基于广义线性模型的针刺足三里脊髓背根神经活动解码

神经系统以时空编码形式刻画外部刺激信息, 针刺作为对穴位的机械作用可以等效为对神经系统的一种外部刺激. 为了揭示神经系统如何表达和传递针刺作用, 本文设计了不同频率的针刺动物实验, 即在针刺大鼠足三里穴位时获取脊髓背根神经节电信号. 首先, 经过数据预处理获得单神经元动作电位序列并转化为点过程序列. 其次, 应用广义线性模型(GLM)编码针刺作用, 产生模拟的神经放电序列. 另外, 在模型基础上应用贝叶斯解码, 根据神经放电序列重构针刺随时间变化的位移波形. 最后, 基于时间重标度理论应用分位数分位数(Q-Q)图方法检验编码模型与点过程数据的一致性. 结果表明, GLM能够模拟针刺神经编码, 并正确解码针刺信息. 本文为针刺研究提供了新的视角, 对于构建神经系统与机器接口以改善针刺的临床研究具有潜在意义. 关键词： 针刺 点过程 广义线性模型 神经解码     

Negative self-feedback induced enhancement and transition of spiking activity for class-3 excitability

Post-inhibitory rebound (PIR) spike, which has been widely observed in diverse nervous systems with different physiological functions and simulated in theoretical models with class-2 excitability, presents a counterintuitive nonlinear phenomenon in that the inhibitory effect can facilitate neural firing behavior. In this study, a PIR spike induced by inhibitory stimulation from the resting state corresponding to class-3 excitability that is not related to bifurcation is simulated in the Morris-Lecar neuron. Additionally, the inhibitory self-feedback mediated by an autapse with time delay can evoke tonic/repetitive spiking from phasic/transient spiking. The dynamical mechanism for the PIR spike and the tonic/repetitive spiking is acquired with the phase plane analysis and the shape of the quasi-separatrix curve. The result extends the counterintuitive phenomenon induced by inhibition to class-3 excitability, which presents a potential function of inhibitory autapse and class-3 neuron in many neuronal systems such as the auditory system.     

神经元电活动不同节律模式的几种变化过程

利用神经元Chay模型,对实验中观察到的三种放电节律模式序列进行数值模拟,并应用余维1极限环分岔分析研究了其产生机理.首先考虑的是周期性放电模式的变化过程;其次,具有不同表象的一种超临界和一种亚临界倍周期簇放电序列产生并导致混沌现象的出现,然后以不同的方式转迁到逆超临界倍周期峰放电序列;最后研究无混沌的加周期簇放电序列,得出加周期分岔仅是一种与倍周期分岔密切相关的分岔现象.     

兴奋性和抑制性自反馈压制靠近Hopf分岔的神经电活动比较

突触输入刺激神经元产生的电活动,在神经编码中发挥着重要作用.通常认为,兴奋性输入增强电活动,抑制性输入压制电活动.本文选取可调节电流衰减速度的突触模型,研究了兴奋性自突触在亚临界Hopf分岔附近压制神经元电活动的反常作用,与抑制性自突触的压制作用进行了比较,并采用相位响应曲线和相平面分析解释了压制作用的机制.对于单稳的峰放电,快速和中速衰减的兴奋性自突触分别可以诱发频率降低的峰放电和混合振荡(峰放电与阈下振荡的交替),而中速和慢速衰减的抑制性自突触也可以分别诱发频率降低的峰放电和混合振荡.对于与静息共存的峰放电,除上述两种行为外,中速衰减的兴奋性和慢速衰减的抑制性自突触还可以诱发静息.兴奋性和抑制性自突触电流在不同的衰减速度下,分别作用在峰放电的不同相位,才能诱发同类压制行为.结果丰富了兴奋性突触压制电活动反常作用的实例,获得了兴奋性和抑制性自突触压制作用机制的不同,给出了调控神经放电的新手段.     

Bursting and spiking due to additional direct and stochastic currents in neuron models

Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to spiking, induced by additional direct and stochastic currents, are explored in rest states corresponding to two values of the parameter $V_{\rm K}$ in the Chay neuron system. Three cases are considered by numerical simulation and fast/slow dynamic analysis, in which only the direct current or the stochastic current exists, or the direct and stochastic currents coexist. Meanwhile, several important bursting patterns in neuronal experiments, such as the period-1 ``circle/homoclinic" bursting and the integer multiple ``fold/homoclinic" bursting with one spike per burst, as well as the transition from integer multiple bursting to period-1 ``circle/homoclinic" bursting and that from stochastic ``Hopf/homoclinic" bursting to ``Hopf/homoclinic" bursting, are investigated in detail.     

