the beam remains important - itcan be expressed as the spot size and spot shape. [7]

Beam temporal character or pulse width is determined by the operating regime of thelaser and with given size of laser media is closely connected with its peak power. A varietyof regimes can produce pulses with vastly different widths and peak powers, as schematicallydepicted on Fig. 2a. Medical continuous wave (cw) lasers typically operate up to some watts.Quasi-cw lasers, which use pulsed pump sources, can produce pulses from microseconds tomillisecond widths, with typical peak powers of some kilowatts. Q-switched lasers modulatethe resonator losses so that all the energy stored in laser media is released in a few round-trip times, producing pulses of nanosecond lengths and peak powers in the megawatt range.Mode-locked lasers, where phases of many oscillating axial modes are matched, can produceextremely short pulses of a few femtoseconds in duration and corresponding peak power ofgigawatts and more. [19]

1The word is an acronym for Light Amplification by Spontaneous Emission of Radiation

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Figure 2: a Spatial parameters of laser beam are its angular (green) and radial (dark green) distribution

of power; for Gaussian beams, the first depends on wavelength, waist size (w0) and divergence (θ), the

latter follows a Gaussian distribution. b Temporal parameters of laser beams are chiefly determined by the

laser operating mode: continuous wave (blue), free-run (red), Q-switched (green) and mode-locked (voilet)

produce pulses of vastly differing durations and peak powers.

3 Skin

Skin is the human body’s largest organ, measuring ∼ 2 m2 and weighting ∼ 5 kg. It is made oftwo distinct layers, the outer epidermis and inner dermis. Below the dermis lies subcutaneouslayer, composed of proteins and adipose tissue (fat), but is not part of the skin itself. Fig. 3aschematically shows the layered structure of the skin. [1]

Epidermis is again made of four to five layers, together measuring around 100 µm. Theyare made of keratinocytes, the cells which produce fibrous protein keratin, and compose 90%of the epidermis. Deeper layers are made of younger cells, which gradually travel outwards,transforming into a hard protective layer along the way. Scattered between the keratinocytesare melanocytes, cells producing the pigment melanin, skin’s main light absorber. Packets ofit are called melanosomes and their main function is to protect the keratinocytes from UVlight coming from the Sun. All people have roughly equal number of melanocytes, but theyproduce different amounts of melanin. Its distribution can also vary (e.g. forming freckles,patches and age spots), hence different skin colors. [1]

A much thicker dermis (∼ 1 mm), unlike the epidermis, is richly supplied with bloodand nerves. Most of the dermis, around 75%, is made of two proteins: collagen and elastin,providing skin’s strength and elasticity. There are many structures in the dermis: tiny loopsof blood vessels with important role in regulation of body temperature, glands, receptors forvarious stimuli, and hair follicles. Hairs protruding from hair follicles are made of keratinwhile melanin gives them color. The heavy presence of blood provides yet another importantpigment, hemoglobin, which is by contrast extremely scarce in the epidermis. [1]

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Figure 3: a Skin has a layered structure of epidermis and dermis, with many small structures embedded.

b Absorption spectra of the skin’s main absorbers: water (blue), melanin (brown) and hemoglobin (red).

Also shown are wavelengths of some important dermatological lasers.

3.1 Skin optics

The absorption in biological tissues is mainly caused by water molecules, proteins and pig-ments. [3] Due to absorption, light intensity decreases with depth according to Beer-Lambertlaw I(z;λ) ∝ e−µa(λ)z, absorption coefficient µa being wavelength dependent. Water stronglyabsorbs above 2 µm with the strongest peak at 3 µm, proteins have a peak absorption in UV(280 nm), leaving pigments dominating the visual and NIR (400 - 2000 nm). Fig. 3b showsthe absorption spectra of water and the body’s two main absorbers, pigments melanin andhemoglobin. Because of the variations of melanin among individuals, the combined absorp-tion coefficient of the skin varies as well; for caucasians at Nd:YAG wavelength it is ∼ 0.1cm−1. [3]

Skin is also a heavy scatterer: its scattering coefficient µs being somewhere between10 and 100 cm−1. Due to its structural diversity, the contributions to scattering are two-fold: atoms and molecules themselves scatter light according to Rayleigh theory, where thescattered intensity Is is inversely proportional to fourth power of light’s wavelength accordingto IS ∝ 1+cos2θ

λ4 ; θ is the deflection angle. The collagen fibers and other structures, havingsize comparable to light’s wavelength, scatter according to Mie theory instead. Scatteredintensity follows a much weaker wavelength dependance IS ∝ λ−x, x being between 0.4 and0.5; scattered direction is mostly forward. The observed scattering in the skin is indeed mostlyforward, but neither of the two theories adequately explain it. [7]

