Extensions to a manifold learning framework for time-series analysis on dynamic manifolds in bioelectric signals.

This paper addresses the challenge of extracting meaningful information from measured bioelectric signals generated by complex, large scale physiological systems such as the brain or the heart. We focus on a combination of the well-known Laplacian eigenmaps machine learning approach with dynamical systems ideas to analyze emergent dynamic behaviors. The method reconstructs the abstract dynamical system phase-space geometry of the embedded measurements and tracks changes in physiological conditions or activities through changes in that geometry. It is geared to extract information from the joint behavior of time traces obtained from large sensor arrays, such as those used in multiple-electrode ECG and EEG, and explore the geometrical structure of the low dimensional embedding of moving time windows of those joint snapshots. Our main contribution is a method for mapping vectors from the phase space to the data domain. We present cases to evaluate the methods, including a synthetic example using the chaotic Lorenz system, several sets of cardiac measurements from both canine and human hearts, and measurements from a human brain.

Reduced-order models for closed-loop wake control.

We review a strategy for low- and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow and stochastic fluctuations. Secondly, their range of validity is restricted by ignoring mode deformations during natural and actuated transients. We address the first challenge by including shift mode(s) and nonlinear turbulence models. The resulting robust least-order model lives on an inertial manifold, which links slow variations in the base flow and coherent and stochastic fluctuation amplitudes. The second challenge, the deformation of coherent structures, is addressed by parameter-dependent modes, allowing smooth transitions between operating conditions. Now, the Galerkin model lives on a refined manifold incorporating mode deformations. Control design is a simple corollary of the distilled model structure. We illustrate the modelling path for actuated wake flows.

Modeling habituation in rat EEG-evoked responses via a neural mass model with feedback.

Habituation is a generic property of the neural response to repeated stimuli. Its strength often increases as inter-stimuli relaxation periods decrease. We propose a simple, broadly applicable control structure that enables a neural mass model of the evoked EEG response to exhibit habituated behavior. A key motivation for this investigation is the ongoing effort to develop model-based reconstruction of multi-modal functional neuroimaging data. The control structure proposed here is illustrated and validated in the context of a biophysical neural mass model, developed by Riera et al. (Hum Brain Mapp 27(11):896-914, 2006; 28(4):335-354, 2007), and of simplifications thereof, using data from rat EEG response to medial nerve stimuli presented at frequencies from 1 to 8 Hz. Performance was tested by predictions of both the response to the next stimulus based on the current one, and also of continued stimuli trains over 4-s time intervals based on the first stimulus in the interval, with similar success statistics. These tests demonstrate the ability of simple generative models to capture key features of the evoked response, including habituation.

Wavefront-based models for inverse electrocardiography.

We introduce two wavefront-based methods for the inverse problem of electrocardiography, which we term wavefront-based curve reconstruction (WBCR) and wavefront-based potential reconstruction (WBPR). In the WBCR approach, the epicardial activation wavefront is modeled as a curve evolving on the heart surface, with the evolution governed by factors derived phenomenologically from prior measured data. The body surface potential/wavefront relationship is modeled via an intermediate mapping of wavefront to epicardial potentials, again derived phenomenologically. In the WBPR approach, we iteratively construct an estimate of epicardial potentials from an estimated wavefront curve according to a simplified model and use it as an initial solution in a Tikhonov regularization scheme. Initial simulation results using measured canine epicardial data show considerable improvement in reconstructing activation wavefronts and epicardial potentials with respect to standard Tikhonov solutions. In particular the WBCR method accurately finds the anisotropic propagation early after epicardial pacing, and the WBPR method finds the wavefront (regions of sharp gradient of the potential) both accurately and with minimal smoothing.

A wavefront-based constraint for potential surface solutions in inverse electrocardiography.

Inverse electrocardiography in recent years has generally been approached using one of two quite distinct source models, either a potential-based approach or an activation-based approach. Each approach has advantages and disadvantages relative to the other, which are inherited by all specific methods based on a given approach. Recently our group has been working to develop models which can bridge between these two approaches, hoping to capture some of the most important advantages of both. In this work we present one such effort, which we term wavefront-based potential reconstruction (WBPR). It is a modification of standard regularization methods for potential-based inverse electrocardiography, into which we incorporate a constraint based on a wavefront-like approximation to the potential-based solution. Initial results indicate significant improvement with respect to localization and characterization of the wavefront in simulations using both epicardially and supra-ventricularly paced heartbeats.

Inverse electrocardiography in the framework of dynamic imaging problems.

We describe several current approaches which include temporal information into the inverse problem of electrocardiography. Some of these approaches operate directly on potential-based source models, and we show how three recent methods, introduced with rather distinct assumptions, can be placed in a common framework and compared. Others operate on parameterized models of the cardiac sources, and we discuss briefly how recent developments in curve evolution methods for inverse problems may allow more physiologically complex parametric models to be employed.