生物多孔介质热输运特性的分形分析

发布时间：2018-04-02 15:38

本文选题：生物多孔介质　切入点：血管树　出处：《华中科技大学》2014年博士论文

【摘要】：随着科学技术、现代医疗水平的发展与进步,生物多孔介质热输运的研究在肿瘤热疗、低温外科、移植器官的冷冻储存、生物组织的切割与焊接、疾病诊断、食物的储存和保鲜及热舒适分析等生物科学与医学领域受到了广泛关注,已成为国际学术界的研究热点之一。大量研究表明生物多孔介质的输运通道如血管树、支气管树、动植物养分输运系统等都具有统计自相似的特征,这种输运系统的微结构在一定尺度范围内具有分形特征,并可采用类分形树状分叉网络来描述。所以,分形几何理论可用于分析这类生物多孔介质的热输运问题。在本文中,作者主要研究由血管树及其周围的组织组成的具有分形特征的生物多孔介质的热输运特性。预计该研究在了解和揭示生物组织的热输运特性、物理机理及临床应用中有重要的科学意义和实际应用价值。本文包括六章。第一章综述了生物多孔介质的热输运的研究背景、理论研究和实际应用方面的进展,并简单介绍了类分形树状分叉网络和分形几何理论。第二章基于随机分布的血管树的母管直径满足分形标度律,我们分析了含有随机分布的血管树的生物多孔介质的热传导特性,提出了含有随机分布的血管树的生物多孔介质的有效热导率的分形模型。理论模型预测与已有的死亡组织的实验数据吻合较好。并分析了有效热导率随血管树的结构参数的定量变化关系。第三章考虑了血液流动的影响,应用分形理论与方法分析了含有随机分布的血管树的活体生物组织的传热特性,提出了含有随机分布的血管树的活体生物组织的有效热导率的分形模型,并详细讨论了考虑血液流动后,血管树的结构参数对有效热导率的影响。活体组织的有效热导率的预测与现有的活体组织的实验数据吻合较好,比死亡组织的实验数据和无血液流动的有效热导率模型的预测高。第四章基于血液循环系统,建立了由一个动脉血管树和静脉血管树构成的血管网络和其周围的组织组成的生物组织模型。根据傅里叶定律和热电模拟的方法,分别推导了死亡组织(无血液流动)和活体组织(有血液流动)的有效热导率的解析表达式。两种模型分别与死亡组织和活体组织的实验数据吻合较好。第五章研究了含有血管树的生物多孔介质径向热传导特性,导出了生物多孔介质径向热流的有效热导率的分布函数。第六章总结了本文的主要内容和创新点,而且对应用分形几何理论研究生物多孔介质物理输运特性等给予了展望。
[Abstract]:With the development and progress of science and technology, modern medical level, the study of thermal transport of biological porous media in tumor hyperthermia, hypothermia surgery, cryopreservation of transplanted organs, cutting and welding of biological tissue, disease diagnosis,Food storage, preservation, thermal comfort analysis and other biomedical and medical fields have received extensive attention, and has become one of the hot research topics in international academia.A large number of studies have shown that the transport channels of biological porous media, such as vascular tree, bronchial tree, plant and animal nutrient transport system, all have the characteristics of statistical self-similarity, and the microstructures of this transport system have fractal characteristics in a certain scale.The fractal tree-like bifurcation network can be used to describe it.Therefore, fractal geometry theory can be used to analyze the thermal transport of this kind of biological porous media.In this paper, the authors mainly study the thermal transport properties of porous media with fractal characteristics, which are composed of vascular trees and their surrounding tissues.It is expected that this study will be of great scientific significance and practical value in understanding and revealing the thermal transport characteristics, physical mechanism and clinical application of biological tissues.This paper includes six chapters.In the first chapter, the research background, theoretical research and practical application of thermal transport in biological porous media are reviewed, and the similar fractal tree bifurcation network and fractal geometry theory are briefly introduced.In the second chapter, based on the fact that the diameter of the parent tube of the randomly distributed vascular tree satisfies the fractal scaling law, we analyze the heat conduction characteristics of the porous medium containing the randomly distributed vascular tree.A fractal model of effective thermal conductivity of biological porous media containing randomly distributed vascular trees is proposed.The theoretical model prediction is in good agreement with the experimental data of existing death tissues.The relationship between effective thermal conductivity and the structural parameters of vascular tree was analyzed.In the third chapter, considering the effect of blood flow, the heat transfer characteristics of living tissues with randomly distributed vascular trees are analyzed by using fractal theory and method.A fractal model of effective thermal conductivity of living tissues with randomly distributed vascular trees is proposed. The effect of the structure parameters of vascular trees on effective thermal conductivity is discussed in detail.The prediction of the effective thermal conductivity of living tissue is in good agreement with the experimental data of living tissue, which is higher than that of the experimental data of dead tissue and the effective thermal conductivity model without blood flow.In chapter 4, based on the circulatory system, a biological tissue model is established, which is composed of a vascular network and its surrounding tissues.Based on Fourier's law and thermoelectric simulation, the analytical expressions of effective thermal conductivity of dead tissue (without blood flow) and living tissue (with blood flow) are derived respectively.The two models agree well with the experimental data of dead tissue and living tissue respectively.In chapter 5, the radial heat conduction characteristics of biological porous media containing vascular tree are studied, and the distribution function of effective thermal conductivity of radial heat flux in biological porous media is derived.In chapter 6, the main contents and innovations of this paper are summarized, and the application of fractal geometry theory to the study of physical transport characteristics of biological porous media is prospected.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：R318.08;O357.3

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