INFORMATION TECHNOLOGIES IN THE STUDY OF THE PROBLEM WITH FREE BOUNDARIES OF THE CONTROLLED CRYODESTRUCTION OF BIOLOGICAL TISSUE IN MEDICINE

F.Kh. Kudayeva, A.A. Kaygermazov, D.A. Khashkhozheva, A.Kh. Zhemukhov , S.B. Balkarova, M.B. Etezova
DOI: 10.25699/SSSB.2019.27.37221 Download PDF
Abstract: In recent years , the low-temperature method of destruction of various pathological formations is widely used in medicine. The results archived in the field of Cryobiology and apparatus method allowed to form a new field of medicine cryosurgery, which has become an important clinical method of treatment. Cryosurgery is considered to be an accurate and controlled process, although a complete solution of its thermal aspects has not been obtained to date. In this regard, along with experimental research is very important mathematical modeling of thermal processes of freezing biological tissue, requiring the development of effective methods for solving the most complex problems of mathematical physics – problems such as Stefan. The proposed work is devoted to the study of one-dimensional problem with free boundaries by means of information and communication technologies. The purpose of the application of information and communication technologies in the study of one-dimensional problem with free boundaries. The exact analytical solution of the stationary problem is found. Using information technology, the graphs of the temperature field versus time in the case of controlled cryodestruction and the process of freezing of biological tissue are constructed. An approximate solution of the unsteady problem is obtained by the equivalent linearization method. The results obtained in this work can be applied to the calculation of low-temperature effects on biological tissue, determining the value of the parameters of freezing, as well as in the design of cryoinstruments. In theoretical terms the issues of existence, uniqueness, monotony and spatial localization remain relevant for solving problems. In terms of applications, approximate analytical and numerical-analytical methods of their solution are important here.
Index terms: information and communication technologies, free boundary problem, stationary problem, controlled cryodestruction, mathematical simulation.

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