Selective cooling of biological tissues: application for thermally mediated therapeutic procedures

The ability to control the degree and spatial distribution of cooling in biological tissues during a thermally mediated therapeutic procedure would be useful for several biomedical applications of lasers. The authors present a theory based on the solution of the heat conduction equation that demonstrates the feasibility of selectively cooling biological tissues. Model predictions are compared with infrared thermal measurements of in vivo human skin in response to cooling by a cryogen spurt. The presence of a boundary layer, undergoing a liquid-vapour phase transition, is associated with a relatively large thermal convection coefficient ( approximately=40 kW m-2 K-1), which gives rise to the observed surface temperature reductions (30-40 degrees C). The degree and the spatial temporal distribution of cooling are shown to be directly related to the cryogen spurt duration.


Introduction
Selective cooling of biological tissues whereby the degree and spatial distribution of cooling can be achieved in a controlled manner would be of benefit for several therapeutic procedures in dermatology where the objective of treatment is to produce irreversible thermal damage to subsurface tissue constituents without destroying or altering superficial structures. Examples of such procedures include laser treatment of port wine stains (pws), telangiectasias, and a haemangiomas in which the ideal therapeutic outcome is photothermolysis of subsurface dermal blood vessels without damage to the normal overlying epidermis (Anderson and Parris 1983). Selective cooling would also be beneficial in the clinical management of paiients with other dermatoses, such as dermal melanocytic lesions and tattoos (Nelson We present a theory, which incorporates thermal and radiometric considerations, that demonstrates the feasibility of selectively cooling biological tissues. Experiments that use infrared radiometry to measure the thermal response of in vivo human skin to cooling by a cryogen spurt are conducted to verify the theoretical results. The heat transfer process resulting from cryogen cooling and the potential dermatologic application to laser treatment of PWS are discussed.

I. Heat transfer
We assume a two-layered semi-infinite medium consisting of skin in contact with a cold film whose thickness may change with time (figure I). Since the film is in contact with both air and skin, we refer to it as a 'boundary layer' (bl) and interpret its formation as follows. During the time course of a cryogen spurt, skin temperature is reduced as a result of supplying the latent heat of vaporization. As the skin surface temperature approaches the boiling point of the cryogen, the rate at which cryogen droplets evaporate becomes less than the accumulation rate. Consequently, a boundary layer of thickness d ( t ) , consisting of a mixture of cryogen and ice (resulting from condensation), is formed on the skin surface at a constant growth rate of d (micrometres per second). Assuming uniform thermal properties and neglecting blood perfusion and sources of internal heat generation (e.g. tissue metabolism), temperature distributions within skin, T ( z > 0, t ) , for the case where the lateral dimensions of the cooled area are much larger than the thermal penetration depth, are calculated by solving the one-dimensional heat conduction equation, where T ( z , r) (degrees Celsius) is the temperature at time t (seconds) and position z (metres), and a is the thermal diffusivity of skin (1.1 x lo-' m2 s-I) (Duck 1990). When cooling the skin by formation of a cold boundary layer, a convective boundary condition is imposed at the skin-film interface: where k (watts per metre per kelvin) is the thermal conductivity of skin (0.45 W m-' K-') (Duck 1990). h (watts per square metre per kelvin) is the thermal convection coefficient (a quantity not known a priori) and T, (degrees Celsius) is the temperature of the boundary layer (i.e. T(-d < z < 0) = T, is assumed to be constant). Using the method of Laplace transformation, the solution to equation (1) with the given boundary condition (equation (2)) and a uniform initial temperature, T ( z =-0, t = 0) = TO is (Carslaw and Jaeger 1959) where and erfc(x) is the complementary error function, 1 -erfc(x). According to equation ( 1 0

Radiometrics
Let Eb,Ah(T(~, f)) (watts per square metre) be the emissive power of a black body within a spectral bandwidth, AA, at a prescribed temperature. Expanding Eb,Ak(T(z, t ) ) in a Taylor series about the initial temperature, TO, and keeping the first two terms in the series gives Eb,AA(T(Z, 2)) R5 Eb,Ak(TO) + [aEb.Ah(T(Z, t))/aT(Z, t)llT=To,[Tk f ) -TO].
The measured radiometric signal, AS@) (degrees Celsius), is proportional to the change in the emissive power of a black body at a prescribed temperature within the by integrating the attenuated infrared emission over all depths. For the two-layered semiinfinite medium shown in figure 1, Spectral bandwidth AA (i.e. proportional to Eb,Ah(T(Z, t ) ) -Eb,Ah(To), and iS computed where pii(z) (per metre) is the infrared attenuation coefficient, assumed to be constant over the spectral bandwidth A?. , and C is a calibration factor that is related to the product of the term [aEb,ah(T(z, t))/aT(z, t ) ] I~= 5 and the specific infrared detection system characteristics (e.g. detector area and responsivity).
With p.ir(z) = j&,l for -d(t) e z < 0, and pjr(z) = p*i. for z > 0, the integral in the argument of the exponential function in equation (8) is evaluated as (9) into equation (8), Using the expressions for T(z, t) given in subsection 2.1, equation (10) becomes AS(t) denotes the 'radiometric temperature' change in the presence of an attenuating boundary layer. The two terms on the RHS of equation (11) represent, from left to right, the attenuated infrared emission from the boundary layer and skin, respectively.

