A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 1. Detection of repeated patterns

The existence of precise temporal relations in sequences of spike intervals, referred to as 'spatiotemporal patterns', is suggested by brain theories that emphasize the role of temporal coding. Specific analytical methods able to assess the significance of such patterned activity are extremely important to establish its function for information processing in the brain. This study proposes a new method called 'pattern grouping algorithm' (PGA), designed to identify and evaluate the statistical significance of patterns which differ from each other by a defined and small jitter in spike timing of the order of few ms. The algorithm performs a pre-selection of template patterns with a fast computational approach, optimizes the jitter for each spike in the template and evaluates the statistical significance of the pattern group using three complementary statistical approaches. Simulated data sets characterized by various types of known non stationarities are used for validation of PGA and for comparison of its performance to other methods. Applications of PGA to experimental data sets of simultaneously recorded spike trains are described in a companion paper (Tetko IV, Villa AEP. A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 2. Application to simultaneous single unit recordings. J Neurosci Method 2000; accompanying article).     

Stochastic description of complex and simple spike firing in cerebellar Purkinje cells

Cerebellar Purkinje cells generate two distinct types of spikes, complex and simple spikes, both of which have conventionally been considered to be highly irregular, suggestive of certain types of stochastic processes as underlying mechanisms. Interestingly, however, the interspike interval structures of complex spikes have not been carefully studied so far. We showed in a previous study that simple spike trains are actually composed of regular patterns and single interspike intervals, a mixture that could not be explained by a simple rate-modulated Poisson process. In the present study, we systematically investigated the interspike interval structures of separated complex and simple spike trains recorded in anaesthetized rats, and derived an appropriate stochastic model. We found that: (i) complex spike trains do not exhibit any serial correlations, so they can effectively be generated by a renewal process, (ii) the distribution of intervals between complex spikes exhibits two narrow bands, possibly caused by two oscillatory bands (0.5-1 and 4-8 Hz) in the input to Purkinje cells and (iii) the regularity of regular patterns and single interspike intervals in simple spike trains can be represented by gamma processes of orders, which themselves are drawn from gamma distributions, suggesting that multiple sources modulate the regularity of simple spike trains.     

Favored patterns in spontaneous spike trains.

By using the modified detection method, favored patterns can be detected in a total of 44 spontaneous spike trains. Among these the 'periodical burst' discharge of one sympathetic preganglionic neuron and the 'fast-slow' alternative discharge of some hypothalamic neurons have visible characteristics, hence we use them to test the reliability of our method by comparing the detected patterns with the non-sequential interval histograms and oscillograms of the spike trains. The comparisons show that our method is reliable. The spike trains of nucleus raphe magnus (NRM) and the locus coeruleus (LC) have no visible characteristics; from these the following results have been observed: (1) all spike trains have one or more favored patterns; (2) some spike trains from neurons in the same nucleus have common fragments of favored patterns; (3) the favored patterns in spike trains recorded from different nuclei are different from each other; (4) some favored patterns in spike trains of the NRM neurons remain unchanged from beginning to end in 35-min records and their repetitions are relatively stable; and (5) microinjection of normal saline or normal serum into the LC has no significant influence on the occurrence of favored patterns in 35-min records of spike trains of the LC neurons. The above results indicate that the favored patterns in spike trains are objective and regular phenomena with relative stability. It seems likely that favored pattern may be used (as an index of the neuronal activity) in combination with the microinjection technique, etc., for various studies including studies on neural coding.     

Wavelet-based processing of neuronal spike trains prior to discriminant analysis

Investigations of neural coding in many brain systems have focused on the role of spike rate and timing as two means of encoding information within a spike train. Recently, statistical pattern recognition methods, such as linear discriminant analysis (LDA), have emerged as a standard approach for examining neural codes. These methods work well when data sets are over-determined (i.e., there are more observations than predictor variables). But this is not always the case in many experimental data sets. One way to reduce the number of predictor variables is to preprocess data prior to classification. Here, a wavelet-based method is described for preprocessing spike trains. The method is based on the discriminant pursuit (DP) algorithm of Buckheit and Donoho [Proc. SPIE 2569 (1995) 540-51]. DP extracts a reduced set of features that are well localized in the time and frequency domains and that can be subsequently analyzed with statistical classifiers. DP is illustrated using neuronal spike trains recorded in the motor cortex of an awake, behaving rat [Laubach et al. Nature 405 (2000) 567-71]. In addition, simulated spike trains that differed only in the timing of spikes are used to show that DP outperforms another method for preprocessing spike trains, principal component analysis (PCA) [Richmond and Optican J. Neurophysiol. 57 (1987) 147-61].     

