Sparse spectral estimation from point process observations

We consider the problem of estimating the power spectral density of the neural covariates underlying the spiking of a neuronal population. We assume the spiking of the neuronal ensemble to be described by Bernoulli statistics. Furthermore, we consider the conditional intensity function to be the logistic map of a second-order stationary process with sparse frequency content. Using the binary spiking data recorded from the population, we calculate the maximum a posteriori estimate of the power spectral density of the process while enforcing sparsity-promoting priors on the estimate. Using both simulated and clinically recorded data, we show that our method outperforms the existing methods for extracting a frequency domain representation from the spiking data of a neuronal population

State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing

Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a challenging problem in functional neuroimaging. The number of potential sources within the brain exceeds by an order of magnitude the number of recording sites. As a consequence, the estimates for the magnitude and location of the neural sources will be ill-conditioned because of the underdetermined nature of the problem. One well-known technique designed to address this imbalance is the minimum norm estimator (MNE). This approach imposes an $L^2$ regularization constraint that serves to stabilize and condition the source parameter estimates. However, these classes of regularizer are static in time and do not consider the temporal constraints inherent to the biophysics of the MEG experiment. In this paper we propose a dynamic state-space model that accounts for both spatial and temporal correlations within and across candidate intracortical sources. In our model, the observation model is derived from the steady-state solution to Maxwell's equations while the latent model representing neural dynamics is given by a random walk process.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robust spectrotemporal decomposition by iteratively reweighted least squares

Classical nonparametric spectral analysis uses sliding windows to capture the dynamic nature of most real-world time series. This universally accepted approach fails to exploit the temporal continuity in the data and is not well-suited for signals with highly structured time–frequency representations. For a time series whose time-varying mean is the superposition of a small number of oscillatory components, we formulate nonparametric batch spectral analysis as a Bayesian estimation problem. We introduce prior distributions on the time–frequency plane that yield maximum a posteriori (MAP) spectral estimates that are continuous in time yet sparse in frequency. Our spectral decomposition procedure, termed spectrotemporal pursuit, can be efficiently computed using an iteratively reweighted least-squares algorithm and scales well with typical data lengths. We show that spectrotemporal pursuit works by applying to the time series a set of data-derived filters. Using a link between Gaussian mixture models, ℓ[subscript 1] minimization, and the expectation–maximization algorithm, we prove that spectrotemporal pursuit converges to the global MAP estimate. We illustrate our technique on simulated and real human EEG data as well as on human neural spiking activity recorded during loss of consciousness induced by the anesthetic propofol. For the EEG data, our technique yields significantly denoised spectral estimates that have significantly higher time and frequency resolution than multitaper spectral estimates. For the neural spiking data, we obtain a new spectral representation of neuronal firing rates. Spectrotemporal pursuit offers a robust spectral decomposition framework that is a principled alternative to existing methods for decomposing time series into a small number of smooth oscillatory components.National Institutes of Health (U.S.) (Transformative Research Award GM 104948)National Institutes of Health (U.S.) (New Innovator Award R01-EB006385

A Unified Point Process Probabilistic Framework to Assess Heartbeat Dynamics and Autonomic Cardiovascular Control

In recent years, time-varying inhomogeneous point process models have been introduced for assessment of instantaneous heartbeat dynamics as well as specific cardiovascular control mechanisms and hemodynamics. Assessment of the model’s statistics is established through the Wiener-Volterra theory and a multivariate autoregressive (AR) structure. A variety of instantaneous cardiovascular metrics, such as heart rate (HR), heart rate variability (HRV), respiratory sinus arrhythmia (RSA), and baroreceptor-cardiac reflex (baroreflex) sensitivity (BRS), are derived within a parametric framework and instantaneously updated with adaptive and local maximum likelihood estimation algorithms. Inclusion of second-order non-linearities, with subsequent bispectral quantification in the frequency domain, further allows for definition of instantaneous metrics of non-linearity. We here present a comprehensive review of the devised methods as applied to experimental recordings from healthy subjects during propofol anesthesia. Collective results reveal interesting dynamic trends across the different pharmacological interventions operated within each anesthesia session, confirming the ability of the algorithm to track important changes in cardiorespiratory elicited interactions, and pointing at our mathematical approach as a promising monitoring tool for an accurate, non-invasive assessment in clinical practice. We also discuss the limitations and other alternative modeling strategies of our point process approach

