Influence of spraying distance and post-cooling on cryogen spray cooling for dermatologic laser surgery

Cryogen spray cooling (CSC) is used to minimize the risk of epidermal damage in various laser dermatological procedures such as treatment of port wine stain birthmarks and hair removal. However, the spray characteristics and combination of CSC and heating (laser) to obtain optimal treatments have not yet been determined. The distance between the nozzle tip and the skin surface for commercial devices was apparently chosen based on the position at which the cryogen spray reached a minimum temperature, presumably with the expectation that such a minimum would correspond to maximal heat flux. We have systematically measured spray characteristics of various nozzles, such as mean droplet diameter, velocity, temperature, and heat transfer coefficient, as a function of distance from the nozzle tip. Among other interesting correlations between these spray characteristics, it is shown that, for nozzle-to-skin distances between 20 to 80 mm, variations in the heat transfer coefficient are larger than those in the spray temperature and, therefore, maximization of the heat flux should be better dictated by the distance at which the heat transfer coefficient is maximized rather than that at which the spray temperature is minimized. Also, the influence of droplet diameter appears to be more influential on the heat transfer coefficient value than that of droplet velocity. Based on spray characteristic correlations, different ranges for positioning the nozzles are recommended, depending on the clinical application. Also, a 2D finite-difference method has been developed to study the spatial and temporal thermal variations within the skin. Our results show that it is possible to decrease significantly the epidermal damage after laser irradiation provided the heat transfer coefficient is significantly increased. The influence of post-cooling has minimal effects for the cases studied.


INTRODUCTION
Cryogen spray cooling (CSC) has been used effectively to cool selectively the epidermis while minimally cooling deeper targets 1 during laser therapy of several dermatoses, such as port wine stains (PWS) birthmarks 2,3 , and cosmetic treatments, such as hair removal 4 . However, to obtain optimal cooling selectivity, the amount of heat removed through the skin surface should be properly controlled. For shallow targets, such as PWS, commercial cryogen spurts do not seem to provide sufficient epidermal protection for skin types with relatively high melanin content (e.g., types III and higher), where an increase of dosage is needed to cause complete photocoagulation of blood vessels. On the other hand, a recent study has indicated that the heat extraction rates produced by commercial devices aimed at deeper targets, e.g., hair follicles, may be unnecessarily large 5 .
Some advances have been made in terms of optimizing spurt durations to provide better cooling selectivity. A recent study has revealed that cryogen spurts of 100-200 ms could result in better epidermal protection than that provided by 30 to 50 ms spurts 1 . Spurts of similar duration have served to increase the threshold of epidermal damage on non-PWS human cadaver skin by a factor of three 6 . Nevertheless, more work is required to better understand how different nozzles and spraying conditions affect spray characteristics, such as droplet diameter (D), velocity (V), and temperature (T) 7,8,9 , and how these, in turn, affect the heat extraction rate which is ultimately dictated by the skin surface temperature (T s ) and the interface heat transfer coefficient (h).
Optimization of CSC parameters is the first step towards an improvement of dermatologic laser treatments. However, a complete assessment of the extent of epidermal and target damage also requires the analysis of laser irradiation parameters, as well as skin optical and thermal properties. As a first approximation, such an assessment can be made through the use of numerical models to determine the spatial and time dependent temperature fields within the skin during CSC and laser irradiation. Paithankar et al. 10 and Pfefer et al. 11 , among others, have recently shown that such models have significant potential as a tool for optimizing heating and cooling parameters.
In this work we determine the effects of nozzle diameter and nozzle-to-skin distance, z, of four spray nozzles varying from 0.5 to 1.4 mm in inner diameter (I.D.) based on the dependence on z of the average values of D, V, T, and h, at the cryogensubstrate interface. Secondly, a 2-D Monte Carlo multi-layer model 12 and a custom-made 2D finite-difference heat diffusion model are used to calculate the light distribution within tissue and the heat diffusion as a function of time, respectively. With the use of both models, and an Arrhenius-type kinetic model used to assess the epidermal and blood vessel damages, we study the influence of the heat transfer coefficient and post-cooling in PWS laser therapy.

