梯度耦合下神经元网络中靶波和螺旋波的诱发研究

神经系统内数量众多的神经元电活动的群体行为呈现一定的节律性和自组织性. 当网络局部区域存在异质性或者受到持续周期性刺激, 则在网络内诱发靶波, 且这些靶波如'节拍器'可调制介质中行波的诱发和传播. 基于Hindmarsh-Rose 神经元模型构造了最近邻连接下的二维神经元网络, 研究在非均匀耦合下神经元网络内有序波的诱发问题. 在研究中, 选定网络中心区域的耦合强度最大, 从中心向边界的神经元之间的耦合强度则按照阶梯式下降. 研究结果表明, 在恰当的耦合梯度下, 神经元网络内诱发的靶波或螺旋波可以占据整个网络, 并有效调制神经元网络的群体电活动, 使得整个网络呈现有序性. 特别地, 当初始值为随机值时, 梯度耦合也可以诱发稳定的有序态. 这种梯度耦合对网络群体行为调制的研究结果有助于理解神经元网络的自组织行为.     

Cortical spreading depression: An enigma

The brain is a complex organ with active components composed largely of neurons, glial cells, and blood vessels. There exists an enormous experimental and theoretical literature on the mechanisms involved in the functioning of the brain, but we still do not have a good understanding of how it works on a gross mechanistic level. In general, the brain maintains a homeostatic state with relatively small ion concentration changes, the major ions being sodium, potassium, and chloride. Calcium ions are present in smaller quantities but still play an important role in many phenomena. Cortical spreading depression (CSD for short) was discovered over 60 years ago by A.A.P. Le?o, a Brazilian physiologist doing his doctoral research on epilepsy at Harvard University, “Spreading depression of activity in the cerebral cortex," J. Neurophysiol., 7 (1944), pp. 359-390. Cortical spreading depression is characterized by massive changes in ionic concentrations and slow nonlinear chemical waves, with speeds on the order of mm/min, in the cortex of different brain structures in various experimental animals. In humans, CSD is associated with migraine with aura, where a light scintillation in the visual field propagates, then disappears, and is followed by a sustained headache. To date, CSD remains an enigma, and further detailed experimental and theoretical investigations are needed to develop a comprehensive picture of the diverse mechanisms involved in producing CSD. A number of mechanisms have been hypothesized to be important for CSD wave propagation. In this paper, we briefly describe several characteristics of CSD wave propagation, and examine some of the mechanisms that are believed to be important, including ion diffusion, membrane ionic currents, osmotic effects, spatial buffering, neurotransmitter substances, gap junctions, metabolic pumps, and synaptic connections. Continuum models of CSD, consisting of coupled nonlinear diffusion equations for the ion concentrations, and a discrete lattice-Boltzmann method approach will be described. Also, we will describe some open problems and remaining challenges.     

在兴奋-抑制混沌神经元网络中有序波的自发形成

大脑皮层在一定条件下可以自发出现螺旋波和平面波,为了了解这些有序波的产生机制,构造了一个双层的二维神经元网络.该网络由最近邻兴奋性耦合和长程抑制性耦合层组成,采用修改后的Hindmarsh-Rose神经元模型研究了该混沌神经元网络从具有随机相位分布的初态演化是否能自发出现各种有序波.数值模拟结果表明:当抑制性耦合强度比较小时,系统一般不会自发出现有序波;在兴奋性耦合强度足够大的情况下,抑制性耦合强度越大,系统越容易产生有序波.系统出现不同的有序波与系统初态和耦合强度有密切关系,适当选择兴奋性和抑制性耦合的耦合强度,系统会自发出现迷宫斑图、平面波、单螺旋波、多螺旋波、旋转方向相反的螺旋波对、双臂螺旋波、靶波、向内方形波等有序波斑图.螺旋波、迷宫斑图和内向方形波出现概率分别达到27.5%, 21.5%和10.0%,这里的迷宫斑图是由不同传播方向的许多平面波组成,其他有序波出现概率比较小.研究结果有助于理解发生在大脑皮层中的自组织现象.     

Control of traveling waves in the Mammalian cortex

We experimentally confirmed predictions that modulation of the neuronal threshold with electrical fields can speed up, slow down, and even block traveling waves in neocortical slices. The predictions are based on a Wilson-Cowan-type integro-differential equation model of propagating neocortical activity. Wave propagation could be modified quickly and reversibly within targeted regions of the network. To the best of our knowledge, this is the first example of direct modulation of the threshold to control wave propagation in a neural system.     

