ORIGINAL RESEARCH REPORT

Laser fractional photothermolysis of the skin: Numerical simulation of microthermal zones

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Mohamad Feras Marqa1,2,3 & Serge Mordon1,2,3 1INSERM

(French National Institute of Health and Medical Research) U703, 2Université de Lille 2 and 3-Lille University Hospital CHRU, Lille, France, and 3Lille University Hospital, CHRU, Lille, France

Abstract Background: Laser Fractional Photothermolysis (FP) is one of the innovative techniques for skin remodeling and resurfacing. During treatment, the control of the Microscopic Thermal Zones’ (MTZs) dimensions versus pulse energy requires detailed knowledge of the various parameters governing the heat transfer process. In this study, a mathematical model is devised to simulate the effect of pulse energy variations on the dimensions of MTZs. Methods: Two series of simulations for ablative (10.6 mm CO2) and non-ablative (1.550 mm Er:Glass) lasers systems were performed. In each series, simulations were carried for the following pulses energies: 5, 10, 15, 20, 25, 30, 35, and 40 mJ. Results of simulations are validated by histological analysis images of MTZs sections reported in works by Hantash et al. and Bedi et al. Results: MTZs dimensions were compared between histology and those achieved using our simulation model using fusion data technique for both ablative FP and non-ablative FP treatment methods. Depths and widths from simulations are usually deeper (21 2%) and wider (12 2%) when compared with histological analysis data. Conclusion: When accounting for the shrinkage effect of excision of cutaneous tissues, a good correlation can be established between the simulation and the histological analysis results. Key Words: bioheat transfer, laser fractional photothermolysis, modeling, simulation, thermal damage

Introduction Laser Fractional Photothermolysis (FP) of the skin is a novel variation on the theory of selective photothermolysis whereby Microscopic Thermal Zones (MTZs) of controlled width, depth, and densities are created. The concept of FP was initially developed to address the shortcomings of traditional ablative and non-ablative device modalities (1,2). The term fractional can be applied to any energy source that delivers high fluence with a small spot diameter, producing pixels of skin damage measuring less than 500 mm in diameter without harming surrounding tissues so as to ensure rapid recovery, typically within 24 to 48 h (3). The controlled zones of thermal heating and tissue damage are surrounded by spared areas of viable epidermis and dermis that allow for rapid repair of the MTZs. The main differences between results of the ablative and non-ablative laser system sources are in microscopic patterns’ depth with

spatial separation of columns of thermally affected epidermal and dermal tissues (4). MTZs are deposited in the skin in random patterns by means of highspeed pulse energies. Therefore, the prediction of the depth to which necrosis will extend is a major issue with respect to the practical implementation of this therapy. Several histological studies have been proposed to examine the effects of pulse energy on the dimensions of MTZs created on human skin ex vivo and in vivo using ablative (4,5) and non-ablative (6) FP. The authors determined that increases in pulse energy led to increases in MTZ depth and width without compromising the structure or viability of interlesional tissue. Also, they considered that, in general, no statistically significant difference was found between in vivo and ex vivo depth and width measurements. In fact, the control of the depth of necrosis versus pulse energy requires in-depth knowledge of the various parameters governing heat transfer processes

Correspondence: Serge Mordon, PhD, INSERM U703, 152, rue du Dr. Yersin, 59120 Loos, France. E-mail: [email protected] (Received 21 August 2013; accepted 30 September 2013) ISSN 1476-4172 print/ISSN 1476-4180 online © 2014 Informa UK, Ltd. DOI: 10.3109/14764172.2013.854642

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deriving from laser energy deposition; namely laser wavelength, laser energy, pulse duration, blood perfusion, and both optical and thermal properties of the tissue involved. Therefore, treatment monitoring is required in order to have precise information about the extent of thermal damage in tissues caused by laser coagulation. Furthermore, skin cooling can be used concurrently to both maximize the efficacy of safety of laser treatment and minimize the patient discomfort (7). Modeling laser–tissue interaction can be a potent tool to help predict the dimension (i.e., the depth and width) of MTZs and by extension, allow for analysis and optimization of the parameters governing planned laser surgical procedures. In this study, we implemented a mathematical model simulating the effect of pulse energy variations on the dimensions of the MTZs in two treatment scenarios: ablative and non-ablative FP published by Hantach et al. (4,5) and Bedi et al. (6). Results of numerical simulations are compared with and validated by histological analysis data previously reported in the literature.

