=Paper=
{{Paper
|id=Vol-3628/short19
|storemode=property
|title=Mathematical, Algorithmic and Software Support for Phonocardiographic Signal Processing to Detect Mitral Insufficiency of Human Heart Valves
|pdfUrl=https://ceur-ws.org/Vol-3628/short19.pdf
|volume=Vol-3628
|authors=Mykola Khvostivskyi,Evhenia Yavorska,Roman Kinash,Roman Boyko
|dblpUrl=https://dblp.org/rec/conf/ittap/KhvostivskyiYKB23
}}
==Mathematical, Algorithmic and Software Support for Phonocardiographic Signal Processing to Detect Mitral Insufficiency of Human Heart Valves==
https://ceur-ws.org/Vol-3628/short19.pdf
Mathematical, Algorithmic and Software Support for
Phonocardiographic Signal Processing to Detect Mitral
Insufficiency of Human Heart Valves
Mykola Khvostivskyi, Evhenia Yavorska, Roman Kinash and Roman Boyko
Ternopil Ivan Puluj National Technical University, Rus’ka Str., 56, Ternopil, 46001, Ukraine
Abstract
Mathematical support for phonocardiographic signal processing has been developed based on
a mathematical model in the form of a periodically correlated stochastic process and a
component processing method. On the basis of mathematical support, algorithmic and software
was developed in the Matlab environment for automated systems of computer diagnostics of
the functional state of the valves of the human heart when mitral insufficiency is detected.
Keywords 1
Mitral valve insufficiency of the human heart, phonocardiographic signal, mathematical
support, periodically correlated stochastic process, component method, algorithmic support,
software, Matlab.
1. Introduction
According to the WHO and the Medical Association of Cardiologists, it has been established that
the development trend of human heart valve lesions occupies a dominant place among all cardiovascular
diseases in Europe [1-19]. The primary causes of such lesions are congenital (arising during fetal
development) and acquired (complications of rheumatism, infectious endocarditis or after surgical
treatment of mitral stenosis) defects of the human heart.
In medical practice, such basic non-invasive instrumental research methods as cardiography [1,2],
auscultation [17,18], echocardiography [4,6,13,14,15] and phonocardiography [17,19] are used to
diagnose mitral insufficiency. Phonocardiography along with other methods makes it possible to
objectify unclear sound phenomena of human heart valves (degree of weakening and presence of heart
sounds, intensity, duration and form of systolic murmur) (Sacks, Roberts and Evans) according to
registered phonocardiographic signals (PCG signals) (Figure 1).
Figure 1: The structure of the PCG signal in mitral insufficiency: the I tone is weakened and merges
with the noise of systole (indicated by the pointing arrow)
Proceedings ITTAP’2023: 3rd International Workshop on Information Technologies: Theoretical and Applied Problems, November 22–24,
2023, Ternopil, Ukraine, Opole, Poland
EMAIL: hvostivskyy@tntu.edu.ua (A. 1); yavorska_eb@yahoo.com (A. 2); roman.kinash97@gmail.com (A. 3); boiko.r.911@ukr.net (A. 4)
ORCID: 0000-0002-2405-4930 (A. 1); 0000-0001-6341-1710 (A. 2); 0009-0007-0904-595X (A. 3); 0000-0003-3671-9917 (A. 4)
©️ 2020 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)
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Of particular value is the possibility of long-term (over a year or more) objective dynamic
monitoring of the PCG signal during the formation of a valve defect. To implement the
phonocardiography method in medical practice, hardware devices in the form of computer
phonocardiographs are used, such as Cardio+ (Ukraine, Metekol LLC), PCG-02 (India, Mumbai),
Techbook Scientech 2356 (India, Scientech Technologies Pvt . Ltd.) and Audio-Technica ATR288W
(Japan). Well-known phonocardiographs based on the principle of obtaining diagnostic information
about the condition of human heart valves are built according to the scheme "bioobject (human heart
valves)-mathematical support (mathematical model-processing method)-algorithmic support-software-
diagnosis result" [21,24,26,28,29,38,39,40]. In phonocardiographs, software and algorithmic support,
which form the result of diagnostics, are implemented on the correlation, spectral and synphase methods
of FCS processing, the core of which is a mathematical model in the form of a deterministic harmonic
function (Dodge and Cabot), periodic functions of different frequencies (Manheimer), almost periodic
functions (Kasyrskyi G.I.), a stationary stochastic process (Metin Akay (Houston)), a mixture of a
stationary stochastic process and a deterministic function (Metin Akay (Houston)), periodically
correlated stochastic process (Osukhivska H.M., Dragan Ya.P. [22,23,35,36], Palianytsia Y.B. [31,32]),
relaxation multipulsator (Osukhivska H.M.) [37]. Such mathematical support (models and methods
developed on their basis) of processing by its structure and properties does not provide tracking the
temporal dynamics of changes in the amplitude and phase indicators of the functioning of the valves of
the human heart, which is important in detecting the manifestations of mitral insufficiency over time.
