Time constants in thermal laser medicine

TLDR

Laser‑induced temperature rise in tissue depends on laser power, spot size, irradiation time, repetition rate, and tissue absorption, scattering, density, heat capacity, and thermal conductivity. The authors approximate the bio‑heat equation by introducing axial and radial time constants that represent parallel heat‑conduction channels, using the laser light extents z₀ and r₀ as the characteristic distances, and apply this model to clinical scenarios such as multi‑pulse irradiation and port‑wine stain treatment. The axial and radial time constants are proportional to the squares of their respective distances, giving an exact solution for short irradiation times and a reasonable approximation up to three times the overall time constant; numerical comparisons confirm accuracy for all penetration‑to‑beam‑radius ratios, with smaller beams yielding better predictions in strongly scattering tissues, and the model predicts clinically relevant outcomes for multi‑pulse irradiation and port‑wine stain treatment.

Abstract

Abstract 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 (τ z ) and radial (τ r ) time constants are found proportional to squared distances ( z O 2 , r O 2 ) that represent the extent of axial and radial temperatures respectively. For convenience, z O and r O are approximated to the axial and radial extent of laser light in the tissue. The resulting solution of the bioheat equation, expressed as temperature rise as function of time and position, is obviously exact for irradiation times short compared to τ z , τ 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.