State space methods for phase amplitude coupling analysis

A dynamic generative model can extract interpretable oscillatory components from multichannel neurophysiological recordings

Modern neurophysiological recordings are performed using multichannel sensor arrays that are able to record activity in an increasingly high number of channels numbering in the 100s to 1000s. Often, underlying lower-dimensional patterns of activity are responsible for the observed dynamics, but these representations are difficult to reliably identify using existing methods that attempt to summarize multivariate relationships in a post hoc manner from univariate analyses or using current blind source separation methods. While such methods can reveal appealing patterns of activity, determining the number of components to include, assessing their statistical significance, and interpreting them requires extensive manual intervention and subjective judgment in practice. These difficulties with component selection and interpretation occur in large part because these methods lack a generative model for the underlying spatio-temporal dynamics. Here, we describe a novel component analysis method anchored by a generative model where each source is described by a bio-physically inspired state-space representation. The parameters governing this representation readily capture the oscillatory temporal dynamics of the components, so we refer to it as oscillation component analysis. These parameters - the oscillatory properties, the component mixing weights at the sensors, and the number of oscillations - all are inferred in a data-driven fashion within a Bayesian framework employing an instance of the expectation maximization algorithm. We analyze high-dimensional electroencephalography and magnetoencephalography recordings from human studies to illustrate the potential utility of this method for neuroscience data.

A dynamic generative model can extract interpretable oscillatory components from multichannel neurophysiological recordings

Modern neurophysiological recordings are performed using multichannel sensor arrays that are able to record activity in an increasingly high number of channels numbering in the 100's to 1000's. Often, underlying lower-dimensional patterns of activity are responsible for the observed dynamics, but these representations are difficult to reliably identify using existing methods that attempt to summarize multivariate relationships in a post-hoc manner from univariate analyses, or using current blind source separation methods. While such methods can reveal appealing patterns of activity, determining the number of components to include, assessing their statistical significance, and interpreting them requires extensive manual intervention and subjective judgement in practice. These difficulties with component selection and interpretation occur in large part because these methods lack a generative model for the underlying spatio-temporal dynamics. Here we describe a novel component analysis method anchored by a generative model where each source is described by a bio-physically inspired state space representation. The parameters governing this representation readily capture the oscillatory temporal dynamics of the components, so we refer to it as Oscillation Component Analysis (OCA). These parameters - the oscillatory properties, the component mixing weights at the sensors, and the number of oscillations - all are inferred in a data-driven fashion within a Bayesian framework employing an instance of the expectation maximization algorithm. We analyze high-dimensional electroencephalography and magnetoencephalography recordings from human studies to illustrate the potential utility of this method for neuroscience data.

A mutual information measure of phase-amplitude coupling using gamma generalized linear models

Introduction

Cross frequency coupling (CFC) between electrophysiological signals in the brain is a long-studied phenomenon and its abnormalities have been observed in conditions such as Parkinson's disease and epilepsy. More recently, CFC has been observed in stomach-brain electrophysiologic studies and thus becomes an enticing possible target for diseases involving aberrations of the gut-brain axis. However, current methods of detecting coupling, specifically phase-amplitude coupling (PAC), do not attempt to capture the phase and amplitude statistical relationships.

Methods

In this paper, we first demonstrate a method of modeling these joint statistics with a flexible parametric approach, where we model the conditional distribution of amplitude given phase using a gamma distributed generalized linear model (GLM) with a Fourier basis of regressors. We perform model selection with minimum description length (MDL) principle, demonstrate a method for assessing goodness-of-fit (GOF), and showcase the efficacy of this approach in multiple electroencephalography (EEG) datasets. Secondly, we showcase how we can utilize the mutual information, which operates on the joint distribution, as a canonical measure of coupling, as it is non-zero and non-negative if and only if the phase and amplitude are not statistically independent. In addition, we build off of previous work by Martinez-Cancino et al., and Voytek et al., and show that the information density, evaluated using our method along the given sample path, is a promising measure of time-resolved PAC.

Results

Using synthetically generated gut-brain coupled signals, we demonstrate that our method outperforms the existing gold-standard methods for detectable low-levels of phase-amplitude coupling through receiver operating characteristic (ROC) curve analysis. To validate our method, we test on invasive EEG recordings by generating comodulograms, and compare our method to the gold standard PAC measure, Modulation Index, demonstrating comparable performance in exploratory analysis. Furthermore, to showcase its use in joint gut-brain electrophysiology data, we generate topoplots of simultaneous high-density EEG and electrgastrography recordings and reproduce seminal work by Richter et al. that demonstrated the existence of gut-brain PAC. Using simulated data, we validate our method for different types of time-varying coupling and then demonstrate its performance to track time-varying PAC in sleep spindle EEG and mismatch negativity (MMN) datasets.

