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Detection of Arrhythmic Cardiac Signals from ECG Recordings Using the Entropy-Complexity Plane
* 1 , 2 , 3
1  PhD student at signal and image processing center from Universidad Tecnológica Nacional - Argentine
2  Director of the signal and image processing center at Universidad Tecnológica Nacional - Argentine
3  Vice Director of the signal and image processing center at Universidad Tecnológica Nacional - Argentine


The aim of this work was to analyze in the Entropy-Complexity plane (HxC) time series coming from ECG, with the objective to discriminate recordings from two different groups of patients: normal sinus rhythm and cardiac arrhythmias.

The HxC plane used in this study was constituted by the Shannon’s Entropy as one of its axis, and the other was composed by the statistical complexity. To compute the entropy the probability distribution function (PDF) of the observed data was obtained using the methodology proposed by Bandt & Pompe (2002) [1].

The database used in the present study was the ECG recordings obtained from PhysioNet, 47 long-term signals of patients with diagnosed cardiac arrhythmias and 18 long-term signals from normal sinus rhythm patients were processed. Average values of statistical complexity and normalized Shannon entropy were calculated and analyzed in the HxC plane for each time series.

The average values of complexity of ECG of patients with diagnosed arrhythmias were bigger than normal sinus rhythm group. On the other hand, the Shannon entropy average values for arrhythmias patients were lower than the normal sinus rhythm group. This characteristic made possible discriminate the position of both signals’ groups in the HxC plane. The results were analyzed through a multivariate statistical test hypothesis.

The methodology proposed has a remarkable conceptual simplicity, and shows a promissory efficiency in the detection of cardiovascular pathologies.

Keywords: entropy-complexity plane; ECG; arrhythmic cardiac signals; Shannon’s entropy; permutation entropy; Bandt & Pompe
Comments on this paper
Luciano Costa
multiscale extensions
I found your work very interesting, especially the combination of the two time series measurements.

Have you considered a multiscale extension of your approach, e.g. considering progressively smoothed
versions of the time series or some other related scheme?

A minor point: in Eq. 5, would there be missing an equal symbol ("=") in the subscript?

All best wishes, Luciano da F. Costa
Pablo Martinezcoq
Dear Luciano,

Thank you very much for your comments.
We were used the multi scale permutation entropy (MPE) but not yet combined in the informational plane.
Upon your suggestion we are planning to join the complexity with the above mentioned version of permutation entropy, to compound a new plane MPExC.

Best regards.

Pablo, Walter and Ricardo.