Limits of radial time constants to approximate thermal response of tissue

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Abstract
The time constant model, as an approximation to the bio-heat equation, was tested for non-ablating, deep penetrating (argon) laser beams in absorbing tissue phantoms (polyacrylamide) in air. Temperature responses were measured with a thermal camera, both during laser irradiation as well as after the laser beam was switched off. The radial time constant model was found to give a reasonable prediction (within 5%) of temperature rise for irradiation times of up to the order of one time constant. The cooling behavior of tissue could not be described by one single time constant. The time constant model was found to fit the early cooling rate (cooling time about equal to irradiation time) for laser pulse durations of up to one time constant. The late cooling rate turned out to be much slower than predicted by the radial time constant model, yet it was faster than the cooling rate predicted by the one-dimensional instantaneous hot cylinder surface model.

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