Conclusions

Our new measure of PAC using Gamma GLMs and mutual information demonstrates a promising new way to compute PAC values using the full joint distribution on amplitude and phase. Our measure outperforms the most common existing measures of PAC, and show promising results in identifying time varying PAC in electrophysiological datasets. In addition, we provide for using our method with multiple comparisons and show that our measure potentially has more statistical power in electrophysiologic recordings using simultaneous gut-brain datasets.

Effect of Repeated Exposure to Sevoflurane on Electroencephalographic Alpha Oscillation in Pediatric Patients Undergoing Radiation Therapy: A Prospective Observational Study

BACKGROUND

Pharmacological tolerance is defined as a decrease in the effect of a drug over time, or the need to increase the dose to achieve the same effect. It has not been established whether repeated exposure to sevoflurane induces tolerance in children.

METHODS

We conducted an observational study in children younger than 6 years of age scheduled for multiple radiotherapy sessions with sevoflurane anesthesia. To evaluate the development of sevoflurane tolerance, we analyzed changes in electroencephalographic spectral power at induction, across sessions. We fitted individual and group-level linear regression models to evaluate the correlation between the outcomes and sessions. In addition, a linear mixed-effect model was used to evaluate the association between radiotherapy sessions and outcomes.

RESULTS

Eighteen children were included and the median number of radiotherapy sessions per child was 28 (interquartile range: 10 to 33). There was no correlation between induction time and radiotherapy sessions. At the group level, the linear mixed-effect model showed, in a subgroup of patients, that alpha relative power and spectral edge frequency 95 were inversely correlated with the number of anesthesia sessions. Nonetheless, this subgroup did not differ from the other subjects in terms of age, sex, or the total number of radiotherapy sessions.

CONCLUSIONS

Our results suggest that children undergoing repeated anesthesia exposure for radiotherapy do not develop tolerance to sevoflurane. However, we found that a group of patients exhibited a reduction in the alpha relative power as a function of anesthetic exposure. These results may have implications that justify further studies.

Different Methods to Estimate the Phase of Neural Rhythms Agree But Only During Times of Low Uncertainty

Rhythms are a common feature of brain activity. Across different types of rhythms, the phase has been proposed to have functional consequences, thus requiring its accurate specification from noisy data. Phase is conventionally specified using techniques that presume a frequency band-limited rhythm. However, in practice, observed brain rhythms are typically nonsinusoidal and amplitude modulated. How these features impact methods to estimate phase remains unclear. To address this, we consider three phase estimation methods, each with different underlying assumptions about the rhythm. We apply these methods to rhythms simulated with different generative mechanisms and demonstrate inconsistency in phase estimates across the different methods. We propose two improvements to the practice of phase estimation: (1) estimating confidence in the phase estimate, and (2) examining the consistency of phase estimates between two (or more) methods.

Multilevel State-Space Models Enable High Precision Event Related Potential Analysis

During cognitive tasks, the elicited brain responses that are time-locked to the stimulus presentation are manifested in electroencephalogram (EEG) as Event Related Potentials (ERPs). In general, ERPs are ~ 1 μ V signals embedded in the background of much stronger neural oscillations, and thus they are traditionally extracted by averaging hundreds of trial responses so that the neural oscillations can cancel out each other. However, often in cognitive science experiments, it is difficult to administer large number of trials due to physical constraints. Additionally, these excessive averaging can also blur fine structures of the ERPs signals, which might otherwise be indicative of various intrinsic factors. Here we propose to model the background oscillations using a novel oscillation state-space representation and identify their time-traces in a data-driven way. This allows us to effectively separate the oscillations from the response signals of interest, thus improving the signal-to-noise of the evoked response, and eventually increasing trial fidelity. We also consider a random-walk like continuity constraint for the ERP waveforms to recover smooth, de-noised estimates. We employ a generalized expectation maximization algorithm for estimating the model parameters, and then infer the approximate posterior distribution of ERP waveforms. We demonstrate the reduced reliance of our proposed ERP extraction technique via a simulation study. Finally, we showcase how the extracted ERPs using our method can be more informative than the traditional average-based ERPs when analyzing EEG data in cognitive task settings with fewer trials.

