We consider the use of a running measure of power spectrum disorder to distinguish between the normal sinus rhythm of the heart and two forms of cardiac arrhythmia: atrial fibrillation and atrial flutter. This spectral entropy measure is motivated by characteristic differences in the power spectra of beat timings during the three rhythms. We plot patient data derived from tenbeat windows on a “disorder map” and identify rhythm-defining ranges in the level and variance of spectral entropy values. Employing the spectral entropy within an automatic arrhythmia detection algorithm enables the classification of periods of atrial fibrillation from the time series of patients’ beats.When the algorithm is set to identify abnormal rhythms within 6 s it agrees with 85.7% of the annotations of professional rhythm assessors; for a response time of 30 s this becomes 89.
5%, and with 60 s it is 90.3%. The algorithm provides a rapid way to detect atrial fibrillation, demonstrating usable response times as low as 6 s. Measures of disorder in the frequency domain have practical significance in a range of biological signals: the techniques described in this paper have potential application for the rapid identification of disorder in other rhythmic signals.
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5.1 Introduction
Cardiovascular diseases are a group of disorders of the heart and blood vessels and are the largest cause of death globally (World Health Organization 2007).
An arrhythmia is a disturbance in the normal rhythm of the heart and can be caused by a range of cardiovascular diseases. In particular, atrial fibrillation is a common arrhythmia affecting 0.4% of the population and 5%–10% of those over 60 years old (Kannel et al. 1982; Cairns & Connolly 1991); it can lead to a very high (up to 15-fold) risk of stroke (Bennett 2002).
Heart arrhythmias are thus a clinically significant domain in which to apply tools investigating the dynamics of complex biological systems (Wessel et al. 2007). Since the pioneering work of Akselrod et al. (1981) on spectral aspects of heart rate variability, such approaches have tended to focus on frequencies lower than the breathing rate. By contrast, we develop a spectral entropy measure to investigate heart rhythms at higher frequencies, similar to the heart rate itself, that can be meaningfully applied to short segments of data.
Conventional physiological measures of disorder, such as approximate entropy (ApEn) and sample entropy (SampEn), typically consider long time series as a whole and require many data points to give useful results (Grassberger & Procaccia 1983; Pincus 1991; Richman & Moorman 2000). With current implant technology and the increasing availability of portable electrocardiogram (ECG) devices (Bai et al. 1999; Anlike et al. 2004), a rapid approach to fibrillation detection is both possible and sought after. Though 114 numerous papers propose rapid methods for detecting atrial fibrillation using the ECG (Xu et al. 2002, 2007; Isa et al. 2007), less work has been done using only the time series of beats or intervals between beats (RR intervals).
In one study, Tateno and Glass use a statistical method comparing standard density histograms of ?RR intervals (Tateno & Glass 2000, 2001). The method requires around 100 intervals to detect a change in behavior and thus may not be a tool suitable for rapid response.Measures of disorder in the frequency domain have practical significance in a range of biological signals. The irregularity of electroencephalography (EEG) measurements in brain activity, quantified using the entropy of the power spectrum, has been suggested to investigate localized desynchronization during some mental and motor tasks (Inouye et al. 1991; Rosso 2007).
Thus, the techniques described here have potential application for the rapid identification of disorder in other rhythmic signals.In this paper we present a technique for quickly quantifying disorder in high frequency event series: the spectral entropy is a measure of disorder applied to the power spectrum of periods of time series data. By plotting patient data on a disorder map, we observe distinct thresholds in the level and variance of spectral entropy values that distinguish normal sinus rhythm from two arrhythmias: atrial fibrillation and atrial flutter. We use these thresholds in an algorithm designed to automatically detect the presence of atrial fibrillation in patient data. When the algorithm is set to identify abnormal rhythms within 6 s it agrees with 85.7% of the annotations of professional rhythm assessors; for a response time of 30 s this becomes 89.
5%, and with 60 s it is 90.3%. The algorithm provides a rapid way to detect fibrillation, demonstrating usable response times as low as 6 s and may complement other detection techniques.The structure of the paper is as follows. Section 5.
2 introduces the data analysis and methods employed in the arrhythmia detection algorithm, including a description of the spectral entropy and disorder map in the context of cardiac data. The algorithm itself is presented in Section 5.3, along with results for a range of detection response times. In Section 5.4, we discuss the results of the algorithm and sources of error, and compare our method to other fibrillation detection techniques. An outline of further work is presented in Section 5.
5, with a summary of our conclusions closing the paper in Section 5.6.
5.2 Data Analysis
After explaining how we symbolize cardiac data in Section 5.2.1, the spectral entropy measure is introduced (Section 5.2.
2) and appropriate parameters for cardiac data are selected (Section 5.2.3). We then show how the various rhythms of the heart can be identified by their position on a disorder map defined by the level and variance of spectral entropy values (Section 5.2.
4).Data were obtained from the MIT-BIH atrial fibrillation database (afdb), which is part of the physionet resource (Goldberger et al. 2000). This database contains 299 episodes of atrial fibrillation and 13 episodes of atrial flutter across 25 subjects (henceforth referred to as “patients”), where each patient’s Holter tape is sampled at 250 Hz for 10 h. The onset and end of atrial fibrillation and flutter were annotated by trained observers as part of the database. The timing of each QRS complex (denoting contraction of the 116 ventricles and hence a single, “normal”, beat of the heart) had previously been determined by an automatic detector (Laguna et al.
1997).
5.2.1 Symbolizing cardiac data
We convert event data into a binary string, a form appropriate for use in the spectral entropy measure. The beat data is an event series: a sequence of pairs denoting the time of a beat event and its type.
We categorize normal beats as N and discretize time into short intervals of length ? (for future reference, symbols are collected with summarizing descriptions in Table 5.1). Each interval is categorized as Ø or N depending on whether it contains no recorded event or a normal beat, respectively. This yields a symbolic string of the form …ØØØN ØØN ØN ØØØN.
… This symbolic string can be mapped to a binary sequence (N ? 1, Ø ? 0). This procedure is shown schematically in Figure 5.1. Naturally, this categorization can be extended to more than two states and applied to other systems. For example, ectopic beats (premature ventricular contractions) could be represented by V to yield a symbolic string drawn from the set {Ø,N,V }.
An additional map could then be used to extract a binary string representing the dynamics of ectopic beats.
5.2.2 Spectral entropy
We now present a physiological motivation for using a measure of disorder in the context of cardiac dynamics, followed by a description of the spectral entropy measure. Following Bennett (2002), atrial fibrillation is characterized by the physiological process of concealed conduction in which the initial
As will be discussed in the following section, H can be normalized by Hmax to give spectral entropy values in the range [0,1].Note that analytical tools relying on various interbeat intervals have been devised in the past (e.
g., Tateno & Glass 2000, 2001; Schulte-Frohlinde et al. 2002; Lerma et al. 2007). Here, we demonstrate how our measure relates to those studies.
Any series of events can be represented by
where tk is the time when an event (beat) occurs.
The corresponding power spectrum is, then, ? X k,k? cos(? | tk ? tk ? |). (5.5)” width=”406″ height=”59″ />The spectral entropy is, by definition,<img class=)
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