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Lasers Surg Med. 2001;29(4):351-9.

Analysis of thermal relaxation during laser irradiation of tissue.

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Biomedical Engineering Laser Laboratory, The University of Texas at Austin, Austin, TX 78712, USA.



Thermal relaxation time (tau(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 tau(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.


One-dimensional (1-D) analytical and numerical and 2-D numerical models were designed and used for calculations of the time tau(eff) required for the peak temperature (T(peak)) to decrease to values slightly over baseline (DeltaT(base)). Temperature values included T(peak)=65 and 100 degrees C, and DeltaT(base) = 5, 10, and 20 degrees 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.


2-D model calculations of tau(eff) demonstrated that tau(eff) (2-D) was as much as 40 times longer than tau(r). For a given combination of T(peak) and DeltaT(base), a linear relationship was calculated between tau(eff) (1-D) and tau(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 tau(eff) than those predicted with a 2-D geometry when the laser spot diameter was equal to or less than the optical penetration depth.


Relatively simple calculations can be performed to estimate tau(eff) for known values of tau(r), T(peak) and DeltaT(base). The parameter tau(eff) may be a better estimate than tau(r) of tissue thermal relaxation during multiple-pulse laser irradiation.

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