Time-varying irregularities in multiple trial spike data

The measurement of neuronal firing rates has been a standard methodology for characterizing properties of neurons. The peri-stimulus time histogram (PSTH) is primarily used for visualizing changes of firing rates in relation to an external stimulus or an event. On the other hand, modulation of other statistics such as distribution and patterns of interspike intervals can be an important index for analysis of neuronal response and may provide insights into the neuronal codes. In particular, it is desirable to visualize the temporal modulation not only of the firing rates but also of the other statistics. In this study, we propose an analysis method for measuring irregularities in multiple trial spike data. The method calculates a local measure by extracting a short segment of data within a predefined time bin and connecting them each other. We compare the different data extraction methods in Poisson and gamma processes and show that our proposed method is effective for estimating the statistics of the irregular spike data.     

非线性物理破解神经编码机制

信息在神经系统中以脉冲点序列的形式传输和处理，神经系统如何通过脉冲点序列对所表达的信息进行编码，一直是一个谜．人们曾普遍认为，神经可能通过发放率（单位时间发放脉冲出现的次数）对信息编码，也有人猜测，神经可通过脉冲点序列的时序编码．由于神经发放的随机性，这就使得任何编码机制都面临着被表达信息的确定性与表达该信息的信号的随机性的矛盾．通过神经非线性随机动力学模型，文章作者发现，神经点序列的发放率对点序列的时序信息传输的影响，揭示了神经点序列时序信息在神经非线性传输中的随机共振特征．由此预期，并进一步通过听觉心理物理实验观察到，在一定条件下噪声对听觉的增强作用．从而通过非线性物理揭示了听觉时序编码机制的存在以及在时序编码中随机性噪声的积极作用．     

Contrast Adaptation Decreases Complexity in Retinal Ganglion Cell Spike Train

The difference in temporal structures of retinal ganglion cell spike trains between spontaneous activity and firing activity after contrast adaptation is investigated. The Lempel-Ziv complexity analysis reveals that the complexity of the neural spike train decreases after contrast adaptation. This implies that the behaviour of the neuron becomes ordered, which may carry relevant information about the external stimulus. Thus, during the neuron activity after contrast adaptation, external information could be encoded in forms of some certain patterns in the temporal structure of spike train that is significantly different, compared to that of the spike train during spontaneous activity, although the firing rates in spontaneous activity and firing activity after contrast adaptation are sometime similar.     

Dynamical origin of independent spiking and bursting activity in neural microcircuits

The relationship between spiking and bursting dynamics is a key question in neuroscience, particularly in understanding the origins of different neural coding strategies and the mechanisms of motor command generation and neural circuit coordination. Experiments indicate that spiking and bursting dynamics can be independent. We hypothesize that different mechanisms for spike and burst generation, intrinsic neuron dynamics for spiking and a modulational network instability for bursting, are the origin of this independence. We tested the hypothesis in a detailed dynamical analysis of a minimal inhibitory neural microcircuit (motif) of three reciprocally connected Hodgkin-Huxley neurons. We reduced this high-dimensional dynamical system to a rate model and showed that both systems have identical bifurcations from tonic spiking to burst generation, which, therefore, does not depend on the details of spiking activity.     

基于抑制性突触可塑性的神经元放电率自稳态机制

神经元放电率自稳态是指大脑神经网络的放电率维持在相对稳定的状态.大量实验研究发现神经元放电率自稳态是神经电活动的重要特征,并且放电率自稳态是实现神经信息处理及维持正常脑功能的基础,因此放电率自稳态的研究是神经科学领域的重要科学问题.脑神经网络是一个高度复杂的动态系统,存在大量输入扰动信号及由于动态链接导致的参数摄动,因此如何建立并维持神经元放电率自稳态及其鲁棒性仍有待深入研究.反馈神经回路是皮层神经网络的典型连接模式,抑制性突触可塑性对神经元放电率自稳态具有重要的调控作用.本文通过构建包含抑制性突触可塑性的反馈神经回路模型对神经元放电率自稳态及其鲁棒性进行计算研究.结果表明:在抑制性突触可塑性的作用下,神经元放电率可自适应地跟踪目标放电率,从而取得放电率自稳态;在有外部输入干扰和参数摄动的情况下,神经元放电率具有良好的抗扰动性能,表明放电率自稳态具有很强的鲁棒性;理论分析揭示了抑制性突触可塑性学习规则是神经元放电率自稳态的神经机制;仿真分析进一步揭示了学习率及目标放电率对放电率自稳态建立过程具有重要影响.     

