基于功率谱的神经元放电早期预警信号  

Power spectrum based early warning signal of neuronal firing

作　　者：李松蔚 谢勇[1] LI Songwei;XIE yong(Shaanxi Engineering Research Center of Nondestructive Testing and Structural Integrity Evaluation,State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安交通大学,复杂服役环境重大装备结构强度与寿命全国重点实验室,陕西省无损检测与结构完整性评价工程技术研究中心,西安710049

出　　处：《物理学报》2025年第1期101-113,共13页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12172269)资助的课题.

摘　　要：在神经系统中,脑疾病的发生往往对应着神经系统的临界转迁与神经元的异常放电,因此对临界转迁的早期预警信号(EWS)的研究有助于预测神经元的放电行为,从而预防脑疾病的发生.传统EWS,如自相关系数、方差等指标,虽然能对动力系统的分岔点进行早期预警,但其无法对分岔类型进行区分.而基于功率谱的EWS可以有效预测分岔点并区分分岔类型,且在气候及生态模型上的预测效果良好.本文将基于功率谱的EWS应用在神经元系统中,先后考察了Morris-Lecar和Hindmarsh-Rose模型神经元放电所对应的4种余维一分岔点前的临界现象,分别计算了传统EWS和基于功率谱的EWS,并进行对比分析.结果表明基于功率谱的EWS能有效预测神经元放电,并且能对不同神经元的Ⅰ型兴奋和Ⅱ型兴奋作出区分.本研究对神经系统的临界转迁的预测有着重要的指导意义,对神经系统疾病的诊断和治疗有着重要的启示作用.Brain diseases often occur simultaneously with critical changes in neural system and abnormal neuronal firing.Studying the early warning signals(EWSs)of critical changes can provide a promising approach for predicting neuronal firing behaviors,which is conducible to the early diagnosis and prevention of brain diseases.Traditional EWSs,such as autocorrelation and variance,have been widely used to detect the critical transitions in various dynamical systems.However,these methods have limitations in distinguishing different types of bifurcations.In contrast,the EWSs with power spectrum have shown a significant advantage in not only predicting bifurcation points but also distinguishing the types of bifurcations involved.Previous studies have demonstrated its predictive capability in climate and ecological models.Based on this,this study applies the EWS with power spectrum to neuronal systems in order to predict the neuronal firing behaviors and distinguish different classes of neuronal excitability.Specifically,we compute the EWSs before the occurrence of saddlenode bifurcation on the invariant circle and subcritical Hopf bifurcation in the Morris-Lecar neuron model.Additionally,we extend the analysis to the Hindmarsh-Rose model,calculating the EWSs before both saddlenode bifurcation and supercritical Hopf bifurcation.This study contains the four types of codimension-1 bifurcations corresponding to the neuronal firing.For comparison,we also calculate two types of conventional EWSs:lag-1 autocorrelation and variance.In numerical simulations,the stochastic differential equations are simulated by the Euler-Maruyama method.Then,the simulated responses are detrended by the Lowess filter.Finally,the EWSs are calculated by using the rolling window method to ensure the detection of EWS before bifurcation points.Our results show that the EWS with power spectrum can effectively predict the bifurcation points,which means that it can predict neuronal firing activities.Compared with the lag-1 autocorrelation and the variance,the

关 键 词：神经动力学 功率谱 临界转迁 早期预警信号 

分 类 号：R338[医药卫生—人体生理学] O59[医药卫生—基础医学]