Faculty Bibliography

Multichannel electroencephalography (EEG) offers a non-invasive tool to explore spatio-temporal dynamics of brain activity. With EEG recordings consisting of multiple trials, traditional signal processing approaches that ignore inter-trial variability in the data may fail to accurately estimate the underlying spatio-temporal brain patterns. Moreover, precise characterization of such inter-trial variability per se can be of high scientific value in establishing the relationship between brain activity and behavior. In this paper, a statistical modeling framework is introduced for learning spatio-temporal decompositions of multiple-trial EEG data recorded under two contrasting experimental conditions. By modeling the variance of source signals as random variables varying across trials, the proposed two-stage hierarchical Bayesian model is able to capture inter-trial amplitude variability in the data in a sparse way where a parsimonious representation of the data can be obtained. A variational Bayesian (VB) algorithm is developed for statistical inference of the hierarchical model. The efficacy of the proposed modeling framework is validated with the analysis of both synthetic and real EEG data. In the simulation study we show that even at low signal-to-noise ratios our approach is able to recover with high precision the underlying spatio-temporal patterns and the dynamics of source amplitude across trials; on two brain-computer interface (BCI) data sets we show that our VB algorithm can extract physiologically meaningful spatio-temporal patterns and make more accurate predictions than other two widely used algorithms: the common spatial patterns (CSP) algorithm and the Infomax algorithm for independent component analysis (ICA). The results demonstrate that our statistical modeling framework can serve as a powerful tool for extracting brain patterns, characterizing trial-to-trial brain dynamics, and decoding brain states by exploiting useful structures in the data.

The ability to accurately infer functional connectivity between ensemble neurons using experimentally acquired spike train data is currently an important research objective in computational neuroscience. Point process generalized linear models and maximum likelihood estimation have been proposed as effective methods for the identification of spiking dependency between neurons. However, unfavorable experimental conditions occasionally results in insufficient data collection due to factors such as low neuronal firing rates or brief recording periods, and in these cases, the standard maximum likelihood estimate becomes unreliable. The present studies compares the performance of different statistical inference procedures when applied to the estimation of functional connectivity in neuronal assemblies with sparse spiking data. Four inference methods were compared: maximum likelihood estimation, penalized maximum likelihood estimation, using either l(2) or l(1) regularization, and hierarchical Bayesian estimation based on a variational Bayes algorithm. Algorithmic performances were compared using well-established goodness-of-fit measures in benchmark simulation studies, and the hierarchical Bayesian approach performed favorably when compared with the other algorithms, and this approach was then successfully applied to real spiking data recorded from the cat motor cortex. The identification of spiking dependencies in physiologically acquired data was encouraging, since their sparse nature would have previously precluded them from successful analysis using traditional methods.

In this article, we present a point process method to assess dynamic baroreflex sensitivity (BRS) by estimating the baroreflex gain as focal component of a simplified closed-loop model of the cardiovascular system. Specifically, an inverse Gaussian probability distribution is used to model the heartbeat interval, whereas the instantaneous mean is identified by linear and bilinear bivariate regressions on both the previous R-R intervals (RR) and blood pressure (BP) beat-to-beat measures. The instantaneous baroreflex gain is estimated as the feedback branch of the loop with a point-process filter, while the RR-->BP feedforward transfer function representing heart contractility and vasculature effects is simultaneously estimated by a recursive least-squares filter. These two closed-loop gains provide a direct assessment of baroreflex control of heart rate (HR). In addition, the dynamic coherence, cross bispectrum, and their power ratio can also be estimated. All statistical indices provide a valuable quantitative assessment of the interaction between heartbeat dynamics and hemodynamics. To illustrate the application, we have applied the proposed point process model to experimental recordings from 11 healthy subjects in order to monitor cardiovascular regulation under propofol anesthesia. We present quantitative results during transient periods, as well as statistical analyses on steady-state epochs before and after propofol administration. Our findings validate the ability of the algorithm to provide a reliable and fast-tracking assessment of BRS, and show a clear overall reduction in baroreflex gain from the baseline period to the start of propofol anesthesia, confirming that instantaneous evaluation of arterial baroreflex control of HR may yield important implications in clinical practice, particularly during anesthesia and in postoperative care.

