Analysis Of Neural Spike Trains Research Articles

Complexity Measures for EEG Microstate Sequences: Concepts and Algorithms

EEG microstate sequence analysis quantifies properties of ongoing brain electrical activity which is known to exhibit complex dynamics across many time scales. In this report we review recent developments in quantifying microstate sequence complexity, we classify these approaches with regard to different complexity concepts, and we evaluate excess entropy as a yet unexplored quantity in microstate research. We determined the quantities entropy rate, excess entropy, Lempel–Ziv complexity (LZC), and Hurst exponents on Potts model data, a discrete statistical mechanics model with a temperature-controlled phase transition. We then applied the same techniques to EEG microstate sequences from wakefulness and non-REM sleep stages and used first-order Markov surrogate data to determine which time scales contributed to the different complexity measures. We demonstrate that entropy rate and LZC measure the Kolmogorov complexity (randomness) of microstate sequences, whereas excess entropy and Hurst exponents describe statistical complexity which attains its maximum at intermediate levels of randomness. We confirmed the equivalence of entropy rate and LZC when the LZ-76 algorithm is used, a result previously reported for neural spike train analysis (Amigó et al., Neural Comput 16:717–736, https://doi.org/10.1162/089976604322860677, 2004). Surrogate data analyses prove that entropy-based quantities and LZC focus on short-range temporal correlations, whereas Hurst exponents include short and long time scales. Sleep data analysis reveals that deeper sleep stages are accompanied by a decrease in Kolmogorov complexity and an increase in statistical complexity. Microstate jump sequences, where duplicate states have been removed, show higher randomness, lower statistical complexity, and no long-range correlations. Regarding the practical use of these methods, we suggest that LZC can be used as an efficient entropy rate estimator that avoids the estimation of joint entropies, whereas entropy rate estimation via joint entropies has the advantage of providing excess entropy as the second parameter of the same linear fit. We conclude that metrics of statistical complexity are a useful addition to microstate analysis and address a complexity concept that is not yet covered by existing microstate algorithms while being actively explored in other areas of brain research.

Inference of Multiplicative Factors Underlying Neural Variability in Calcium Imaging Data.

Understanding brain function requires disentangling the high-dimensional activity of populations of neurons. Calcium imaging is an increasingly popular technique for monitoring such neural activity, but computational tools for interpreting extracted calcium signals are lacking. While there has been a substantial development of factor analysis-type methods for neural spike train analysis, similar methods targeted at calcium imaging data are only beginning to emerge. Here we develop a flexible modeling framework that identifies low-dimensional latent factors in calcium imaging data with distinct additive and multiplicative modulatory effects. Our model includes spike-and-slab sparse priors that regularize additive factor activity and gaussian process priors that constrain multiplicative effects to vary only gradually, allowing for the identification of smooth and interpretable changes in multiplicative gain. These factors are estimated from the data using a variational expectation-maximization algorithm that requires a differentiable reparameterization of both continuous and discrete latent variables. After demonstrating our method on simulated data, we apply it to experimental data from the zebrafish optic tectum, uncovering low-dimensional fluctuations in multiplicative excitability that govern trial-to-trial variation in evoked responses.

A Spike Train Distance Robust to Firing Rate Changes Based on the Earth Mover's Distance.

Neural spike train analysis methods are mainly used for understanding the temporal aspects of neural information processing. One approach is to measure the dissimilarity between the spike trains of a pair of neurons, often referred to as the spike train distance. The spike train distance has been often used to classify neuronal units with similar temporal patterns. Several methods to compute spike train distance have been developed so far. Intuitively, a desirable distance should be the shortest length between two objects. The Earth Mover’s Distance (EMD) can compute spike train distance by measuring the shortest length between two spike trains via shifting a fraction of spikes from one spike train to another. The EMD could accurately measure spike timing differences, temporal similarity, and spikes time synchrony. It is also robust to firing rate changes. Victor and Purpura (1996) distance measures the minimum cost between two spike trains. Although it also measures the shortest path between spike trains, its output can vary with the time-scale parameter. In contrast, the EMD measures distance in a unique way by calculating the genuine shortest length between spike trains. The EMD also outperforms other existing spike train distance methods in measuring various aspects of the temporal characteristics of spike trains and in robustness to firing rate changes. The EMD can effectively measure the shortest length between spike trains without being considerably affected by the overall firing rate difference between them. Hence, it is suitable for pure temporal coding exclusively, which is a predominant premise underlying the present study.