Parafascicular thalamic nucleus activity in a rat model of Parkinson's disease

Parkinson's disease is associated with increased oscillatory firing patterns in basal ganglia output, which are thought to disrupt thalamocortical activity. However, it is unclear how specific thalamic nuclei are affected by these changes in basal ganglia activity. The thalamic parafascicular nucleus (PFN) receives input from basal ganglia output nuclei and directly projects to the subthalamic nucleus (STN), striatum and cortex; thus basal ganglia-mediated changes on PFN activity may further impact basal ganglia and cortical functions. To investigate the impact of increased oscillatory activity in basal ganglia output on PFN activity after dopamine cell lesion, PFN single-unit and local field potential activities were recorded in neurologically intact (control) rats and in both non-lesioned and dopamine lesioned hemispheres of unilateral 6-hydroxydopamine lesioned rats anesthetized with urethane. Firing rates were unchanged 1–2 weeks after lesion; however, significantly fewer spontaneously active PFN neurons were evident. Firing pattern assessments after lesion showed that a larger proportion of PFN spike trains had 0.3–2.5 Hz oscillatory activity and significantly fewer spike trains exhibited low threshold calcium spike (LTS) bursts. In paired recordings, more PFN–STN spike oscillations were significantly correlated, but as these oscillations were in-phase, results are inconsistent with feedforward control of PFN activity by inhibitory oscillatory basal ganglia output. Furthermore, the decreased incidence of LTS bursts is incompatible with inhibitory basal ganglia output inducing rebound bursting in PFN after dopamine lesion. Together, results show that robust oscillatory activity observed in basal ganglia output nuclei after dopamine cell lesion does not directly drive changes in PFN oscillatory activity.     

Spectral analysis of oscillatory neural circuits

Oscillatory dynamics are found at all levels of the nervous system. The goal of our current research on the control of rhythmic motor output by the lamprey spinal cord is to determine the features of neuronal coupling that lead to stable oscillatory activity and precisely-controlled intersegmental phase. Since our experimental manipulations can greatly increase the variability of the ventral root bursting pattern, it is important for us to employ a data analysis method which remains valid independent of this variability. Traditional analysis approaches which rely on identification of burst event times do not generally satisfy this requirement. In this paper, we illustrate the application of a straightforward statistically-based method for determining important parameters of oscillatory motor circuits using Fourier spectral analysis of spike trains. The frequency, phase, and their variabilities can be quantified; and the relative strength of coupling between different parts of the circuit can be tested for statistical significance. The approach we adopt is highly convenient for neuroscientists who study oscillatory systems as it operates directly on trains of action potentials stored as lists of event times (point-processes). Basic concepts and practical issues concerning use of Fourier analysis are discussed.     

Properties of favored patterns in spontaneous spike trains and responses of favored patterns to electroacupuncture in evoked trains.

By using 'the modified detection method', our previous study has shown that all spontaneous spike trains recorded from several areas of brain and spinal cord have favored patterns (FPs). The present study further shows that: (1) all newly detected spike trains from substantia nigra zona compacta, nucleus periventricularis hypothalami and nucleus hypothalamicus posterior also have FPs, and some spike trains from neurons in the same nucleus have a common favored pattern (CF, i.e. they share the same FP), indicating that FP and CF in spike trains are common phenomena; (2) all serial correlation coefficients of FP repetitions (in serial order) in different spike trains detected are less than 0.3 (close to 0), revealing that the repetition of FPs is a renewal process; (3) in different periods of the spike trains evoked by electroacupuncture (EA), the number of different FPs and the number of repetitions of the same representative FP either increase or decrease along with the change of firing rate. The tendencies of these changes are very similar, but after EA the repetitions of different FPs in the same spike trains change differently, showing that different (hidden) responses exist at the same time. The above results suggest that the FPs in spike trains may represent various neural codes, and 'the modified detection method of FP' can pick up more information from spike trains than the firing rate analysis, hence it is a very useful tool for the study of neural coding.     

