Quantifying spike train oscillations: biases, distortions and solutions

Detecting rhythmic spiking through the power spectra of point process model residuals

Objective. Oscillations figure prominently as neurological disease hallmarks and neuromodulation targets. To detect oscillations in a neuron's spiking, one might attempt to seek peaks in the spike train's power spectral density (PSD) which exceed a flat baseline. Yet for a non-oscillating neuron, the PSD is not flat: The recovery period ('RP', the post-spike drop in spike probability, starting with the refractory period) introduces global spectral distortion. An established 'shuffling' procedure corrects for RP distortion by removing the spectral component explained by the inter-spike interval (ISI) distribution. However, this procedure sacrifices oscillation-related information present in the ISIs, and therefore in the PSD. We asked whether point process models (PPMs) might achieve more selective RP distortion removal, thereby enabling improved oscillation detection.Approach. In a novel 'residuals' method, we first estimate the RP duration (nr) from the ISI distribution. We then fit the spike train with a PPM that predicts spike likelihood based on the time elapsed since the most recent of any spikes falling within the precedingnrmilliseconds. Finally, we compute the PSD of the model's residuals.Main results. We compared the residuals and shuffling methods' ability to enable accurate oscillation detection with flat baseline-assuming tests. Over synthetic data, the residuals method generally outperformed the shuffling method in classification of true- versus false-positive oscillatory power, principally due to enhanced sensitivity in sparse spike trains. In single-unit data from the internal globus pallidus (GPi) and ventrolateral anterior thalamus (VLa) of a parkinsonian monkey-in which alpha-beta oscillations (8-30 Hz) were anticipated-the residuals method reported the greatest incidence of significant alpha-beta power, with low firing rates predicting residuals-selective oscillation detection.Significance. These results encourage continued development of the residuals approach, to support more accurate oscillation detection. Improved identification of oscillations could promote improved disease models and therapeutic technologies.

Detecting rhythmic spiking through the power spectra of point process model residuals

Objective

Oscillations figure prominently as neurological disease hallmarks and neuromodulation targets. To detect oscillations in a neuron's spiking, one might attempt to seek peaks in the spike train's power spectral density (PSD) which exceed a flat baseline. Yet for a non-oscillating neuron, the PSD is not flat: The recovery period ("RP", the post-spike drop in spike probability, starting with the refractory period) introduces global spectral distortion. An established "shuffling" procedure corrects for RP distortion by removing the spectral component explained by the inter-spike interval (ISI) distribution. However, this procedure sacrifices oscillation-related information present in the ISIs, and therefore in the PSD. We asked whether point process models (PPMs) might achieve more selective RP distortion removal, thereby enabling improved oscillation detection.

Approach

In a novel "residuals" method, we first estimate the RP duration (nr) from the ISI distribution. We then fit the spike train with a PPM that predicts spike likelihood based on the time elapsed since the most recent of any spikes falling within the preceding nr milliseconds. Finally, we compute the PSD of the model's residuals.

Main results

We compared the residuals and shuffling methods' ability to enable accurate oscillation detection with flat baseline-assuming tests. Over synthetic data, the residuals method generally outperformed the shuffling method in classification of true- versus false-positive oscillatory power, principally due to enhanced sensitivity in sparse spike trains. In single-unit data from the internal globus pallidus (GPi) and ventrolateral anterior thalamus (VLa) of a parkinsonian monkey -- in which alpha-beta oscillations (8-30 Hz) were anticipated -- the residuals method reported the greatest incidence of significant alpha-beta power, with low firing rates predicting residuals-selective oscillation detection.

Significance

These results encourage continued development of the residuals approach, to support more accurate oscillation detection. Improved identification of oscillations could promote improved disease models and therapeutic technologies.

Impulsivity Markers in Parkinsonian Subthalamic Single-Unit Activity

BACKGROUND

Impulsive-compulsive behaviors are common in Parkinson's disease (PD) patients. However, the basal ganglia dysfunctions associated with high impulsivity have not been fully characterized. The objective of this study was to identify the features associated with impulsive-compulsive behaviors in single neurons of the subthalamic nucleus (STN).

METHODS

We compared temporal and spectral features of 412 subthalamic neurons from 12 PD patients with impulsive-compulsive behaviors and 330 neurons from 12 PD patients without. Single-unit activities were extracted from exploratory microrecordings performed during deep brain stimulation (DBS) implant surgery in an OFF medication state.

RESULTS

Patients with impulsive-compulsive behaviors displayed decreased firing frequency during bursts and a larger fraction of tonic neurons combined with weaker beta coherence. Information carried by these features led to the identification of patients with impulsive-compulsive behaviors with an accuracy greater than 80%.

CONCLUSIONS

Impulsive-compulsive behaviors in PD patients are associated with decreased bursts in STN neurons in the OFF medication state. © 2021 International Parkinson and Movement Disorder Society.