Many special empirical scattering (or phase) functions were introduced instead to fit themeasured data and describe the angular probability after the scattering ”event”. They can beused together with the scattering coefficient, stating the probability for the scattering event,and absorption coefficient, to model light propagation in the skin or other tissues. [4]

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4 Modelling light propagation

The most fundamental approach on calculating light propagation is based on physics ofMaxwell’s equations. However, because of the complexities involved, such approach can be oflimited applicability. [7] Due to its simplicity, universality and good practical results, photontransport theory is frequently used instead. [3]

4.1 Photon transport theory

A beam of light is described with its radiance J(r, s), expressing the power at the position rflowing in the direction s. Radiance is governed by the radiative transport equation as follows

dJ(r, s)ds

= −µtJ(r, s) +µs

4π

∫4π

p(s, s’)J(r, s’)dΩ′. (1)

Radiance J(r, s) is being diminished proportionally to the total attenuation coefficient µt =µa + µs which is a sum of absorption and scattering attenuation coefficients. On the otherhand, radiance J(r, s) is being augmented by the light scattered from direction s’ to directions, magnitude of which is described the phase function p(s, s’). Commonly used is a Henyey-Greenstein phase function, which can be expressed as [7]

p(s, s’) = p(θ) =µs

µt

1− g2

(1 + g2 − 2gcosθ)32

, (2)

depending on the average cosine or anisotropy factor g = cos θ: g = 1 denotes purely forwardscattering, g = −1 purely backward and g = 0 isotropic scattering. Most tissues are mainlyforward scattering; for skin g was found to be around from 0.8 to 0.9. [3, 4]

Radiative transport equation is difficult to solve directly and many approximations exist,among others the Kubelka-Munk, inverse adding-doubling and the diffusion approximation.Since the mean free path of the light propagating in skin is much smaller than the typicaldimensions involved, propagation quickly becomes effectively random. [7] The Monte-Carlosimulation is then the preferred method for numerically solving the radiative transport prob-lem. [3, 4]

4.1.1 Monte-Carlo simulations

In Monte-Carlo simulation the laser beam is represented as a stream of a large number N

of ”photons”, each having the coordinate, direction and and energy weight. Each photon isstatistically ray-traced through tissue following five steps (depicted on Fig. 4):

1. Photon generation: Initial location and direction of propagation are randomly de-termined according the original beam.

2. Pathway generation: Path to the next event is determined: the direction of propa-gation is determined according to the phase function p(θ). The traveled distance ∆r

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is determined by choosing a random number ξ between 0 and 1 and using logarithmicdistribution

∆r = − log(ξ)µt

. (3)

3. Absorption: The photon energy weight E is decreased after each event according toabsorption and scattering coefficient

∆E = −µa

µtE. (4)

4. Elimination: When the photon energy weight goes below some predetermined thresh-old, its propagation is terminated and a new photon is launched.

5. Detection: The absorbed energy ∆E is registered at the event coordinates after eachevent.

At the end of procedure a three-dimensional distribution of absorbed energy is produced.More details of Monte-Carlo algorithm implementation for light propagation through skin canbe found in [6, 20].

Figure 4: a Schematic representation of Monte-Carlo simulation steps of laser beam propagation in skin.

It consists of five steps (see text above): 1 - photon generation, 2 - pathway generation, 3 - absorption,

4 - elimination and detector count. Black dots represents scattering events and blue squares detector cell

counts. Grid size is exaggerated for clarity. b Side view of actual calculation for N = 100 photons.

4.1.2 Calculated absorbed light distributions

We used optical ray-tracing program Zemax, which features a highly efficient Monte-Carloimplementation, to obtain the distributions of absorbed light. Simulation consisted of threelayers of skin (epidermis, dermis and subcutaneous tissue) hit by Nd:YAG, λ = 1064 nm laserbeams. Distributions of absorbed light were calculated for various spot sizes of square (or”top-hat”) collimated beams. We observed the absorbed power densities at the surface andin the depth for each spot size and also intraspot variations on the surface. The calculated

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distributions are presented for 4 mm spot size. On the surface distribution (Fig. 5a) the scat-tering ”tails” can be observed, while the depth distribution reveals penetration depth (Fig.5b). Interestingly, aplot of maximum power densities versus spot size reveals strong depen-dence and saturation effect (Fig. 5c), which is explained by the fact that the scattered ”tail”is somewhate invariant to the spot size, making ratio of scattered energy inversely propor-tional to spot size. Similar reasoning can be applied for spot-size dependence of penetrationdepth (Fig. 5d). Furthermore, because optical parameters of skin are strongly wavelengthdependant (see Sec. 3.1), laser wavelength as well as the skin type, i.e. its absorption andscattering coefficients, are also of essential importance in determining the beam penetrationdepth.

