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.

Electrodermal activity (EDA) is a direct read-out of sweat-induced changes in the skin's electrical conductance. Sympathetically-mediated pulsatile changes in skin sweat measured as EDA resemble an integrate-and-fire process, which yields an inverse Gaussian model as the inter-pulse interval distribution. We have previously showed that the inter-pulse intervals in EDA follow an inverse Gaussian distribution. However, the statistical structure of EDA pulse amplitudes has not yet been characterized based on the physiology. Expanding upon the integrate-and-fire nature of sweat glands, we hypothesized that the amplitude of an EDA pulse is proportional to the excess volume of sweat produced compared to what is required to just reach the surface of the skin. We modeled this as the difference of two inverse Gaussian models for each pulse, one which represents the time required to produce just enough sweat to rise to the surface of the skin and one which represents the time requires to produce the actual volume of sweat. We proposed and tested a series of four simplifications of our hypothesis, ranging from a single difference of inverse Gaussians to a single simple inverse Gaussian. We also tested four additional models for comparison, including the lognormal and gamma distributions. All models were tested on EDA data from two subject cohorts, 11 healthy volunteers during 1 hour of quiet wakefulness and a different set of 11 healthy volunteers during approximately 3 hours of controlled propofol sedation. All four models which represent simplifications of our hypothesis outperformed other models across all 22 subjects, as measured by Akaike's Information Criterion (AIC), as well as mean and maximum distance from the diagonal on a quantile-quantile plot. Our broader model set of four simplifications offered a useful framework to enhance further statistical descriptions of EDA pulse amplitudes. Some of the simplifications prioritize fit near the mode of the distribution, while others prioritize fit near the tail. With this new insight, we can summarize the physiologically-relevant amplitude information in EDA with at most four parameters. Our findings establish that physiologically based probability models provide parsimonious and accurate description of temporal and amplitude characteristics in EDA.

Brain source imaging is an important method for noninvasively characterizing brain activity using Electroencephalogram (EEG) or Magnetoencephalography (MEG) recordings. Traditional EEG/MEG Source Imaging (ESI) methods usually assume the source activities at different time points are unrelated, and do not utilize the temporal structure in the source activation, making the ESI analysis sensitive to noise. Some methods may encourage very similar activation patterns across the entire time course and may be incapable of accounting the variation along the time course. To effectively deal with noise while maintaining flexibility and continuity among brain activation patterns, we propose a novel probabilistic ESI model based on a hierarchical graph prior. Under our method, a spanning tree constraint ensures that activity patterns have spatiotemporal continuity. An efficient algorithm based on an alternating convex search is presented to solve the resulting problem of the proposed model with guaranteed convergence. Comprehensive numerical studies using synthetic data on a realistic brain model are conducted under different levels of signal-to-noise ratio (SNR) from both sensor and source spaces. We also examine the EEG/MEG datasets in two real applications, in which our ESI reconstructions are neurologically plausible. All the results demonstrate significant improvements of the proposed method over benchmark methods in terms of source localization performance, especially at high noise levels.

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.

The anesthetic propofol elicits many different spectral properties on the EEG, including alpha oscillations (8-12 Hz), Slow Wave Oscillations (SWO, 0.1-1.5 Hz), and dose-dependent phase-amplitude coupling (PAC) between alpha and SWO. Propofol is known to increase GABAA inhibition and decrease H-current strength, but how it generates these rhythms and their interactions is still unknown. To investigate both generation of the alpha rhythm and its PAC to SWO, we simulate a Hodgkin-Huxley network model of a hyperpolarized thalamus and corticothalamic inputs. We find, for the first time, that the model thalamic network is capable of independently generating the sustained alpha seen in propofol, which may then be relayed to cortex and expressed on the EEG. This dose-dependent sustained alpha critically relies on propofol GABAA potentiation to alter the intrinsic spindling mechanisms of the thalamus. Furthermore, the H-current conductance and background excitation of these thalamic cells must be within specific ranges to exhibit any intrinsic oscillations, including sustained alpha. We also find that, under corticothalamic SWO UP and DOWN states, thalamocortical output can exhibit maximum alpha power at either the peak or trough of this SWO; this implies the thalamus may be the source of propofol-induced PAC. Hyperpolarization level is the main determinant of whether the thalamus exhibits trough-max PAC, which is associated with lower propofol dose, or peak-max PAC, associated with higher dose. These findings suggest: the thalamus generates a novel rhythm under GABAA potentiation such as under propofol, its hyperpolarization may determine whether a patient experiences trough-max or peak-max PAC, and the thalamus is a critical component of propofol-induced cortical spectral phenomena. Changes to the thalamus may be a critical part of how propofol accomplishes its effects, including unconsciousness.

