Modeling optical and thermal distributions in tissue during laser irradiation

The propagation of light energy in tissues is an important problem in phototherapy, especially with the increased use of lasers as light sources. Often a slight difference in delivered energy separates a useless, efficacious, or disastrous treatment. Methods are presented for experimental characterization of the optical properties of a tissue and computational prediction of the distribution of light energy within a tissue. A standard integrating sphere spectrophotometer measured the total transmission, Tt, total reflectance, Rt, and the on-axis transmission, Ta, for incident collimated light that propagated through the dermis of albino mouse skin, over the visible spectrum. The diffusion approximation solution to the one-dimensional (1-D) optical transport equation computed the expected Tt and Rt for different combinations of absorbance, k, scattering, s, and anisotropy, g, and by iterative comparison of the measured and computed Tt and Rt values converged to the intrinsic tissue parameters. For example, mouse dermis presented optical parameters of 2.8 cm-1, 239 cm-1, and 0.74 for k, s, and g, respectively, at 488 nm wavelength. These values were used in the model to simulate the optical propagation of the 488-nm line of an argon laser through mouse skin in vivo. A 1-D Green's function thermal diffusion model computed the temperature distribution within the tissue at different times during laser irradiation. In vitro experiments showed that the threshold temperature range for coagulation was 60 degrees-70 degrees C, and the kinetics were first order, with a temperature-dependent rate constant that obeyed an Arrhenius relation (molar entropy 276 cal/mol-degrees K, molar enthalpy 102 kcal/mol). The model simulation agreed with the corresponding in vivo experiment that a 2-s pulse at 55 W/cm2 irradiance will achieve coagulation of the skin.