Clinical Electroencephalography for Anesthesiologists

The widely used electroencephalogram-based indices for depth-of-Anesthesia monitoring assume that the same index value defines the same level of unconsciousness for all anesthetics. In contrast, we show that different anesthetics act at different molecular targets and neural circuits to produce distinct brain states that are readily visible in the electroencephalogram. We present a two-part review to educate anesthesiologists on use of the unprocessed electroencephalogram and its spectrogram to track the brain states of patients receiving anesthesia care. Here in part I, we review the biophysics of the electroencephalogram and the neurophysiology of the electroencephalogram signatures of three intravenous anesthetics: propofol, dexmedetomidine, and ketamine, and four inhaled anesthetics: sevoflurane, isoflurane, desflurane, and nitrous oxide. Later in part II, we discuss patient management using these electroencephalogram signatures. Use of these electroencephalogram signatures suggests a neurophysiologically based paradigm for brain state monitoring of patients receiving anesthesia care.National Institutes of Health (U.S.) (Grant DP1-OD003646)National Institutes of Health (U.S.) (Grant TR01-GM104948

Spatial variation in automated burst suppression detection in pharmacologically induced coma

Burst suppression is actively studied as a control signal to guide anesthetic dosing in patients undergoing medically induced coma. The ability to automatically identify periods of EEG suppression and compactly summarize the depth of coma using the burst suppression probability (BSP) is crucial to effective and safe monitoring and control of medical coma. Current literature however does not explicitly account for the potential variation in burst suppression parameters across different scalp locations. In this study we analyzed standard 19-channel EEG recordings from 8 patients with refractory status epilepticus who underwent pharmacologically induced burst suppression as medical treatment for refractory seizures. We found that although burst suppression is generally considered a global phenomenon, BSP obtained using a previously validated algorithm varies systematically across different channels. A global representation of information from individual channels is proposed that takes into account the burst suppression characteristics recorded at multiple electrodes. BSP computed from this representative burst suppression pattern may be more resilient to noise and a better representation of the brain state of patients. Multichannel data integration may enhance the reliability of estimates of the depth of medical coma.National Institutes of Health (U.S.) (Grant K23 NS090900)National Institute of Neurological Diseases and Stroke (U.S.) (Grant K23 NS090900)National Institutes of Health (U.S.) (Grant DP2-OD006454)National Institutes of Health (U.S.) (Grant TROI-GMI04948

Reference-free removal of EEG-fMRI ballistocardiogram artifacts with harmonic regression

Combining electroencephalogram (EEG) recording and functional magnetic resonance imaging (fMRI) offers the potential for imaging brain activity with high spatial and temporal resolution. This potential remains limited by the significant ballistocardiogram (BCG) artifacts induced in the EEG by cardiac pulsation-related head movement within the magnetic field. We model the BCG artifact using a harmonic basis, pose the artifact removal problem as a local harmonic regression analysis, and develop an efficient maximum likelihood algorithm to estimate and remove BCG artifacts. Our analysis paradigm accounts for time-frequency overlap between the BCG artifacts and neurophysiologic EEG signals, and tracks the spatiotemporal variations in both the artifact and the signal. We evaluate performance on: simulated oscillatory and evoked responses constructed with realistic artifacts; actual anesthesia-induced oscillatory recordings; and actual visual evoked potential recordings. In each case, the local harmonic regression analysis effectively removes the BCG artifacts, and recovers the neurophysiologic EEG signals. We further show that our algorithm outperforms commonly used reference-based and component analysis techniques, particularly in low SNR conditions, the presence of significant time-frequency overlap between the artifact and the signal, and/or large spatiotemporal variations in the BCG. Because our algorithm does not require reference signals and has low computational complexity, it offers a practical tool for removing BCG artifacts from EEG data recorded in combination with fMRI.National Institutes of Health (U.S.) (Award DP1-OD003646)National Institutes of Health (U.S.) (Award TR01-GM104948)National Institutes of Health (U.S.) (Grant R44NS071988)National Institute of Neurological Diseases and Stroke (U.S.) (Grant Grant R44NS071988

State space methods for phase amplitude coupling analysis

Phase amplitude coupling (PAC) is thought to play a fundamental role in the dynamic coordination of brain circuits and systems. There are however growing concerns that existing methods for PAC analysis are prone to error and misinterpretation. Improper frequency band selection can render true PAC undetectable, while non-linearities or abrupt changes in the signal can produce spurious PAC. Current methods require large amounts of data and lack formal statistical inference tools. We describe here a novel approach for PAC analysis that substantially addresses these problems. We use a state space model to estimate the component oscillations, avoiding problems with frequency band selection, nonlinearities, and sharp signal transitions. We represent cross-frequency coupling in parametric and time-varying forms to further improve statistical efficiency and estimate the posterior distribution of the coupling parameters to derive their credible intervals. We demonstrate the method using simulated data, rat local field potentials (LFP) data, and human EEG data.P01GM118269 - NIH HHS; R01AG056015 - NIH HHS; R01AG054081 - NIH HHS; R21DA048323 - NIH HHSPublished versio