−2r 2 ( x , y , z ) Φ( r , t ) Φ 0 exp ϕ(t ) σ2

(1)

Where r( x, y,z ) x 2 y 2 z 2 is the radial distance (mm), s is the standard deviation of the laser beam’s radial spread (mm), ϕ(t) is the temporal distribution of the pulse train (s), this function is considered as a rectangular profile (8). I0 is the initial laser intensity (W/mm3), which can be expressed by the following equation: I0

2 µ a Pow π σ2

(2)

Where ma is the coefficient of absorption (mm 1), Pow is the power of the laser source (W), The optical parameters used in the model were reported and summarized in the Table I. The time-dependent laser light intensity distribution in medium is given by the approximation equation: ∇ ⋅ D ⋅ ∇Φ( r , t ) µ a ⋅ Φ( r , t ) Q( r , t )

Material and methods The model to simulate the ablative and non-ablative FP of the skin uses the Finite Element Method (FEM) to solve light diffusion approximation, bioheat, and thermal damage equations. Optical, thermal, and damage parameters of the epidermal wall were reported in the literature. Modeling In the following sections, we will describe the different stages required to construct the model: Geometrical model. Dimensions of microscopic images of the histological specimens of the skin, in the order of mm, were used to define the dimensions of our geometrical model which consisted of a cube of 2 2 2 mm3. Tissue of epidermal layer skin was considered homogenous. MTZ density per cm2 used on our model was 225 MTZ/cm2. Spot diameter was 120 mm for 10.6 mm CO2 laser ablative FP used in (4,5) and 70 mm for 1.550 mm Er:Glass laser non-ablative FP used in (6). The inter-spot space was 500 mm. Also, laser beams were perpendicular to the surface of the skin. Light distribution in tissue (Laser light source). The laser beams carried a near diffraction limited 1/e2 Gaussian spot size of approximately 120 mm for ablative FP and 70 mm for non-ablative FP, with pulse energies ranging from 5 to 40 mJ. The beam is considered Gaussian in the radial direction and therefore a cylindrical co-ordinate system is chosen to describe its geometry.

(3)

Where F is the light fluence rate (W.mm 2), Q is the source term (W.mm 3). It represents the energy injected by unit of volume. D is the diffusion coefficient (mm) and is defined by the following equation: D

µ 1 2a 3( µ a µ ′s ) µ eff

(4)

Where ma is the absorption coefficient (mm 1) and m′s is the reduced scattering coefficient in tissue (mm 1), described as follows: µ′s µ s (1 − g )

(5)

Table I. Optical and thermal parameters of epidermis used in the numerical simulation extracted from references (9,10). Epidermis parameters Absorption coefficients

Heat capacity Density Thermal conductivity Frequency factor Activation energy Universal gas constant

Value ma (mm 1) Laser CO2 (10.600 mm) m′s (mm 1) Laser CO2 (10.600 mm) ma (mm 1) Laser Er: Glass (1.550 mm) m′s (mm 1) Laser Er: Glass (1.550 mm) C (J.g 1.K 1) r (g.mm 3) 𝓀 (W.mm 1.°K 1) Af(s 1) Ea (J.mole 1) R (J.mole 1.°K 1)

102 ∼102 1 2.219 1.70 1.10 4.2 10 4 3.1 1098 6.28 105 8.3144

Laser fractional photothermolysis of the skin 59

With g being the anisotropy factor incorporating the effects of directionally dependent scattering. meff is the effective attenuation coefficient (mm 1), and it can be described by the following equation: µ eff 3µ a ( µ a µ′s )

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(6) The optical parameters used in the model are reported in (9). Heat distribution. The temperature distribution within the skin calculated from the temporal decay of skin surface temperature using the well-known bioheat transfer equation (Pennes equation): Cp ⋅

∂T( r ,t )

(

)

− ∇⋅ k ⋅ ∇T( r ,t ) ∂t wb ⋅ Cp ⋅ Tb T( r ,t ) + I( r ,t ) + Qmet

(7)

Where T is temperature (°K), Cp C*r is heat capacity (J.mm 3.°K 1), r is tissue density (g.mm 3), C is specific heat capacity of tissue (J.g 1.°K 1), 𝓀 is thermal conductivity of tissue (W.mm 1.°K 1), wb is blood flow rate (ml.g 1.min 1), Tb is the blood temperature (°K), r is the radial distance (mm), t is time (s), I(r,t) is the heat source (W.mm 3). The thermal parameters used in the model were also reported in (10). They are summarized in Table I. As previously described in the literature, the metabolic heat source is considered as insignificant (11), so was ignored that in our model. To solve equation (3), the FEM was used. The simulated laser source was considered as a spot, which has the same dimensions of the spot of laser used in the experiments. The tissues were considered as a regular finite element grid of 2 2 2 mm3 corresponding to the microscopic images (see section Geometrical model). The initial temperature was set to T0 37°C. The boundary conditions for the bioheat equationwere as follows: n ⋅ k ⋅ ∇T 0 for all surfaces. Where n is the direction of the heat flux. To obtain a stable and convergent numerical solution, the GMRES (Generalized Minimum RESidual) algorithm was used. GMRES is an iterative method introduced by Saad and Schultz (12) to solve linear equations systems. It was tuned with the following settings: time steps were 10 2 ms and convergence tolerance was set to10 3. Thermal damage. Thermal damage in cells and tissue can be described mathematically by a first-order thermo-chemical rate equation, in which temperature

history determines damage. Damage is quantified using a single parameter W, which ranges on the entire positive real axis. It is calculated from the Arrhenius law (9,13). W is dimensionless, exponentially dependent on temperature and on time of exposure. It is calculated from the Arrhenius law as follows: τ − Ea Ω( r , τ ) Af ∫ exp dt R. T( r,t ) 0