The sleep onset process (SOP) is a dynamic process correlated with a multitude of behavioral and physiological markers. A principled analysis of the SOP can serve as a foundation for answering questions of fundamental importance in basic neuroscience and sleep medicine. Unfortunately, current methods for analyzing the SOP fail to account for the overwhelming evidence that the wake/sleep transition is governed by continuous, dynamic physiological processes. Instead, current practices coarsely discretize sleep both in terms of state, where it is viewed as a binary (wake or sleep) process, and in time, where it is viewed as a single time point derived from subjectively scored stages in 30-second epochs, effectively eliminating SOP dynamics from the analysis. These methods also fail to integrate information from both behavioral and physiological data. It is thus imperative to resolve the mismatch between the physiological evidence and analysis methodologies. In this paper, we develop a statistically and physiologically principled dynamic framework and empirical SOP model, combining simultaneously-recorded physiological measurements with behavioral data from a novel breathing task requiring no arousing external sensory stimuli. We fit the model using data from healthy subjects, and estimate the instantaneous probability that a subject is awake during the SOP. The model successfully tracked physiological and behavioral dynamics for individual nights, and significantly outperformed the instantaneous transition models implicit in clinical definitions of sleep onset. Our framework also provides a principled means for cross-subject data alignment as a function of wake probability, allowing us to characterize and compare SOP dynamics across different populations. This analysis enabled us to quantitatively compare the EEG of subjects showing reduced alpha power with the remaining subjects at identical response probabilities. Thus, by incorporating both physiological and behavioral dynamics into our model framework, the dynamics of our analyses can finally match those observed during the SOP.

We consider the problem of recovering a sequence of vectors, $(x_k)_{k=0}^K$, for which the increments $x_k-x_{k-1}$ are $S_k$-sparse (with $S_k$ typically smaller than $S_1$), based on linear measurements $(y_k = A_k x_k + e_k)_{k=1}^K$, where $A_k$ and $e_k$ denote the measurement matrix and noise, respectively. Assuming each $A_k$ obeys the restricted isometry property (RIP) of a certain order---depending only on $S_k$---we show that in the absence of noise a convex program, which minimizes the weighted sum of the $\ell_1$-norm of successive differences subject to the linear measurement constraints, recovers the sequence $(x_k)_{k=1}^K$ \emph{exactly}. This is an interesting result because this convex program is equivalent to a standard compressive sensing problem with a highly-structured aggregate measurement matrix which does not satisfy the RIP requirements in the standard sense, and yet we can achieve exact recovery. In the presence of bounded noise, we propose a quadratically-constrained convex program for recovery and derive bounds on the reconstruction error of the sequence. We supplement our theoretical analysis with simulations and an application to real video data. These further support the validity of the proposed approach for acquisition and recovery of signals with time-varying sparsity.

We develop a state space approach to multimodal integration of simultaneously recorded EEG and fMRI. The EEG is represented with a distributed current source model using realistic MRI-based forward models, whose temporal evolution is governed by a linear state space model. The fMRI signal is similarly modeled by a linear state space model describing the hemodynamic response to underlying EEG current activity. We explore the feasibility of high dimensional dynamic estimation of simultaneous EEG/fMRI using simulation studies of the alpha wave.

Evaluation of baroreflex control of heart rate (HR) has important implications in clinical practice of anesthesia and postoperative care. In this paper, we present a point process method to assess the dynamic baroreflex gain using a closed-loop model of the cardiovascular system. Specifically, the inverse Gaussian probability distribution is used to model the heartbeat interval, whereas the instantaneous mean is identified by a linear or bilinear bivariate regression on the previous R-R intervals and blood pressure (BP) measures. The instantaneous baroreflex gain is estimated in the feedback loop with a point process filter, while the RR→BP feedforward frequency response is estimated by a Kalman filter. In addition, the instantaneous cross-spectrum and cross-bispectrum (as well as their ratio) can also be estimated. All statistical indices provide a valuable quantitative assessment of the interaction between heartbeat dynamics and hemodynamics during general anesthesia.

We consider signal estimation for functional MRI studies on multiple subjects. There are two major issues; alignment or registration of images across subjects, and using the multisubject information to capture covariance information; we discuss only the latter. Capturing this covariance information properly can lead to great improvements in statistical efficiency beyond what simple averaging can offer as well as compact description of group features.

In the last half decade, fast methods of magnetic resonance imaging have led to the possibility, for the first time, of non-invasive dynamic brain imaging. This has led to an explosion of work in the Neurosciences. From a signal processing viewpoint the problems are those of nonlinear spatio-temporal system identification. In this paper, we develop new methods of identification using novel spatial regularization. We also develop a new model comparison technique and use that to compare our method with existing techniques on some experimental data.

We consider a model comparison based on a new model selection criterion. We treat fMRI as a spatio-temporal system identification problem and compare our model fitting method based on spatial regularization methods with the so-called statistical parametric map technique currently popular in the fMRI literature. We illustrate our results with data from the brain obtained during a combined visual and motor experiment.

The authors consider spatio-temporal modelling of functional MRI data from an inverse problems point of view. Most of the modelling to date has been on a pixel by pixel basis with no acknowledgment given to spatial smoothness when it exists. The authors discuss regularization methods that address that issue and illustrate their results with experimental data.