Evaluating the estimation accuracy in random point processes for the analysis of neural spike trains

Evaluating the estimation accuracy in random point processes for the analysis of neural spike trains

A Functional Connectivity Analysis Toolbox for Multiple Spike Trains Data: �ToolConnect�

A Functional Connectivity Analysis Toolbox for Multiple Spike Trains Data: �ToolConnect�

Multiscale analysis of neural spike trains

This paper studies the multiscale analysis of neural spike trains, through both graphical and Poisson process approaches. We introduce the interspike interval plot, which simultaneously visualizes characteristics of neural spiking activity at different time scales. Using an inhomogeneous Poisson process framework, we discuss multiscale estimates of the intensity functions of spike trains. We also introduce the windowing effect for two multiscale methods. Using quasi-likelihood, we develop bootstrap confidence intervals for the multiscale intensity function. We provide a cross-validation scheme, to choose the tuning parameters, and study its unbiasedness. Studying the relationship between the spike rate and the stimulus signal, we observe that adjusting for the first spike latency is important in cross-validation. We show, through examples, that the correlation between spike trains and spike count variability can be multiscale phenomena. Furthermore, we address the modeling of the periodicity of the spike trains caused by a stimulus signal or by brain rhythms. Within the multiscale framework, we introduce intensity functions for spike trains with multiplicative and additive periodic components. Analyzing a dataset from the retinogeniculate synapse, we compare the fit of these models with the Bayesian adaptive regression splines method and discuss the limitations of the methodology. Computational efficiency, which is usually a challenge in the analysis of spike trains, is one of the highlights of these new models. In an example, we show that the reconstruction quality of a complex intensity function demonstrates the ability of the multiscale methodology to crack the neural code.

An overview of Bayesian methods for neural spike train analysis.

Neural spike train analysis is an important task in computational neuroscience which aims to understand neural mechanisms and gain insights into neural circuits. With the advancement of multielectrode recording and imaging technologies, it has become increasingly demanding to develop statistical tools for analyzing large neuronal ensemble spike activity. Here we present a tutorial overview of Bayesian methods and their representative applications in neural spike train analysis, at both single neuron and population levels. On the theoretical side, we focus on various approximate Bayesian inference techniques as applied to latent state and parameter estimation. On the application side, the topics include spike sorting, tuning curve estimation, neural encoding and decoding, deconvolution of spike trains from calcium imaging signals, and inference of neuronal functional connectivity and synchrony. Some research challenges and opportunities for neural spike train analysis are discussed.

NSTAT: Open-source neural spike train analysis toolbox for Matlab

Over the last decade there has been a tremendous advance in the analytical tools available to neuroscientists to understand and model neural function. In particular, the point process – generalized linear model (PP-GLM) framework has been applied successfully to problems ranging from neuro-endocrine physiology to neural decoding. However, the lack of freely distributed software implementations of published PP-GLM algorithms together with problem-specific modifications required for their use, limit wide application of these techniques. In an effort to make existing PP-GLM methods more accessible to the neuroscience community, we have developed nSTAT – an open source neural spike train analysis toolbox for Matlab®. By adopting an object-oriented programming (OOP) approach, nSTAT allows users to easily manipulate data by performing operations on objects that have an intuitive connection to the experiment (spike trains, covariates, etc.), rather than by dealing with data in vector/matrix form. The algorithms implemented within nSTAT address a number of common problems including computation of peri-stimulus time histograms, quantification of the temporal response properties of neurons, and characterization of neural plasticity within and across trials. nSTAT provides a starting point for exploratory data analysis, allows for simple and systematic building and testing of point process models, and for decoding of stimulus variables based on point process models of neural function. By providing an open-source toolbox, we hope to establish a platform that can be easily used, modified, and extended by the scientific community to address limitations of current techniques and to extend available techniques to more complex problems.

