Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2023. №8
ContentsFull text in Russian (pdf)
DOI: https://doi.org/10.30898/1684-1719.2023.8.1
DOES THE ACOUSTOBRIGHTNESS TEMPERATURE SATISFY
THE HEAT EQUATION?
A.A. Anosov 1,2, A.A. Sharakshane 2
1 Sechenov First Moscow State Medical University (Sechenov University)
119991, Russia, Moscow, st. Trubetskaya, d. 8, building 2
2 Kotelnikov IRE RAS
125009, Russia, Moscow, Mokhovaya str., 11, b.7
The paper was received January 29, 2023.
Abstract. In medicine, the monitoring of local hyperthermia requires painless measurements of the deep temperature with an error not exceeding 0.5–1 К and spacial resolution no worse than 5 mm. For temperature measurements, the use of passive acoustic thermometry is proposed based on the registration of the inherent thermal acoustic noise of the object. The measurements of the noise signal require a considerable integration time: in the megahertz range, attaining a desired accuracy requires that the signal be averaged during 30–50 s. To reduce this time without loss of accuracy, we propose to restore the temperature using the heat equation with blood flow. Local deep hyperthermia of the human soft tissues was examined. The three-dimensional heat equation (governing the deep temperature) was integrated with respect to depth, with a weight coefficient accounting for the absorption of ultrasound, subject to the instrument function of the receiving detector, to obtain a differential equation for the acoustobrightness temperature (measured signal). It was shown that, during the initial stage of the heating (~ 5 min), the distribution of the acoustobrightness temperature on the body surface satisfies approximately the 2D heat equation whose parameters are uniquely determined by the 3D heat equation governing the distribution of the deep temperature. Computations were carried out using the values of the thermal conductivity coefficient, specific blood flow, and ultrasound absorption coefficient typical for the soft tissues of the human organism as well as typical parameters of the source in the local, five-minute heating of soft tissues. The acoustobrightness temperature was computed in the standard way, using the known integral expression, with and without the detector instrument function, as well as through the solution of the obtained 2D heat equation. The discrepancy between the acoustobrightness temperatures computed through the different procedures grows with time but after five minutes of heating, it does not exceed the measurement error. A condition was introduced to determine the acceptability of the approximation made. The proposed approximation enables determination of the heat equation parameters from acoustobrightness temperature measurements, which makes it possible to compute the deep temperature distribution at any point in time.
Key words: passive acoustic thermometry; thermal acoustic radiation; temperature reconstruction; the Pennes heat equation; acoustobrightness temperature.
Financing: The investigation was supported by a grant from the Russian Science Foundation No 23-22-00175, https://rscf.ru/project/23-22-00175/
Corresponding author: Anosov Andrey Anatol’evich, anosov_a_a@staff.sechenov.ru
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For citation:
Anosov A.A., Sharakshane A.A. Does the acoustobrightness temperature satisfy the heat equation? Zhurnal radioelektroniki [Journal of Radio Electronics].
2023. №8. https://doi.org/10.30898/1684-1719.2023.8.1 (In Russian)