A theoretical study of the thermal response of skin to cryogen spray cooling and pulsed laser irradiation: implications for treatment of port wine stain birthmarks

The successful treatment of port wine stain (PWS) patients undergoing laser therapy is based on selective thermal coagulation of blood vessels without damaging the normal overlying epidermis. Cryogen spray cooling of skin may offer an effective method for minimizing epidermal thermal injury. Inasmuch as the density of melanosomes and depth of PWS blood vessels can vary considerably, an optimum cooling strategy is required on an individual patient basis. The authors present a theoretical study of the thermal response of various pigmented PWS lesions to spray cooling in conjunction with flashlamp-pumped pulsed dye laser irradiation (585 nm). Results of the authors' model indicate that precooling of skin using tetrafluoroethane as the cryogen spray is sufficient to eliminate epidermal thermal injury when using incident fluences less than 10 J cm-2 and 8 J cm-2 on patients with intermediate and high epidermal melanin content, respectively. Cryogens that have lower boiling points than tetrafluoroethane may allow successful treatment when using fluences equal to or greater than those indicated.


Introduction
Successful laser treatment of port wine stain (PWS) birthmarks is based on selective photothermolysis whereby absorption of the laser light by haemoglobin in PWS blood vessels results in irreversible thermal injury (Anderson and Parrish 1983). The ideal laser treatment should cause irreversible laser injury to the PWS blood vessels without damaging the overlying epidermis. Unfortunately, the native epidermal melanin acts as an 'optical shield' that absorbs the laser light and reduces the heat generated in PWS blood vessels.
In recent years, cooling of skin has been used as a technique for preventing thermal injury to epidermis. One method has involved use of ice or chilled water prior to or during laser irradiation (Gilchrest et al 1982, Dreno et al 1985. Although epidermal thermal injury has been reported to be prevented with use of these cooling methods, deeper layers of skin including PWS blood vessels may also be cooled and as a result remain resistant to photothermolysis (Nelson et al 1995a). Therefore, an appropriate cooling and irradiation method should cool selectively the epidermal layer but allow photocoagulation of deeper PWS blood vessels.
Evaporation of a cryogen sprayed on skin has been shown to provide a mechanism for selectively cooling the skin, whereby the degree and spatial distribution of cooling within skin can be achieved in a controlled manner by adjusting the cryogen spurt duration (Anvari er al 1995). Transient temperature reductions of the order of 3040°C have been achieved on the skin surface in 5-80 ms using tetrafluoroethane (CzHzF4: b.p. = -25OC. an environmentally compatible, non-toxic, and non-flammable freon substitute) as a cryogenic spray.
Encouraging preliminary clinical results in PWS patients have been reported by spraying the skin with millisecond spurts of tetrafluoroethane in conjunction with pulsed dye laser irradiation (Nelson et nl 1995a, b). Nevertheless, the optimum cooling strategy needs to be determined on individual patient basis as density of melanosomes as well as depth of the PWS blood vessels vary considerably. We present a theoretical study of the thermal response of skin resulting from spray cooling in conjunction with temperature increases due to pulsed laser irradiation for various pigmented PWS lesions. In particular, we calculate temperature distributions within skin when precooling the skin with a cryogen spray prior to laser irradiation as well as cooling it during and after laser irradiation, and compare the results with the temperature distribution obtained in the absence of cooling. Results of this study can be used as a guide to select the optimum cooling strategy in clinical studies of treatment of PWS birthmarks on an individual patient basis.

