@article{jacques87a,
  author = {S. L. Jacques and S. A. Prahl},
  title = {Modeling Optical and Thermal Distributions in Tissue During Laser Irradiation},
  journal = {Lasers Surg. Med.},
  year = {1987},
  volume = {6},
  pages = {494--503},
  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 spectrophotometer 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 \textit{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$^\circ$C, and the kinetics were first order, with a temperature-dependent rate constant that obeyed an Arrhenius relation (molar entropy 276\,cal/mol$^\circ$K, molar enthalpy 102\,kcal/mol). The model simulation agreed with the corresponding \textit{in vivo} experiment that a 2\,s pulse at 55\,W/cm $^2$ irradiance will achieve coagulation of the skin.},
}