Therefore, the development of mathematical support (a processing method based on its adequate
mathematical model) and algorithmic-software processing of PCG signal for detecting mitral valve
insufficiency of the human heart is an urgent scientific task.
2. Mathematical support for phonocardiographic signal processing
The experimentally recorded implementation of the PCG signal in the case of mitral insufficiency
is shown in Figure 2.
Figure 2: Experimentally recorded PCG signal (mitral regurgitation)
The PCG signal in mitral insufficiency as a stochastic and cyclical process by the nature of the
correlation function satisfies the conditions of cyclicity of the average characteristics and their
variations:
mt T mt , (1)
r t T , s T r t , s . (2)
In this case, T corresponds to the duration of one PCG signal cycle in mitral insufficiency.
Expressions (1-2) indicate the cyclic nature of the characteristics, namely that the values of the average
characteristics and their variations due to the cardiac cycle are repeated, but with changes caused by
chance.
PCG signal in the case of mitral class insufficiency provides the study of its type of harmonicity as
a process of stochastic and cyclic nature in the form of PСSP from the standpoint of the energy approach
(developer Ya.P. Dragan [20,22,23,30,31,32,33,34]).
Since the PCG signal in mitral insufficiency is presented in a stochastic process with cyclic
characters of a finite nature, it can be represented through the expression of translational components
[20]:
t H t pT k t qt , (3)
pZ k Z
where is a H single function that indicates the place of generation of the PCG signal tone in mitral
insufficiency; T - is the cycle period of the PCG signal in case of mitral insufficiency; k t -
PCG signal tones in case of mitral insufficiency within the cardiac cycle; k - cardiac cycle number.
But based on the equivalence of representations through translational components (3) and stationary
components, the expression of the PCG signal model in mitral insufficiency has the form [20-
23,28,31,32]:
2
t k t e
ik t
T , t R (4)
k Z
where are k t the steady-state components of the PCG signal in mitral insufficiency.
Mitral insufficiency by nature has the appearance of a noise similar in shape to white noise. Such
similarity should be reflected in model (4) additively in the form of an expression:
2
t k t e , t R
ik t
T n t (5)
k Z
where nt is white noise as a sign of mitral insufficiency in the realization of the PCG signal (according
to the nature of its formation).
Expression (5) ensures the use of the component method for the processing of the PCG signal in the
case of mitral insufficiency as a stochastic process with cyclic characters of a finite nature.
The component method of PCG signal processing based on model (5) ensures the calculation of
correlation components according to the expression [20,24,27,28]:
2
1T0 0 ik
B k u t u kT t kT e T dt , t R
t
T0
(6)
0 0
where is t t m t a centered PCG signal with mitral valve insufficiency; m t - the average
PCG signal in the case of mitral valve insufficiency.