Figure 5: Calculated absorbed light distribution cross-sections for 4 mm diameter beam viewed from a top,

where scattering ”tails” can be observed and b side, where strong absorption in epidermis is evident. Both

c average superficial absorbed power density (horizontal line in a) and d penetration depth (vertical line in

b) significantly depend on beam diameter.

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5 Modelling thermal interaction

Light that is absorbed in tissue can induce many light-tissue interactions. Five such in-teractions are empirically classified today. Two governing parameters, which determine theinteraction, were identified: the peak power density and exposure time, which can simply beequated with the pulse duration. [3] The five interaction zones are depicted on Fig. 6a.

Figure 6: a Circles roughly represent regions of five laser-tissue interaction mechanisms that are classified

today. Main determining parameter is the pulse duration (with interdependent power density), while total

deposited energy is of lesser importance and mostly lies between 1 J and 1000 J. b For irreversible thermal

effects to take place, the duration of the elevated temperature is important as well. Red line is empirically

estimated critical temperature.

5.1 Estimation of thermal interaction effects

Thermal interaction is itself a family of biological effects following tissue exposure to increasedlocal temperatures. The irreversible cell effects range from hyperthermia (at 45 C), reductionin enzyme activity and cell immobility (at 50 C), denaturation of proteins and coagulation(at 60 C), vaporization and thermal ablation (at 100 C) to carbonization (> 150 C) andfinal melting (> 300 C). [3]

The duration of the elevated temperature is important as well. Correlation of criticaltemperature and exposure time τ can be estimated by Arrhenius type damage integral [4]

ln

(C(0)C(τ)

)= Γ

∫ τ

0e− Ea

RT (r,t) dt, (5)

using ratio of initial and final concentrations of native cells as the measure of damage. The twoparameters, frequency factor Γ and activation energy Ea, must be experimentally obtained byobserving optical or histological changes of the irradiated tissue. A plot of critical temperatureversus duration of exposition is shown on Fig. 6b. [3]

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5.2 Thermokinetic selectivity theory

Once distribution of absorbed light is obtained as presented in Sec. 4, the full time evolutionof temperature in irradiated and surrounding tissue can be modeled by the 3D heat equation

∂T (r, t)∂t

=k

ρcp∇2T (r, t) +

j(r, t)ρcp

, (6)

using calculated absorbed power density j(r,t) as the heat source; its temporal part is deter-mined by the laser pulse evolution with time. Skin thermal parameters are contained in thethermal conductivity k and volumetric heat capacity ρcp of the skin.

Temperature increase in skin’s stronger absorbing structures can be much higher thanthe bulk temperature raise, depending on the particle absorption coefficient, its depth, sizeand laser pulse duration. [8, 4] A theory designated as thermokinetic selectivity exposes thestrong correlation between particle size and its thermal relaxation time (TRT ). [8] A one-dimensional model of spherical heat source (depicted on Fig. 7b) is used to calculated theTRT and temperature evolution with time depending on laser pulse duration. The governingequation for difference between particle and surrounding tissue temperature ∆T is then

∂T (r, t)∂t

=k

ρcp

∂

r2∂r

(r2 ∂T (r, t)

∂r

)+

a j(x, t)ρcp

, (7)

where a is the absorption ratio of a small structure versus bulk skin and j(x, t) the calculatedlaser intensity at depth x multiplied with the pulse temporal function. Thermal relaxationtime (TRT ) depends only on skin thermal diffusivity k

ρcpand particle radius r0, while obtain-

ing actual temperatures also requires knowing a j(x, t).

Figure 7: a Skin is an inhomogenous tissue, having embedded many small structures like melanosomes (1),

hair follicles (2) and vascular lesions (3). b Their temperature increase due to laser irradiation is treated

with thermokinetic selectivity theory, where small structures are represented as small source of radius r0

embedded in sphere of skin with radius R >> r0.

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5.2.1 Calculated TRTs and temperature evolutions

By definition thermal relaxation time is the time it takes a particle at initial high temper-ature T0 to cool down to T0/e. I’s proportional to the second power of particle’s radiusTRT [µs] ∼ r2[µm2]. [8] Laser pulses with durations shorter than particle’s TRT cause maxi-mum temperature raise, on the contrary, pulses with durations much longer than TRT don’tchange its temperature significantly, as can be seen on Fig. 8. The laser pulse duration isthus a crucial selectivity parameter when targeting small skin ”imperfections”.

Figure 8: Time evolution of temperature difference in 10 µm particle with TRT ∼ 100 µs, irradiated with

pulses of different durations and same energy density 1 J/mm3, leads to significantly different temperature

differences.