Statistical technique for analysing functional connectivity of multiple spike trains

A new statistical technique, the Cox method, used for analysing functional connectivity of simultaneously recorded multiple spike trains is presented. This method is based on the theory of modulated renewal processes and it estimates a vector of influence strengths from multiple spike trains (called reference trains) to the selected (target) spike train. Selecting another target spike train and repeating the calculation of the influence strengths from the reference spike trains enables researchers to find all functional connections among multiple spike trains. In order to study functional connectivity an "influence function" is identified. This function recognises the specificity of neuronal interactions and reflects the dynamics of postsynaptic potential. In comparison to existing techniques, the Cox method has the following advantages: it does not use bins (binless method); it is applicable to cases where the sample size is small; it is sufficiently sensitive such that it estimates weak influences; it supports the simultaneous analysis of multiple influences; it is able to identify a correct connectivity scheme in difficult cases of "common source" or "indirect" connectivity. The Cox method has been thoroughly tested using multiple sets of data generated by the neural network model of the leaky integrate and fire neurons with a prescribed architecture of connections. The results suggest that this method is highly successful for analysing functional connectivity of simultaneously recorded multiple spike trains.     

Multineuronal vectorization is more efficient than time-segmental vectorization for information extraction from neuronal activities in the inferior temporal cortex

In order for patients with disabilities to control assistive devices with their own neural activity, multineuronal spike trains must be efficiently decoded because only limited computational resources can be used to generate prosthetic control signals in portable real-time applications. In this study, we compare the abilities of two vectorizing procedures (multineuronal and time-segmental) to extract information from spike trains during the same total neuron-seconds. In the multineuronal vectorizing procedure, we defined a response vector whose components represented the spike counts of one to five neurons. In the time-segmental vectorizing procedure, a response vector consisted of components representing a neuron’s spike counts for one to five time-segment(s) of a response period of 1 s. Spike trains were recorded from neurons in the inferior temporal cortex of monkeys presented with visual stimuli. We examined whether the amount of information of the visual stimuli carried by these neurons differed between the two vectorizing procedures. The amount of information calculated with the multineuronal vectorizing procedure, but not the time-segmental vectorizing procedure, significantly increased with the dimensions of the response vector. We conclude that the multineuronal vectorizing procedure is superior to the time-segmental vectorizing procedure in efficiently extracting information from neuronal signals.     

Modeling and analyzing higher-order correlations in non-Poissonian spike trains

Measuring pairwise and higher-order spike correlations is crucial for studying their potential impact on neuronal information processing. In order to avoid misinterpretation of results, the tools used for data analysis need to be carefully calibrated with respect to their sensitivity and robustness. This, in turn, requires surrogate data with statistical properties common to experimental spike trains. Here, we present a novel method to generate correlated non-Poissonian spike trains and study the impact of single-neuron spike statistics on the inference of higher-order correlations. Our method to mimic cooperative neuronal spike activity allows the realization of a large variety of renewal processes with controlled higher-order correlation structure. Based on surrogate data obtained by this procedure we investigate the robustness of the recently proposed method empirical de-Poissonization (Ehm et al., 2007). It assumes Poissonian spiking, which is common also for many other estimation techniques. We observe that some degree of deviation from this assumption can generally be tolerated, that the results are more reliable for small analysis bins, and that the degree of misestimation depends on the detailed spike statistics. As a consequence of these findings we finally propose a strategy to assess the reliability of results for experimental data.     

A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 2. Application to simultaneous single unit recordings

This study demonstrates the practical application of the pattern grouping algorithm (PGA), presented in the companion paper (Tetko IV, Villa AEP. A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 1. Detection of repeated patterns. J. Neurosci. Methods 2000; accompanying article), to data sets including up to 30 simultaneously recorded spike trains. The analysis of a large network of simulated neurons shows that the incidence of patterns cannot be simply related to an increase in firing rates obtained after Hebbian learning. Patterns that disappeared and reappeared in the thalamus of anesthetized rats when the cerebral cortex was reversibly inactivated suggest that widespread cell assemblies contribute to the generation and propagation of precisely timed activity. In an another experiment multiple spike trains were recorded from the temporal cortex of freely moving rats performing a complex two-choice discrimination task. The presence or absence of particular patterns in the period preceding the cue was associated with changes in reaction time. In conclusion, neuronal network interactions may generate spatiotemporal firing patterns detectable by PGA. We provide evidence of such patterned activity associated with specific animal's behavior, thus suggesting the existence of complex temporal coding schemes in the higher nervous centers of the brain.     

