Distribution of the acoustobrightness temperature satisfies heat equation

Abstract

Passive acoustic thermometry (PAT), a method proposed for medical applications, involves direct measurement of the acoustobrightness temperature which is the intensity of the thermal acoustic radiation expressed in degrees. The hypothesis has been proposed that the acoustobrightness temperature measured on the surface of the object under study obeys the 2D heat equation whose parameters coincide or are uniquely connected with the parameters of the 3D heat equation governing the deep temperature of the object. Since in PAT a noise signal is measured, the achievement of an acceptable error level (0.5–1 K) requires a considerable integration time (about a minute). The proposed hypothesis will enable linking together the data obtained by acoustothermometric sensors separated in space, at different points in time. This, in turn, will lower the dimensionality of the problem of temperature distribution reconstruction and enable reducing the integration time without loss of accuracy. The proposed hypothesis has been confirmed experimentally and with the aid of computer simulation for the case where local hyperthermia of soft tissues of the human organism is modeled.