METHODOLOGICAL APPROACH TO THE MATHEMATICAL MODELS CONSTRUCTION OF BIOOBJECT PROBLEMS - KRAVTSOV, Andrii; LEVKIN, Dmytro; BEREZHNA, Natalija; LEVKIN, Artur (Herald of Khmelnytskyi National University. Technical sciences, 2023)
This article reveals a technique for the mathematical modeling of biotechnological systems that contain sources of laser action. Calculation and optimization mathematical models for finding rational values of the technical parameters of the emitters are the basis for this. The authors researched the main aspects of the theory of analysis and synthesis of complex systems that contain concentrated, moving sources of physical fields. To ensure the viability of embryo cells, it is necessary to carefully monitor the level of embryo heating not only at the points closest to the laser dissection site but also at the end of the laser action. It should also be noted that at the end of the short-term effect of laser radiation, the flow of heat from the border of the embryo dissection passes to other parts of it. The non-stationary process of thermal distribution will occur until a stationary mode is established, which is necessary to maintain the viability of the embryo. Due to the peculiarities of the microbiological object, the authors perform mathematical modeling of a non-stationary, nonlinear, multidimensional biotechnological system, which contains a discrete, moving source of laser action. It is quite difficult to implement applied optimization mathematical models that are used to optimize the modeled system. Therefore, it is advisable to obtain approximate solutions to boundary value problems with averaged values of thermophysical parameters of laser emitters without considering the three-layer structure of the embryo. To increase the level of viability of germ cells, the authors propose to implement an applied optimization mathematical model for minimizing the deviation of the temperature of laser action from its acceptable value. This will make it possible to obtain rational technical parameters of the emitters, which are close to reality and satisfy the needs of the technical use of laser emitters.