Analysis of thermal relaxation during laser irradiation of tissue

Background and Objective Thermal relaxation time (τ r ) is a commonly‐used parameter for estimating the time required for heat to conduct away from a directly‐heated tissue region. Previous studies have demonstrated that temperature superposition can occur during multiple‐pulse irradiation, even if the interpulse time is considerably longer than τ r . The objectives of this study were (1) to analyze tissue thermal relaxation following laser‐induced heating, and (2) to calculate the time required for a laser‐induced temperature rise to decrease to near‐baseline values. Study Design/Materials and Methods One‐dimensional (1‐D) analytical and numerical and 2‐D numerical models were designed and used for calculations of the time τ eff required for the peak temperature ( T peak ) to decrease to values slightly over baseline (Δ T base ). Temperature values included T peak =65 and 100°C, and Δ T base  = 5, 10, and 20°C. To generalize the calculations, a wide range of optical and thermal properties was incorporated into the models. Flattop and gaussian spatial beam profiles were also considered. Results 2‐D model calculations of τ eff demonstrated that τ eff (2‐D) was as much as 40 times longer than τ r . For a given combination of T peak and Δ T base , a linear relationship was calculated between τ eff (1‐D) and τ r and was independent of optical and thermal properties. A comparison of 1‐D and 2‐D models demonstrated that 1‐D models generally predicted longer values of τ eff than those predicted with a 2‐D geometry when the laser spot diameter was equal to or less than the optical penetration depth. Conclusion Relatively simple calculations can be performed to estimate τ eff for known values of τ r , T peak and Δ T base . The parameter τ eff may be a better estimate than τ r of tissue thermal relaxation during multiple‐pulse laser irradiation. Lasers Surg. Med. 29:351–359, 2001. © 2001 Wiley‐Liss, Inc.