Mechanism for propagation of rate signals through a 10-layer feedforward neuronal network

Using numerical simulations, we explore the mechanism for propagation of rate signals through a 10-layer feedforward network composed of Hodgkin--Huxley (HH) neurons with sparse connectivity. When white noise is afferent to the input layer, neuronal firing becomes progressively more synchronous in successive layers and synchrony is well developed in deeper layers owing to the feedforward connections between neighboring layers. The synchrony ensures the successful propagation of rate signals through the network when the synaptic conductance is weak. As the synaptic time constant τ_syn varies, coherence resonance is observed in the network activity due to the intrinsic property of HH neurons. This makes the output firing rate single-peaked as a function of τ_syn, suggesting that the signal propagation can be modulated by the synaptic time constant. These results are consistent with experimental results and advance our understanding of how information is processed in feedforward networks.     

Coherent to incoherent ultrasonic wave conversion in heterogeneous media

An initially coherent acoustic wave propagating in a heterogeneous medium becomes progressively incoherent. The diffusion of the acoustic wave on randomly distributed heterogeneities leads to a progressive frequency-dependent conversion from coherent to incoherent waves along the propagation direction. A simplified statistical model for this propagation of ultrasonic waves is presented. This model is valid when both the mechanical impedance mismatch and acoustical frequency are sufficiently small to approximate the effect of each heterogeneity to a single-phase lead or lag. The propagation of acoustical waves is studied by a phase gradient model which shows the progressive loss of phase coherence of the wave, i.e. the progressive transition from the coherent to the incoherent state. A critical length beyond which the loss of coherence is so high that the classical phase reconstruction methods of imaging are no longer applicable is defined and evaluated. An experimental set-up is described and the experimental results are presented and discussed and good fit between experiment and theory is found.     

大气湍流间歇性及其对光波传播的影响

当光波在大气中传播时,由于大气湍流的作用,其光束质量将会极大地恶化。对于这类问题的处理,长期以来都是以Tartask ii等人的理论为指导,而他们的理论是根据Kolmogrov于1941年建立的局地均匀各向同性湍流理论(K41)建立的,所以K41理论是这一领域奠基的基石。然而,随着湍流研究的深入,人们已经逐渐意识到K41湍流理论的各方面的缺点,其中尤其明显的是,K41理论忽略了湍流的间歇特征。在湍流现代理论中,湍流间歇性的研究一直是处于中心位置。经过数十年的不懈的努力,目前人们已经对湍流间歇性有了一些初步的成果和认识。本文综述了试图将湍流间歇性引入随机介质中光传播问题的考虑之中的各种尝试。我们首先结合光学问题的需要对湍流及其间歇性研究现状及重要成果进行了概要的回顾和说明。在此基础上,我们以两种方式对间歇性大气湍流中光传播问题进行分析:首先,我们以一种简单的非Gauss场模型为基础分析间歇性大气湍流中的光场统计性质;然后,我们将统计矩方程展开到四阶累积函数,分析了近Gauss场附近的光场统计性质。我们还以层次结构模型为基础对二阶统计矩进行了进一步的研究。     

大气湍流间歇性及其对光波传播的影响

当光波在大气中传播时，由于大气湍流的作用，其光束质量将会极大地恶化。对于这类问题的处理，长期以来都是以Tartaskii等人的理论为指导，而他们的理论是根据Kolmogrov于1941年建立的局地均匀各向同性湍流理论（K41）建立的，所以K41理论是这一领域奠基的基石。然而，随着湍流研究的深入，人们已经逐渐意识到K41湍流理论的各方面的缺点，其中尤其明显的是，K41理论忽略了湍流的间歇特征。在湍流现代理论中，湍流间歇性的研究一直是处于中心位置。经过数十年的不懈的努力，目前人们已经对湍流间歇性有了一些初步的成果和认识。本文综述了试图将湍流间歇性引入随机介质中光传播问题的考虑之中的各种尝试。我们首先结合光学问题的需要对湍流及其间歇性研究现状及重要成果进行了概要的回顾和说明。在此基础上，我们以两种方式对间歇性大气湍流中光传播问题进行分析：首先，我们以一种简单的非Gauss场模型为基础分析间歇性大气湍流中的光场统计性质；然后，我们将统计矩方程展开到四阶累积函数，分析了近Gauss场附近的光场统计性质。我们还以层次结构模型为基础对二阶统计矩进行了进一步的研究。     

