Rapidly Detecting Disorder in Rhythmic Biological Signals

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 initialSchematic of cardiac data analysis and the automatic arrhythmia detection algorithm. A full description of the data analysis (stages 1-3) is given in the Data Analysis section, Section 5.2, of the text; the remaining steps (stages 4-5) are described in the Algorithm section, Section 5.3.</p>
<p> MIT-BIH atrial fibrillation database event data (stage 1) are discretized at sampling interval ? , then mapped to give a binary series representing the dynamics of regular beats N (stage 2). A sequence of spectral entropy windows, of length ?, is applied with overlap parameter a to obtain a series of spectral entropy values (stage 3). Variance windows, of length ? with overlap parameter b, are applied to obtain a series of variance values. Threshold conditions in the level and variance of spectral entropy values allows for the classification of periods of atrial fibrillation (AF) and other rhythms (N), typically normal sinus rhythm (stage 4). Finally, the most frequent prediction in each modal smoothing window, of length ? with overlap parameter c, is identified {AF? , N?} to obtain the final algorithm output (stage 5).</p>
<p> For definitions and typical values for algorithm parameters, see Table 5.1.” width=”563″ height=”773″ />regular electrical impulses from the atria (upper chamber of the heart) are conducted intermittently by the atrioventricular node to the ventricles (lower chamber of the heart).</p>
<p> This process is responsible for the irregular ventricular rhythm that is observed. Atrial flutter has similar causes to atrial fibrillation but is less common; incidences of flutter can degenerate into periods of fibrillation. Commonly, alternate electrical waves are conducted to the ventricles, maintaining the initial regular impulses originating from the atria. This results in a rhythm with pronounced regularity.</p>
<p> Normal sinus rhythm can be characterized by a slightly less regular beating pattern occurring at a slower rate compared to atrial flutter. Example electrocardiograms for the three rhythms are shown in the boxed-out areas of Figure 5.3, below.</p>
<p>Given these physiological phenomena, the spectral entropy can be used as a natural measure of disorder, enabling one to distinguish between these three rhythms of the heart. Presented with a possibly very short period of heart activity one can create a length-L, duration-L? , binary string. One then obtains the corresponding power spectrum of this period of heart activity using the discrete Fourier transform (Cooley & Tukey 1965).</p>
<p> Given a (discrete) power spectrum with the ith frequency having power Ci , one can define the “probability” of having power at this frequency as<img class=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 byf(t) = X k ?(t ? tk), (5.4)where tk is the time when an event (beat) occurs.

The corresponding power spectrum is, then,Spectral entropy time series (top), professional rhythm annotation (middle), and arrhythmia detection algorithm prediction (bottom) for patient 08378 from the MIT-BIH atrial fibrillation database.</p>
<p> Event data is sampled at 30-ms intervals approximately 200 times such that there are on average ten beats per spectral entropy window. Each window, of length 6 s for a typical patient, contributes one value of the spectral entropy; windows have a typical overlap of 1.5 s. For the rhythm annotation and algorithm prediction: AF denotes atrial fibrillation, AFL denotes atrial flutter, and N represents all other rhythms.</p>
<p> The algorithm prediction (primed symbols omitted for clarity) demonstrates good agreement with professional annotations; shown for a response time of 30 s, thresholds: ?f ib = 0.84, ?f l = 0.70 and ?f ib = 0.018.” width=”569″ height=”561″ /></p>
<h4>5.2.</p>
<p>4 Cardiac disorder map</h4>
<p>Having identified differences in the level of the spectral entropy measure corresponding to different rhythms of the heart, we suggest that there should be a similar distinction in the variance of a series of spectral entropy values. We propose that the fibrillating state may represent an upper limit to the spectral entropy measure; once this state is reached, variations in the measure’s value are unlikely until a new rhythm is established. By contrast, the beating pattern of normal sinus rhythm is not as disordered as possible and can therefore show variation in the spectral entropy values taken. Inspecting the data, one frequently observes transitions between periods of very regular and more irregular (though still clearly sinus) beating.Thus, normal sinus rhythm will naturally explore more of the spectral entropy value range than atrial fibrillation, which is consistently irregular in character (including some dominant frequencies, see Ng & Goldberger 2007). Furthermore, in defining the spectral entropy window to be constant for a given patient, some dependence on the heart rate is retained, despite accounting for each patient’s average heart rate. This dependence can cause additional harmonics to appear in the power spectrum, increasing the variation of spectral entropy values explored during normal sinus rhythm.</p>
<p> Last, windows straddling transitional periods of the heart rate will also demonstrate atypical power spectra, further compounding the increase in the variance when comparing normal sinus rhythm to atrial fibrillation. We do not conjecture on (and do not observe) a characteristic difference in the variance of spectral entropy values for atrial flutter, relying on the spectral entropy level to distinguish<img class=Algorithm and DiscussionPrevious Page – Discussion and Appendix