Modeling optical and thermal distributions in tissue during laser irradiation

TLDR

Light propagation in tissues is a key issue for phototherapy, and small variations in delivered energy can determine whether a treatment is ineffective, effective, or harmful. The authors develop experimental techniques to measure tissue optical properties and computational models to predict the distribution of light energy within tissue. They measured transmission and reflection with an integrating sphere, fitted a diffusion‑approximation model to obtain absorption, scattering, and anisotropy parameters, and then used those parameters in a 1‑D Green’s‑function thermal diffusion model to simulate 488‑nm argon‑laser propagation and heating in mouse skin. The resulting optical parameters (k = 2.8 cm⁻¹, s = 239 cm⁻¹, g = 0.74 at 488 nm) and the model predict that a 2‑s, 55 W cm⁻² pulse induces coagulation, with an in‑vitro coagulation threshold of 60–70 °C following first‑order Arrhenius kinetics, and the simulation agrees with in‑vivo experiments.

Abstract

Abstract 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 spectrophototneter measured the total transmission, T t , total reflectance, R t , and the on‐axis transmission, T a , 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 T t , and R t , for different combinations of absorbance, k , scattering, s , and anisotropy, g , and by iterative comparison of the measured and computed T t , and R t , 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°–70° C, and the kinetics were first order, with a temperature‐dependent rate constant that obeyed an Arrhenius relation (molar entropy 276 cal/mol‐°K, molar enthalpy 102 kcal/mol). The model simulation agreed with the corresponding in vivo experiment that a 2‐s pulse at 55 W/cm 2 irradiance will achieve coagulation of the skin.