Assumptions
(i) We classify PWSs into three categories based on the epidermal melanin content and on the depth of the PWS (Barsky et ol 1980). Category I is defined as a thin PWS (200 pm thickness) below an epidermis with low melanin content. Category JJ is a thick PWS (700-850 pm thickness) below an epidermis with intermediate melanin content (corresponding to an olive complexion). Category III is a thick PWS below an epidermis with high melanin content (corresponding to a black complexion). Each category of PWS is divided into two subclasses: (A) superficial, where the depth of the most superficial dermis-PWS interface is 150 pm below the surface of skin, and (B) deep, where the depth of the most superlicial dermis-PWS interface is at 300 pm.
(ii) We represent skin by a one dimensional, semi-infinite medium and model the effect of laser irradiation by assuming an instantaneous deposition of energy that induces temperature increases at skin locations where light is absorbed by (a) melanin within epidermis and @) blood within PWS vessels. This simplified representation of conversion of laser energy into heat generation within the skin does not explicitly take into account the laser light distribution withii the tissue (van Gemert et al 1986, Jacques and Prahl 1987, Keijzer et ai 1989, Miller and Veitch 1993. However, we assume laser-induced initial temperature distributions that are consistent with predicted temperature rises based on pulsed photothermal radiomelry (PPTR) of PWS lesions .
We assume that at t = ifase,, the time when laser energy is deposited, the instantaneous temperature rise due to light absorption by melanin is constant over the epidermis. This assumption is based on the belief that in the region near the surface where melanin absorption takes place, optical backscatter of laser light induces a nearly uniform temperature rise (van Gemert et al 1991, Verkruysse et al 1993. We assume that at t = the temperature distribution withii the PWS layer decreases exponentially with depth with an effective blood absorption coefficient pifmd (m-') for a dermis composed of p% blood by volume . The reduced scattering coefficient within the PWS layer can be neglected since it is much smaller than .the absorption coefficient at 585 nm (Verkruysse et al 1993).
Laser-induced temperature rises in one dimension are given by A %epidermal for z1 < z 4 z2

A U z , Gaser) = (ATo,Pws/~=,~=)~[-'(Z-'~)~ for z3 < z 4 z4
(1) l o for all other z where positions z1 and z2 define the interval over which epidermal melanin absorption takes place, 23 and z4 define the interval where blood absorption takes place (i.e., the region within the skin where the PWS is located) (figure 1). ATO.cpidPrmol ("C) is the epidermal temperature rise due to melanin absorption, h T 0 . p~~ is the average temperature rise at the most superficial dermis-PWS interface (~3 ) . and fore= is the fractional vascular area in a plane parallel to the skin-air interface. It is related to the fractional vascular volume, Assuming that the laser pulse is sufficiently short (e.g., FS 450 ps) that there is no significant heat diffusion during-the irradiation time, the epidermal temperature rise at the end of the laser pulse is computed as (Anderson et a1 1989) where Eo (J m-' ) is the incident laser fluence, p~pidermol ( m -' ) IS ' the epidermal absorption coefficient (e.g., 500, 1800, and 2700 m-' at 585 nm corresponding to types I, II, and ID, respectively) (Svaasand et a1 1995), p is the density (kg m"), c is the specific heat capacity (J kg-' "C-I), ri is the averaged internal reflectance at the air-tissue interface, and Rd is the diffuse reflectance resulting from light that enters the tissue, is scattered, and subsequently reemerges from the tissue, and can be approximated as (Jacques et al 1993) .p,*n.nl From diffusion theory, the optical penetration depth, 8, i s calculated as where ps is the scattering coefficient (e.g., 47 000 m-' for epidermis at 585 nm), and g is the anisotropy factor (e.g., 0.79 for epidermis at 585 nm) (Verkruysse et al 1993). For example, with an incident fluence of 7 J cm-' and assuming minimal loss of optical fluence within a thin 10 p m stratum corneum, the term 2(1 + rL)/(lr,) = 7.1 (Jacques et a1 1993), and the term pc = 3.76 x IO6 J mW3 "C-' for tissue with 75% water content by weight (Jacques et a1 1993). ATO.eprd.rmui is 82°C for a category II PWS.
We calculate ATOJWS in a similar manner as calculatlng A T~,~~i d~~~~l except that we assume matched refractive indices at dermis-PWS interface so that

ATo,pws E(z = ~3 ) / 1 : '~~~/ p C .
We estimate the value of fluence at the most superficial dermis-PWS interface (i.e., (iii) We assume cooling starts at t = 0 and represent the thermal boundary condition at the skin surface as where K (W m-' K-') is the thermal conductivity of skin (0.45 W m-l K-I) (Duck 1990), T ("C) is the temperature within the skin, z (m) is the distance into the skin (with the origin at the skin surface), t (s) is the time, h (W m-z K-') is the heat transfer coefficient, and Tm ("C) is the temperature of the resulting cryogen-ice film (formed as a result of water condensation) at the skin surface during the cryogen spurt, t. The value of h has been determined experimentally to be about 40000 W m-' K-' (Anvari et al 1995). and is assumed here to be constant during the cryogen spurt. With tetrafluoroethane as the cryogen spray, i", ("C) is measured to be about -1O"C, and is assumed to be constant.

