基于分岔理论的全脑动力学建模分析

郭琪丽 ,  魏静 ,  刘宇轩 ,  许亚茹 ,  郝志鹏 ,  杨艳丽

科学技术与工程 ›› 2025, Vol. 25 ›› Issue (18) :7700-7709

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科学技术与工程 ›› 2025, Vol. 25 ›› Issue (18) :7700-7709 DOI: 10.12404/j.issn.1671-1815.2405388
自动化技术、计算机技术

基于分岔理论的全脑动力学建模分析

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Whole-brain Dynamical Modeling Based on Bifurcation Theory

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摘要

传统的全脑动力学模型反演技术采用静态的单一特征来约束,忽略了脑网络的动态波动,缺少对相应特征的定性分析,导致建模精度不高、解释性不够。针对这一问题,在基于分岔分析的基础上提出了一种多目标期望最大化算法。该方法利用动态平均场模型,结合基于多模态影像数据提取的脑结构功能特征进行建模。进一步利用分岔理论对模型的多个约束特征定性分析,选取其中的功能连接、动态功能连接和亚稳态特征联合约束模型反演。通过分岔分析确定初始参数值,使用期望最大化算法迭代优化参数组合,定量分析的结果证明了该方法的准确性和稳定性。

Abstract

Traditional whole-brain dynamical modeling techniques are typically constrained by static single features, neglecting dynamic fluctuations in brain networks and lacking qualitative analysis of corresponding indicators, which limits modeling accuracy and comprehensibility. In order to address this issue, a multi-objective expectation maximization algorithm based on bifurcation analysis was proposed. This approach integrates a dynamic mean-field model with brain structural-functional features extracted from multi-mode imaging data for modeling purposes. Bifurcation theory was employed to qualitatively analyze multiple constraint indicators of the model, including functional connectivity, dynamic functional connectivity, and metastability for model inversion. Initial parameter values were determined through bifurcation analysis, and parameter combinations were iteratively refined using an expectation maximization algorithm. Quantitative analysis validates the accuracy and stability of this method.

关键词

动态平均场模型 / 分岔分析 / 多模态 / 多目标

Key words

dynamic mean field / bifurcation analysis / multi-mode / multi-objective

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郭琪丽, 魏静, 刘宇轩, 许亚茹, 郝志鹏, 杨艳丽. 基于分岔理论的全脑动力学建模分析[J]. 科学技术与工程, 2025, 25(18): 7700-7709 DOI:10.12404/j.issn.1671-1815.2405388
GUO Qi-li, WEI Jing, LIU Yu-xuan, XU Ya-ru, HAO Zhi-peng, YANG Yan-li. Whole-brain Dynamical Modeling Based on Bifurcation Theory[J]. Science Technology and Engineering, 2025, 25(18): 7700-7709 DOI:10.12404/j.issn.1671-1815.2405388

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基金资助

山西省科技厅基础研究计划面上项目(20210302123099)

山西省基础研究计划(自由探索类)青年项目(202303021212166)

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