Abstract
Implantable cardioverter defibrillators (ICD) are the most effective therapy to terminate malignant ventricular arrhythmias (VA) and therefore to prevent sudden cardiac death. Until today, there is no way to predict the onset of such VA. Our aim was to develop a mathematical model that could predict VA in a timely fashion. We analyzed the time series of R-R intervals from 3 groups. Two groups from the Spontaneous Ventricular Tachyarrhythmia Database (v 1.0) were analyzed from a set of 81 pairs of R-R interval time series records from patients, each pair containing one record before the VT episode (Dataset 1A) and one control record which was obtained during the follow up visit (Dataset 1B). A third data set was composed of the R-R interval time series of 54 subjects without a significant arrhythmia heart disease (Dataset 2). We developed a new method to transform a time series into a network for its analysis, the ε-regular graphs. This novel approach transforms a time series into a network which is sensitive to the quantitative properties of the time series, it has a single parameter (ε) to be adjusted, and it can trace long-range correlations. This procedure allows to use graph theory to extract the dynamics of any time series. The average of the difference between the VT and the control record graph degree of each patient, at each time window, reached a global minimum value of -2.12 followed by a drastic increase of the average graph until reaching a local maximum of 5.59. The global minimum and the following local maxima occur at the windows 276 and 393, respectively. This change in the connectivity of the graphs distinguishes two distinct dynamics occurring during the VA, while the states in between the 276 and 393, determine a transitional state. We propose this change in the dynamic of the R-R intervals as a measurable and detectable "early warning" of the VT event, occurring an average of 514.625 seconds (8:30 minutes) before the onset of the VT episode. It is feasible to detect retrospectively early warnings of the VA episode using their corresponding ε-regular graphs, with an average of 8:30 minutes before the ICD terminates the VA event.
Highlights
Implantable cardioverter defibrillators (ICD) are the cornerstone of sudden cardiac death prevention through termination of ventricular tachycardia/ventricular fibrillation
The global minimum and the following local maxima occur at the windows 276 and 393, respectively. This change in the connectivity of the graphs distinguishes two distinct dynamics occurring during the ventricular arrhythmias (VA), while the states in between the 276 and 393, determine a transitional state. We propose this change in the dynamic of the R-R intervals as a measurable and detectable “early warning” of the ventricular tachyarrhythmias (VT) event, occurring an average of 514.625 seconds (8:30 minutes) before the onset of the VT episode
Several methods have been developed to transform time series into networks for its analysis. Such methods include the visibility graphs method [8], and a plethora of its modifications [9, 10], which consider the topological properties of the time series, the recurrence analysis of time series [11, 12], and the analysis based on the phase space [13]
Summary
Implantable cardioverter defibrillators (ICD) are the cornerstone of sudden cardiac death prevention through termination of ventricular tachycardia/ventricular fibrillation. We usher in a new method to transform a time series into a network for its analysis, the ε−regular graphs. This novel approach transforms a time series into a network which is sensitive to the quantitative properties of the time series, it has a single parameter (ε) to be adjusted, and it can capture long-range correlations. This procedure permits using graph theory to extract the dynamics of any time series. The failure in heart function is the result of malfunctions in the myocardium, heart valves, pericardium, or the endocardium [16]
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