Methodology for Estimation of Time-Dependent Surface Heat Flux due to Cryogen Spray Cooling JAMES W. TUNNELL,JORGE H. T ORRES, and BAHMAN ANVARI Department of Bioengineering, Rice University, Houston, TX (Received 13 March 2001; accepted 1 November 2001) Abstract—Cryogen spray cooling CSC is an effective tech- nique to protect the epidermis during cutaneous laser therapies. Spraying a cryogen onto the skin surface creates a time-varying heat flux, effectively cooling the skin during and following the cryogen spurt. In previous studies mathematical models were developed to predict the human skin temperature profiles dur- ing the cryogen spraying time. However, no studies have ac- counted for the additional cooling due to residual cryogen left on the skin surface following the spurt termination. We formu- late and solve an inverse heat conduction IHC problem to predict the time-varying surface heat flux both during and fol- lowing a cryogen spurt. The IHC formulation uses measured temperature profiles from within a medium to estimate the surface heat flux. We implement a one-dimensional sequential function specification method SFSM to estimate the surface heat flux from internal temperatures measured within an in vitro model in response to a cryogen spurt. Solution accuracy and experimental errors are examined using simulated tempera- ture data. Heat flux following spurt termination appears sub- stantial; however, it is less than that during the spraying time. The estimated time-varying heat flux can subsequently be used in forward heat conduction models to estimate temperature profiles in skin during and following a cryogen spurt and pre- dict appropriate timing for onset of the laser pulse. © 2002 Biomedical Engineering Society. DOI: 10.1114/1.1432691 Keywords—Inverse heat conduction problem, Sequential func- tion specification, Skin, Selective cooling, Epidermal protec- tion, Heat transfer coefficient. INTRODUCTION Cutaneous laser therapy is based on the principle of selective photothermolysis. 2 Light is preferentially ab- sorbed by subsurface chromophores causing irreversible thermal damage. Applications include port wine stain therapy and removal of tattoos, unwanted hair, and facial rythides. Theoretically, by choosing appropriately short pulse durations and proper wavelength, thermal energy remains confined to the targeted structures. 2,9,12 However, melanin within the overlying epidermis absorbs light over a broad spectrum. 30 This absorption of light by melanin causes nonspecific thermal damage to the epi- dermis and underlying dermis, clinically resulting in blis- tering, dyspigmentation, and, rarely, hypertrophic scarring. 1,8,11,13,15,22,23,32 Cryogen spray cooling CSC has recently been de- veloped to selectively cool the epidermis during cutane- ous laser therapies. 3–6,17,18 The principle of this method is to spray the skin surface with an appropriately short cryogen spurt on the order of tens of milliseconds im- mediately prior to laser exposure so that only the super- ficial skin layers are cooled while the temperature of the deeper targeted chromophores remain unchanged. Thus, in response to the subsequent laser pulse, the temperature within the superficial layer remains below the threshold for thermal damage while the targeted chromophores are thermally destroyed. Spraying a cryogen onto the skin surface creates a time-varying heat flux, effectively cooling the skin dur- ing and following the cryogen spurt. In previous studies, mathematical models were developed to predict the hu- man skin temperature profiles during the cryogen spurt application time. 6,19,25,31,33 However, recent studies have shown that the presence of the residual cryogen remain- ing on the skin surface may result in substantial cooling following spurt termination. 25,26,28 To properly character- ize skin thermal response to the interactions between CSC and laser irradiation during treatment of various dermatologic disorders, an appropriate thermal boundary condition needs to be used at the skin surface following spurt application time. Inasmuch as thermal boundary conditions such as a time-varying heat flux are difficult to measure directly, indirect techniques using internal temperature measure- ments are often used. 24 With these techniques, an inverse heat conduction problem IHCP is solved to estimate the boundary condition from internal temperature measure- ments. We use the sequential function specification SFS method 7 to solve the IHCP and estimate the surface heat flux due to CSC. In doing so, we first analyze the accu- racy and sensitivity of this method to measurement Address correspondence to Bahman Anvari, Department of Bioengineering, Rice University, P.O. Box 1892, Houston, TX 77251. Electronic mail: anvari@rice.edu Annals of Biomedical Engineering, Vol. 30, pp. 19–33, 2002 0090-6964/2002/301/19/15/$15.00 Printed in the USA. All rights reserved. Copyright © 2002 Biomedical Engineering Society 19