=Paper=
{{Paper
|id=Vol-2864/paper17
|storemode=property
|title=Software for Statistical Processing and Modeling of a Set of Synchronously Registered Cardio Signals of Different Physical Nature
|pdfUrl=https://ceur-ws.org/Vol-2864/paper17.pdf
|volume=Vol-2864
|authors=Serhii Lupenko,Iaroslav Lytvynenko,Andrii Sverstiuk,Borys Shelestovskyi,Andrii Horkunenko
|dblpUrl=https://dblp.org/rec/conf/cmis/LupenkoLSSH21
}}
==Software for Statistical Processing and Modeling of a Set of Synchronously Registered Cardio Signals of Different Physical Nature==
https://ceur-ws.org/Vol-2864/paper17.pdf
Software for statistical processing and modeling of a set of
synchronously registered cardio signals of different physical
nature
Serhii Lupenkoa, Iaroslav Lytvynenkoa, Andrii Sverstiukb, Andrii Horkunenkob and
Borys Shelestovskyia
a
Ternopil Ivan Puluj National Technical University, Ruska Street 56, Ternopil, 46000, Ukraine
b
I. Horbachevsky Ternopil National Medical University, Maidan Voli 1, Ternopil, 46000, Ukraine
Abstract
It has been developed the software complex, that allows to perform mutual statistical
processing of synchronously registered cardiosignals on the basis of the vector model of the
cyclic rhythmically connected stochastic processes.
The developed software provides the ability to form a discrete rhythm function, depending on
the number of cycles and zones of the cardio signal to be modeled. The developed set of
programs allows to perform statistical processing of synchronously registered cardiosignals
of different physical nature and to obtain estimates of mathematical expectation, dispersion,
autocorrelation and mutual correlation functions taking into account the rhythm function and
the period. The software also allows you to simulate cardio signals, using the loaded input
data of the cardiosignal, rhythm functions, the number of cycles and zones of the signal to be
modeled.
Keywords 1
Synchronously registered cardiosignals, statistic processing methods, software complex
1. Introduction
Cardiovascular diseases in the world are a serious problem. The medical-social burden of the
circulatory system diseases, especially exacerbated by the rapid spread of COVID-19 and is that they
significantly affect the duration and life quality, the loss economic potential indicators of countries.
That is why the fight against diseases of the circulatory system at the present stage is a priority
problem of modern medicine [1, 2]. Therefore, the development of modern technologies for
instrumental diagnosis of the cardiovascular system (CVS) pathology in the early disease stages,
monitoring the effectiveness of preventive and curative measures, as well as monitoring the vital
functions of the body in critical conditions is an urgent problem of modern medicine and technology
[3, 4].
A promising direction to overcome this problem is to improve existing methods of instrumental
diagnosis of CVS by developing new diagnostic and prognostic features based on the choosing
adequate mathematical analysis methods of synchronously registered signals. To date, a significant
number of functional methods for studying the state of the CVS, which uses the synchronous
registration of several identical or different in origin cardiosignals. One of the main ones is the
synchronous registration of the electrocardiogram (ECG) in different leads 5 and in standardized
formats [6].
CMIS-2021: The Fourth International Workshop on Computer Modeling and Intelligent Systems, April 27, 2021, Zaporizhzhia, Ukraine
EMAIL: lupenko.san@gmail.com (S. Lupenko); iaroslav.lytvynenko@gmail.com (I. Lytvynenko); sverstyuk@tdmu.edu.ua (A. Sverstiuk);
horkunenkoab@tdmu.edu.ua (A. Horkunenko); kaf_vm@tu.edu.te.ua (B. Shelestovskyi)
ORCID: 0000-0002-6559-0721 (S. Lupenko); 0000-0001-7311-4103 (I. Lytvynenko); 0000-0001-8644-0776 (A. Sverstiuk); 0000-0002-
2021-006X (A. Horkunenko); 0000-0002-5606-6290 (B. Shelestovskyi)
© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
When monitoring the vital functions of the body, which occurs during the provision of emergency
and urgent medical care, synchronously recorded key indicators of the body: ECG, curves of arterial
and central venous pressure, external respiration, oxygen and carbon dioxide in the blood and others,
depending on specific clinical situation and capabilities of the applied equipment 7, 8. Mechanical
devices to support blood circulation in advanced heart failure are considered in the work [9].