Revealing Spectrum Features of Stochastic Neuron Spike Trains

Power spectra of spike trains reveal important properties of neuronal behavior. They exhibit several peaks, whose shape and position depend on applied stimuli and intrinsic biophysical properties, such as input current density and channel noise. The position of the spectral peaks in the frequency domain is not straightforwardly predictable from statistical averages of the interspike intervals, especially when stochastic behavior prevails. In this work, we provide a model for the neuronal power spectrum, obtained from Discrete Fourier Transform and expressed as a series of expected value of sinusoidal terms. The first term of the series allows us to estimate the frequencies of the spectral peaks to a maximum error of a few Hz, and to interpret why they are not harmonics of the first peak frequency. Thus, the simple expression of the proposed power spectral density (PSD) model makes it a powerful interpretative tool of PSD shape, and also useful for neurophysiological studies aimed at extracting information on neuronal behavior from spike train spectra.

Long-range temporal correlations in scale-free neuromorphic networks

Biological neuronal networks are the computing engines of the mammalian brain. These networks exhibit structural characteristics such as hierarchical architectures, small-world attributes, and scale-free topologies, providing the basis for the emergence of rich temporal characteristics such as scale-free dynamics and long-range temporal correlations. Devices that have both the topological and the temporal features of a neuronal network would be a significant step toward constructing a neuromorphic system that can emulate the computational ability and energy efficiency of the human brain. Here we use numerical simulations to show that percolating networks of nanoparticles exhibit structural properties that are reminiscent of biological neuronal networks, and then show experimentally that stimulation of percolating networks by an external voltage stimulus produces temporal dynamics that are self-similar, follow power-law scaling, and exhibit long-range temporal correlations. These results are expected to have important implications for the development of neuromorphic devices, especially for those based on the concept of reservoir computing.

Biological neuronal networks exhibit well-defined properties such as hierarchical structures and scale-free topologies, as well as a high degree of local clustering and short path lengths between nodes. These structural properties are intimately connected to the observed long-range temporal correlations in the network dynamics. Fabrication of artificial networks with similar structural properties would facilitate brain-like (“neuromorphic”) computing. Here we show experimentally that percolating networks of nanoparticles exhibit similar long-range temporal correlations to those of biological neuronal networks and use simulations to demonstrate that the dynamics arise from an underlying scale-free network architecture. We discuss similarities between the biological and percolating systems and highlight the potential for the percolating networks to be used in neuromorphic computing applications.

Longer β oscillatory episodes reliably identify pathological subthalamic activity in Parkinsonism

BACKGROUND

The efficacy of deep brain stimulation (DBS) - primarily of the subthalamic nucleus (STN) - for advanced Parkinson's disease (PD) is commonly attributed to the suppression of pathological synchronous β oscillations along the cortico-thalamo-basal ganglia network. Conventional continuous high-frequency DBS indiscriminately influences pathological and normal neural activity. The DBS protocol would therefore be more effective if stimulation was only applied when necessary (closed-loop adaptive DBS).

OBJECTIVES AND METHODS

Our study aimed to identify a reliable biomarker of the pathological neuronal activity in parkinsonism that could be used as a trigger for adaptive DBS. To this end, we examined the oscillatory features of paired spiking activities recorded in three distinct nodes of the basal ganglia network of 2 African green monkeys before and after induction of parkinsonism (by MPTP intoxication).

RESULTS

Parkinsonism-related basal ganglia β oscillations consisted of synchronized time-limited episodes, rather than a continuous stretch, of β oscillatory activity. Episodic basal ganglia β oscillatory activity, although prolonged in parkinsonism, was not necessarily pathological given that short β episodes could also be detected in the healthy state. Importantly, prolongation of the basal ganglia β episodes was more pronounced than their intensification in the parkinsonian state-especially in the STN. Hence, deletion of longer β episodes was more effective than deletion of stronger β episodes in reducing parkinsonian STN synchronized oscillatory activity.

CONCLUSIONS

Prolonged STN β episodes are pathological in parkinsonism and can be used as optimal trigger for future adaptive DBS applications. © 2018 International Parkinson and Movement Disorder Society.

Desynchronization of slow oscillations in the basal ganglia during natural sleep

Slow oscillations of neuronal activity alternating between firing and silence are a hallmark of slow-wave sleep (SWS). These oscillations reflect the default activity present in all mammalian species, and are ubiquitous to anesthesia, brain slice preparations, and neuronal cultures. In all these cases, neuronal firing is highly synchronous within local circuits, suggesting that oscillation-synchronization coupling may be a governing principle of sleep physiology regardless of anatomical connectivity. To investigate whether this principle applies to overall brain organization, we recorded the activity of individual neurons from basal ganglia (BG) structures and the thalamocortical (TC) network over 70 full nights of natural sleep in two vervet monkeys. During SWS, BG neurons manifested slow oscillations (∼0.5 Hz) in firing rate that were as prominent as in the TC network. However, in sharp contrast to any neural substrate explored thus far, the slow oscillations in all BG structures were completely desynchronized between individual neurons. Furthermore, whereas in the TC network single-cell spiking was locked to slow oscillations in the local field potential (LFP), the BG LFP exhibited only weak slow oscillatory activity and failed to entrain nearby cells. We thus show that synchrony is not inherent to slow oscillations, and propose that the BG desynchronization of slow oscillations could stem from its unique anatomy and functional connectivity. Finally, we posit that BG slow-oscillation desynchronization may further the reemergence of slow-oscillation traveling waves from multiple independent origins in the frontal cortex, thus significantly contributing to normal SWS.

