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

Visualization of Complex Processes in Cardiovascular System during Electrical Auricular Vagus Nerve Stimulation

The analysis of human physiological systems from the point of view of complex systems theory remains a very ambitious task. The complexity of the problem often encourages the use of innovative mathematical methods analyzing the processes that take place in space and time. The main goal of this paper is to visualize the cardiovascular system during auricular vagus nerve stimulation (aVNS) using the matrix differences to evaluate the dynamic signal interfaces by cointegrating the initial signal data into the matrices during each case. Algebraic relationships between RR/JT and JT/QRS cardiac intervals are used not only to track the cardiovascular changes during aVNS but also to characterize individual features of the person during the transit through the therapy. This paper presents the computational techniques that can visualize the complex dynamical processes taking place in the cardiovascular system using the electrical aVNS therapy. Four healthy volunteers participated in two verum and two placebo experiments. We discovered that the body's reaction to the stimulation was very different in each of the cases, but the presented techniques opened new possibilities for a novel interpretation of the dynamics of the cardiovascular system.

Sequential and efficient neural-population coding of complex task information

Recent work has highlighted that many types of variables are represented in each neocortical area. How can these many neural representations be organized together without interference and coherently maintained/updated through time? We recorded from excitatory neural populations in posterior cortices as mice performed a complex, dynamic task involving multiple interrelated variables. The neural encoding implied that highly correlated task variables were represented by less-correlated neural population modes, while pairs of neurons exhibited a spectrum of signal correlations. This finding relates to principles of efficient coding, but notably utilizes neural population modes as the encoding unit and suggests partial whitening of task-specific information where different variables are represented with different signal-to-noise levels. Remarkably, this encoding function was multiplexed with sequential neural dynamics yet reliably followed changes in task-variable correlations throughout the trial. We suggest that neural circuits can implement time-dependent encodings in a simple way using random sequential dynamics as a temporal scaffold.

Characterizing the transient electrocardiographic signature of ischemic stress using Laplacian Eigenmaps for dimensionality reduction

OBJECTIVE

Despite a long history of ECG-based monitoring of acute ischemia quantified by several widely used clinical markers, the diagnostic performance of these metrics is not yet satisfactory, motivating a data-driven approach to leverage underutilized information in the electrograms. This study introduces a novel metric for acute ischemia, created using a machine learning technique known as Laplacian eigenmaps (LE), and compares the diagnostic and temporal performance of the LE metric against traditional metrics.

METHODS

The LE technique uses dimensionality reduction of simultaneously recorded time signals to map them into an abstract space in a manner that highlights the underlying signal behavior. To evaluate the performance of an electrogram-based LE metric compared to current standard approaches, we induced episodes of transient, acute ischemia in large animals and captured the electrocardiographic response using up to 600 electrodes within the intramural and epicardial domains.

RESULTS

The LE metric generally detected ischemia earlier than all other approaches and with greater accuracy. Unlike other metrics derived from specific features of parts of the signals, the LE approach uses the entire signal and provides a data-driven strategy to identify features that reflect ischemia.

CONCLUSION

The superior performance of the LE metric suggests there are underutilized features of electrograms that can be leveraged to detect the presence of acute myocardial ischemia earlier and more robustly than current methods.

SIGNIFICANCE

The earlier detection capabilities of the LE metric on the epicardial surface provide compelling motivation to apply the same approach to ECGs recorded from the body surface.

Uncovering transitions in paleoclimate time series and the climate driven demise of an ancient civilization

We present a hybrid framework appropriate for identifying distinct dynamical regimes and transitions in a paleoclimate time series. Our framework combines three powerful techniques used independently of each other in time series analysis: a recurrence plot, manifold learning through Laplacian eigenmaps, and Fisher information metric. The resulting hybrid approach achieves a more automated classification and visualization of dynamical regimes and transitions, including in the presence of missing values, observational noise, and short time series. We illustrate the capabilities of the method through several pragmatic numerical examples. Furthermore, to demonstrate the practical usefulness of the method, we apply it to a recently published paleoclimate dataset: a speleothem oxygen isotope record from North India covering the past 5700 years. This record encodes the patterns of monsoon rainfall over the region and covers the critically important period during which the Indus Valley Civilization matured and declined. We identify a transition in monsoon dynamics, indicating a possible connection between climate change and the decline of the Indus Valley Civilization.