However, and in this situation the diagnostic analysis is conducted on each signal in particular
which is compared with age norm or magnitude which is defined and corrected by the doctor. An
urgent problem today is the improvement of existing methods of instrumental diagnosis of the
cardiovascular system by developing a software package for the analysis of cardio signals.
A smart system for monitoring and predicting heart disease, which is based on in-depth training, is
presented in the work [10]. The article [11] presents cardio diagnostic systems that use artificial
intelligence and machine learning, as it concerns the health of the cardiovascular system. Cyclic
analysis between meteorological rhythms of respiratory and cardiovascular diseases is considered in
[12]. Diseases of the circulatory system under the influence of ionizing radiation are considered in this
work [13].
Algorithms and methods of cardiac signal processing are created on the basis of their adequate
mathematical models. Thus, it can be stated that today the methods of compatible automated
processing of the set of synchronously registered cardiosignals (SRCS) have not received significant
development. This is due to the insufficient level of development of unifying ideas in the construction
of mathematical models of different types of cardiosignals and diversity of methods for their
processing. The development of other highly informative diagnostic methods also had a significant
impact. However, it can be stated that the development of optimal ways to analyze SRCS or vital
parameters of the organism with access to new integrated indicators and empirical confirmation of
their higher diagnostic value, compared to existing ones, can raise to a new level the nature of
diagnostic process and health management treatment.
Despite significant advances in mathematical modeling of cyclic heart signals, their existing
models do not take into account the following facts. For example, new diagnostic features for cardio
diagnostic systems based on the model of electrocardiographic signals in the form of a vector of
cyclic random processes are considered in [14].
The above arguments indicate the relevance of software for statistical processing and
modeling of cardiosignals based on a mathematical model in the form of a vector of synchronously
registered cardio signals for the needs of automated cardiodiagnostics.
The effectiveness of modern cardiodiagnostic systems largely depends on the hardware and
software components on which they are based. The use of various processing methods included in the
software significantly expands the functionality and increases the reliability of human heart diagnosis
[15]. While the methods are based on mathematical models that establish the possibility and specifics
of processing. In particular, the simultaneous processing of cardiosignals of different physical nature
can be performed only if their mathematical models are in some way correlated and have a similar
structure.
2. Analysis of recent researches
A stochastic approach to their simulation is mainly used in the direction of cardiac signal
processing. Thus, for this purpose, use the mathematical models of cyclostationary signals [16-18],
modeling diagnostic features [19-20], analytical approaches for myocardial fibrillation signals [21],
modeling the pulse signal by wave-shape function [22]. An interesting approach to the description of
cardio signals is the mathematical model presented in [23]. It allows to take into account both
morphological features of cardiac signals and their rhythmic structure. It is important that this
mathematical model takes into account the common rhythm of synchronously recorded cyclic cardio
signals of different physical nature, which do not allow to implement other mathematical models
using a stochastic approach. In order to be able to apply the proposed mathematical model, a
necessary condition is the availability of information about the characteristic elements of cardio
signals (cycles and zones, such as zones P, Q, R, S, T - electrocardiogram). It is possible to obtain tau
information about the characteristic elements of cyclic cardiac signals by applying their segmentation
methods, for example, the methods presented in [24], other methods of analysis of cardio signals are
presented in [25-27].
3. Objectives
The work is devoted to the creation and application of software for statistical processing and
modeling of synchronously registered cardiac signals as components of cardio diagnostic systems.
The importance of these studies lies in the possibility of using a common rhythm in the modelling
and static processing of different in nature cyclic signals but formed by a single source.
4. Method
According to paper [22], we give a definition of the vector of cyclic rhythmically connected
stochastic processes.
Definition 1. If there is a function such as T t , n , which satisfies the conditions of the rhythm
function that finitely measurable vectors {i1 ( , t1 ), i2 ( , t 2 ),..., ik ( , tk )} and
{i1 ( , t1 T (t1 , n)), i2 ( , t2 T (t2 , n)),..., ik ( , tk T (tk , n))} n Z, i1 ,..., ik 1, N , where
t1 ,..., tk - multiple separability of the vector Θ , t , for all the integers k 1 are stochastic
N
equivalent in the broadest sense, we will call the vector Θ N , t of cyclic stochastic processes
____
i , t , i 1, N , ∈Ω, t ∈W as the vector of strictly rhythmically connected stochastic
processes and the processes as strictly rhythmically connected.