Towards statistical summaries of spike train data

AbstractStatistical inference has an important role in analysis of neural spike trains. While current approaches are mostly model-based, and designed for capturing the temporal evolution of the underlying stochastic processes, we focus on a data-driven approach where statistics are defined and computed in function spaces where individual spike trains are viewed as points. The first contribution of this paper is to endow spike train space with a parameterized family of metrics that takes into account different time warpings and generalizes several currently used metrics. These metrics are essentially penalized Lp norms, involving appropriate functions of spike trains, with penalties associated with time-warpings. The second contribution of this paper is to derive a notion of a mean spike train in the case when p=2. We present an efficient recursive algorithm, termed Matching-Minimization algorithm, to compute the sample mean of a set of spike trains. The proposed metrics as well as the mean computations are demonstrated using an experimental recording from the motor cortex.

Correlation-based approach to analysis of spiking networks

The correlation structure of neural activity is believed to play a major role in the encoding and possibly decoding of information in neural populations. In addition, some of the most fundamental and widely applied tools for the identification of systems rely on the use of second order statistical properties (correlation or spectral). An arsenal of tools for identifying spike train models from their correlations, rather than from their full observed realizations could thus form a welcome bridge between ‘classical’ signal processing ideas and tools and the field of neural spike train analysis. Recently, several methods were developed for controlling the correlation structure of multi-channel synthetic spike trains [1,3-5], and in related work, correlation based analysis of spike trains was used for blind identification of single-neuron models [5], for identifying compact autoregressive models for multi-channel spike trains, and for facilitating their causal network analysis [6]. However, the diversity of correlation structures that can be explained by the non-recurrent generative models used in these studies is limited, and hence, methods based on such models occasionally fail while analyzing correlation structures that are observed in neural activity. Here, we extend this framework by deriving closed-form expressions for the correlation structure of a more powerful multivariate self- and mutually-exciting Hawkes model class that is driven by exogenous non-negative inputs. We demonstrate that the resulting Linear-Nonlinear-Hawkes (LNH) framework is capable of capturing the dynamics of spike trains with a generally richer multi-correlation structure. We explore several new applications of this framework including highly compact representation of multi-channel spike train data and causal analysis of network information flow.

Correlation-Based Analysis and Generation of Multiple Spike Trains Using Hawkes Models with an Exogenous Input

The correlation structure of neural activity is believed to play a major role in the encoding and possibly the decoding of information in neural populations. Recently, several methods were developed for exactly controlling the correlation structure of multi-channel synthetic spike trains (Brette, 2009; Krumin and Shoham, 2009; Macke et al., 2009; Gutnisky and Josic, 2010; Tchumatchenko et al., 2010) and, in a related work, correlation-based analysis of spike trains was used for blind identification of single-neuron models (Krumin et al., 2010), for identifying compact auto-regressive models for multi-channel spike trains, and for facilitating their causal network analysis (Krumin and Shoham, 2010). However, the diversity of correlation structures that can be explained by the feed-forward, non-recurrent, generative models used in these studies is limited. Hence, methods based on such models occasionally fail when analyzing correlation structures that are observed in neural activity. Here, we extend this framework by deriving closed-form expressions for the correlation structure of a more powerful multivariate self- and mutually exciting Hawkes model class that is driven by exogenous non-negative inputs. We demonstrate that the resulting Linear–Non-linear-Hawkes (LNH) framework is capable of capturing the dynamics of spike trains with a generally richer and more biologically relevant multi-correlation structure, and can be used to accurately estimate the Hawkes kernels or the correlation structure of external inputs in both simulated and real spike trains (recorded from visually stimulated mouse retinal ganglion cells). We conclude by discussing the method's limitations and the broader significance of strengthening the links between neural spike train analysis and classical system identification.

Signal Processing for Neural Spike Trains

Signal Processing for Neural Spike Trains

Encoding of Information Into Neural Spike Trains in an Auditory Nerve Fiber Model With Electric Stimuli in the Presence of a Pseudospontaneous Activity

