=Paper=
{{Paper
|id=Vol-2843/shortpaper31
|storemode=property
|title=Classification of the Functional State of the Respiratory System Based on the Spectral Analysis of the Electrocardio Signal (short paper)
|pdfUrl=https://ceur-ws.org/Vol-2843/shortpaper031.pdf
|volume=Vol-2843
|authors=Maksim B. Myasnyankin,Alexandr A. Kuzmin,Sergey A. Filist,Leonid V. Shulga
}}
==Classification of the Functional State of the Respiratory System Based on the Spectral Analysis of the Electrocardio Signal (short paper)==
https://ceur-ws.org/Vol-2843/shortpaper031.pdf
Classification of the Functional State of the Respiratory
System Based on the Spectral Analysis of the
Electrocardio Signal *
Maksim B. Myasnyankin, Alexandr A. Kuzmin [0000-0001-7980-0673], Sergey A. Filist [0000-
0003-1358-671X]
and Leonid V. Shulga [0000-0002-6793-7362]
Southwest State University, 19, Chelyuskintsev Street, Kursk, 305004, Russian Federation
SFilist@gmail.com
Abstract. The aim of the study is to develop a method for forming descriptors
for neural network classifiers of the functional state of the respiratory system,
based on the analysis of slow waves of the time-frequency spectrum of the elec-
trocardiosignal. The essence of the proposed method is to study the interaction
of the rhythms of the cardiovascular, respiratory system and higher-order
rhythms, which is carried out on the wavelet plane of the electrocardiosignal.
The lines are highlighted on this plane, the frequency range of which corre-
sponds to the breathing rhythm. These lines are modulated by VLF (very low
frequency) waves, which determine the variability of the respiratory rate. We
carry out Fourier analysis of these lines of the wavelet plane and find descrip-
tors for the trained classifier of the functional state of the respiratory system.
The signals of slow waves, reflecting the variations in the breathing rhythm, are
extracted from the monitoring electrocardiosignal by means of exploratory
analysis in the frequency range of the breathing rhythm and subsequent wavelet
analysis in the frequency range corresponding to the frequency range of the
breathing rhythm. The components of the relevant strings of the wavelet plane
are used to calculate descriptors of a trained neural network, which makes a de-
cision on assigning the current state of the respiratory system to the tested state.
Keywords: Cardiac Rhythm, Respiratory System, Systemic Rhythms, Fourier
Transform, Wavelet Transform, Respiration Rhythm, Trained Classifier.
1 Introduction
The fundamental property of an organism is the functioning of its systems in certain
rhythms, with a certain “rhythmic variability” [1-2]. Respiratory rhythm is formed on
the basis of receptor information received from various receptors (for example,
chemoreceptors, mechanoreceptors), which allows the central respiratory regulator to
select optimal ventilation modes. Respiratory rhythm formation in humans largely
*
Copyright © 2021 for this paper by its authors. Use permitted under Creative Commons License Attribu-
tion 4.0 International (CC BY 4.0).
depends on their psycho-emotional state, which is due to the influence of the limbic
system on the activity of the respiratory center. A number of experimental studies
show that the electromyogram of the respiratory muscles is an indicator of the state of
the respiratory system. And the electrical activity of the respiratory muscles is an
informative parameter in the diagnosis of violations of the functional state of the res-
piratory system [3-5].
The body's biorhythms carry information about the functional state of its systems
and subsystems. Consequently, the analysis of biorhythm variability makes it possible
to assess the functional state of the system as a whole. We use electrocardiosignal
(ECS) to study biorhythms in a living organism. This signal is unique in that waves of
various origins can be observed in it in the form of modulation of the main rhythm of
the electrocardiosignal by waves of a higher order. Since the main rhythm of the
pacemaker is a quasi-periodic signal, the spectrum of the pacemaker is continuous
(not discrete), which makes it difficult to isolate slow waves from it.
Control of the cardiac rhythm is carried out both from the side of the cardiovascu-
lar system and from the side of the respiratory system. The sinus node is a self-
contained oscillator with a resonant frequency of about 1 Hz. Its frequency can be
slowed down (parasympathetic influence) or accelerated (sympathetic influence) un-
der the influence of control factors. The goal of autonomic heart rate control is to
stabilize blood pressure (BP). However, not only the autonomic nervous system, but
also the central nervous system (CNS) affects the wave structure of the pacemaker.
HF-waves (high frequency waves) are presented in the ECS spectrum with a peak
in the range of 0.2 ... 0.3 Hz. The presence of these waves is determined by the respi-
ratory system. The peak of these waves in the spectral region, as a rule, coincides with
the rhythm of breathing.
