Faculty Bibliography

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.

Tracking the autonomic control and respiratory sinus arrhythmia (RSA) from electrocardiogram and respiratory measurements is an important problem in cardiovascular control. We propose a point process adaptive filter algorithm based on an inverse Gaussian model to track heart beat intervals that incorporates respiratory measurements as a covariate and provides an analytic form for computing a dynamic estimate of RSA gain. We use Kolmogorov-Smirnov tests and autocorrelation function analyses to assess model goodness-of-fit. We illustrate the properties of the new dynamic estimate of RSA in the analysis of simulated heart beat data and actual heart beat data recorded from subjects in a four-state postural study of heart beat dynamics: control, sympathetic blockade, parasympathetic blockade, and combined sympathetic and parasympathetic blockade. In addition to giving an accurate description of the heart beat data, our adaptive filter algorithm confirms established findings pointing at a vagally mediated RSA and provides a new dynamic RSA estimate that can be used to track cardiovascular control between and within a broad range of postural, pharmacological, and age conditions. Our paradigm suggests a possible framework for designing a device for ambulatory monitoring and assessment of autonomic control in both laboratory research and clinical practice.

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.

Robustness in signal processing is crucial for the purpose of reliably interpreting physiological features from noisy data in biomedical applications. We present a robust algorithm based on the reformulation of a well-known spatial filtering and feature extraction algorithm named Common Spatial Patterns (CSP). We cast the problem of learning CSP into a probabilistic framework, which allows us to gain insights into the algorithm. To address the overfitting problem inherent in CSP, we propose an expectation-maximization (EM) algorithm for learning robust CSP using from a Student-t distribution. The efficacy of the proposed robust algorithm is validated with both simulated and real EEG data.

Identification of multiple simultaneously recorded neural spike train recordings is an important task in understanding neuronal dependency, functional connectivity, and temporal causality in neural systems. An assessment of the functional connectivity in a group of ensemble cells was performed using a regularized point process generalized linear model (GLM) that incorporates temporal smoothness or contiguity of the solution. An efficient convex optimization algorithm was then developed for the regularized solution. The point process model was applied to an ensemble of neurons recorded from the cat motor cortex during a skilled reaching task. The implications of this analysis to the coding of skilled movement in primary motor cortex is discussed.

Quantitative evaluation of respiratory sinus arrhythmia (RSA) may provide important information in clinical practice of anesthesia and postoperative care. In this paper, we apply a point process method to assess dynamic RSA during propofol general anesthesia. Specifically, an 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 respiratory measures. The estimated second-order bilinear interaction allows us to evaluate the nonlinear component of the RSA. The instantaneous RSA gain and phase can be estimated with an adaptive point process filter. The algorithm's ability to track non-stationary dynamics is demonstrated using one clinical recording. Our proposed statistical indices provide a valuable quantitative assessment of instantaneous cardiorespiratory control and heart rate variability (HRV) during general anesthesia.

Evaluation of arterial baroreflex in cardiovascular control is an important topic in cardiology and clinical medicine. In this paper, we present a point process approach to estimate the dynamic baroreflex gain in 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 modulated by a bivariate autoregressive model that contains the previous R-R intervals and systolic blood pressure (SBP) measures. The instantaneous baroreflex gain is estimated in the feedback loop with a point process filter, while the RR→SBP feedforward frequency response gain can be estimated by a Kalman filter. The proposed estimation approach provides a quantitative assessment of interacting heartbeat dynamics and hemodynamics. We validate our approach with real physiological signals and evaluate the proposed model with established goodness-of-fit tests.

Electroencephalogram (EEG) is often used in the confirmatory test for brain death diagnosis in clinical practice. Because EEG recording and monitoring is relatively safe for the patients in deep coma, it is believed to be valuable for either reducing the risk of brain death diagnosis (while comparing other tests such as the apnea) or preventing mistaken diagnosis. The objective of this paper is to study several statistical methods for quantitative EEG analysis in order to help bedside or ambulatory monitoring or diagnosis. We apply signal processing and quantitative statistical analysis for the EEG recordings of 32 adult patients. For EEG signal processing, independent component analysis (ICA) was applied to separate the independent source components, followed by Fourier and time-frequency analysis. For quantitative EEG analysis, we apply several statistical complexity measures to the EEG signals and evaluate the differences between two groups of patients: the subjects in deep coma, and the subjects who were categorized as brain death. We report statistically significant differences of quantitative statistics with real-life EEG recordings in such a clinical study, and we also present interpretation and discussions on the preliminary experimental results.

In this paper, we compare and validate different probabilistic models of human heart beat intervals for assessment of the electrocardiogram data recorded with varying conditions in posture and pharmacological autonomic blockade. The models are validated using the adaptive point process filtering paradigm and Kolmogorov-Smirnov test. The inverse Gaussian model was found to achieve the overall best performance in the analysis of autonomic control. We further improve the model by incorporating the respiratory covariate measurements and present dynamic respiratory sinus arrhythmia (RSA) analysis. Our results suggest the instantaneous RSA gain computed from our proposed model as a potential index of vagal control dynamics.