Methods and materials
In vivo human skin on fingers and forearm was cooled with a cryogen spray (1.1.1.2. tetrafluoroethane, CzHzF4, an environmentally compatible, non-toxic, non-flammable freon substitute, BP = -26.2"C) (figure 3). Cryogen was contained in a pressurized steel canister (-5 atm), and delivered through an electronically controlled standard fuel injection valve (aperture diameter % 1 mm) covering a 7 mm diameter area on the skin. The duration of the cryogen spurt, r (5-80 ms), was controlled by a programmable digital delay generator (DG535, Stanford Research Systems). The distance between the aperture of the solenoid valve and the skin surface was maintained at 20 mm.
Infrared emission from the cooled skin site was detected using a 1 mm2 liquid N2 cooled HgCdTe detector (MDD-IOEO-S1, Cincinnati Electronics) placed at the focal plane of a 25 mm diameter f/l Ge lens, and optically filtered by a 7-1 1 j m handpass filter (RL-7500-F, Corion). The collection optics was configured for unit magnification and had an exit pupil of 5 mm diameter positioned 50 mm from the detector, resulting in an f/IO system. The optical axis was oriented normal to the cooled skin site. For improved signal to noise ratio, the infrared radiation was amplitude modulated (3 kHz) using a mechanical chopper, and synchronously detected by a lock-in amplifier (SRXSO, Stanford Research Systems).
The temperature response of the detection system was calibrated by measuring the lockin amplifier voltage as a function of the surface temperature of an AI block, coated with highly emissive ( E % 0.97) black paint (TC-303 black, GIE Corp.), and heated from 23 to 45 "C by a resistive element. The surface temperature of the AI block was measured using a precision thermistor (86x1, Keithley) attached to the block; the measured voltage was proportional to the surface temperature (1.05 mV "C-').
In order to investigate the effect of stratum corneum thickness on the measured infrared signal, we compared spraying skin on fingers to that on the forearm where the stratum B Anvari et ul corneum is thinner. The skin water content is known to increase from the surface towards the stratum corneum-ganulosum interface (Bommannan et al 1990, von Zglinick er al 1993. Thus, the radiomelric temperature in response to a cryogen spurt at these anatomical sites may be different under similar experimental conditions. Each site was sprayed eight times for a given r and the resulting signals averaged. A Michelson intefierometer using an He-Ne laser (A = 632 nm) as a coherent light source was used to estimate the thickness of the boundary layer. One mirror of the interferometer was sprayed with the cryogen and the resulting boundary layer thickness, d , was related to the number of fringes, N , and the index of refraction of the cryogen, n (assumed to be w 1.5), as d = N1/2(n-1). (12)