Understanding the way in which groups of cortical neurons change their individual and mutual firing activity during the induction of general anesthesia may improve the safe usage of many anesthetic agents. Assessing neuronal interactions within cell assemblies during anesthesia may be useful for understanding the neural mechanisms of general anesthesia. Here, a point process generalized linear model (PPGLM) was applied to infer the functional connectivity of neuronal ensembles during both baseline and anesthesia, in which neuronal firing rates and network connectivity might change dramatically. A hierarchical Bayesian modeling approach combined with a variational Bayes (VB) algorithm is used for statistical inference. The effectiveness of our approach is evaluated with synthetic spike train data drawn from small and medium-size networks (consisting of up to 200 neurons), which are simulated using biophysical voltage-gated conductance models. We further apply the analysis to experimental spike train data recorded from rats' barrel cortex during both active behavior and isoflurane anesthesia conditions. Our results suggest that that neuronal interactions of both putative excitatory and inhibitory connections are reduced after the induction of isoflurane anesthesia.

Neurons in the Primary Motor Cortex (MI) are known to form functional ensembles with one another in order to produce voluntary movement. Neural network changes during skill learning are thought to be involved in improved fluency and accuracy of motor tasks. Unforced errors during skilled tasks provide an avenue to study network connections related to motor learning. In order to investigate network activity in MI, microwires were implanted in the MI of cats trained to perform a reaching task. Spike trains from eight groups of simultaneously recorded cells (95 neurons in total) were acquired. A point process generalized linear model (GLM) was developed to assess simultaneously recorded cells for functional connectivity during reaching attempts where unforced errors or no errors were made. Whilst the same groups of neurons were often functionally connected regardless of trial success, functional connectivity between neurons was significantly different at fine time scales when the outcome of task performance changed. Furthermore, connections were shown to be significantly more robust across multiple latencies during successful trials of task performance. The results of this study indicate that reach-related neurons in MI form dynamic spiking dependencies whose temporal features are highly sensitive to unforced movement errors.

We present a comprehensive probabilistic point process framework to estimate and monitor the instantaneous heartbeat dynamics as related to 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 (BRS), can be rigorously derived within a parametric framework and instantaneously updated with an adaptive algorithm. Instantaneous metrics of nonlinearity, such as the bispectrum of heartbeat intervals, can also be derived. We have applied the proposed point process framework to experimental recordings from healthy subjects in order to monitor cardiovascular regulation under propofol anesthesia. Results reveal interesting dynamic trends across different pharmacological interventions, 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, noninvasive assessment of general anesthesia.

Human heartbeat intervals are known to have nonlinear and nonstationary dynamics. In this paper, we propose a model of R-R interval dynamics based on a nonlinear Volterra-Wiener expansion within a point process framework. Inclusion of second-order nonlinearities into the heartbeat model allows us to estimate instantaneous heart rate (HR) and heart rate variability (HRV) indexes, as well as the dynamic bispectrum characterizing higher order statistics of the nonstationary non-gaussian time series. The proposed point process probability heartbeat interval model was tested with synthetic simulations and two experimental heartbeat interval datasets. Results show that our model is useful in characterizing and tracking the inherent nonlinearity of heartbeat dynamics. As a feature, the fine temporal resolution allows us to compute instantaneous nonlinearity indexes, thus sidestepping the uneven spacing problem. In comparison to other nonlinear modeling approaches, the point process probability model is useful in revealing nonlinear heartbeat dynamics at a fine timescale and with only short duration recordings.

Modeling heartbeat variability remains a challenging signal-processing goal in the presence of highly non-stationary cardiovascular control dynamics. We propose a novel differential autoregressive modeling approach within a point process probability framework for analyzing R-R interval and blood pressure variations. We apply the proposed model to both synthetic and experimental heartbeat intervals observed in time-varying conditions. The model is found to be extremely effective in tracking non-stationary heartbeat dynamics, as evidenced by the excellent goodness-of-fit performance. Results further demonstrate the ability of the method to appropriately quantify the non-stationary evolution of baroreflex sensitivity in changing physiological and pharmacological conditions.

UP and DOWN states, the periodic fluctuations between increased and decreased spiking activity of a neuronal population, are a fundamental feature of cortical circuits. Understanding UP-DOWN state dynamics is important for understanding how these circuits represent and transmit information in the brain. To date, limited work has been done on characterizing the stochastic properties of UP-DOWN state dynamics. We present a set of Markov and semi-Markov discrete- and continuous-time probability models for estimating UP and DOWN states from multiunit neural spiking activity. We model multiunit neural spiking activity as a stochastic point process, modulated by the hidden (UP and DOWN) states and the ensemble spiking history. We estimate jointly the hidden states and the model parameters by maximum likelihood using an expectation-maximization (EM) algorithm and a Monte Carlo EM algorithm that uses reversible-jump Markov chain Monte Carlo sampling in the E-step. We apply our models and algorithms in the analysis of both simulated multiunit spiking activity and actual multi- unit spiking activity recorded from primary somatosensory cortex in a behaving rat during slow-wave sleep. Our approach provides a statistical characterization of UP-DOWN state dynamics that can serve as a basis for verifying and refining mechanistic descriptions of this process.