Abstract
The linear bio-heat transfer equation proposed by Pennes is widely used to predict temperature rise in perfused media. In this article, a mathematical relationship between the predicted temperature increase under perfused and nonperfused conditions is derived based on an analysis of the Pennes equation. The perfused temperature at time t and position r , T perf ( r, t) , can be calculated from the unperfused temperature history T unperf ( r, t) and the time constant for perfusion, τ: T perf( r,t)=T unperf( r,t) exp(−t/τ)+ 1 τ ∫ 0 t exp(−t′/τ)T unperf( r,t′) dt′ When the full nonperfused temperature history is not available, a simpler approximate method of estimating the perfused temperature is also suggested, requiring only a knowledge of the time constant for perfusion. Results are given showing the effects of perfusion after different exposure times for a range of beamwidths and perfusion time constants.
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