Inferring oscillatory modulation in neural spike trains

Oscillations are observed at various frequency bands in continuous-valued neural recordings like the electroencephalogram (EEG) and local field potential (LFP) in bulk brain matter, and analysis of spike-field coherence reveals that spiking of single neurons often occurs at certain phases of the global oscillation. Oscillatory modulation has been examined in relation to continuous-valued oscillatory signals, and independently from the spike train alone, but behavior or stimulus triggered firing-rate modulation, spiking sparseness, presence of slow modulation not locked to stimuli and irregular oscillations with large variability in oscillatory periods, present challenges to searching for temporal structures present in the spike train. In order to study oscillatory modulation in real data collected under a variety of experimental conditions, we describe a flexible point-process framework we call the Latent Oscillatory Spike Train (LOST) model to decompose the instantaneous firing rate in biologically and behaviorally relevant factors: spiking refractoriness, event-locked firing rate non-stationarity, and trial-to-trial variability accounted for by baseline offset and a stochastic oscillatory modulation. We also extend the LOST model to accommodate changes in the modulatory structure over the duration of the experiment, and thereby discover trial-to-trial variability in the spike-field coherence of a rat primary motor cortical neuron to the LFP theta rhythm. Because LOST incorporates a latent stochastic auto-regressive term, LOST is able to detect oscillations when the firing rate is low, the modulation is weak, and when the modulating oscillation has a broad spectral peak.

Oscillatory modulation of neural activity in the brain is widely observed under conditions associated with a variety of cognitive tasks and mental states. Within individual neurons, oscillations may be uncovered in the moment-to-moment variation in neural firing rate. This, however, is often challenging because many factors may affect fluctuations in neural firing rate and, in addition, neurons fire irregular sets of action potentials, or spike trains, due to an unknown combination of meaningful signals and extraneous noise. We have devised a statistical Latent Oscillatory Spike Train (LOST) model with accompanying model-fitting technology, that is able to detect subtle oscillations in spike trains by taking into account both spiking noise and temporal variation in the oscillation itself. The method couples two techniques developed for other purposes in the literature on Bayesian analysis. Using data simulated from theoretical neurons and real data recorded from cortical motor neurons, we demonstrate the method’s ability to track changes in the modulatory structure of the oscillation across experimental trials.

Temporal dynamics of saccades explained by a self-paced process

Sensory organs are thought to sample the environment rhythmically thereby providing periodic perceptual input. Whisking and sniffing are governed by oscillators which impose rhythms on the motor-control of sensory acquisition and consequently on sensory input. Saccadic eye movements are the main visual sampling mechanism in primates, and were suggested to constitute part of such a rhythmic exploration system. In this study we characterized saccadic rhythmicity, and examined whether it is consistent with autonomous oscillatory generator or with self-paced generation. Eye movements were tracked while observers were either free-viewing a movie or fixating a static stimulus. We inspected the temporal dynamics of exploratory and fixational saccades and quantified their first-order and high-order dependencies. Data were analyzed using methods derived from spike-train analysis, and tested against mathematical models and simulations. The findings show that saccade timings are explained by first-order dependencies, specifically by their refractory period. Saccade-timings are inconsistent with an autonomous pace-maker but are consistent with a "self-paced" generator, where each saccade is a link in a chain of neural processes that depend on the outcome of the saccade itself. We propose a mathematical model parsimoniously capturing various facets of saccade-timings, and suggest a possible neural mechanism producing the observed dynamics.

Dynamical systems, attractors, and neural circuits

Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic—they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.

Beta oscillations in the parkinsonian primate: Similar oscillations across different populations

Parkinson's disease (PD) is characterized by excessive beta band oscillations (BBO) in neuronal spiking activity across basal ganglia (BG) nuclei. High frequency stimulation of the subthalamic nucleus, an effective treatment for PD, suppresses these oscillations. There is still a heated debate on the origin and propagation of BBO and their association to clinical symptoms. The key prerequisite in addressing these issues is to obtain an accurate estimation of the subpopulation of oscillatory neurons and the magnitude of their oscillations. Studies have shown that neurons in different BG nuclei vary dramatically in the magnitude of their oscillations. However, the stochastic nature of neuronal activity subsamples the oscillatory neuronal rate functions, thus causing standard spectral analysis methods to be dramatically biased by biological and experimental factors such as variations in the neuronal firing rate across BG nuclei. In order to overcome these biases, and directly analyze the expression of BBO within BG nuclei, we used a novel objective method, the modulation index. This method reveals that unlike previous spectral results, individual neurons in the different nuclei display similar magnitudes of oscillations, whereas only the size of the oscillatory subpopulation varies between nuclei. During stimulation, the magnitude of the BBO does not change but the fraction of oscillatory neurons decreases in the globus pallidus internus, leading to a significant change in BG output. This non-biased oscillation quantification thus enables the reconstruction of oscillations at the single neuron and nuclei population levels, and calls for a reassessment of the role of BBO during PD.