title: A new mathematical approach to the diffusion approximation theory for selective photothermolysis modeling and its implication in laser treatment of port-wine stains.
abstract: OBJECTIVE
  Monte Carlo (MC) simulations of light-tissue interactions and analytical solutions for the diffusion approximation theory have been used to determine the optimal laser wavelength and radiant exposure to treat port-wine stains (PWS). Both approaches suggest that optimal parameters are a wavelength of 585 or 595-nm with pulse times of 0.45-20 milliseconds. However, which parameters are optimal is still unclear. As differences in vessel size and in temperature distribution within vessels appeared to be the main reasons for the varied responses to the same laser treatments, we sought to develop a solution to the diffusion approximation in order to calculate temperature distribution and the resulting coagulation pattern within specific blood vessels.
  
  
  METHODS
  The light and heat diffusion equations were simultaneously solved with the finite element method (FEM). The latent heat of evaporation was included in the thermal analysis. The temperature and coagulation patterns across specific blood vessels, within a heterogeneous medium, were calculated for laser wavelengths of 585 and 595-nm with clinical parameters.
  
  
  RESULTS
  At 1.2 mm deep, the calculations predicted that vessels ranging from 50 to 100 microm in diameter would be coagulated from top to bottom, small vessels (10 microm) would be spared, and vessels larger than 150 microm would be partially coagulated. Coagulation across vessels was more uniform for the 595-nm than for the 585-nm wavelength. Maximal temperatures did not exceed 100 degrees C because of the inclusion of latent heat in the thermal calculations.
  
  
  CONCLUSIONS
  To study laser treatments of PWS with the diffusion approximation, FEM is an effective method to calculate the coagulation patterns within specific blood vessels. To improve coagulation efficacy at 585 and 595-nm wavelengths, the radiant exposure should be increased without increasing the irradiance.
authors.affiliation: Vascular Anomalies Center, Arkansas Children's Hospital and University of Arkansas for Medical Sciences, Little Rock, Arkansas 72202, USA. shafirsteingal@uams.edu
authors.forename: Gal
authors.initials: G
authors.lastname: Shafirstein
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Bäumler
authors.forename: Moshe
authors.initials: M
authors.lastname: Lapidoth
authors.forename: Scott
authors.initials: S
authors.lastname: Ferguson
authors.forename: Paula E
authors.initials: PE
authors.lastname: North
authors.forename: Milton
authors.initials: M
authors.lastname: Waner
mesh_terms: D001831:Body Temperature / Q000528:radiation effects*; D006801:Humans; D017075:Laser Coagulation / Q000379:methods; D028022:Low-Level Light Therapy / Q000379:methods*; D008962:Models, Theoretical; D009010:Monte Carlo Method; D019339:Port-Wine Stain / Q000628:therapy*