Astrocyte signaling in the presence of spatial inhomogeneities

Astrocytes, a special type of glial cells, were considered to have just a supporting role in information processing in the brain. However, several recent studies have shown that they can be chemically stimulated by various neurotransmitters, such as ATP, and can generate Ca2+ and ATP waves, which can propagate over many cell lengths before being blocked. Although pathological conditions, such as spreading depression and epilepsy, have been linked to abnormal wave propagation in astrocytic cellular networks, a quantitative understanding of the underlying characteristics is still lacking. Astrocytic cellular networks are inhomogeneous, in the sense that the domain they occupy contains passive regions or gaps, which are unable to support wave propagation. Thus, this work focuses on understanding the complex interplay between single-cell signal transduction, domain inhomogeneity, and the characteristics of wave propagation and blocking in astrocytic cellular networks. The single-cell signal transduction model that was employed accounts for ATP-mediated IP3 production, the subsequent Ca2+ release from the ER, and ATP release into the extracellular space. The model is excitable and thus an infinite range of wave propagation is observed if the domain of propagation is homogeneous. This is not always the case for inhomogeneous domains. To model wave propagation in inhomogeneous astrocytic networks, a reaction-diffusion framework was developed and one-gap as well as multiple-gap cases were simulated using an efficient finite-element algorithm. The minimum gap length that blocks the wave was computed as a function of excitability levels and geometric characteristics of the inhomogeneous network, such as the length of the active regions (cells). Complex transient patterns, such as wave reflection, wave trapping, and generation of echo waves, were also predicted by the model, and their relationship to the geometric characteristics of the network was evaluated. Therefore, the proposed model can help in the formulation of testable hypotheses to explain the observed abnormal wave propagation in pathological situations.     

Propagation of electromagnetic waves in two-dimensionally periodic thin-film waveguides

A simplified mathematical model of two-dimensionally(2D) periodic thin-film wavegmide is proposed and the characteristics of wave propagation are shown to be governed by a five-term recurrence relation with dyadic admittance coefficients. The generalized transverse resonance method can be used to analyze any complicated 2D periodic thin-film waveguide. The dispersion characteristics are described by both approximation analysis and numerical calculation. The theoretical explanation and physical understanding of the effecis of 2D periodic modulation provided by our analysis and resulis can give sound support to the engineering applications.     

Natural beam focusing of non-axisymmetric guided waves in large-diameter pipes

The propagation of non-axisymmetric guided waves in larger diameter pipes is studied in this paper by treating the guided waves as corresponding Lamb waves in an unwrapped plate. This approximation leads to a simpler method for calculating the phase velocities of hollow cylinder guided waves, which reveals a beam focusing nature of non-axisymmetric guided waves generated by a partial source loading. The acoustic fields in a pipe generated by a partial-loading source includes axisymmetric longitudinal modes as well as non-axisymmetric flexural modes. The circumferential distribution of the total acoustic field, also referred as an angular profile, diverges circumferentially while guided waves propagate with dependence on such factors as mode, frequency, cylinder size, propagation distance, etc. Exact prediction of the angular profile of the total field can only be realized by numerical calculations. In particular cases, however, when the wall thickness is far less than the cylinder diameter and the wavelength is smaller than or comparable to the pipe wall thickness, the acoustic field can be analyzed based on the characteristics of Lamb waves that travel along a periodic unwrapped plate. Based on this assumption, a simplified model is derived to calculate the phase velocities of non-axisymmetric flexural mode guided waves. The model is then applied to discussions on some particular characteristics of guided-wave angular profiles generated by a source loading. Some features of flexural modes, such as cutoff frequency values are predicted with the simpler model. The relationship between the angular profiles and other factors such as frequency, propagation distance, and cylinder size is obtained and presented in simple equations. The angular profile rate of change with respect to propagation distance is investigated. In particular, our simplified model for non-axisymmetric guided waves predicts that the wave beam will converge to its original circumferential shape after the wave propagates for a certain distance. A concept of "natural focal point" is introduced and a simple equation is derived to compute the 1st natural focal distance of non-axisymmetric guided waves. The applicable range of the simplified equation is provided. Industrial pipes meet the requirement of wall thickness being far less than the pipe diameter. The approximate analytical algorithms presented in this paper provides a convenient method enabling quick acoustic field analysis on large-diameter industrial pipes for NDE applications.     

