van Gemert, 1989
Title: Time constants in thermal laser medicine.
Authors: van Gemert MJ, Welch AJ
Journal: Lasers Surg Med 1989;9(4):405-21
PMID: 2761336, UI: 89343474
Affiliated institution: University of Texas, Austin 78712.
Temperature rise of laser-irradiated tissue due to direct absorption of laser light is related to laser parameters (power, spot size, irradiation time, and repetition rate) and tissue parameters (absorption and scattering coefficients, density, heat capacity, and thermal conductivity). Solutions to the bio-heat equation are approximated by introducing axial (z) and radial (r) time constants for heat conduction that represent two parallel channels for heat conduction. These axial (tau z) and radial (tau r) time constants are found proportional to squared distances (z02, r02) that represent the extent of axial and radial temperatures respectively. For convenience, z0 and r0 are approximated to the axial and radial extent of laser light in the tissue. The resulting solution of the bio-heat equation, expressed as temperature rise as function of time and position, is obviously exact for irradiation times short compared to ta z, tau r (adiabatic heating), but is also a quite reasonable approximation up to irradiation times three times the overall time constant. Comparison with (exact) numerical computations show that this holds for all ratios of (light) penetration depth to laser-beam radius; for strongly scattering materials, smaller laser beams give better predictions than do larger laser beams. Several examples of clinical relevance are discussed, such as multiple-laser-pulse irradiation of high- and low-absorbing tissues and laser treatment of port-wine stains, with some unexpected results that also show potential clinical relevance.