Introduction Biological tissues of human body emit electromag- netic waves in a wide frequency range. Microwaves emit- ted by tissues bear information that can be used for non- invasive detection of thermal anomalies located at a depth of several centimeters by the method of microwave radiometry (MR). Development of noise-proof radiome- ters made unnecessary the electromagnetic shielding of the room where measurements are taken and opened pos- sibilities for wide use of MR in medicine [1]. In particu- lar, MR can be used for cancer diagnosis. Increased metabolism and vascularization of tumors result in high- er temperatures at early stages of carcinogenesis (pro- nounced proliferation and atypical changes). The tem- perature of the tumor depends on its doubling time. This allows the most aggressive tumors to be detected by MR [2, 3]. Interest to MR can be explained by the high sensi- tivity of this method when used to detect patients at risk of breast cancer, as well as by possibility of ultra-early diagnosis and painlessness of the diagnostic procedure. Another advantage of the method is that it does not involve exposure to radiation. The procedure of MR diag- nosis is based on measuring the internal and skin temper- atures. Besides oncology, this procedure is used in such branches of medicine as treatment of strokes and cranio- cerebral injuries [4]; detection of inflamed atheromatous plaques and stroke prognosis [5]; diagnosis of spine and joint diseases [6], small pelvis diseases [8], and pyelonephritis [8]; monitoring in the process of treatment of pathologies of the lower limb vessels [9], etc. Until recently, MR had been performed based mainly on exper- imental data or simplified models allowing the measure- ment depth to be determined. Thus, it is of particular interest to carry out mathematical simulation of microwave emission of biological tissues, such as breast tissues with or without a malignant tumor. Simulation should be performed with due regard to the structure of the measuring antennas and the thermophysical parame- ters of biological tissues. Methods The brightness temperature (BT) T rad is determined from the power of emission of breast tissues. The rela- tionship between BT and thermodynamic temperature is as follows: (1) Biomedical Engineering, Vol. 52, No. 3, September, 2018, pp. 190-194. Translated from Meditsinskaya Tekhnika, Vol. 52, No. 3, May-Jun., 2018, pp. 33-36. Original article submitted November 28, 2017. 190 0006-3398/18/5203-0190  2018 Springer Science+Business Media, LLC 1 Main Research and Testing Robotics Centre of the Ministry of Defense of the Russian Federation (MRTRC), Moscow, Russia. 2 Hyperion Ltd., Moscow, Russia; E-mail: ooo.giperion@gmail.com 3 Bauman Moscow State Technical University, Moscow, Russia. 4 RES Company, Moscow, Russia. 5 JSC Radio Engineering Corporation “Vega”, Moscow, Russia. 6 Peoples’ Friendship University of Russia, Moscow, Russia. * To whom correspondence should be addressed. Mathematical Simulation of Heat Transfer Processes in a Breast with a Malignant Tumor M. K. Sedankin 1 , V. Yu. Leushin 2 *, A. G. Gudkov 3 , S. G. Vesnin 4 , I. A. Sidorov 5 , S. V. Agasieva 6 , and A. V. Markin 3 Mathematical simulation of heat-exchange processes in a breast with a malignant tumor was carried out taking into account thermophysical properties of internal tissues. The results of calculation of the physical temperature in the breast and the brightness temperature for four antennas used in breast care are presented. The obtained results can be used in developing new medical antennas and radiometers with improved characteristics. DOI 10.1007/s10527-018-9811-2