Accurate spike sorting for multi‐unit recordings

Simultaneous recordings with multi‐channel electrodes are widely used for studying how multiple neurons are recruited for information processing. The recorded signals contain the spike events of a number of adjacent or distant neurons and must be sorted correctly into spike trains of individual neurons. Several mathematical methods have been proposed for spike sorting but the process is difficult in practice, as extracellularly recorded signals are corrupted by biological noise. Moreover, spike sorting is often time‐consuming, as it usually requires corrections by human operators. Methods are needed to obtain reliable spike clusters without heavy manual operation. Here, we introduce several methods of spike sorting and compare the accuracy and robustness of their performance by using publicized data of simultaneous extracellular and intracellular recordings of neuronal activity. The best and excellent performance was obtained when a newly proposed filter for spike detection was combined with the wavelet transform and variational Bayes for a finite mixture of Student’s t‐distributions, namely, robust variational Bayes. Wavelet transform extracts features that are characteristic of the detected spike waveforms and the robust variational Bayes categorizes the extracted features into clusters corresponding to spikes of the individual neurons. The use of Student’s t‐distributions makes this categorization robust against noisy data points. Some other new methods also exhibited reasonably good performance. We implemented all of the proposed methods in a C++ code named ‘EToS’ (Efficient Technology of Spike sorting), which is freely available on the Internet.     

Bilateral oscillations for lateralized spikes in benign rolandic epilepsy

PURPOSES: To elucidate the oscillatory dynamics with respect to interictal spike occurrence in benign rolandic epilepsy (BRE). METHODS: Using a whole-scalp magnetoencephalography (MEG), we recorded scalp EEG and MEG signals in 10 BRE patients (age 8-12 years) and visually identified unilateral interictal spikes that were simultaneously present on both EEG and MEG channels. We obtained the peak timing of individual spike complex based on MEG single-dipole modeling, and then applied wavelet transform to analyze the time-frequency components of corresponding MEG signals with respect to spike occurrence. RESULTS: In the hemisphere with time-domain spike waveforms, we identified a clear increase of 0.5-40 Hz activity around the spike peak, most prominent at alpha band (8-13 Hz). Notably, at the approximate timing we also observed an increase in 0.5-25 Hz oscillations over the homotopic area in the other hemisphere where no spike signals were found. CONCLUSIONS: Our results indicate bilateral increases in 0.5-25 Hz oscillations during unilateral spike formation in BRE patients. By using wavelet transform analysis, one could be able to detect some irritative feature that would in visual analysis remain undetected.     

Developments in understanding neuronal spike trains and functional specializations in brain regions.

Understanding information processing at the neuronal level would provide valuable insights to computational intelligence research and computational neuroscience. In particular, understanding constraints on neuronal spike trains would provide indication about the type of syntactic rules used by neurons when processing information. A recent discovery, reported here, was made through analyzing microelectrode recordings (MER) made during surgical procedure in humans. Analysis of MERs of extracellular neuronal activity has gained increasing interest due to potential improvements to surgical techniques involving ablation or placement of deep brain stimulators, done in the treatment of advanced Parkinson's disease. Important to these procedures is the identification of different brain structures such as the globus pallidus internus from the spike train being recorded from the intracranial probe tip during surgery. Spike train data gathered during surgical procedure from multiple patients were processed using a novel feature extraction method reported here. Distinct structures within the spike trains were identified and used to build an effective brain region classifier. The extracted features upon analysis provide some insight into the 'syntactic' constraint on spike trains.     

Information trains. The technique and its uses in spike train and network analysis, with examples taken from the nucleus parabrachialis medialis during sleep-waking states

We describe an analytical procedure for assessing functional interactions between neuronal spike trains based on the outcome of cross-correlation procedures. Subsets of a reference cell spike train in a two-train recording are extracted, based on their time-locked relationship to spikes in the dependent train. Such timing relationships comprise the significant primary structures in the cross-correlogram. Different subsets can be extracted for different primary structures in the same correlogram (i.e. a subset responsible for an interaction effect, a subset responsible for a shared input effect, etc.) These new spike trains represent an information transfer process across synapses. These ‘information trains’ may be compared and correlated to different cells of the network across different functional conditions such as sleep-waking states, and may also be subjected to conventional spike train analysis techniques such as rate histogram, auto-correlation and cross-correlation procedures. We illustrate the information train procedures with a network analysis of a set of cells recorded in the nucleus parabrachialis medialis during different sleep-waking states.     

Evidence for spatiotemporal firing patterns within the auditory thalamus of the cat

Multiple spike trains were recorded in the auditory thalamus of cats. Each unit was studied before, during and after cooling of the ipsilateral primary auditory cortex, during spontaneous activity and acoustically evoked activity. The search for spatiotemporal firing patterns provided evidence that excess of patterns does exist and that the acoustical stimulation increased their number. Cortical cooling did not affect the probability of finding the firing pattern.     

