具有异质化功能特性的微血管网络数学模型研究

Microvascular network is the fundamental functional unit in circulatory system. Due to the features of microvascular network, such as small size, high density, complex connection structure and uncertain boundary conditions and comprehensive regulatory processes, the mathematical model for the microvascular network has become one of the challenges in the research of simulation and modeling of physiological system. Fractal theory provides a basic modeling strategy for describing complex microvascular system. However, the existing methods failed to mimic the important functions like substance exchange and network regulation, mostly limited in the statistical analysis of blood vessel topological structure and parameters because of the neglecting of the network heterogeneity. The present study aims to develop the functional model of microvascular network based on the heterogeneous fractal theory. The work will introduce the topological and functional fractal characteristics of the microvascular network in the modeling, focusing on the heterogeneous expression of the fractal dimension in the microvascular network, the construction of the capillary elasticity network, as well as the heterogeneous regulation mechanism. Finally, a heterogeneous fractal mathematical model for the microvascular network will be established based on the experimental data of model animals. The outcome of the proposal will produce a complete solution for the study of functional microvascular network models, offer a reliable technical approach for physiological and clinical application, and contribute to the international development in this field.

微血管网络是循环系统最基本的功能单位，由于尺寸微小、密度高、结构复杂、边界条件不确定、调控过程繁多等特点，使得微血管网络数学模型成为生理系统仿真建模研究的难点之一。分形理论可以为描述复杂微血管系统提供基本建模方法，但由于缺乏对网络异质性的研究，现有方法多限于血管拓扑结构及参数的统计分析，难以仿真物质交换、网络调控等最为重要的功能特性。本申请拟开展基于异质化分形理论的微血管网络功能模型研究，引入微血管网络的拓扑及功能分形特性，重点解决微血管网络异质化表达方法、毛细血管功能性弹性网络构建、网络分形调控机制等关键问题，最终基于模式动物实验数据建立具有异质化特性的功能性微血管网络分形数学模型。本申请预计将形成微血管网络功能模型研究较为完整的解决方案，为微血管网络的生理、临床研究提供可靠技术方法，并在国际相关研究领域中产生影响。

本项目重点开展了微循环网络调控机制、微循环网络的拓扑及功能异质化特性等研究。解决了微循环网络长时程-短时程调控机制耦合难题，基于模式动物实验数据建立了脉动血流调制的长短时程微循环网络调控模型，定量分析了一氧化氮等对血管网络的调控过程。解决了兼顾表征异构血管网络中局部-全局信息的难题，应用分形分析技术建立了描述异质化血管网络空间及时间特征的数学模型，并实现了分形维数的可视化，研究结果揭示血管网络存在形态及功能的异质化特征，对深入了解血管再生中的时间及空间分布模式及其生理属性具有重要意义。本项目还开展了组织灌注模型技术研究，建立了重要脏器如肾脏、肺的微循环血流灌注分形模型，提出了基于小样本生理数据建立机器学习模型的方案，为研究成果在重症疾病诊疗中的临床转化及应用打下了基础。获得了1项省级科技进步二等奖，在国际微循环研究主流学术期刊发表了一批高水平论文，培养了多名青年研究人才，并开展了活跃的国内外学术交流活动，助力提升了我国微循环研究的国际影响力。