(8)

Where Af (s 1) is the frequency factor, Ea (J.mole 1) is the activation energy, R (J.mole 1.°K 1) is the universal gas constant (R 8.3144), and T (°K) is the temperature. The parameters Af and Ea, called the kinetic parameters, are temperature dependent and can be determined from experimental data. Numerical values of these parameters used in the model were reported in (9,10) (Table I). Equation (4) indicates that the measure of damage (W) describes the probability of tissue being destroyed. The damage threshold for tissue necrosis is commonly selected as omega 1 (a damage concentration of 63% for a unimolecular system). Experimental validation The histological detection was used to define MTZs dimensions by representing collagen denaturation and cell necrosis within the irradiated field after FP treatment. The vertical section can be used to estimate the degree and the depth of the damage. This method is widely used to validate the results of the FP treatment (2,4–6). Histological images of the MTZs sections are used to validate the thermal damage estimated from the simulation model, whereas a fusion data from the histological image section and the corresponding section of damage from simulation is used to validate the mathematical model. Numerical implementation The mathematical model was implemented using the COMSOL Multiphysics V4.2 software (COMSOL AB, Grenoble, France). This Finite Element computer aided design software specifies the Partial Differential Equations (PDE), variables, geometry, and boundary conditions.

Results Figure 1 displays the thermal damages (corresponding to W 1) using the ablative (10.6 mm CO2, 30 mJ) lasers.

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Figure 1. 3D lesions distribution (Thermal damage corresponding to W 1) versus pulse energy of 30 mJ, using 10.6 mm CO2 ablative laser.

Figures 2 and 3 display results from fusing data between the histological section and the corresponding section of simulated damage, which will help in

comparing dimensions of lesions (MTZs) between histological analysis and simulations. Depths and widths of lesions are 970 mm and 266 mm, respectively, in histological analysis image section versus 1235 mm (˜21%) and 360 mm (˜26%), respectively, in simulation using ablative FP (Figure 4). Also, Depths and widths of lesions are 800 mm and 225 mm, respectively, in histological analysis image section versus 920 mm (˜13%) and 154 mm (˜30%), respectively, in simulation using non-ablative FP (Figure 5). To simplify the understanding of variations of MTZs dimensions with laser energy pulse, graphical illustrations of depths and widths of lesions for series of pulses energies: 5, 10, 15, 20, 25, 30, 35, and 40 mJ for ablative and non-ablative lasers were extracted from simulations and presented in Figures 4 and 5, respectively. Figures 6 and 7 present a comparison of thermal damages dimensions (depth and width) of MTZs between histological analysis reported in (4,6) and simulations. these figures show that increasing pulse energies from 5 to 40 mJ leads to a quasi-linear increase in depth and width of the MTZs . This

Figure 2. Comparative illustration between depth and width of lesion zone from histological analysis reported in (4) and simulation versus 30 W, 10.6 mm CO2, for 30 mJ pulse energy.

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Figure 3. Comparative illustration between depth and width of lesion zone from histological analysis reported in (6) and simulation versus 30 W, 1.550 mm Er: Glass, for 30 mJ pulse energy.

quasi-linear increase in result was confirmed histologically by Tannous (14). On the other hand, differences between widths from histological measures and simulations varied from 2 to 124 mm for ablative lasers and from 10 to 67 mm for non-ablative lasers. Differences between depths from histological measures and simulations varied from 42 to 247 mm for ablative lasers and from 13 to 312 mm for non-ablative lasers. Discussion Laser FP is a new technique producing numerous small regions of MTZs lesions, each of which affecting a fractional part of the tissue while sparing the skin around the lesion for a faster treatment. However, the optimum depth of skin damage for each lesion area and the volume of coagulated or necrotized tissue have not been determined. We also do not have a clear idea of what percentage of skin area should be covered or treated in each session or the optimal number of sessions necessary, and the

most appropriate parameters have yet to be optimized for each system. At present, there is evidence that fractional techniques are effective with one of the most important indications being acne scarring (primary indication), fine and moderate wrinkles, rejuvenation, and actinic keratosis. What seems clear is that all these techniques are effective and their popularity will depend on the level of training and competency when selecting the appropriate parameters in each particular case. Histologic studies were proposed as methods to validate results and examine the effects of pulse energy variations on the dimensions of MTZs created on the skin (4–6,14–19). Bedi et al. proposed ex vivo and in vivo studies using non-ablative FP with pulse energy ranging from 4.5 to 40 mJ (6). The authors determined that increases in pulse energy led to increases in MTZ depth and width without compromising the structure or viability of interlesional tissue. Also, they considered that, in general, no statistically significant difference was found between in vivo and ex vivo depth and width measurements.