Short-term plasticity optimizes synaptic information transmission

Short-term synaptic plasticity (STP) is widely thought to play an important role in information processing. This major function of STP has recently been challenged, however, by several computational studies indicating that transmission of information by dynamic synapses is broadband, i.e., frequency independent. Here we developed an analytical approach to quantify time- and rate-dependent synaptic information transfer during arbitrary spike trains using a realistic model of synaptic dynamics in excitatory hippocampal synapses. We found that STP indeed increases information transfer in a wide range of input rates, which corresponds well to the naturally occurring spike frequencies at these synapses. This increased information transfer is observed both during Poisson-distributed spike trains with a constant rate and during naturalistic spike trains recorded in hippocampal place cells in exploring rodents. Interestingly, we found that the presence of STP in low release probability excitatory synapses leads to optimization of information transfer specifically for short high-frequency bursts, which are indeed commonly observed in many excitatory hippocampal neurons. In contrast, more reliable high release probability synapses that express dominant short-term depression are predicted to have optimal information transmission for single spikes rather than bursts. This prediction is verified in analyses of experimental recordings from high release probability inhibitory synapses in mouse hippocampal slices and fits well with the observation that inhibitory hippocampal interneurons do not commonly fire spike bursts. We conclude that STP indeed contributes significantly to synaptic information transfer and may serve to maximize information transfer for specific firing patterns of the corresponding neurons.     

Stimulus-Dependent Neuronal Oscillations in Cat Visual Cortex: Receptive Field Properties and Feature Dependence

Previously we have demonstrated that neurons in the striate cortex of lightly anaesthetized cats exhibit oscillatory responses at a frequency near 50 Hz in response to their preferred stimuli. Here we have used both single and multiple unit recording techniques to determine: (i) the receptive field properties and laminar distribution of cells exhibiting oscillatory responses; and (ii) the influence of changing stimulus properties on the temporal behaviour of the oscillatory responses. Oscillatory responses were detected and evaluated by computation of the autocorrelation function of the neuronal spike trains. We recorded oscillatory responses in 56% of the standard complex cells and in 12% and 11% of the simple and special complex cells. Cells exhibiting oscillatory responses were located primarily in supra- and infragranular layers. The oscillatory modulation amplitude of the autocorrelation function was enhanced by binocular stimulation (9 out of 16 cells) and reduced by combined stimulation with optimal and orthogonally orientated light bars (16 out of 21 cells). Changing stimulus orientation caused no change in the oscillation frequency of the sampled population of cells, while oscillation frequency increased monotonically with respect to stimulus velocity within the range of 1 - 12 degrees per second (10 out of 11 cells). The oscillatory modulation of the autocorrelation function increased as a function of stimulus length within the boundary of the cell's receptive field (11 out of 11 cells). In 6 out of these 11 cells, the responses did not show an oscillatory modulation if elicited by small moving spots of light. Moving stimuli were much more effective in evoking oscillatory responses than were stationary stimuli (19 out of 20 cells). In no instance, using either stationary or moving stimuli, was the phase of the oscillatory response synchronized with the stimulus. These results demonstrate functional heterogeneity among cells within striate cortex based on their temporal firing patterns and provide evidence that the temporal pattern of oscillatory cellular activity is influenced by changes in stimulus properties.     

Measurement of variability dynamics in cortical spike trains

We propose a method for the time-resolved joint analysis of two related aspects of single neuron variability, the spiking irregularity measured by the squared coefficient of variation (CV(2)) of the ISIs and the trial-by-trial variability of the spike count measured by the Fano factor (FF). We provide a calibration of both estimators using the theory of renewal processes, and verify it for spike trains recorded in vitro. Both estimators exhibit a considerable bias for short observations that count less than about 5-10 spikes on average. The practical difficulty of measuring the CV(2) in rate modulated data can be overcome by a simple procedure of spike train demodulation which was tested in numerical simulations and in real spike trains. We propose to test neuronal spike trains for deviations from the null-hypothesis FF=CV(2). We show that cortical pyramidal neurons, recorded under controlled stationary input conditions in vitro, comply with this assumption. Performing a time-resolved joint analysis of CV(2) and FF of a single unit recording from the motor cortex of a behaving monkey we demonstrate how the dynamic change of their quantitative relation can be interpreted with respect to neuron intrinsic and extrinsic factors that influence cortical variability in vivo. Finally, we discuss the effect of several additional factors such as serial interval correlation and refractory period on the empiric relation of FF and CV(2).