Stochastic resonance and synchronization behaviors of excitatory-inhibitory small-world network subjected to electromagnetic induction

The phenomenon of stochastic resonance and synchronization on some complex neuronal networks have been investigated extensively.These studies are of great significance for us to understand the weak signal detection and information transmission in neural systems.Moreover,the complex electrical activities of a cell can induce time-varying electromagnetic fields,of which the internal fluctuation can change collective electrical activities of neuronal networks.However,in the past there have been a few corresponding research papers on the influence of the electromagnetic induction among neurons on the collective dynamics of the complex system.Therefore,modeling each node by imposing electromagnetic radiation on the networks and investigating stochastic resonance in a hybrid network can extend the interest of the work to the understanding of these network dynamics.In this paper,we construct a small-world network consisting of excitatory neurons and inhibitory neurons,in which the effect of electromagnetic induction that is considered by using magnetic flow and the modulation of magnetic flow on membrane potential is described by using memristor coupling.According to our proposed network model,we investigate the effect of induced electric field generated by magnetic stimulation on the transition of bursting phase synchronization of neuronal system under electromagnetic radiation.It is shown that the intensity and frequency of the electric field can induce the transition of the network bursting phase synchronization.Moreover,we also analyze the effect of magnetic flow on the detection of weak signals and stochastic resonance by introducing a subthreshold pacemaker into a single cell of the network and we find that there is an optimal electromagnetic radiation intensity,where the phenomenon of stochastic resonance occurs and the degree of response to the weak signal is maximized.Simulation results show that the extension of the subthreshold pacemaker in the network also depends greatly on coupling strength.The presented results may have important implications for the theoretical study of magnetic stimulation technology,thus promoting further development of transcranial magnetic stimulation(TMS) as an effective means of treating certain neurological diseases.     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

Multilayer adaptive networks in neuronal processing

The connectome is a wiring diagram mapping all the neural connections in the brain. At the cellular level, it provides a map of the neurons and synapses within a part or all of the brain of an organism. In recent years, significant advances have been made in the study of the connectome via network science and graph theory. This analysis is fundamental to understand neurotransmission (fast synaptic transmission) networks. However, neurons use other forms of communication as neuromodulation that, instead of conveying excitation or inhibition, change neuronal and synaptic properties. This additional neuromodulatory layers condition and reconfigure the connectome. In this paper, we propose that multilayer adaptive networks, in which different synaptic and neurochemical layers interact, are the appropriate framework to explain neuronal processing. Then, we describe a simplified multilayer adaptive network model that accounts for these extra-layers of interaction and analyse the emergence of interesting computational capabilities.     

The role of neural architecture and the speed of signal propagation in the process of synchronization of bursting neurons

Synchronized neuronal activity has been observed at all levels of human and any other nervous systems and was suggested as particularly relevant in information processing and coding. In the present paper we investigate the synchronization of bursting neuronal activity. Motivated by the fact that in neural systems the interplay between the network structure and the dynamics taking place on it is closely interrelated, we develop a spatial network representation of neural architecture in which we can tune the network organization between a scale-free network with dominating long-range connections and a homogeneous network with mostly adjacent neurons connected. Our results reveal that the most synchronized response is obtained for the intermediate regime where long- as well as short-range connections constitute the neural architecture. Moreover, the optimal response is additionally enhanced when the speed of signal propagation is optimized.     

A high-order discontinuous Galerkin method for wave propagation through coupled elastic–acoustic media

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic–acoustic media. A velocity–strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic–acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic–acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.     

Lamb waves propagation in elastic plane layers with a joint strip

The Lamb waves are used for the ultrasonic characterization of welds because of their relative long-range propagation. In this paper, a simplified model of a weld-strip between two identical semi-infinite elastic layers is investigated. The reflected and transmitted ultrasonic fields are expressed by modal series whose coefficients are obtained by application of orthogonality relation. Comparisons with solutions obtained by finite elements wave propagation simulations are made. The energy balance between the incident and the scattered waves is also used to verify the accuracy of the obtained modal amplitudes.     

A model of wave propagation in an inhomogeneous excitable meduim

Wave propagation in an inhomogeneous excitable medium is modeled by a two-dimensional, multi-state cellular automaton with absorbing boundary conditions. The inhomogeneity of the meduim affects the normal pattern of wave propagation and various phenomena like delayed propagation and circular wave formation are observed. The different types of wave propagation observed in our computer simulations are summarized in a phase diagram and the predictions of the stochastic models for two of the wave propagation phenomena are presented. This system has been suggested as a simple model of the atrioventricular (AV) node.     

非均匀圆柱壳中非线性波传播模型的同伦分析解法

圆柱形壳中非线性波传播问题的研究具有重要的理论和现实意义.本文用同伦分析方法,研究了描述非均匀圆柱壳中非线性波传播的一种新模型,得到了该模型的高精度近似孤波解和周期波解.这表明同伦分析方法是研究非线性波传播问题的一种十分有效的方法.