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Figure 4. Thermal damages (Lesions) depth and width versus 30W, 10.6 mm CO2 pulse energy pulse energies: 5, 10, 15, 20, 25, 30, 35, and 40 mJ extracted from simulation.

Also, Initial ex vivo histologic study proposed by Hantash et al., where a prototype novel device ablative 10.6 mm CO2 laser (30 W, 120 mm spot size, and 0.7 ms pulse duration) with pulses energies 9.2, 13.8, 18.0, and 23.3 mJ were used to reveal discrete MTZs of epidermal and partial-thickness dermal coagulation that increase in both depth and width with increasing pulse energies (5). MTZs were spaced approximately at 500 mm.The authors found that at 23.3 mJ, the lesion width was approximately 350 mm and the depth was 1 mm. Hantash et al. expanded their study to evaluate their novel device in vivo histologically, where a range of pulse energies between 5 and 40 mJ was tested and lesion dimensions were assessed histologically. The results of the extension study confirmed the ex vivo findings and showed for the first time in vivo, that a controlled array of MTZs of ablation and coagulation could be deposited in human skin by varying treatment pulse energy (4). Few studies have been realized to predict the reproducible parameters and time-dependence of

heat distribution and thermal damage in the epidermal layer after laser FP. Some of these studies presented a Monte Carlo simulation with features that calculate photon propagation and energy deposition, reflection, and transmission in multi layered skin explicitly for each skin layer (20). The authors considered that the results will contribute to a better understanding of light tissue interaction and its effect on dermatological applications relating to surgery and skin rejuvenation. In this study, we were interested by the simulation of laser FP outcomes. Results of simulations are validated histologically to confirm the theoretical model. In this model, solving the Arrhenius equation for time increasing temperature returns a relatively constant damage threshold value of 50 1°C (21). Although this model greatly simplifies the understanding of thermal tissue damage by assuming a single first-order rate process and to not directly modeling the energy of the laser light, it has been successfully used to describe the threshold of tissue

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Figure 5. Thermal damage (Lesion) depth and width versus 30 W, 1.550 mm Er:Glass pulse energies: 5, 10, 15, 20, 25, 30, 35, and 40 mJ extracted from simulation.

Figure 6. Comparison between the thermal damage (lesion) depth and width from the histological analysis reported in Hantash et al. (4) and from simulation versus 30 W, 10.6 mm CO2 pulses energies: 5, 10, 15, 20, 25, 30, 35, and 40 mJ.

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Figure 7. Comparison between the thermal damage (lesion) depth and width from the histological analysis reported in Bedi et al. (6) and from simulation versus 30 W, 1.550 mm Er: Glass pulses energies: 5, 10, 15, 20, 25, 30, 35, and 40 mJ.

damage as a function of temperature and exposure time (13,21,22). Figures 6 and 7 suggest that dimensions of estimated MTZs from simulations are larger than those achieved from histological analysis. These differences can be explained by the shrinkage effect due to the histology technique (23). In fact, there is a shrinkage effect due to laser treatment (24), but the main effect comes from shrinkage from excision of cutaneous tissues, primarily because of the intrinsic contractile properties of the skin. Kerns et al. presented a study to estimate the shrinkage effect of excision of cutaneous tissues prior to formalin fixation. The authors found that the main shrinkage was 21 2% in length and 12 2% in width (25). Formalin fixation does not cause cutaneous tissue shrinkage (25) and the majority of tissue shrinkage occurred prior to Formalin fixation (26,27).

cutaneous tissues. With this in mind when analyzing the histological data, a good correlation can be established between the results of simulation and those from the histological analysis. Acknowledgements The authors wish to thank Pascal Servell for his careful review of the English language of this manuscript and Le Groupe Laser de la Société Française de Dermatologie for its support. Declaration of interest: The authors report no declaration of interest. The authors alone are responsible for the content and writing of the paper. This work was supported by the French National Institute of Health and Medical Research (INSERM). References

Conclusion Laser FP is a promising technique for skin remodeling and resurfacing. Further evaluation and understanding of heat dissipation in tissues to control the MTZs’ dimensions with laser parameters is warranted. In this article, we presented a numerical simulation of the laser FP and then compared the results with the histological analysis data. The differences can be easily explained by the shrinkage effect resulting from the excision of

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Notice of Correction Changes have been made to this article since its original online publication date of 10 January 2014.

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