Phase-amplitude coupling during maintenance of general anaesthesia: towards a better understanding of anaesthetic-induced brain dynamics in children

Electroencephalogram signatures associated with anaesthetic-induced loss of consciousness have been widely described in adult populations. A recent study helps verify our understanding of brain dynamics induced by anaesthetics in a paediatric population by describing a specific pattern in terms of an interaction of the phase of delta oscillations and the amplitude of alpha oscillations. This feature has potential translational implications for optimising future monitoring technologies.

Switching state-space modeling of neural signal dynamics

Linear parametric state-space models are a ubiquitous tool for analyzing neural time series data, providing a way to characterize the underlying brain dynamics with much greater statistical efficiency than non-parametric data analysis approaches. However, neural time series data are frequently time-varying, exhibiting rapid changes in dynamics, with transient activity that is often the key feature of interest in the data. Stationary methods can be adapted to time-varying scenarios by employing fixed-duration windows under an assumption of quasi-stationarity. But time-varying dynamics can be explicitly modeled by switching state-space models, i.e., by using a pool of state-space models with different dynamics selected by a probabilistic switching process. Unfortunately, exact solutions for state inference and parameter learning with switching state-space models are intractable. Here we revisit a switching state-space model inference approach first proposed by Ghahramani and Hinton. We provide explicit derivations for solving the inference problem iteratively after applying a variational approximation on the joint posterior of the hidden states and the switching process. We introduce a novel initialization procedure using an efficient leave-one-out strategy to compare among candidate models, which significantly improves performance compared to the existing method that relies on deterministic annealing. We then utilize this state inference solution within a generalized expectation-maximization algorithm to estimate model parameters of the switching process and the linear state-space models with dynamics potentially shared among candidate models. We perform extensive simulations under different settings to benchmark performance against existing switching inference methods and further validate the robustness of our switching inference solution outside the generative switching model class. Finally, we demonstrate the utility of our method for sleep spindle detection in real recordings, showing how switching state-space models can be used to detect and extract transient spindles from human sleep electroencephalograms in an unsupervised manner.

Delta power during sleep is modulated by EEG-gated auricular vagal afferent nerve stimulation (EAVANS)

Vagus nerve stimulation (VNS) has many clinical applications under development. In particular, there is a large interest in transcutaneous auricular VNS (taVNS) because it is non-invasive and provides easy access to neuromodulation. The present study proposes a novel approach for electroencephalography (EEG)-gated taVNS, with the ultimate goal of enhancing therapeutic outcomes, including for the treatment of delirium. Delirium arises from an altered state of consciousness and is the most common neuropsychiatric disorder observed in hospitalized patients, especially the elderly. Delirium has been linked to specific disturbances in EEG rhythms. Here, we propose an EEG-gated auricular vagal afferent nerve stimulation (EAVANS) approach to deliver stimulation targeting a specific instantaneous phase of the EEG Delta rhythm to modulate arousal and downstream reduction of neuroinflammation, two of the contributing factors to delirium. We hypothesize that treatment with EAVANS will modulate Delta power, which has been linked with delirium. As dominant Delta power is also a typical feature of non-rapid eye movement (NREM) sleep, we applied a prototype of an EAVANS device on healthy volunteers during sleep to establish preliminary validation. We successfully employed our closed-loop approach to target vagal afference during the rising Delta phase in the range [-π/2 0] radians. We found a significant reduction in Delta wave power for stimulation during the rising Delta phase compared to 1) absence of stimulation, 2) active stimulation during the descending Delta phase, and 3) active stimulation targeting non-vagal territory (i.e. greater auricular nerve) during the rising Delta phase. Further validation of our EEG-gated taVNS approach in the peri-operative period will be needed. As there is presently a lack of effective treatments for delirium, our non-pharmacological and non-invasive approach, if validated, could be easily deployed in clinical settings.Clinical Relevance- Given the serious health consequences and costs associated with delirium, and the absence of effective non-pharmacological treatments, the proposed neuromodulatory approach may be a promising option for reducing delirium and other disorders of consciousness. Our EAVANS prototype system has been tested on healthy volunteers during a NREM sleep state and will require further validation in different patient populations to optimize the proposed technology and gather more evidence to support its clinical utility. This novel non-pharmacological and non-invasive closed-loop neuromodulatory device could be used peri-operatively and in inpatient hospital settings to treat patients at risk of developing delirium. For instance, in a pre-operative setting, this technology may provide an effective preventative "pre-habilitation" approach for patients at high risk of developing delirium. Post-operatively, our technology may help manage patients with delirium more effectively.