1063-7710/05/5104- $26.00 © 2005 Pleiades Publishing, Inc. 0376 Acoustical Physics, Vol. 51, No. 4, 2005, pp. 376–384. Translated from Akusticheskiœ Zhurnal, Vol. 51, No. 4, 2005, pp. 447–455. Original Russian Text Copyright © 2005 by Anosov, Gavrilov. An important characteristic of a human body is the spatial distribution of the in-depth temperature. Tem- perature monitoring is necessary for various therapeu- tic procedures, such as, for example, hyperthermia in oncology. In this procedure, it is important to heat a tumor up to a certain optimal temperature, for example, to 43–44°ë, and, then, to maintain the temperature for several or several tens of minutes. Monitoring is effec- tive if it is possible to measure the temperature at a depth of 3–8 cm in a volume of about 1 cm 3 with an accuracy of about 0.5 K. For such measurements it is desirable to use nondestructive and noninvasive tech- niques, for example, to receive the thermal acoustic radiation from a biological object in the ultrasonic fre- quency range. In the previous publications [1, 2], the problem of reconstructing the in-depth temperature of a biological object was theoretically investigated and the recon- struction parameters were evaluated. However, in solv- ing this problem, the directivity patterns of receivers were approximated by beams and the ultrasonic absorption coefficient in a biological object was assumed to be known, which is not always possible. Experiments on the reconstruction (using the indicated assumptions) of the in-depth temperature in glycerol and in a human hand were carried out in [2]. The authors of [3–5] theoretically and experimentally reconstructed the position of a heat source within model objects, in some cases, with the use of focused receivers [4, 5]. However, the temperature parameters of the distribution were not evaluated. The authors of [2, 6–8] theoretically and experimentally investigated the abilities of the correlation detection of thermal acoustic radiation in determining the internal tempera- ture of a biological object. In this case, the accuracy of the reconstruction was not estimated. The purpose of the present study is to theoretically investigate the feasibility of the reconstruction of a two- dimensional temperature distribution with the use of linear phased arrays by taking into account the actual directivity patterns of the arrays and by assuming that data on the absorption coefficient are absent. We pro- pose to determine the form of the temperature distribu- tion in two mutually perpendicular directions from the results of electronic scanning of a biological object by two phased arrays and to reconstruct the absorption coefficient in the medium from the difference between the signals measured by these arrays. Then, using the information on the form of the distribution and on the absorption coefficient, we propose to calculate the amplitude of the temperature peak and, thus, to com- pletely reconstruct the temperature distribution. Let us consider the measurement scheme (Fig. 1) proposed for the solution of a two-dimensional prob- lem. (1) A biological object is located within the right angle formed by two rays, 0x and 0z. We assume that ultrasonic absorption within the biological object is constant and determined by the absorption coefficient α 0 . The value of α depends on the frequency of the received signal. We assume that the measurement of thermal acoustic radiation is performed in soft tissue in a frequency range of about 1 MHz and that the ampli- tude absorption coefficient is α ≈ 0.1 cm –1 [9]. We also assume that the attenuation coefficient α is numerically equal to α 0 , since the contribution of scattering to atten- uation in soft tissues (usually no greater than 10–15% Reconstruction of the In-Depth Temperature Distribution for Biological Objects by Linear Phased Arrays A. A. Anosov* and L. R. Gavrilov** * ELDIS Research Center for Electronic Diagnostic Systems, Russian Academy of Sciences, Starosadskiœ per. 8, Moscow, 101000 Russia ** Andreev Acoustics Institute, Russian Academy of Sciences, ul. Shvernika 4, Moscow, 117036 Russia e-mail: anosov@hotmail.ru Received December 2, 2003 Abstract—The feasibility of the reconstruction of two-dimensional temperature distributions in biological objects with the use of linear phased arrays is investigated theoretically with allowances made for the actual array directivity patterns and without using the data on the absorption coefficient. The method provides an opportunity to reconstruct the temperature distribution in the region under investigation with an accuracy of about 0.5 K from the data of 1.5-min-long measurements when the temperature of the region of interest is raised by 5–10 K. © 2005 Pleiades Publishing, Inc.