LF waves (low frequency waves) are represented by a spectrum with a peak at 0.1
Hz. These are the so-called L. Traube waves with a period of 10 s. As in the case of
HF, several hypotheses have been put forward about the genesis of LF waves. In
them, the formation of a rhythm of 0.1 Hz is explained by mechanisms of baroreflex,
central and myogenic origin. In practice, the analysis of this rhythm is used to esti-
mate the state of sympathetic regulation of the heart rhythm [6-8].
The VLF (very low frequency) range is the least studied, which corresponds to
slow waves with a period of 25… 330 seconds. Many hypotheses explain the genesis
of these waves. One of them, described in [8], believes that the variability of the
breathing rhythm is based on the mechanism of gas exchange. If this assumption is
correct, then the intensity of pulmonary gas exchange, which reflects the rate of oxy-
gen consumption, has the structure of slow waves of the second order and can be used
as a marker of the functional state (FS) of the respiratory system. To analyze such
indicators of external respiration, long-term recording of pneumogram and registra-
tion of pulmonary gas exchange is necessary. It is very difficult to obtain such pa-
rameters, since this requires special equipment, with continuous recording of signals
at an interval of at least 30 minutes.
2 Materials and methods
The mechanism of changes in the heart rate during breathing is associated with the
functioning of the baroreflex system for stabilizing blood pressure (BP). It is known
that the heart rate rises with inspiration and decreases with expiration due to changes
in pressure in the chest cavity. These processes cause fluctuations in blood pressure
[6].
Consider the morphology of the ECS wavelet plane. Figure 1 shows an example of
the ECS wavelet plane with a duration of 3 minutes. The image contains 300 lines
(wavelets). The lower frequency on the wavelet plane is 0.25 Hz and the upper fre-
quency is 40 Hz. The contrast stripes in Figure 1 correspond to the cardiocycle har-
monics: the 1.2 Hz harmonic occupies a 0.64 Hz band; harmonic 2.4 Hz - 0.4 Hz; the
3.6 Hz harmonic occupies a 0.6 Hz bandwidth. Breathing rhythm waves correspond to
vertical stripes in the lower part of the wavelet plane. They characterize the variability
of the breathing rhythm in frequency.
We will consider one line of the wavelet plane, the dislocation of which corre-
sponds to the respiration rate to assess the temporal variability of the respiration rate.
The diagram of this line is shown in Figure 2. It characterizes the so-called energy
variability, that is, the change in the intensity of the corresponding harmonic over
time.
3,6 Hz
0,5 Hz
frequency
2,4 Hz
0,27 Hz
1,2 Hz
time
Fig. 1. The structure of the wavelet of the electrocardiosignal.
н е р г и яrel.
ЭEnergy, л . ед .
, у сunits
τ,sec.
с
Fig. 2. Plot of the wavelet plane line of the electrocardiosignal corresponding to one of the
respiratory rhythm frequencies.
We will also highlight the frequency variability, by which we mean the variability
of the frequency band occupied by the respiratory train (frequency packet) over time.
According to the results of the analysis of the image in Figure 2, we must identify
changes in the selected segments that occur during pathological processes for the
formation of descriptors. For this, each segment of the wavelet plane can be character-
ized by some vector, consisting of the minimum number of components. In this case,
we managed to identify two informative zones (waves of the first and second order)
with the same parameters of image synthesis. The Fourier spectrum of the wavelet
plane line is morphologically similar to the spectrum of the respiratory rhythm train,
and morphologically and topologically (in the sense of frequency dislocation) it is
similar to the spectrum of the respiratory rhythm obtained by spectral analysis of the
pneumogram [8-9].
Summarizing the above, we can present a method for forming descriptors for clas-
sifiers of the functional state of the respiratory system by means of spectral analysis
of the monitoring electrocardiosignal. The method includes the following processing
steps:
─ the Fourier spectrum of the electrocardiosignal is determined with the allocation of
a train of breathing rhythm;
─ frequency band, occupying a train of breathing rhythm is determined;
─ the ECS wavelet plane is constructed with parameters allowing to observe lines
with breathing rhythm trains on it;
─ Fourier spectra of the wavelet plane lines are determined, which correspond to the
breathing rhythm frequency band;
─ indicators of variability are determined in the spectra of lines of the wavelet plane
(indicators of variability in time), corresponding to the respiratory rhythm trains;
─ variability indices are defined in lines of the wavelet plane in frequency.
Thus, the method allows one to obtain two groups of descriptors that determine the
variability of the breathing rhythm. These two groups of descriptors correspond to
two groups of classifiers, the solutions of which are combined by means of an aggre-
gator [10-13].
3 Results
We will consider the process of implementing the method of forming descriptors for
classifiers of the functional state of the respiratory system on a specific signal. Ac-
cording to the above method, we must determine the train of the breathing rhythm in
the Fourier spectrum of the electrocardiosignal for the formation of descriptors. The
parameters for constructing the wavelet plane of the electrocardiosignal should be
selected in а such way that the lines corresponding to the frequency range of the ob-
tained breathing rhythm train are reflected on the wavelet plane.