Results
The radiometric temperature showed a rapid decrease (figure 4) in response to spraying the skin for various spurt durations. For r = 5 ms, an immediate radiomehic temperature reduction to 0°C was measured; longer spurts resulted in radiometric temperatures between -4°C and -10°C. After termination-of the cryogen spurt the radiometric temperature began to increase. Increased spurt duration resulted in a longer relaxation time to the initial baseline temperature.
., , , , . ,, , , , , . , , , , , , .. For r = 80 ms, ice formation (presumably by condensation of water vapour present in the air) on the skin surface was observed. Measurements using laser interferometry indicated the, thickness of the boundary layer to be -20 pm. The presence of a quasiequilibrium state, during which the temperature was constant for -100 ms, is probably due to iceliquid (i.e. melting) and/or ice-vapour (i.e. sublimation) phase transitions. For shorter spurt durations, smaller quantities of ice may have formed, resulting in an imperceptible phase transition time.
Measurements of the thermal response of fingers and forearm for r = 5 ms are shown in figure 5: spraying the forearm consistently resulted in significantly lower radiometric temperatures. A discussion of this observation is presented later (section 5). and -1O"C, respectively. Considering that water is the major constituent of the skin, we used &kin = 0.06 ,urn-', characteristic of liquid water in the 7-11 pm spectral region (Hale andQueny 1973, Marechal 1991).
For a 20 p m thick film that accumulates in 80 ms (2 = 0.25 pm ms-'), increased infrared attenuation by the boundary layer is predicted to result in lower values of the radiometric temperature. As infrared attenuation of the boundary layer increases, there is a greater conhibution to the detected signal from the boundary layer and the radiometric temperature approaches that of the boundary layer. Conversely, as p~u + 0, the detected signal originates from the skin. The physical model of the boundary layer described above gives good agreement with infrared thermal measurements for all spurt durations; we present results for r = 80 ms (figure 7). We used h = 40 kW m-2 K-I and T, = -9 "C to fit the results of the radiometric temperature for the fingers (figure 7(a)), and h = 90 kW mU2 K-' and T, = -1 1 "C to fit the results of the measurements on the forearm (figure 7(b)). Values of pbl = 0.3 fim-' and d = 0.25 wm ms-I were used in both cases. Values of h are well within the range of known heat transfer coefficienti representing convective heat transfer due to a liquid-vapour phase transition (Incropera and Dewitt 1981).
To examine the uniqueness of the parameters used in fitting the experimental data, a sensitivity study on T, and d revealed that T, had a more pronounced effect on the predicted temperatures. As T , was lowered by a factor of two, the radiometric surface temperature decreased by a few degrees (-3°C) in the first few milliseconds and approached T, with increasing time. Increasing d by a factor of two resulted in a reduction of the radiometric surface temperature by about 2°C in the first few milliseconds without affecting the response for t > 30 ms.
The instantaneous heat flux, q , at the skin surface is maximum at the instant when the cryogen is deposited, as the induced thermal gradient is greatest at this time (figure 8). After 10 ms, the heat flux has diminished appreciably, whereas the total amount of heat removed at the surface, Q, continues to increase,^ albeit both at reduced rates.
Calculated values of T ( z ) within skin (using h = 40 kW m-* K-l, and Tm = -9°C) illustrate the feasibility of selectively cooling biological tissue (figure 9). The duration of the cryogen spurt can be used to control the degree and spatial/temporal distribution of cooling in tissue. For example, locations 20 pm below the surface can be cooled by 20°C in response to a cryogen spurt of r = 20 ms duration, while temperatures of deeper layers located below 100 p m remain'unchanged. At positions below 300 pm, temperatures are unaffected by the spurt duration (for 5 < 80 ms).  (-) and measured (0) radiometric temperature, for a clyogen spurt duration T = 80 ms, of (a) fingers and (b) forearm.

Discussion
Our theory predicts that temperature reductions to less than 0°C at the skin surface can be obtained by large thermal convection coefficients that are associated with a liquid-vapour

m,
of the detected infrared signal originates from the more superficial, less attenuating layers of skin. Conversely, on the fingers, where the stratum corneum is thicker, a greater portion of the detected infrared signal originates from the deeper and warmer layers. Therefore, on the fingers, the infrared detection system probes deeper into the skin and the radiometric temperature in response to a cryogen spurt is expected to be higher than for corresponding measurements on the forearm (fi,pe 7). An equivalent explanation can be presented in terms of emissivity rather than absorbance of water. Selective cooling of tissue as an integral part of a therapeutic procedure could be useful for various biomedical applications, for example in the laser treatment of PWS. Ideally, such a treatment method should result in irreversible thermal damage to blood vessels that comprise the PWS while preserving the normal overlying epidermis. Encouraging results have been reported in a preliminary clinical study using millisecond cryogen spurts to protect the skin surface from damaging thermal effects associated with light absorption by epidermal melanin (Nelson et a1 1994). However, further development of the cooling strategy is needed for optimal treatment of PWS. For example, the relative timing between laser irradiation and cryogen spurt delivery is important. When irradiating with a flashlamp pumped pulsed dye laser, an effective strategy might be one that delivers a laser pulse during a relatively long spurt. Prior to laser irradiation, cooling reduces the temperature in the pigmented epidermis, while the presence of the boundary layer during and after laser exposure provides a heat sink for dissipation of epidermal heat generated by melanin absorption. Studies are currently under way in OUT laborat07 to examine the resulting thermal response of skin to cryogen spray cooling during laser irradiation.

Conclusions
We have developed a theory for radiometric temperature in the presence of an attenuating convective boundary layer in contact with a semi-infinite medium. The theory, in combination with radiomehic temperature measurements, can be used to estimate the value of the convective heat eansfer coefficient.
The time controlled formation of a boundary layer on the skin surface can be used for selective cooling. The liquid-vapour phase transition of a cryogen (e.g. tetrafluoroethane) is sustained by heat transferred from the skin and results in subsequent cooling of tissue. Large temperature drops (3MO"C) in thin superficial layers (50-150 pm) are obtained in short periods of time (5-80 ms). The degree and spatialkemporal distribution of tissue cooling can be achieved in a controlled manner by adjusting the cryogen spurt duration.