3. Algorithmic support for phonocardiographic signal processing
Having considered the expression (6), the main operations of its implementation are highlighted:
1. Finding the T period of the FСG signal in the case of mitral valve insufficiency [25].
2. Calculation of the estimate of the mathematical expectation m of the PCG signal in the case of
mitral valve insufficiency.
0
3. Centering of the PCG signal in the case of mitral valve insufficiency t .
0 0
4. Calculation of the covariance t u kT t kT of the PCG signal in the case of mitral valve
insufficiency.
5. Counting the components Bˆ k u of the PCG signal in case of mitral valve insufficiency.
In Figure 3, we show all the listed operations in the form of an algorithm, which displays all the
operations of implementing the component method of processing.
Figure 3: Algorithm of component processing of PCG signal in case of mitral valve insufficiency
Figure 3 shows K the number of components, U the maximum length of the time shift, and T the
duration of the heart cycle.
4. Software and results of phonocardiographic signal processing
Software with a graphical user interface was developed in the MATLAB environment to automate
the process of processing the PCG signal when mitral insufficiency is detected.
The results of processing PCG signals in the normal state (Patient A) and in the presence of mitral
insufficiency (Patient B) are shown in Figure 4-7.
Figure 4: Realization of correlated (spectral) components of the PCG signal (Patient A - norm) (axis X
– number of components, Y – shift, Z – power)
Figure 5: Realization of the components of the PCG signal (Patient A - norm) (axis X – component
number, Y – offset) (top view)
Figure 6: Realization of correlated (spectral) components of the PCG signal (Patient B - mitral valve
insufficiency) (axis X – number of components, Y – shift, Z – power, V2)
Figure 7: Realization of correlated (spectral) components of the PCG signal (Patient B - mitral valve
insufficiency) (X axis – component number, Y – shift) (top view)
A comparison of the magnified view of the components from above is shown in Figure 8.
(Patient A - norm)
(Patient B - mitral insufficiency)
Figure 8: Magnified samples of correlation (spectral) components of the PCG signal (top view)
According to the results of the analysis of the correlation components, a slight change in the power
intensity of the components is visible, namely, with mitral insufficiency, the power is more scattered
than in the normal state. The components allow only visual detection of changes in the operation of
human heart valves without quantitative evaluation.
For the quantitative evaluation of correlation (spectral) components, the evaluation of their
averaging by time shifts was used (Figure 9-10).
Figure 9: Realization of the averaged components of the PCG signal (Patient A - norm)
Figure 10: Implementation of the averaged spectral components of the PCG signal (Patient B - mitral
valve insufficiency)
In Figure 9-10 it is visually and quantitatively visible that the maximum values of the averaged
components for a patient in a physiologically normal state (patient A) and a patient with mitral valve
insufficiency (patient B) are concentrated at the same frequencies (identical in structure), but the
amplitude values of the estimates slightly differ from each other, namely, for patients A and B, the
maximum amplitudes are concentrated on the 1st and 7th components. However, an increased power
level of the 2nd, 3rd, 4th, and 5th components, as well as an increase in the maximums of the 1st and
7th components, were noticed in patient B. Such changes quantitatively reflect the manifestations of
mitral valve insufficiency of the human heart.
Therefore, the calculation of correlation (spectral) components is a quantitative parameter for
detecting early changes in the functioning of the valves of the human heart, in particular valve
insufficiency.
5. Conclusions
The work substantiates the mathematical model of the PCG signal as a mixture of a periodically
correlated stochastic process and noise for solving the problem of detecting the insufficiency of the
mitral valves of the human heart. A method and algorithm for processing the PCG signal based on the
component method was developed, which provided a procedure for detecting the insufficiency of the
mitral valves of the human heart based on the averaged estimates of the correlation components.
Software was developed using the MATLAB tool for processing the empirical data of the PCG signal,
which provided the process of calculating correlation components as diagnostic signs that quantitatively
reflect indicators of mitral valve insufficiency of the human heart.
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