Abstract

Mathematical models are described in which the circulatory system of an organism is considered as a multifractal object. The solution to two problems is given. The first one is associated with the normal state of the body’s life support system, namely, to heat transfer in human skin. The equations of hydrodynamics and heat transfer are the basis of the model. Quantitative results of calculating heat fluxes in three layers of the dermis are presented. The second problem is a violation of fractality due to the presence of arteriovenous malformation in the vascular system of the brain. Blood flow modeling in the presence of malformation was performed using the SolidWorks 2017 Flow Simulation software product. Data on blood velocity and blood flow in vessels for various cases of malformation are presented.

中文翻译：

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畸形是对生物循环系统分形结构的侵犯

摘要

描述了将生物体的循环系统视为多重分形对象的数学模型。给出了两个问题的解决方案。第一个与人体生命维持系统的正常状态有关，即人体皮肤中的热传递。流体力学和传热方程是该模型的基础。给出了计算真皮三层中热通量的定量结果。第二个问题是由于脑血管系统中动静脉畸形的存在而导致的分形性破坏。使用SolidWorks 2017 Flow Simulation软件产品在存在畸形的情况下进行血流建模。给出了各种畸形情况下血管速度和血流量的数据。