Spray Formation
A total of four nozzles were used for this study: Two commercial cryogen spray nozzles used for laser treatment of vascular lesions and hair removal (ScleroPLUS TM (SP), and GentleLASE TM (GL), Candela, Wayland, MA), with approximate inner diameters of 0.8 and 0.5 mm, respectively; and two custom made nozzles (narrow nozzle, N, and wide nozzle, W) of 0.7 and 1.4 mm I.D. Liquid cryogen (tetrafluoroethane, R-134a, boiling temperature, T b = -26 o C, at atmospheric pressure) was delivered through a standard high-pressure hose connecting the container to a control valve. The container is pressurized at the saturation pressure of this cryogen (6.7 bar at 25 o C). Spurt durations-defined by the time the valve remains open, were electronically controlled. In this study, we have characterized sprays that were at least 50 ms long, so only characteristics of fully developed sprays were considered 13,16 , i.e., sprays that do not vary with time.

Droplet Size and Velocity Measurements
An Ensemble Particle Concentration & Sizing apparatus (EPCS by Insitec/Malvern, Worcestershire,UK) was used to measure average diameters (D) of the spray droplets. This instrument is based on the principle of diffraction of a parallel beam of monochromatic light (provided by a 670 nm diode laser) caused by the obstruction of spray droplets with the beam. When this happens, a diffraction pattern made of a series of alternate light and dark concentric rings (Fraunhofer diffraction) is formed, and the spacing between these rings is related to droplet diameter. A more detailed description may be found in Lefevbre 14 . In order to obtain more localized measurements of D, the beam was reduced from its normal diameter of 10 mm to 3.3 mm with the aid of an inverted beam expander (OptoSigma, Santa Ana, CA). A positioning system was used to displace the nozzle tip perpendicularly to the laser beam, from 15 to 200 mm. In addition, a Phase Doppler Particle Analyzer (PDPA by TSI, St. Paul, MN) was utilized to provide statistical averages of both droplet diameters (D) and velocities (V). PDPA captures and analyzes light scattered by droplets traveling through interfering laser beams of different wavelengths, focused on a probe volume, typically smaller than 1 mm 3 . When droplets interfere with these beams, they generate a Doppler signal with a frequency shift proportional to droplet velocity. The phase difference between the signals collected by two adjacent detectors is proportional to droplet diameter.

Temperature Measurements
A type-K thermocouple with bead diameter of approximately 0.3 mm (5SC-TT-E-36 by Omega, Stamford, CT) was used to measure average spray temperature as a function of distance from the nozzle tip, T (z). Cryogen spurt durations of at least 1 second were used, which ensured steady state conditions for the thermocouple. The temperature sensor was supported by a rigid stick and inserted into the center of the spray cone at varying distances from the nozzle. The estimated uncertainty in nozzle-to-skin distance, z, is ± 0.5 mm. Since water condensation and freezing on the thermocouple bead could affect temperature measurements, these experiments were conducted in a chamber filled with dry air (relative humidity below 5%). Under such conditions, most of the tests did not show appreciable condensation, except for z > 100 mm, where signs of frost formation were observed on the thermocouple bead.

Heat transfer coefficient measurements
A custom-made device was built to measure the heat transfer coefficient (h). In short, the device consists of a silver disk (10.48 mm diameter, 0.42 mm thickness), embedded in a thermal insulator, e.g., epoxy. The upper surface of the disk is exposed to the cryogen spray, and the disk temperature is monitored by a type-K thermocouple attached to its lower surface. The energy equation, which describes the disk temperature evolution is: where ρ m , C m , V m and A m are the density, specific heat, volume, and exposed surface area of the metallic disk, respectively; h is the heat transfer coefficient, and T and T cryo are the temperatures of the disk and the cryogen, respectively. This equation assumes that T is uniform over the whole disk at any given time. This assumption means that the disk relaxation time-given by (ρ m V m C m )/(A m h), is much larger than the diffusion time across the disk thickness, d m 2 /α, where d m is the disk thickness and α its thermal diffusivity. Substituting T cryo with measured spray temperature, h can be calculated from measurements of disk temperature during CSC.