Area of definition W vector of cyclic rhythmically connected stochastic processes can be as ordered
discretely W R {t ml R , m Z, l 1, L} or continuous W R set of real numbers. In the case of
discrete domain definition W D for its elements if m2 m1 , or if m2 m1 , а l 2 l1 , in other cases
t m1l1 t m2l2 ; m1 , m2 Z , l1 , l2 1, L there is a type of linear ordering: t m1l1 t m2l2 . Moreover
0 t m , l 1 t m , l .
The rhythm function T t , n determines the law of changing the time intervals between the single-phase
values of the vector of cyclic rhythmically connected stochastic processes. The function of the rhythm satisfies
such conditions according to the theorem which is proved in the paper:
а) T t , n 0 , if n 0 ( T t ,1 ∞ );
b) T t , n 0 , if n 0 ;
с) T t , n 0 , if n 0 , t ∈W ; (1)
for any t1 ∈W and t2 ∈W , for which t1 t2 , for function T t , n should be performed a
strict inequality:
T t1 , n t1 T t2 , n t2 , ∀ n ∈Z ; (2)
function T t , n is the smallest modulo ( T t , n ≤ T t , n ) among all such functions
T t, n, ∈Γ, which satisfy (1) and (2).
In the partial case, if the rhythm function is T t , n n T T 0, n ∈Z , we will call the
vector Θ N , t as the vector T - periodically connected stochastic processes.
Let us consider the properties of some probabilistic characteristics of the vector Θ N , t
cyclic rhythmically connected stochastic processes. So, for its compatible k - measurable distribution
function takes place equation:
Fk ... ( x1 ,..., xk ; t1 ,..., t k )
i1 k1
Fki ... k ( x1 ,..., xk ; t1 T (t1 , n),..., t k T (t k , n)), n Z, i1 ,..., ik 1, N , t1 ,..., t k W (3)
1 1
k
Combined central moments function of order p R :
j 1
j
rpi ...i (t1 ,..., t k ) M{( i1 ( , t1 ) mi1 (t1 )) R1 ... ( i p ( , t k ) mik (t k )) Rk }
1
(4)
k
rpi ...i (t1 T (t1 , n),..., t k T (t k , n)), t1 , t 2 ,..., t k W, i1 ,..., ik 1, N , n Z.
1 k
5. Results and Discussion
It was made the series of experiments on processing of the cardiaosignals of the same and
different physical origin which were investigated for the purpose of approving of the greater
effectiveness of the simultaneous processing of synchronously registered cardiosignals (SRCS) based
on the model of the vector of cyclic rhythmically connected stochastic processes in comparison with
the well-known method of their processing.
As the example it is shown on the Figure 1 the realizations of SRCS electrocardiosignal
(ECS) and phonocardiosignal (PCS) and on the figures 2-4 are represented the results of a
comparative analysis.
(t ), mV (t ), conditional units
0,3
0,5
0,2
0,4
0,1
0,3
0
0,2
0,1 -0,1
0 -0,2
-0,1 t , s -0,3 t, s
0 2 4 6 8 10 0 2 4 6 8 10
a) b)
Figure 1: The realizations of SRCS: (a) electrocardiogram, (b) phonocardiogram.
RˆT (t1 , t2 ), mV 2 RˆT (t ,1) (t1 , t2 ), mV 2
0,06 0,06
0 0
-0,06 -0,06
t2 , c t2 , c
0,8 0,8
0,6 0,8
t1 , s 0,6 0,8
t1 , s
0,4 0,6 0,4 0,6
0,4 0,4
0,2 0,2 0,2 0,2
0 0
а) b)
Figure 2: The realization graphs of statistical estimations of the autocorrelation function of the ECS
while its processing on the basis of: (a) the vector of periodically connected stochastic processes; (b)
the vector of cyclic rhythmically connected stochastic processes.
RˆT (t1 , t2 ), conditional units 2 RˆT (t,1) (t1 , t2 ), conditional units 2
0,012
0,012
0
0
-0,012
-0,012
t2 , c t 2 , 0,8
c
0,8
0,6 0,8
t1 , s 0,6 t1 , s
0,8
0,4 0,6 0,4 0,6
0,4 0,4
0,2 0,2 0,2 0,2
0 0
a) b)
Figure 3: The realization graphs of statistical estimations of the autocorrelation function of PCS while
its processing on the basis of: (a) the vector of periodically connected stochastic processes; (b) the
vector of cyclic rhythmically connected stochastic processes.