6 Measurements of skin temperature

Infrared (or thermal) imaging is the method of choice for fairly accurate, fast and non-contact measurements of temperature distributions. It can be used to obtain in vivo timedependent temperature distributions from skin surface. [15, 16] Moreover, using the model-based parameter estimation by setting such model parameters for solution to fit the measuredtemperature spatial distributions or temporal course, some structural and optical parameterstogether with their uncertainties can be estimated. [17]

In order to get quality images with well-defined timings, laser pulse and camera frame-taking must be exactly synchronized. Two general techniques of measurement are possible asdepicted on Fig. 9a:

1. Immediately after laser pulse an usual recording is triggered. Each frame is taken sothe frame-rate determines the temporal resolution ∆tf = 1

FPS

2. Only the first frame after the laser pulse is taken. Repeating the measurement by varyingthe delay between the laser pulse and camera frame taking time, temporal resolutionsmuch lower than ∆tf can be reached.

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Figure 9: a Every frame (black high) can be taken immediately after laser pulse (green high) is triggered

and the frame-rate determines resolution ∆tf . Conversely, only the first frame after the laser pulse is

taken. The delay between them roughly determines the resolution ∆tp instead. b Thermovision camera

(yellow) with IR optics (blue) was used to record distributions of skin surface temperature after laser pulse

irradiation (green) emerging from a handpiece (grey).

6.1 Measured temperature distributions

We employed both techniques using a thermovision camera with spatial resolution of 320 by240 pixels, frame-rate of 50 Hz interlaced and detector integration time of 1.5 ms in a set-upas depicted schematically on Fig. 9b. The composite video output from the camera was usedfor recording while its sync part was used for triggering the Nd:YAG laser. Pulse durationsranged from 100 µs to 2 ms. By overlapping the camera integration time with the laser pulseand varying the delay as shown on lower part of Fig. 9a, temporal resolution ∆tp of less than100 µs was reached. Laser light was delivered to skin on arms of three different people by anoptical fiber ended with handpiece, which determined the beam shape and spot size.

Surface temperature evolution following a single pulse (shown on Fig. 10) reveals timescaleof skin surface cooling. The presence of hot-spots due to skin inhomogenity is clearly visibleon the first frame. Fig. 11 shows skin temperatures obtained with different spot sizes andthe same fluence of 40 J/cm2 where spot dependence can be noted. Fig. 12 shows skintemperatures obtained with same spot size and fluence of 40 J/cm2, but on different people.The role of local skin type is apparent.

Additional data can be extracted with some computer image analysis. Assuming circu-lar symmetry and rolling out hot-spots, the angular average of surface temperature (shownFig. 13a) reveals scattering ”tails”, which can be used to validate the scattering parameters:coefficient µs and anisotropy factor g. The evolution with time (not shown) further revealsthe cooling direction, which is mainly vertical. Average spot temperature versus spot size(Fig. 13b) show strong dependence with saturation around spot diameter of 6 mm, which isin decent agreement with calculations (Fig. 5c). Measured temporal evolution of the aver-age spot temperatures agree very well with the calculated ones (Fig. 13c), found by solvingplanar heat equation with initial temperature distribution obtained from the Monte-Carlo

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simulation. By using model-based parameter estimation, it appears that the relaxation timeof the fast part (∼ 20 ms) is mainly determined by epidermis thickness, the relaxation timeof the slow part (∼ 10 s, not shown) by penetration depth and the ratio of amplitudes by theratio of epidermis/dermis absorption coefficients. Finally, probing for relaxation time of skinhot-spots (Fig. 13d) gives a rough estimate of less than 100 µs, meaning their size is in therange of 10 µm.

Figure 10: Skin surface temperature evolution after irradiation with a pulse of collimated Nd:YAG laser

beam with 4 mm spot size.

Figure 11: Skin surface temperature immediately after irradiation with a pulse of collimated Nd:YAG laser

beam with different spot sizes.

Figure 12: Skin surface temperature immediately after irradiation with a pulse of collimated Nd:YAG laser

beam on different people.

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Figure 13: a Angular averaged temperature of skin surface immediately after laser pulse. b Spot averaged

temperatures of skin surface for different spot-sizes and same fluences. c Temporal evolutions of skin

temperature measured with direct recording agree well with calculated ones. d Temporal evolutions of

hot-spots measured with pump-probe technique gives estimation of relaxation time.

7 Conclusion

A basic overview of studying the thermal laser-skin interaction, which is an essential part oflaser dermatology, was given in the seminar. All the steps from laser beam characterization,skin optical properties determination, light propagation in the tissue, thermal relaxation timeand damage modelling were concisely covered. Thermal imaging was presented as a measuringmethod, which can be used to validate the models, determine the skin properties or tunelaser application parameters. Additionally, some calculated as well as measured results werepresented with good agreement obtained between them.

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