E(z
The boundary condition during the spurt represents the presence of the evaporating cryogen on skin surface. Once the cryogen is turned off, we assume an insulated boundary (i.e., h = 0) as most of the cryogen has evaporated shortly after the spurt.

Cooling modalities
We consider two distinct cooling modalities and compare the resulting temperature distributions with those in the absence of cooling. In the first modality, cooling is restricted to the time prior to laser energy deposition, whereas in the second modality, cooling continues for a limited time following laser irradiation. In both modalities, temperatures within skin at any time are calculated by solving the heat conduction equation. With uniform thermal properties and effects of blood perfusion neglected, the heat conduction equation becomes a2T(z, t ) / a z 2 = ( i / + w ( z , w a r (7) where a is the thermal diffusivity of skin (1.1 x equation (7) for both cooling modalities against no cooling are analysed.

2.2.1.
The thermal response with no cooling. The solution of equation (7) with the initial temperature distributions (1) is the sum of the responses to epidermal and PWS temperature rises: m2 s-l) (Duck 1990). Solutions to
Equation (11) gives the temperature distribution within skin before the laser energy is deposited. Since an analytical solution to equation (7) with an initial temperature distribution given in (11) (before laser irradiation) is not readily obtainable, we approximate the initial temperature distribution (11) with an exponential function, T,e-kL, and choose k so that Temperature dishibutions following the laser energy deposition are then obtained by superposition of the thermal response due to cooling, and laser-induced epidermal and PWS temperature changes: 15) AG is the change in surface temperature at the end of the cryogen spurt and k = kJor(ttioser). Expressionk for ATpidcrmoi(~, t > tiorer) and ATpws(z. t z tia$er) are given in (9a) and (9b), respectively.

The thermal response with precooling and postcooling.
In this modality, cryogen spraying continues after laser irradiation. The thermal response in skin after laser irradiation is obtained by superposition of responses due to spray cooling, epidermal heating, and PWS heating (equation (14)). The expression for ATcoo~ing(zr t) is given in equation (11); expressions for ATePipidcrm.j(z, t > tioscr) and ATpw~(z, f > tiarar) are now given as (see ( 1 W and

Epidermal thermal ohmage assessment
We use an index, Q, to quantify the severity of epidermal thermal damage and assume that the rate of change of Q follows an Arrhenius relationship (Glasstone et a1 1941): where A (s-') and AE (J mol-') are constants, R is the universal gas constant (8.314 J mol-' K-I), and T (K) is the absolute temperature. Total damage accumulated over a period t* is obtained by integrating equation (18). We assume complete epidermal necrosis occurs when $2 = 1 (Mckenzie 1990, van Gemert etal 1991 and use the empirical values of A = 3.1 x lo9' s-' and AE = 6.3 x IO5 J mol-' (Henriques 1947): Threshold temperatures, Ch,&old, for epidermal necrosis as a function of time are generated according to equation (19) (figure 2).
io6 lo5 ioa io-* ioL loo 10' Exposure time, t* (s) To specify an optimum cooling modality, we require that (i) the time-averaged temperature of the mean temperature between z = 0 and z = zz remain below T f h r e s h j d , and (ii) in the PWS layer, areas of specified regions that remain above a coagulation threshold temperature (e.g. 60°C) for at least 10 ms after the laser pulse do not differ by more than 5% in the cases of cooling and no cooling, [AGO cooling(Z, t = timer + 10 ms) + To -601 dz < 0.05 (21) where we have specified z* to be the distance over which the temperature distribution within the PWS layer has decreased exponentially with depth by 22% (e-' .").
The latter requirement is imposed to ensure that sufficient time exists for blood vessel photocoagulation and that cooling does not affect the PWS layer.