This paper presents an information-theoretic analysis of neural spike trains in an auditory nerve fiber (ANF) model stimulated extracellularly with Gaussian or sinusoidal waveforms in the presence of a pseudospontaneous activity of spike firings. In the computer simulation, stimulus current waveforms were applied repeatedly to a stimulating electrode located 1 mm above the 26th node of Ranvier, in an ANF axon model having 50 nodes of Ranvier, each consisting of stochastic sodium and potassium channels. From spike firing times recorded at the 36th node of Ranvier, a post-stimulus time histogram (PSTH) was generated, and raster plots were depicted for 30 stimulus presentations, in order to investigate the temporal precision and reliability of the spike firing times. Also, inter spike intervals were generated and then "total" and "noise" entropies were estimated to obtain the mutual information and the information rate of the spike trains. It was shown in the case of Gaussian electric stimuli that the temporal precision of spike firing times and the reliability of spike firings were found to increase as the standard deviation (SD) of the Gaussian electric stimuli increased. It was also shown in the case of sinusoidal electric stimuli where there was a specific amplitude of sinusoidal waveforms, the information rate being maximized. It was implied that setting the parameters of electric stimuli to the specific values which maximize the information rate might contribute to efficiently encoding information into the spike trains in the presence of a pseudospontaneous activity of spike firings.

Analyzing Functional Connectivity Using a Network Likelihood Model of Ensemble Neural Spiking Activity

Analyzing the dependencies between spike trains is an important step in understanding how neurons work in concert to represent biological signals. Usually this is done for pairs of neurons at a time using correlation-based techniques. Chornoboy, Schramm, and Karr (1988) proposed maximum likelihood methods for the simultaneous analysis of multiple pair-wise interactions among an ensemble of neurons. One of these methods is an iterative, continuous-time estimation algorithm for a network likelihood model formulated in terms of multiplicative conditional intensity functions. We devised a discrete-time version of this algorithm that includes a new, efficient computational strategy, a principled method to compute starting values, and a principled stopping criterion. In an analysis of simulated neural spike trains from ensembles of interacting neurons, the algorithm recovered the correct connectivity matrices and interaction parameters. In the analysis of spike trains from an ensemble of rat hippocampal place cells, the algorithm identified a connectivity matrix and interaction parameters consistent with the pattern of conjoined firing predicted by the overlap of the neurons' spatial receptive fields. These results suggest that the network likelihood model can be an efficient tool for the analysis of ensemble spiking activity.

Analysis of neural spike trains with interspike interval reconstruction.

As a method for the analysis of neural spike trains, we examine fundamental characteristics of interspike interval (ISI) reconstruction theoretically with a leaky-integrator neuron model and experimentally with cricket wind receptor cells. Both the input to the leaky integrator and the stimulus to the wind receptor cells are the time series generated from the Rossler system. By numerical analysis of the leaky integrator, it is shown that, even if ISI reconstruction is possible, sometimes the entire structure of the Rössler attractor may not be reconstructed with ISI reconstruction. For analysis of the in vivo physiological responses of cricket wind receptor cells, we apply ISI reconstruction, nonlinear prediction and the surrogate data method to the experimental data. As a result of the analysis, it is found that there is a significant deterministic structure in the spike trains. By this analysis of physiological data, it is also shown that, even if ISI reconstruction is possible, the entire attractor may not be reconstructed.

Stochastic methods for neural systems

This paper is a survey of recent developments in the application of stochastic modeling and statistical analysis of biological and artificial neuron systems. We focus first on a general description of information processing in the central nervous system including the basic physiology of synaptic communications. We discuss some of the current models of and inference for membrane potential including temporal models. We discuss some of the stochastic modeling and analysis of neural spike trains. From a focus on communications between individual pairs of neurons, we turn our attention to broader scale neural network considerations, closing our discussion with models of networks with hidden layers.

Computer analysis of vestibular responses to putative neurotransmitters

An inexpensive microcomputer (Commodore 64K) based system was developed for the analysis of neural spike trains. The trains were recorded from single ampullary units in response to mechanical stimulation of the isolated semicircular canal of the bullfrog ( Rana catesbeiana). A BASIC program provided a number of options while machine language subroutines generated interstimulus interval (ISI) and peristimulus time (PST) histograms. Up to thirty 5-s spike trains could be combined for analysis (0.1 ms resolution ISI, 100 ms bin width PST). Histograms and summary statistics were saved on floppy disks. The cost of adding this computer system to an existing neurophysiology laboratory is less than US $600 (printed, tape, and disk versions of these programs are available). The system was used to measure vestibular responses to putative vestibular neurotransmitters such as carbachol (an acetylcholine mimic) (Rossi et al., 1980) and gamma-aminobutyric acid (GABA) (Flock and Lam, 1974).