Numerical Simulation of Energy Absorption and Cryogen Spray Cooling
A numerical model was developed using a 2D finite-difference (FD) approximation to the heat equation in cylindrical coordinates. The cross section area of the skin model was 15 mm wide and 1mm thick, and was discretized into 61 nodes spaced 250 µm in the radial direction and 101 nodes spaced 10 µm in the axial direction. Time steps of 100 µs ensured stability and convergence criteria. Starting with a constant temperature of 35 o C, the temperature field resulting from a 100 ms spurt was first computed by imposing a constant convective boundary condition at the skin surface (constant h and constant T cryo ). Values of h used in this study varied from 2,400 to 30,000 W/m 2 K, and T cryo was fixed at -58 o C. No delay between the end of the spurt and the beginning of the laser pulse was allowed, as suggested by Verkruysse et al. 1 . Then, a source term (q) was incorporated into the heat diffusion model (Eq. 2) to simulate the energy absorption of the laser pulse by epidermal melanin and PWS.
The source term, q, was previously generated using MCML, a Monte Carlo software package developed by Wang et. al. 12 .
Given the specific optical properties of the skin layers and the geometry and energy of the laser beam, MCML determined the optical transport of photons in the skin layers. For consistency, the skin layer depths and optical properties, as well as the thermal properties we used in this study are the same as those used by Pfefer et al. 11 , and are listed in Tables 1 and 2, respectively. All Monte Carlo simulations used four layers: an epidermal melanin layer, a normal dermis layer, a PWS layer, and another normal dermis layer with the same optical and thermal properties as the second layer ( Fig. 1). The absorption coefficients (µ a ) of the epidermal layers were set to 8, 20, and 52 cm -1 , to describe skin types ranging from light skin to olive skin. These absorption coefficients corresponded to melanin volume fractions of 2, 5, and 13%, respectively, assuming a melanin absorption coefficient of 400 cm -1 at 585 nm wavelength 15 . For the normal dermis and blood energy absorption coefficients we used 2.4 and 19.1 cm -1 , respectively. The latter values were used in all simulations. Scattering coefficients (µ s ), scattering anisotropies (g), and indices of refraction (n) used for all layers are also listed in Table 1. All simulations used 100,000 photons. The grid spacing for the MCML simulation was the same as that of the FD heat diffusion model. The adjunct program to MCML, CONV, was used to take the infinitesimally narrow photon beam from the MCML simulations and create a flat top, circular beam with 5 mm diameter.

Assessment of Tissue Thermal Damage
Tissue thermal damage was computed using the Arrhenius-type kinetic model, given by Eq. 3, as follows: where A is a frequency factor [1/s], E a an activation energy barrier [J/mole], R the universal gas constant [8.32 J/mole K], and T the absolute temperature [K]. The parameters A and E a used in this study are listed in Table 3, and also correspond to the values used in Pfefer et al. 11 .  Figure 2 shows the average droplet diameter (D), velocity (V), temperature (T) and heat transfer coefficient (h) as a function of z for sprays from all four nozzles. As seen in Figure 2a, the maximum droplet diameter for the nozzles with inner diameters between 0.5 and 0.8 mm, i.e., SP, GL, and N, is D max = 8.7 ± 0.2 µm, measured at z = 60-70 mm. In contrast, D measurements for the 1.4 mm nozzle (W) vary between 12 to 14 µm. The measurements of V for all nozzles are presented in Figure 2b. Although to a different extent, these results show a similar behavior to that of D, with an increasing trend within the first 40 mm from the nozzle. At greater distances, V monotonically decreases, reaching 15 m/s at z = 200 mm in all cases. Measurements of T are depicted in Figure 2c. The temperature trends indicate that the exit temperature, T 0 , may gradually vary between -26 o C for the 1.4 mm nozzle (W), to -50 o C for the 0.5 mm nozzle (GL). The minimum temperature, T min , for the nozzles with inner diameters between 0.5 and 0.8 mm is around -58 o C, reached at z = 60-120 mm, and it is slightly lower than T min for the W nozzle at the same z. For the SP, GL and N nozzles, T starts to increase between z = 80 -120 mm, indicating evaporation of cryogen droplets at such distances. Finally, Figure 2d shows the variation of h with z. The measurements for SP and GL were carried out using the method described above, and the values shown represent averages over the duration of the spurt (100 ms) as well as over the detector area. The h value for the W nozzle is a conservative estimate of the range of values reported in Verkruysse et al. 7 (5,900 -30,000 W/m 2 K). Measurements of those values, however, were carried out with a different procedure described therein (epoxy block / dynamical method), and the measurements were only taken between z = 50-60 mm.

