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New Geometric Method of Heart Rate Variability Estimation based on the Multiscale Crrelation Analysis Representation


V.E. Antsiperov
Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences,
Mokhovaya 11–7, Moscow, Russia

The nature and characteristics of ECG signals have been
the subject of research for more than 100 years. This is
because ECG signals contain a valuable diagnostic information
about the functioning of the heart and, indirectly,
about some other organs. Now, despite the impressive track
record of the diagnostics and recommendations already developed
[1], ECG signals continue to be the subject of intensive
study both in the field of cardiology and biomedical
engineering. Cardiologists search for new diagnostic
properties of ECG signals, while engineers are interested
in new approaches and methods for such signals processing
and analysing. New methods imply, in particular, new
techniques of noise suppression, efficient signal representation
and feature extraction.
Feature extraction is an essential step in ECG processing.
It consists in formation of some feature patterns – a set of
descriptors most adequately describing the signal. Among
these features / descriptors the most important are those
with diagnostic properties. As a rule, they represent time
domain parameters, though sometimes they can be defined
in the frequency domain. Basing on ECG patterns, one can
make some initial diagnosis [1]. For example, an “irregular”
QRS complex without P wave is the hallmark of atrial
fibrillation, the shape of the QRS with a left bundle branch
block indicates a risk of cardiomyopathy, etc.
ECG patterns, especially P–QRS–T complexes, are also the
basis for the subsequent heart rate analysis. Usually it is a
more complex phase of ECG signal processing. However,
now there are many methods and approaches related, for
example, to the heart rate variability (HRV) analysis [2].
Quantitative evaluation of the HRV is usually based on the
calculation of some indices connected with the variability
of sequential NN intervals (normal–to–normal intervals between
adjacent QRS complexes). Some of these indices
are determined in the time domain – SDNN, CV, RMSSD,
PNN5O, etc. Others – in the frequency domain – VLF, LF,
HF spectral power components, IC index, etc. It should
be noted that, due to the complexity of the EEG signal, its
fractal–like nature, the values of almost all indices can essentially
diverge for different lengths of time intervals analysed,
even for the same record. Therefore, the European
Society of Cardiology suggests differentiating the diagnostic
methodologies based on HRV indices obtained from the
short–term recordings (of 2 to 5 min) and from the long–
term recordings (of entire 24–h period) [3].
The above discussion is illustrated in Figure 1 by cardioin-

tervalograms (CIG, the NN interval dependences on time)
for a healthy person (A) and a heart disease person (B). It
is clear from the figure that both CIGs are qualitatively different.
For example, at a small temporal scale, the variability
(spread) of NN intervals in a healthy person is greater,
which is a well known fact [5] – but on large scales the variability
becomes equal in both cases. This observation suggests
that the diagnosis based on HRV is adequte, but diagnostic
procedures (automatic in particular) may be nontrivial.
This circumstance gives high relevance to the development
of new ECG processing methods based on long
records – more than 10 minutes, for example, Holter.


[1] J.S. Coviello. ECG interpretation made incredibly easy!
Philadelphia: Wolters Kluwer, 3 edition, 2017.
[2] R.M. Baevsky and A.G. Chernikova. Heart rate variability
analysis: physiological foundations and main methods.
Cardiometry, (10):66–76, 2017.
[3] Task Force of the European Society of Cardiology, the
North American Society of Pacing, and Electrophysiology.
Heart rate variability. standards of measurement,
physiological interpretation, and clinical use. Eur Heart
J, 7(3):354–381, 1996.
[4] A.L. Goldberger and H.E. Stanley et al. Long-range anticorrelations
and non-gaussian behavior of the heartbeat.
Phys Rev Letters, 70(9):1343–1346, 1996.
[5] S.S.Yamamoto J.F. Thayer and J.F. Brosschot. The relationship
of autonomic imbalance, heart rate variability
and cardiovascular disease risk factors. Phys Rev Letters,
141(2):122–131, 2010.
[6] M. Malik. Geometrical methods for heart rate variability
assessment. In M. Malik and A. Camm, editors, Heart
Rate Variability, pages 47–61. Armonk, Futura Publishing
Company -New York, 1995.
[7] V.E. Antsiperov and I.V. Zabrosaev. New results for the
pvc / spb detection using based on the mca heart rhythm
estimation method. In Proceedings of the 12th Russian-
German Conference on Biomedical Engineering, pages
182–186. Vladimir State University, jul 2016.
[8] V.E. Antsiperov. Syclic renewal point processes for heart
rate variability modeling. In Extended abstracts of the second
Russian Conference with international participation
"Physics for Life Sciences", page 61. Ioffe Institute siencetech
information department, sen 2017.
[9] R. Serfozo. Basics of Applied Stochastic Processes.
Springer, -Berlin, -Heidelberg, 2009.
[10] L.A.N. Amaral A.L. Goldberger and et al. P.h. Ivanov.
Physiobank, physiotoolkit, and physionet: Components of
a new research resource for complex physiologic signals.
Circulation, 101(23):e215–e220, 2000.

June 24, 2020
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