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0USING COMSOLE MULTYPYSICS IN THE CARDIOVESSEL 1Dilafruz Nurjabova, 2Elmira Nazirova, 3Talipova Ozoda
1,2,3Tashkent University of Information Technologies,"Multimedia Technologies ",100084 1dilyaranur1986@gmail.com, 2elmira nazirova@mail.ru, 3ozoda.talipova.70@mail.ru
https://doi.org/10.5281/zenodo.10659593
Abstract. This abstract discusses the process of solving a differential equation ofparabolic type by the finite difference method. The method is based on discretization of space and time, approximation of derivatives and subsequent calculation offunction values on a grid. The solution of a system of equations is performed using an explicit or implicit scheme. In an explicit scheme, the function values in the new time layer are calculated based on the function values in the previous layer. In the implicit scheme, the function values in the new layer are found as a solution to a system of equations. For the implicit scheme, iterative methods are used.
Keywords: Differential equation, explicit scheme, implicit scheme, mathematical model of blood vessels, discretization of space and time.
The differential equation used to create a mathematical model of blood vessels is usually of the parabolic type.
Modeling blood vessels using parabolic differential equations allows one to study the dynamics of blood flow, the distribution of nutrients and oxygen in organs and tissues, and also predict the effects of various factors on the circulatory system.
The use of differential equations of parabolic type in modeling blood vessels allows one to study phenomena such as blood transport inside vessels, diffusion of nutrients through capillary walls, gas exchange between blood and tissues, etc.
These equations allow us to take into account various parameters, such as the size and shape of blood vessels, their elasticity, blood pressure, vascular resistance and other factors that affect the functioning of the circulatory system. Modeling blood vessels using differential equations of parabolic type helps to better understand and predict various processes occurring in the body, and can be useful for the development of new methods for diagnosing and treating diseases associated with blood circulation. One of the most common parabolic differential equations used in blood vessel modeling is called the diffusion equation or heat equation. This equation describes the distribution of the concentration of a substance or temperature in space and time.
This equation allows one to model the distribution of nutrients, oxygen, or other substances within blood vessels and surrounding tissues. It takes into account the diffusion of a substance along vessels and through their walls, as well as the transfer of a substance under the influence of a concentration gradient.
In addition to the diffusion equation, other parabolic differential equations can be used in modeling blood vessels, including equations that describe the propagation of electrical or chemical signals in the nervous system or the propagation of heat in tissue during laser treatment, for example. The choice of a particular equation depends on the specific characteristics of the system and the physical processes that need to be modeled.
Fig 1. Model of arteries velocity blood flow with oriented place
Fig 2. Model of arteries velocity blood flow with oriented place
Fig 3. Model of arteries velocity blood flow with oriented place
Fig 4. Model of arteries velocity blood flow with oriented place
Fig 5. Model of arteries velocity blood flow with oriented place
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