Rhythm Synchronization of Coupled Neurons with Temporal Coding Scheme

Encoding information by firing patterns is one of the basic neural functions, and synchronization is important collective behaviour of a group of coupled neurons. Taking account of two schemes for encoding information （that is, rate coding and temporal coding）, rhythm synchronization of coupled neurons is studied. There are two types of rhythm synchronization of neurons： spike and burst synchronizations. Firstly, it is shown that the spike synchronization is equivalent to the phase synchronization for coupled neurons. Secondly, the similarity function of the slow variables of neurons, which have relevant to the bursting process, is proposed to judge the burst synchronization. It is also found that the burst synchronization can be achieved more easily than the spike synchronization, whatever the firing patterns of the neurons are. Hence the temporal encoding scheme, which is closely related to both the spike and burst synchronizations, is more comprehensive than the rate coding scheme in essence.     

Phase description of the Huber-Braun neuron model for mammalian cold receptors

The spiking activity of mammalian cold receptors is described by the Huber-Braun neuron model. Sweeping temperature as a control parameter across a biologically relevant range this model exhibits a complex bifurcation structure seen in the sequence of interspike intervals. The model’s distinctive feature is the interaction between a fast spike generating dynamics and a slow subthreshold oscillation. Viewing the spike generation as a cycle, the dynamics may also be modeled phenomenologically by two phases, one for the spike cycle and the second for the slow subthreshold oscillation. In fact, a phase model of temperature-dependent mammalian cold receptors was already proposed by Roper et al. (2000). Here we follow their approach and investigate to what extent this model is able to reproduce the bifurcation patterns of the Huber-Braun model. Special attention is paid to the tonic firing to bursting transition observed in the low temperature range.     

针刺足三里的脊髓背根神经电信号非线性特征提取

神经系统在外部刺激下会呈现出丰富的放电模式,针刺作为对穴位的机械作用可以等效为对神经系统的一种外部刺激,在针刺刺激下神经系统会产生不规则的电信号.由于神经系统是高度复杂的非线性动力学系统,神经电信号具有很强的非线性,所以本文设计了提插补法、提插泻法、捻转补法、捻转泻法等四种针刺手法的动物实验,获取针刺大鼠足三里穴位的脊髓背根神经束动作电位序列.采用峰峰间期的思想,应用非线性时间序列的方法分析此动作电位序列,通过计算Lyapunov指数、关联维数以及Lempel-Ziv复杂度等参数,提取神经电信号的非线性特征,得到不同针刺手法的神经电信息的编码;并证明了针刺作用下脊髓背根的神经电信号具有明显的混沌特性. 关键词： 针刺 神经电信号 非线性分析 混沌     

Dynamics analysis on neural firing patterns by symbolic approach

Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh--Rose (HR) neuronal model is simulated with the external stimuli gradually decreasing, and various firing activities with different topological structures are orderly numbered. Through constructing first-return maps of interspike intervals, all firing patterns are described and identified by symbolic expressions. On the basis of ordering rules of symbolic sequences, the corresponding relation between parameters and firing patterns is established, which will be helpful for encoding neural information. Moreover, using the operation rule of $\ast$ product, generation mechanisms and intrinsic configurations of periodic patterns can be distinguished in detail. Results show that the symbolic approach is a powerful tool to study neural firing activities. In particular, such a coarse-grained way can be generalized in neural electrophysiological experiments to extract much valuable information from complicated experimental data.     