Results
For a category IIB PWS (thick, deep, with intermediate epidermal melanin content) and an incident fluence of 6 J cm?, the centre of the epidermal layer (assumed to be located IC-50 pm below the surface of the skin) reaches a temperature of 100°C immediately after the laser pulse in absence of cooling ( figure 3). Precooling the skin with a tetrafluoroethane spurt duration of 70 ms keeps the initial temperature jump due to laser irradiation below 80°C. Heat generated in the PWS diffuses to the skin surface as a delayed thermal wave and the temperature peaks to a local maximum value. Precooling the skin results in an overall temperature reduction within the epidermis. for an incident fluence of 7 J on a category IIA PWS, precooling the skin with telrafluoroethane for 70 ms reduces the peak epidermal temperature by almost 30°C, while the temperatures within the PWS layer remain unaffected by cooling ( figure 4). Postcooling the skin for 20 ms after 10 ms of precooling reduces the peak epidermal temperature by approximately 80"C, but also results in almost 40°C temperature reduction at the dermis-PWS interface.  Spraying with tetrafluomethane does not sufficiently reduce the epidermal temperature when using fluences geater than 7 J cm-' on category III PWSs. With a fluence of 8 J cm-' on a category IJIB PWS, temperatures withiin the epidermal layer, 2 ms following the laser pulse, remain above 80°C even after precooling the skin for 100 ms with telratluoroethane (figure 5). By reducing Tm to -3OoC, corresponding to the temperature of the chlorodifluoromethane-ice film at the skin surface (as measured by infrared radiometry in OUT laboratory), the peak temperature within the epidermal layer is reduced to 70°C when precooling the skin with a spurt duration of 80 ms. When using fluences greater than 8 J on a category 111 PWS, relatively long spurts of chlorodifluoromethane are required that can result in cooling of PWS blood vessels as well.

Discussion
Ideal laser treatment of PWS should result in irreversible thermal damage to blood vessels that compromise the PWS while preserving the overlying normal epidermis. Spray cooling of skin with a cryogen such as tetrafiuoroethane has been suggested as a promising technique for eliminating thermal injury during pulsed laser treatment of PWSs (Nebon et al 1995a, b, Anvari et al 1995. The degree and spatial distribution of cooling has been shown to be directly related to the cryogen spurt duration (Anvari et al 1995). Although preliminary clinical results have indicated successful blanching of the PWS without any adverse epidermal thermal injury when using spray cooling in conjunction with flashlamp pumped pulsed dye laser therapy, an optimum cooling modality should be selected on an individual patient basis based on knowledge of the PWS vessel depth distribution (Jacques et al 1993, Milner etal 1994. Recently, an algorithm has been developed to estimate the depth of PWS vessels from the recordings of time-resolved infrared radiometric measurements of the skin surface . The appropriate cooling modality on an individual patient basis may be selected in conjunction with this algorithm or an alternative diagnostic technique.
Our calculations indicate that precooling of skin is sufficient to eliminate epidermal thermal injury. Although postcooling of skin enhances the heat sink capacity available for dissipation of the excessive heat generated within the epidermis, it can also result in cooling of the PWS blood vessels when greater than 10-20 ms in duration.
on patients with intermediate and high epidermal melanin content, respectively, spray cooling the skin by tetrafluoroethane is not sufficient to eliminate epidermal injury. A cryogen that has a lower boiling point than tetrafluoroethane (e.g., chlorodifluoromethane) may be more. appropriate. Larger temperature drops can be obtained in a shorter time and the presence of a larger thermal gradient toward the surface allows for more rapid heat dissipation. Experiments utilizing our theoretical analyses are currently underway in our laboratory to optimize the cooling technique for clinical applications.
For fluences greater than 9 and 7 J

Conclusions
We have presented a theoretical study to examine the thermal response of skin to cryogen spray cooling in conjunction with pulsed laser treatment of PWS at 585 nm. Our calculations indicate that precooling the skin with tetrafluomethane is effective in eliminating epidermal thermal injury when using fluences of less than 10 and 8 J on patients with intermediate and high epidermal melanin content, respectively. Chlorodifluoromethane is shown to be a potentially effective cryogen for eliminating epidermal injury when using fluences greater than those indicated.

Appendix B. Derivations of equations (1Q) and (16b)
With the initial temperature distribution (1) at t = tfase, and the boundary condition (6). the resulting thermal response due to epidermal melanin or blood absorption can be written as (Carslaw and Jaeger 1959)