Novel Metric Using Laplacian Eigenmaps to Evaluate Ischemic Stress on the Torso Surface

The underlying pathophysiology of myocardial ischemia is incompletely understood, resulting in persistent difficulty of diagnosis. This limited understanding of underlying mechanisms encourages a data driven approach, which seeks to identify patterns in the ECG data that can be linked statistically to disease states. Laplacian Eigen-maps (LE) is a dimensionality reduction method popularized in machine learning that we have shown in large animal experiments to identify underlying ischemic stress both earlier in an ischemic episode, and more robustly, than typical clinical markers. We have now extended this approach to body surface potential mapping (BSPM) recordings acquired during acute, transient ischemia episodes from animal and human PTCA studies. Our previous studies, suggest that the LE approach is sensitive to the spatiotemporal electrocardiographic consequences of ischemia-induced stress within the heart and on the epicardial surface. In this study, we expand this technique to the body surface of animals and humans. Across 10 episodes of induced ischemia in animals and 200 human recordings during PTCA, the LE algorithm was able to detect ischemic events from BSPM as changes in the morphology of the resulting trajectories while maintaining the superior temporal performance the LE-metric has shown previously.

Application of a Hybrid Model Based on Echo State Network and Improved Particle Swarm Optimization in PM2.5 Concentration Forecasting: A Case Study of Beijing, China

With the acceleration of urbanization, there is an increasing trend of heavy pollution. PM2.5, also known as fine particulate matter, refers to particles in the atmosphere with a diameter of less than or equal to 2.5 microns. PM2.5 has a serious impact on human life, a sustainable city, national economic development, and so on. How to forecast the PM2.5 concentration accurately, and then formulate a scientific air pollution prevention and monitoring program is of great significance. This paper proposes a hybrid model based on echo state network (ESN) and an improved particle swarm optimization (IPSO) algorithm for the Beijing air pollution problem, and provides a method for PM2.5 concentration forecasting. Firstly, the PSO algorithm is improved to speed up the search performance. Secondly, the optimal subset of the original data is selected by the convergence cross-mapping (CCM) method. Thirdly, the phase space reconstruction (PSR) process is combined with the forecasting model, and some parameters are optimized by the IPSO. Finally, the optimal variable subset is used to predict PM2.5 concentration. The 11-dimensional air quality data in Beijing from January 1 to December 31, 2016 are analyzed by the proposed method. The experimental results show that the hybrid method is superior to other comparative models in several evaluation indicators, both in one-step and multi-step forecasting of PM2.5 time series. The hybrid model has good application prospects in air quality forecasting and monitoring.

Temporal Performance of Laplacian Eigenmaps and 3D Conduction Velocity in Detecting Ischemic Stress

BACKGROUND

Myocardial ischemia has a complex and time-varying electrocardiographic signature that is used to diagnose and stratify severity. Despite the ubiquitous clinical use of the ECG to detect ischemia, the sensitivity and specificity of ECG based detection of myocardial ischemia are still inadequate.

PURPOSE

The purpose of this study was to compare, using animal models, the performance of several traditional ECG-based metrics for detecting acute ischemia against two novel metrics, the Laplacian Eigenmap (LE) parameters and a three-dimensional estimate of Conduction Velocity (CV).

METHODS

LE is a machine learning technique that reduces the dimensions of simultaneously recorded time signals using a non-linear embedding followed by an singular value decomposition to represent each multichannel recording as a single trajectory on a manifold. Perturbations in the trajectories suggest the presence of myocardial ischemia. CV was computed using a tetrahedral mesh created from the electrode locations of transmural plunge needles. To validate the results, we used electrograms collected over 95 episodes of acutely induced myocardial ischemia in 15 canine and 2 porcine subjects. The LE and CV metrics were compared against traditional metrics derived from the ST segment, the T wave, the QRS of the same electrograms. The response time and robustness of each metric was quantified using parameters we defined as time to threshold (TTT) and contrast ratio (CR).

RESULTS

The temporal performance of the metrics evaluated throughout the ischemic episodes showed a consistent relationship; the LE metrics changed earlier than those from the T wave, which were followed by those from the ST segment, and finally from the QRS. The CV results showed median drops in conduction velocity throughout the perfusion bed of more than 23% in canines and over 12% during half of the induced ischemia episodes in swine. The other half of the episodes in swine produced a 76% drop.

CONCLUSIONS

Our results suggest that the LE metric is more sensitive to acute ischemia than traditional single parameters used in previous studies, likely because it incorporates the entire QRST across multiple electrodes in a way that captures their most salient features in a low-dimensional space. The estimates of conduction velocity suggest substantial, in some cases dramatic slowing of the spread of activation, a finding that is not surprising but has not been documented in such three-dimensional detail before. The experiments and these new metrics provide a means to both explore details of the acute ischemic response not available from humans and suggest a path to translate this knowledge into improvements in clinical scoring of ischemia.