Implications of heterogeneous inputs and connectivity on the synchronization in excitable networks

We study the combined implications of connectivity and heterogeneous inputs on the synchronization features of a one-dimensional chain of diffusively coupled FitzHugh Nagumo (FHN) systems. The uncoupled systems are triggered into a regime of chaotic firing by periodic parametric forces modeling external stimuli. Due to the parameter dispersion involved in randomly distributed amplitudes and/or phases of the forces the units are nonidentical and the firing events on the chain of uncoupled units will be asynchronous leading to a distribution of the spiking times. Interest is focused on mutually synchronized spikings arising through the coupling where the connectivity of the network may range from nearest-neighbor interaction to global interactions. From our studies we conclude that increasing the interaction radius does not necessarily entail better spike synchrony and the coupling strength plays a more important role than connectivity. It is found that for driving with random amplitudes together with random phases a critical interaction radius exists beyond which firing becomes suppressed if the coupling between the units is too strong. In such cases of ‘firing death’ the units perform only small-amplitude oscillations which are mutually synchronous. The optimal coupling for spike synchrony is of intermediate strength and altering the connectivity does not really matter for the degree of spike synchrony. Distinct to that, when all the phases are equal and only the amplitudes of the forces are randomly distributed enhanced spike synchrony is achieved for sufficiently strong coupling regardless of the interaction radius.     

Parameter-dependent synchronization transition of coupled neurons with co-existing spiking and bursting

A firing pattern transition is simulated in the Leech neuron model, firstly from bursting to co-existence of spiking and bursting and then to spiking. The attraction domain of spiking and bursting for three different parameter values are calculated. Synchronization transition processes of two coupled Leech neurons, one is bursting and the other the co-existing spiking, are simulated for the three parameters. The three synchronization processes appear similar as the coupling strength increases, beginning from non-synchronization to complete synchronization through a complex dynamical procedure, but their detailed processes are different depending on the parameter values. The transition procedure is complex and the complete synchronization is in bursting for larger parameter values, while the process is simple with complete synchronization of spiking for smaller values. The potential relationship between complete synchronization and the attraction domain is also discussed. The results are instructive to understanding the synchronization behaviors of the coupled neuronal system with co-existing attractors.     

Experimental evidence of a chaotic region in a neural pacemaker

In this Letter, we report the finding of period-adding scenarios with chaos in firing patterns, observed in biological experiments on a neural pacemaker, with fixed extra-cellular potassium concentration at different levels and taken extra-cellular calcium concentration as the bifurcation parameter. The experimental bifurcations in the two-dimensional parameter space demonstrate the existence of a chaotic region interwoven with the periodic region thereby forming a period-adding sequence with chaos. The behavior of the pacemaker in this region is qualitatively similar to that of the Hindmarsh–Rose neuron model in a well-known comb-shaped chaotic region in two-dimensional parameter spaces.     

Two Different Bifurcation Scenarios in Neural Firing Rhythms Discovered in Biological Experiments by Adjusting Two Parameters

Two different bifurcation scenarios, one is novel and the other is relatively simpler, in the transition procedures of neural firing patterns are studied in biological experiments on a neural pacemaker by adjusting two parameters. The experimental observations are simulated with a relevant theoretical model neuron. The deterministic non-periodic firing pattern lying within the novel bifurcation scenario is suggested to be a new case of chaos, which has not been observed in previous neurodynamical experiments.     

Determination of the Phase Shift of a Plasma Wave Reflected from the Edge of a Small-Scale Irregularity

In our papers [1,2], a nonlinear theory has been developed for excitation of plasma-wave eigenmodes inside field-aligned small-radius inhomogeneities in experiments on ionospheric heating by powerful radio waves. This theory takes into account the striction effects of plasma expulsion near the plasma resonance level where a trapped wave is reflected from the edge of the irregularity. The results of this theory depend strongly on the phase of the linear (i.e., weak-field) reflection coefficient. In this paper, we calculate this parameter for irregularities of different shapes.     

Second order phase transition in neural rate coding: binary encoding is optimal for rapid signal transmission

Here, we derive optimal tuning functions for minimum mean square reconstruction from neural rate responses subjected to Poisson noise. The shape of these tuning functions strongly depends on the length T of the time window within which action potentials (spikes) are counted in order to estimate the underlying firing rate. A phase transition towards pure binary encoding occurs if the maximum mean spike count becomes smaller than approximately three. For a particular function class, we prove the existence of a second-order phase transition. The analytically derived critical decoding time window length is in precise agreement with numerical results. Our analysis reveals that binary rate encoding should dominate in the brain wherever time is the critical constraint.