Numerical Simulations
Effect of h on light skin (µ µ µ µ a = 8 cm -1 ) PWS laser therapy Figure 3 shows the temperature profiles computed for the lightest skin type chosen for this study (µ a = 8 cm -1 ). The dotted lines represent temperature as a function of depth at the end of 100 ms spurts for two cases: h = 2,400 W/m 2 K, which is the lowest value of h for CSC reported in the literature 3 , and h = 6,000 W/m 2 K, which is a conservative value corresponding to the measurements presented above. In both cases, cryogen temperature, T cryo , was -58 o C, i.e., the minimum spray temperature measured for the SP, GL, and N sprays. The dashed and solid lines represent, respectively, temperature profiles at the end of 1.5 ms laser pulses with a fluence of 12 J/cm 2 for each of the values of h.
Effect of post-cooling on tanned light skin (µ µ µ µ a = 20 cm -1 ) PWS laser therapy Figure 4 shows the results of temperature profiles computed for µ a = 20 cm -1 , i.e., for the mid-tanned light skin chosen for this study. The dotted line represents temperature as a function of depth at the end of a 1.5 ms laser pulse with a fluence of 13 J/cm 2 . Prior to this pulse, a 100 ms spurt with a heat transfer coefficient, h, of 8,400 W/m 2 K was imposed. According to the measurements shown above, this is the maximum value of h that could be obtained with the SP nozzle if it was positioned at 30 mm from the skin surface (Fig. 2d). The dashed and solid lines represent the temperature profiles 12.5 ms after the end of the laser pulse (114.0 ms from start of pre-cooling), when no post-cooling and post-cooling are applied, respectively.     Figure 5 shows temperature profiles computed for the same skin-type shown in Fig. 4 (µ a = 20 cm -1 ), i.e., for the mid-tanned skin-type chosen for this study. The dotted lines represent temperature as a function of depth at the end of 1.5 ms laser pulses with a fluence of 13 J/cm 2 . Prior to these pulses, 100 ms spurts with heat transfer coefficients of 8,400 W/m 2 K and 30,000 W/m 2 K were imposed, respectively. The latter value of h was chosen as an extreme upper limit, which would be desirable to reach to optimize epidermal protection. In both cases, cryogen temperature, T cryo , was fixed at -58 o C. The dashed and solid lines represent the temperature profiles 4.5 ms after the end of the laser pulses for each of the values of h. Post-cooling was applied in both cases with identical values of h to those used during the pre-cooling. Effect of h and post-cooling in olive skin (µ µ µ µ a = 52 cm -1 ) PWS laser therapy Figure 6 shows temperature profiles computed for the darkest skin-type chosen for this study (µ a = 52 cm -1 ). The dotted lines represent temperature as a function of depth at the end of 1.5 ms laser pulses with a fluence of 10 J/cm 2 . Prior to these pulses, 100 ms spurts with heat transfer coefficients of 8,400 W/m 2 K and 60,000 W/m 2 K were imposed, respectively. Clearly, the temperature reached is excessively high within the epidermis, and no correction is made to take into account phase and chemical changes that would likely occur after such a large energy absorption. The dashed and solid lines represent the temperature profiles 12.5 ms after the end of the laser pulses for each of the values of h. In both cases, post-cooling (PC) is applied with identical values of h to those used during the pre-cooling, i.e., 8,400 and 60,000 W/m 2 K, respectively.   Table 5 shows values of Ω computed from Eq. 3 to assess the levels of epidermal (Ω E ) and PWS (Ω PWS ) damages for the cases shown in Figs. 3-6. Also, the ratios between the epidermal damages were calculated to qualitatively represent the effects of increasing heat transfer coefficients and benefits of use of post-cooling.

