Ex vivo determined experimental correction factor for the ultrasonic source term in the bioheat equation

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Abstract

The objective of this work is to propose an effective absorption coefficient (αeffec) as an empirical correction factor in the source term of the bioheat equation. The temperature rise in biological tissue due to ultrasound insonification is produced by energy absorption. Usually, the ultrasonic absorption coefficient (αA) is used as a source term in the bioheat equation to quantify the temperature rise, and the effect of scattering is disregarded. The coefficient αeffec includes the scattering contribution as an additional absorption term and should allow us to make a better estimation of the thermal dose (TD), which is important for clinical applications. We simulated the bioheat equation with the source term considering αA or αeffec, and with heating provided by therapeutic ultrasound (1 MHz, 2.0 W cm−2) for about 5.5 min (temperature range 36–46 °C). Experimental data were obtained in similar heating conditions for a bovine muscle tissue (ex vivo) and temperature curves were measured for depths 7, 30, 35, 40 and 45 mm. The TD values from the experimental temperature curves at each depth were compared with the numerical solution of the bioheat equation with the classical and corrected source terms. The highest percentual difference between simulated and experimental TD was 42.5% when assuming the classical αA, and 8.7% for the corrected αeffec. The results show that the effective absorption coefficient is a feasible parameter to improve the classical bioheat transfer model, especially for depths larger than the mean free propagation path.

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