Manifold learning for analysis of low-order nonlinear dynamics in high-dimensional electrocardiographic signals

Abstract

The dynamical structure of electrical recordings from the heart or torso surface is a valuable source of information about cardiac physiological behavior. In this paper, we use an existing data-driven technique for manifold identification to reveal electrophysiologically significant changes in the underlying dynamical structure of these signals. Our results suggest that this analysis tool characterizes and differentiates important parameters of cardiac bioelectric activity through their dynamic behavior, suggesting the potential to serve as an effective dynamic constraint in the context of inverse solutions.

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

“…In practice, however, the algorithm is readily applied to data with time-varying dynamics by assuming that a static manifold underlies the data, with the consequence of increasing the dimensionality of the reconstructed phase space. Although it may be possible to obtain a more parsimonious representation with an alternative approach, in our experience the algorithm can be quite sensitive to even small signal changes [28, 29]. Moreover, in general, it would be useful to have a method to validate that the changes in LE coordinates can be directly attributed to meaningful changes in the bioelectric signals themselves.…”

“…, by mapping vectors representative of these changes between the two domains), and then confirming that the estimated signal changes match those that were known a priori . In our analyses, we used this approach to validate that LE is sensitive to a number of important signal changes in both ECG and EEG data, which are known to exhibit time-varying behavior [28–30]. Of course, the same methods can be used for data exploration when there is no a priori knowledge of what causes changes in the data.…”

A statistical approach to incorporate multiple ECG or EEG recordings with artifactual variability into inverse solutions

“…In previous work, Erem et al . observed that the measured potentials can be represented as a curve embedded in a high dimensional vector space defined by the potentials at each electrode [5]. 1 However, biological noise, such as respiration, alters the trajectory of the potentials such that samples at equivalent time instances of different epochs appear at different positions along the curve.…”

Combined delay and graph embedding of epileptic discharges in EEG reveals complex and recurrent nonlinear dynamics

“…Recently there has been some interest in analyzing low-order nonlinear dynamics with manifold learning techniques, which can reduce the dimensionality of data when they can be modeled as points sampled from a low-dimensional manifold embedded in a vector space [3, 4, 5, 6]. Indeed, many of those methods also use ideas from nonlinear dynamical analysis ( e.g.…”

“…We have previously applied manifold learning methods to characterize electrocardiographic (ECG) signal dynamics [4] and then we later built low-order models based on those characterizations of dynamics in order to constrain the ECG inverse problem [9]. While the dynamics observed in ECG signals are generally less complex than those in EEGs, we have found dynamic manifolds in both types of data using similar manifold learning techniques.…”