DISCUSSION
Various features may be pointed out in Fig. 2. First, for the driving pressure corresponding to this cryogen (6.7 bar), nozzles with I.D. between 0.5 to 0.8 mm do not produce significant differences in terms of average droplet diameters, as illustrated in Fig. 2a. This is also evident in spray images reported recently in Aguilar et al. 16 . In contrast, for the 1.4 mm I.D. nozzle (W), droplet diameters are about twice as large throughout the range measured. It was not possible to obtain reliable diameter measurements closer than 90 mm from the nozzle tip for this nozzle. This is because of a high droplet density spray, or even an unbroken jet 16 . The droplet diameter growth seen in Figure 2a between 0 < z < 60 mm for the SP, GL, and N nozzles, is an indication of droplet coalescence 17,18 , a phenomenon which may contribute more to the average droplet diameter variation than the evaporation process 9 . However, evaporation becomes the dominant process in determining average droplet size for z > 60 mm, as demonstrated by decreasing D at greater z.
For all nozzles shown in Fig. 2b there is an increase in V within the first 40 mm from the nozzle tip. This can be explained by the coalescence of large fast droplets, with slower smaller ones. The decrease of V for z > 40 mm results from droplet deceleration due to drag as droplets move through quiescent air 8,9 .
The variation of spray temperature with distance for all nozzles shown in Fig. 2c is to be anticipated. Sprays produced by smaller I.D. nozzles are more finely atomized, i.e., have a larger surface area, removal of latent heat of vaporization from the remaining liquid droplets is more effective and, thus, somewhat lower spray temperatures are achieved. Notice that the initial temperature T 0 , does not seem to be the same for all nozzles. For example, for the W nozzle (nozzle with the largest I.D.), T 0 is close to -26 o C, which coincides with the boiling temperature of the cryogen, and is the expected cryogen temperature after a sudden expansion through the valve (provided evaporation within the hose and nozzle are negligible). This means that the cryogen has not been significantly atomized and, thus, that the liquid cryogen has not been able to undercool. On the other hand, the T 0 estimated for the GL nozzle (nozzle with the smallest I.D.) is equal to -49 o C, which indicates better atomization right at the exit of the nozzle (and perhaps even some degree of evaporation within the nozzle) and, therefore, a larger undercooling.
An interesting observation is that the ratio between the N and the GL nozzle diameters is 1.4, and no significant differences are appreciable in terms of their droplet diameter and temperature evolutions. On the other hand, the ratio between the N and the W nozzle I.D. is slightly greater (2.0), and yet the differences in terms of their droplet diameter and temperature evolutions are noteworthy. This large change in spray characteristics for a relatively similar nozzle diameter ratio indicates that there is a critical nozzle diameter-somewhere between 0.8 and 1.4 mm, at which a change in the atomization mechanism takes place (at least, for the particular conditions under which this cryogen is sprayed).
This study shows that variations of h can be achieved by positioning the nozzles at different distances from the skin surface, and even more significant variations can be achieved by varying the nozzle diameter. The effect of nozzle-to skin distance (z) in the resulting h is shown in Fig. 2d. Our results demonstrate that values between 6,000 to 8,400 W/m 2 K may be obtained for the SP and GL nozzles in the range of z between 30 and 50 mm. Significantly larger values of h may be obtained by increasing nozzle diameter to about 1.4 mm (W nozzle). In a previous study 7 , the differences in h due to changes in nozzle diameter were attributed to build up of a cryogen layer on the sprayed surface, which appeared to be thicker in the case of the N nozzle as compared with the W nozzle, and thus constituted a higher thermal barrier for heat extraction. It was speculated then that the different cryogen layer thicknesses were due to the larger momentum (given by the product of D and V) of large and fast moving droplets, such as those produced by W nozzle, in contrast to the smaller and slower moving droplets produced by N nozzle. This hypothesis is supported in this study by the larger droplet diameter and velocity seen for the W nozzle in comparison with the SP, GL, and N nozzles (Figs. 2a and 2b). Additionally, note that T starts to increase between 80 and 120 mm for the SP, GL, and N nozzles. This increase is consistent with D and V measurements, since the higher momentum droplets move further downstream before evaporating completely. Clearly, the complexity of the problem is such that establishing a correlation between D, V, T, and h, is not straightforward. Nevertheless, it is noted that a relatively invariant value of h is reached between 40 and 70 mm for the SP and GL nozzles, the same range where D is maximum. This is perhaps an indication that the influence of D on h may actually be more dominant than that of V.
For laser therapy of PWS or other superficial targets, it is important that the effect of cooling remains spatially confined to the superficial 100-200 µm of the skin 2,19 . Such spatial selectivity requires the use of short cryogen spurts and the highest possible heat transfer rates. Therefore, aiming at the highest h a nozzle can produce, should be the most important criterion to determine its appropriate position with respect to the skin surface. One should be aware, however, that the use of larger diameter nozzles may not be viable for clinical applications, since they produce more confined jet-like sprays, and larger droplet momentum may produce patient discomfort. In contrast, smaller diameter nozzles produce a finely atomized spray, which is more acceptable to patients and cover a wider sprayed area. The downside of fine atomization is, as mentioned above, that it may induce the formation of a thicker liquid layer, which adversely affects the heat extraction rate due to low thermal conductivity of cryogen 20 . Maximizing h may not be the ultimate goal for CSC aimed at therapy of deeper targets (e.g., hair removal). In fact, the GL nozzle is currently used with an Alexandrite laser for the treatment of deep targets and for such targets, it may actually be beneficial to reduce h in order to have a more prolonged and less aggressive heat extraction, while still obtaining sufficient epidermal protection 5,21 .
The results presented in Fig. 3 demonstrate that for very light skin (µ a =8 cm -1 ), even a heat transfer coefficient of 2,400 W/m 2 K 3 , would provide sufficient epidermal protection, while significant PWS damage would be obtained. In fact, an increase in h to values similar to those measured for the SP and GL nozzles (≈ 6,000 W/m 2 K), would further reduce the epidermal damage, while sufficient PWS thermal damage would still be induced. For slightly darker skin types, e.g., µ a = 20 cm -1 , the increase in epidermal temperature could be significant for the dose used (13 J/cm 2 ), as exemplified in Figs. 4 and 5. Fig. 4 shows that a post-cooling with an h value similar to the maximum measured for the SP nozzle, would help reduce the epidermal damage by a small amount only (≈ 2%), while the PWS damage would be basically unaffected but yet large enough to induce irreversible thermal damage. In Fig. 5 the heat transfer coefficient was increased from 8,400 W/m 2 K to the upper estimate value we have previously reported (30,000 W/m 2 K) 7 and post-cooling was applied in both cases. As seen in Table 5, for this choice of parameters the epidermal damage is significantly minimized (by more than a factor of 170) and, although the PWS damage is also reduced, it is still be large enough to induce the desired thermal damage. This is a good example of the importance of maximizing h to be able to treat skin types that may be otherwise not viable. Finally, Fig. 6 shows that for darker skin types (µ a = 52 cm -1 ), the increase in epidermal temperature with a dose of 10 J/cm 2 would be excessive, and yet no significant damage would be induced to the PWS. Even an increase in h up to 60,000 W/m 2 K and postcooling, would not be sufficient to avoid extensive epidermal damage.