The Figure 3 shows an electrocardiosignal wavelet plane, consisting of 800 lines.
Its lines cover the frequency range of the breathing rhythm, which lies in the lower
part of the wavelet plane. Discrete electrocardiosignal was obtained with a sampling
frequency of 100 Hz. To obtain the wavelet plane, 11000 samples of the electrocardi-
osignal were used. With such input parameters, the wavelet plane covers the fre-
quency range from 40 Hz to 0.125 Hz.
Fig. 3. Wavelet plane of an electrocardiosignal with a second-order slow wave sector with
modulation of the respiratory cycle by 15 ... 20 s waves.
In the image in Figure 3, the region of the breathing rhythm train covers lines with
numbers from 250 to 800, according to the Fourier spectrum shown in Figure 2. The
wavelet plane displays rhythms that are modulated by systemic rhythms with a period
of approximately 15 ... 20 s. A sweep of several lines in the breathing rhythm sector is
shown in Figure 4. Here you can see that the 0.2 Hz breath wave is modulated by a
slower wave of higher order, in this case 0.04 Hz.
rel.от.units
ед.
n n+1 n+2 n+3
Энергия,
Energy,
Wavelet
Эпюры plane
строк line plots
вейвлет-плоскости
Fig. 4. Scanning of wavelet plane lines in the respiratory rhythm segment: breath wave
(0.2 Hz), modulated by 0.04 Hz waves.
Weak classifiers can be constructed for each line from this range. But Figure 6 in-
dicates an excessive correlation of adjacent lines of this wavelet plane, which indi-
cates a weak variability of the breathing rhythm in frequency. This does not contradict
either theoretical or experimental studies, since the respiratory rate is modulated by
VLF waves, the period of which is 25… 330 seconds (Figure 2).
To construct classifiers of the functional state of the respiratory system, it was pro-
posed to use hierarchical systems of classifiers based on the principle of strengthening
the quality indicators of "weak" classifiers [11-13]. The structural diagram of the
hierarchical classifier is shown in Figure 5.
NET 3
2-1 P1
1 NET
NET 3-3
Descriptor
generation
module
3-1
electrocardiosignal
P1
Wavelet plane of
Р
P
2-2 P2
NET
Descriptor
generation
module
3-2
P2
Fig. 5. Structural diagram of a hierarchical classifier.
It consists of two autonomous feed-forward neural networks NET 13-1 and NET
13-2 and an aggregating neural network NET 13-3. The indicators of the variability of
the selected lines of the wavelet plane in time are used as descriptors of the first
autonomous neural network, and the indicators of the variability of the selected lines
of the wavelet plane in frequency are used as descriptors of the second autonomous
neural network.
4 Discussion
As a result of the analysis of numerous wavelet planes of the electrocardiosignal, as
well as the study of the works of other scientists [14-16], we concluded that the as-
sessment of the functional state of the respiratory system depends on the modulation
of slow waves of a lower order by slow waves of a higher order. To construct classifi-
ers of the functional state of the respiratory system, we proposed using hierarchical
systems of classifiers based on the principle of enhancing the quality indicators of
“weak” classifiers [12-13]. The descriptors based on the analysis of the respiratory
rhythm variability, the indicators of which can be obtained by analyzing the pneu-
mogram signal and the lung gas exchange indicators, were used as descriptors of
"weak" classifiers. It was shown that similar information on the variation of the
breathing rhythm can be obtained by analyzing the monitoring electrocardiosignal, the
observation aperture of which corresponds to the wavelengths of the VLF range.
The segment of the wavelet plane of the electrocardiosignal was used to determine
the indicators of the variability of the breathing rhythm. The lines of this segment
corresponded to the frequency range occupied by the breathing rhythm. Since the
frequency range of the breathing rhythm is unique for each individual, the Fourier
spectrum of the electrocardiosignal was calculated to determine the boundaries, and
the spectral composition of its train belonging to the breathing rhythm was analyzed.
The parameters for constructing the wavelet plane of the electrocardiosignal were
calculated using the found frequency range of the train.
5 Conclusion
The proposed method for the formation of descriptors for classifiers of the functional
state of the respiratory system made it possible to highlight from the monitoring elec-
trocardiosignal slow waves corresponding to the rhythm of respiration and a wave of
the second order. Analysis of the spectral characteristics of these waves makes it pos-
sible to form a space of informative features for classifiers of the functional state of
the respiratory system, including classifiers of the premorbid state.
6 Acknowledgments
Acknowledgments: The reported study was funded by RFBR, project number 20-38-
90058.
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