Rapidly detecting disorder in rhythmic biological signals: A spectral entropy measure to identify cardiac arrhythmias

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 ten-beat 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 $6\mathrm{s}$, it agrees with 85.7% of the annotations of professional rhythm assessors; for a response time of $30\mathrm{s}$, this becomes 89.5%, and with $60\mathrm{s}$, it is 90.3%. The algorithm provides a rapid way to detect atrial fibrillation, demonstrating usable response times as low as $6\mathrm{s}$. 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.

Figure 1

Schematic 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, Sec. 2, of the text; the remaining steps (stages 4 and 5) are described in the Algorithm section, Sec. 3. MIT-BIH atrial fibrillation database event data (stage 1) are discretized at sampling interval $\tau$, then mapped to give a binary series representing the dynamics of regular beats $N$ (stage 2). A sequence of spectral entropy windows, of length $\alpha$, is applied with overlap parameter $a$ to obtain a series of spectral entropy values (stage 3). Variance windows, of length $\beta$ with overlap parameter $b$, are applied to obtain a series of variance values. Threshold conditions in the level and variance of spectral entropy values allow 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 $\gamma$ with overlap parameter $c$, is identified $\{{\mathrm{AF}}^{\prime },{\mathrm{N}}^{\prime }\}$ to obtain the final algorithm output (stage 5). For definitions and typical values for algorithm parameters, see Table .

Figure 2

(Color online) 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. Event data is sampled at $30\text{−}\mathrm{ms}$ intervals approximately 200 times such that there are on average ten beats per spectral entropy window. Each window, of length $6\mathrm{s}$ for a typical patient, contributes one value of the spectral entropy; windows have a typical overlap of $1.5\mathrm{s}$. For the rhythm annotation and algorithm prediction, AF denotes atrial fibrillation, AFL denotes atrial flutter, and N represents all other rhythms. The algorithm prediction (primed symbols omitted for clarity) demonstrates good agreement with professional annotations; shown for a response time of $30\mathrm{s}$, thresholds ${\Gamma }_{\mathit{fib}}=0.84$, ${\Gamma }_{\mathit{fl}}=0.70$, and ${\Phi }_{\mathit{fib}}=0.018$.

Figure 3

(Color online) Cardiac disorder map for all 25 patients in the MIT-BIH atrial fibrillation database (afdb). Boxed-out area: example electrocardiograms for normal sinus rhythm, atrial fibrillation, and atrial flutter, taken from patient 04936. Spectral entropy values are obtained from windows of event data expected to contain ten beats; data are sampled at $30\text{−}\mathrm{ms}$ intervals. For a typical patient, each spectral entropy window is around $6\mathrm{s}$ in length and has an overlap with adjacent windows of $1.5\mathrm{s}$. For each point on the disorder map, the standard deviation and average spectral entropy level are calculated from $M$ adjacent spectral entropy values: we call this the variance window $\beta$. Here, we have $M$ equal to 20, and so $\beta$ has a typical length of $30\mathrm{s}$; $\beta$ represents the response time of the algorithm. Normalized frequency histograms are disorder map projections onto the relevant axes. Rhythm assessments {N, AF, AFL} are provided in the afdb. Atrial fibrillation is situated in the upper left of the disorder map, consistent with having a high value for the spectral entropy and a low value for the variance. Atrial flutter has a lower average value for the spectral entropy, as expected. Fibrillation thresholds for the arrhythmia detection algorithm are set at ${\Gamma }_{\mathit{fib}}=0.84$ for the spectral entropy level and ${\Phi }_{\mathit{fib}}=0.018$ for the standard deviation, as indicated on the disorder map.