Detecting Ischemic Stress to the Myocardium Using Laplacian Eigenmaps and Changes to Conduction Velocity

The underlying pathophysiology of ischemia and its electrocardiographic consequences are poorly understood, resulting in unreliable diagnosis of this disease. This limited knowledge of underlying mechanisms suggests a data driven approach, which seeks to identify patterns in the ECG that can be linked statistically to underlying behavior and conditions of ischemic stress. The gold standard ECG metrics for evaluating ischemia monitor vertical deflections within the ST segment. However, ischemia influences all portions of the electrogram. Another metric that targets the QRS complex during ischemia is Conduction Velocity (CV). An even more inclusive, data driven approach is known as "Laplacian Eigenmaps" (LE), which can identify trajectories, or "manifolds", that respond to different spatiotemporal consequences of ischemic stress, and these changes to the trajectories on the manifold may serve as a clinically relevant biomarker. On this study, we compared the LE- and CV-based markers against two gold standards for detecting ischemic stress, both derived from the ST segment. We evaluated the response time and fidelity of each biomarker using a Time to Threshold (TTT) and Contrast Ratio (CR) measure, over 51 episodes recorded as cardiac electrograms from a canine model of controlled ischemia. The results show that metrics designed to monitor regions beyond the ST segment can perform at least as well, if not better, than traditional ST segment based metrics.

New approach for visualization of relationships between RR and JT intervals

This paper presents the concept of perfect matrices of Lagrange differences which are used to analyze relationships between RR and JT intervals during the bicycle ergometry exercise. The concept of the perfect matrix of Lagrange differences, its parameters, the construction of the load function and the corresponding optimization problem, the introduction of internal and external smoothing, embedding of the scalar parameter time series into the phase plane—all these computational techniques allow visualization of complex dynamical processes taking place in the cardiovascular system during the load and the recovery processes. Detailed analysis is performed with one person’s RR and JT records only—but the presented techniques open new possibilities for novel interpretation of the dynamics of the cardiovascular system.

Dynamic Electrical Source Imaging (DESI) of Seizures and Interictal Epileptic Discharges Without Ensemble Averaging

We propose an algorithm for electrical source imaging of epileptic discharges that takes a data-driven approach to regularizing the dynamics of solutions. The method is based on linear system identification on short time segments, combined with a classical inverse solution approach. Whereas ensemble averaging of segments or epochs discards inter-segment variations by averaging across them, our approach explicitly models them. Indeed, it may even be possible to avoid the need for the time-consuming process of marking epochs containing discharges altogether. We demonstrate that this approach can produce both stable and accurate inverse solutions in experiments using simulated data and real data from epilepsy patients. In an illustrative example, we show that we are able to image propagation using this approach. We show that when applied to imaging seizure data, our approach reproducibly localized frequent seizure activity to within the margins of surgeries that led to patients' seizure freedom. The same approach could be used in the planning of epilepsy surgeries, as a way to localize potentially epileptogenic tissue that should be resected.

Novel Biomarker for Evaluating Ischemic Stress Using an Electrogram Derived Phase Space

The underlying pathophysiology of ischemia is poorly understood, resulting in unreliable clinical diagnosis of this disease. This limited knowledge of underlying mechanisms suggested a data driven approach, which seeks to identify patterns in the ECG data that can be linked statistically to underlying behavior and conditions of ischemic tissue. Previous studies have suggested that an approach known as Laplacian eigenmaps (LE) can identify trajectories, or manifolds, that are sensitive to different spatiotemporal consequences of ischemic stress, and thus serve as potential clinically relevant biomarkers. We applied the LE approach to measured transmural potentials in several canine preparations, recorded during control and ischemic conditions, and discovered regions on an approximated QRS-derived manifold that were sensitive to ischemia. By identifying a vector pointing to ischemia-associated changes to the manifold and measuring the shift in trajectories along that vector during ischemia, which we denote as Mshift, it was possible to also pull that vector back into signal space and determine which electrodes were responsible for driving the observed changes in the manifold. We refer to the signal space change as the manifold differential (Mdiff). Both the Mdiff and Mshift metrics show a similar degree of sensitivity to ischemic changes as standard metrics applied during the ST segment in detecting ischemic regions. The new metrics also were able to distinguish between sub-types of ischemia. Thus our results indicate that it may be possible to use the Mshift and Mdiff metrics along with ST derived metrics to determine whether tissue within the myocardium is ischemic or not.