Rˆ , (t1 , t 2 ), m V conditional un its Rˆ , (t1 , t2 ), mV conditional units
0,09 0,012
0 0
-0,09 -0,012
t2 , c t2 , c
0,8 0,8
0,6 0,8
t1 , s 0,6 0,8
t1 , s
0,4 0,6 0,4 0,6
0,4 0,4
0,2 0,2 0,2 0,2
0 0
а) b)
Figure 4: The realization graphs of statistical estimations of the mutual correlation function of the
ECS and PCS while its processing on the basis of: (a) the vector of periodically connected stochastic
processes; (b) the vector of cyclic rhythmically connected stochastic processes.
It was set in the result of the comparative analysis of the statistical processing of sets of SRCS
which was made that the method of statistical processing of the analyzed cardiosignals on the basis of
the vector of cyclic rhythmically connected stochastic processes significantly reduces the negative
effect of "blurring" of statistical estimations of mutual correlation functions as a part of set of
synchronous cyclic signals of a heart that is strongly-pronounced in results of statistical processing of
the cardiac signals which were investigated on the basis of the vector of periodically connected
stochastic processes. It is proved by the fact that the new method of compatible statistical processing
takes into account the variability of the SRCS rhythm, in contrast to the well-known methods.
5.1 Software operating principle
It was developed the software complex which allows to perform SRCS statistical processing
and its structural scheme is shown in Figure 5.
In this complex was implemented: block of SRCS formation, SRCS filtering block, trend
removal block, SRCS segmentation block, block for determining the SRCS rhythm function,
statistical analysis block of the rhythm function, valuation block of statistical estimates of SRCS,
statistical analysis block of SRCS, dimension minimization block of the vector of informative
features, diagnostic block.
The exported synchronously registered cardio signals were used from PhysioNet in
accordance with the article [28] in the SRCS implementation generation unit. Pre-processing units are
designed to filter and extract trends from SRCS. The segmentation unit is used to obtain the time-time
structure of SRCS to determine their rhythmic functions. Blocks of statistical processing are intended
for the normalization of statistical estimations, the analysis of investigated cardiac signals. The block
of minimization of dimensionality of a vector of informative signs is necessary for minimization of
their quantity representing norm or a certain pathology of the cardiovascular system. The diagnostic
unit allows you to diagnose the cardiovascular system using SRCS (Fig. 5).
BLOCKS OF SRCS PRE-PROCESSING
BLOCK OF SRCS SRCS TREND SRCS
FORMATION FILTERING REMOVAL SEGMENTATION
BLOCK BLOCK BLOCK
BLOCKS OF SRCS STATISTICAL PROCESSING
BLOCK FOR VALUATION
DETERMINING STATISTICAL BLOCK OF STATISTICAL
THE SRCS ANALYSIS BLOCK OF STATISTICAL ANALYSIS BLOCK
RHYTHM THE RHYTHM ESTIMATES OF OF SRCS
FUNCTION FUNCTION SRCS
DIMENSION
MINIMIZATION
BLOCK OF THE DIAGNOSTIC
VECTOR OF BLOCK
INFORMATIVE
FEATURES
Figure 5: Software complex for statistical processing of synchronously registered cardiosignals.
For the compatible statistical processing of SRCS (electrical, magnetic, acoustic nature) the
module “Compatible statistical processing of SRCS” is used, the structural-functional scheme of
which is shown in fig. 6.
Data entry Estimation of compatible correlation
(two synchronously registered function taking into account
cardiosignals and their rhythm functions
mathematical expectations)
Data storage
Data visualization
Visualization of the obtained results
Figure 6: Structural‐functional module scheme of the program "Compatible statistical processing
SRCS".
The input data for compatible statistical processing are oversampled values of signals and
their estimates of mathematical expectation. The result of joint statistical processing is a cross-
correlation function obtained taking into account the rhythm function (Fig. 6).
To simulate cardiosignals, a simulation unit SRCS was developed taking into account the
rhythm function, the structural-functional scheme of which is shown in Fig. 7.
In order to simulate cardio signals taking into account the rhythm function, it is first necessary
to open the input data of the cardio signal and rhythm function, set the number of cycles and signal
zones, load the input cycle (Fig. 7).
Data entry Data entry of a new
(cardio signal, rhythm rhythm function (zones
function) and cycles)
Enter quantity Forming a durations table
cycles and zones of the rhythm function
cardiosignal
Cardio signal modeling taking Formation of a new
into account the rhythm rhythm function
function
Saving of modeling results
Visualization of results
and new rhythm function
Figure 7: Structural‐functional scheme of the SRCS simulation unit taking into account the rhythm
function.