CONCLUSIONS
This study shows that variations of the heat transfer coefficient, h, can be achieved by positioning nozzles at different distances from the skin surface, and significant increases in h can also be achieved by increasing nozzle inner diameter (I.D.) For the SP and GL nozzles, variations in the heat transfer coefficient are larger than those in the spray temperature and, therefore, maximization of the heat flux-which is needed to improve PWS treatments for skin types III and higher, should be determined by adjusting the nozzle-to-skin distance within the range where the heat transfer coefficient is maximized rather than that at which the spray temperature is minimized. Sprays produced by all the studied nozzles appear to reach very similar minimal temperatures (≈ -60 o C), but for nozzles with I.D. ranging from 0.5 to 0.8, relatively invariant values of h are reached within the ranges of z where D is maximal. This suggests that the influence of droplets mass (D) may actually be the most determinant variable on the value of h. Preliminary results of a heat diffusion numerical simulation using a Monte Carlo technique to determine laser energy absorption and distribution within human skin, indicate that for light skin types (µ a = 8 cm -1 ), h values that are measured for commercial devices (5,000 to 10,000 W/m 2 K) are large enough to offer adequate epidermal protection, while enduring PWS photothermal damage. For somewhat darker skin types (e.g., µ a = 20 cm -1 ), an increase in h would significantly help reduce the risk for epidermal damage for doses beyond 12 J/cm 2 , while the benefits of using post-cooling would be minimal. Unfortunately, however, not even an increase in h to about 60,000 W/m 2 K and post-cooling would be sufficient to avoid severe epidermal damage for skin types where µ a = 52 cm -1 or higher.