5.2 Software design
In Fig. 8 the general view of program interfaces for data input (cardiosignals, rhythm functions)
and their visualization is given.
a) b)
Figure 8: General view of the program interfaces for data entry (a) and their visualization (b).
Two methods were used in the program for statistical processing of SRCS: the method of
averaging the values of signal realization taking into account the period and the method of averaging
the values of signal realization taking into account the rhythm function. An example of the program
interface for statistical processing taking into account the period is shown in Fig. 9.
The method of averaging the values of signal realization taking into account the rhythm
function, in comparison with known methods, significantly reduces the negative effect of "blurring"
of statistical estimates of probabilistic characteristics of SRCS, which allows to increase the accuracy,
reliability and informative of complex automated diagnosis of the human cardiovascular system by
synchronous cyclic heart signals (Fig. 9).
a) b)
Figure 9: General view of the program interfaces for statistical processing through period (a) and
taking into account the rhythm function (b).
During statistical processing, taking into account the rhythm function, it is necessary to specify
additional parameters, namely: the sampling step of the signal and rhythm function (required during
resampling of signal and rhythm function), as well as the number of heartbeat cycles and the zones
number (per cycle) of registered signal implementation. Performing consistent steps: rhythm function
interpolation; signal interpolation; rhythm function resampling; signal oversampling we obtain the
necessary data for statistical processing, taking into account the rhythm function.
In Fig. 9 shows that as a result of statistical processing we can obtain estimates of the following
probabilistic characteristics: mathematical expectation, variance and autocorrelation function. All
received data can be saved in text files if necessary.
The general view of the program interfaces for visualization of the estimation of the
mathematical expectation of the phonocardiogram (a) and the integrated rheogram (b), by the method
of statistical processing taking into account the rhythm function, is given in Fig. 10.
a) b)
Figure 10: General view of the program interfaces for estimation visualization of the mathematical
expectation of the phonocardiogram (a) and the integrated rheogram (b).
The input data for compatible statistical processing are oversampled values of signals and their
estimates of mathematical expectation. The result of compatible statistical processing is a mutual
correlation function obtained taking into account the rhythm function.
An example of the program interface for entering synchronously registered data (a) and their
compatible processing (b) is shown in Fig. 11.
a) b)
Figure 11: General program interface view for entering synchronously registered data (a) and their
compatible processing (b).
In order to simulate cardiosignals taking into account the rhythm function, it is first necessary
to open the input data of the cardiosignal and rhythm function, set the number of cycles and signal
zones, load the input cycle. The program interfaces are used for input data (Fig. 12 (a)) and for
visualization of the input cycle (Fig. 12 (b)).
а) b)
Figure 12: General view of the interface of the program of input data input (a) and visualization of
the input cycle (b).
The developed software provides the ability to form a discrete rhythm function, depending on
the number of cycles and zones of the cardiosignal to be modeled. The program interfaces for forming
the rhythm function and visualization of the modeled cardio signal are shown, respectively, in Fig. 13
(a, b).
а) b)
Figure 13: General view of the program interface for forming the rhythm function (a) and the
modeled cardiosignal generated by the rhythm function (b).
The developed set of programs makes it possible to perform statistical processing of SRCS of
different physical nature and obtain estimates of mathematical expectation, dispersion, autocorrelation
and mutual correlation functions (taking into account the rhythm function and taking into account the
period). The software also allows you to simulate cardio signals. The developed software provides the
ability to form a discrete rhythm function, depending on the number of cycles and zones of the cardio
signal to be modeled.
6. Conclusions
A set of programs has been developed that allows for statistical processing of cardiac signals
of different physical origin and to obtain estimates of mathematical expectation, variance,
autocorrelation and cross-correlation (taking into account the function of rhythm and period). The
software allows you to simulate the implementation of cardio signals of different physical nature,
taking into account their constant rhythm (taking into account the period), variable (taking into
account the rhythm function) and the common rhythm. The modeling method includes information
obtained at the stage of statistical processing of cardiac signals, in particular, morphological features
are taken into account on the basis of estimates of mathematical expectation and variance of cardiac
cycle cycles.
The developed software provides the possibility of forming a discrete rhythm function
depending on the number of cycles and zones of the simulated cardio signal.
This software can be used as a component of diagnostic systems of the human heart.
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