314
ANALYSIS OF ELECTROCARDIOSIGNALS WAVELET-SPECTRUM
FACTOR DISTRIBUTION AIMED AT CLASSIFYING CARDIOVASCULAR
DISEASES 1
D.G. Khafizov2, N.V. Parsaev2
2Mari
State Technical University, Lenin Sq. 3, 424000 Yoshkar-Ola, Russian Federation.
tel.: (8362) 455412 e-mail: [email protected]
Histograms of factor distribution of electrocardiosignals wavelet-spectrum are determined and analyzed in normal state and under various pathologies. Probabilities of electrocardiosignals correct recognition by histograms of wavelet-spectrum factor distribution are obtained.
Introduction
Cardiovascular diseases (CVD) are the most
widespread reasons of lethality. The analysis
of the electrocardiogram allows the skilled expert to judge a damage rate of a myocardium.
Thus computer diagnostics of cardiovascular
system condition is meant to help the cardiologist with the analysis of electrocardiograms.
Wavelet transform is the ideal instrument for
the analysis of non-stationary signals such as
electrocardiosignal [1].
Wavelet transform
Wavelet transform allows to localize the characteristic features of electrocardiosignals by
time and frequency, resolving the problem of
signal particularization. Time-scale localization of characteristic features of electrocardiosignals by the results of wavelet transform
depends on the principle of construction the
orthogonal basis of decomposition. Unlike the
Fourier transform traditionally applied for signal analysis the wavelet transform provides
two-dimensional
presentation
of
onedimensional signal under study, for this purpose frequency and coordinate are considered
independent variables. Eventually there is an
opportunity to analyze the properties of a signal simultaneously in both physical and frequency spaces.
By the results of research, given in [2], a
wavelet «Mexican hat» was chosen as a parent
wavelet,
 1

 1

mhat t   exp    t 2   t 2  exp    t 2  ,
 2

 2

which is more adaptive to the reference electrocardiosignal by criterion of resolution in the
field of low frequencies where the greatest
self-descriptiveness of electrocardiograms is
incorporated.
The power spectrum of "Mexican hat" wavelet
without stretch is located within the frequencies ranging from 0 up to 4 Hz, therefore to
study the whole frequency range of electrocardiosignal it is necessary to apply stretching
and compression of parent wavelet.
1 
 t 
 mhat   .
 a, t  
a
 a 
Since the useful spectrum of electrocardiosignal is located within the range between 0,05
and 100 Hz, if we conduct a wavelet analysis
of electrocardiosignal with the change of
wavelet stretch factor а "Mexican hat" within
the range between 1/64 and 16 with gradual
increase as much again the whole useful spectrum of the signal will be studied.
Factors of electrocardiosignals wavelet–
notation are defined as follows:
N 1
1
 k T  j T 
Сi, j 
  f k  mhat 
.
j
i
a
0

2


a0  2 k 0
_______________________________________________________________________
1
Work is executed under the financial support of RFFI, project 07-01-00058а
315
Thus, wavelet notations of electrocardiosignals
(ECS) were obtained (Fig. 1-5).
Fig. 4. Wavelet plane of the electrocardiogram at hypertrophy of the left ventricle
Fig. 1. Wavelet plane of the normal electrocardiogram
Fig. 5 Wavelet plane of the electrocardiogram at an
acute cardiac infarction
Fig. 2. Wavelet plane of the electrocardiogram at WPW
syndrome
Fig. 6. Histogram of factor distribution of normal ECS
wavelet-notation
Fig. 3. Wavelet plane of the electrocardiogram at hypertrophy of the right auricle
The analysis of wavelet-spectra
On the basis of the obtained wavelet-spectra,
the histograms of factor distribution of ECS
wavelet notation were calculated and built
(Fig. 6-10).
Fig. 7. Histogram of factor distribution of waveletnotation at WPW syndrome
316
Fig. 8. Histogram of factor distribution of waveletnotation at hypertrophy of the right auricle (RA)
Fig. 9. Histogram of factor distribution of waveletnotation at hypertrophy of the left ventricle (LV)
Fig. 10 Histogram of factor distribution of waveletnotation at an acute cardiac infarction (CI)
On the basis of the criterion  2 widely used in
biometry the degree of distinction of these histograms (table) was evaluated.
Values
 2 for distributions of wavelet-notation fac-
Cardiovascular diseases
Normal
ECS
WPW
syndrome
Hypertrophy of RA
Hypertrophy of LV
tors of ECS at CVD
WPW Hyper- HyperNormal
Acute
syn- trophy trophy
ECS
CI
drome of RA of LV
0
287,7
287,7 1,3·103 1,8·103 1,7·103
0
1,3·103 1,4·103
1,4·103 1,3·103 1,9·103
0
1,8·103 1,3·103 1,1·103
1,1·103 2,9·103
0
1,7·103 1,9·103 2,9·103 2,5·103
2,5·103
0
From the table it can be seen that for all pairs
of compared histograms actual values of 2
exceed the critical value 2кр  37,65 on the
confidence level   0,05 . Taking this into
account it is possible to draw a conclusion
about the opportunity of electrocardiosignals
recognition of the considered cardiovascular
diseases, on the basis of distribution of wavelet-notation factors.
Conclusion
For classification of CVD diseases we chose
diseases with infringement of cardiac conduction and the possibility of their diagnostics
with the help of II standard lead: WPW syndrome (syndrome of preexcitation of ventricles), hypertrophy of the right auricle, hypertrophy of the left ventricle and acute cardiac
infarction. To find a wavelet-transform we
chose a parent wavelet MHAT ("Mexican
hat") and defined its stretch boarders taking
into account useful spectrum of electrocardiosignals.
On the basis of electrocardiosignal models of
these cardiovascular diseases their waveletnotations were obtained and histograms of
their factor distribution were calculated.
On the basis of  2 method the algorithm of
cardiovascular diseases classification by factor
distributions of electrocardiosignals waveletnotations was developed.
References
1. Dobeshi I. Ten lectures on wavelets. – Izhevsk: Scientific center «regular and chaotic dinamics», 2001,
464 p.
2. Badin О.N., Burukina I.P. Peculiarities of electrocardiographic information analysis with the use of
velevet-transform // Medical equipment. – 2004. –
№ 4. – p.26 – 29.
3. Astafeva N.М. wavelet-analysis: basics of theory
and examples of application (actual problems reviews). – М.: – 1996. 26 p.
4. Bala Y.М. et. al. Atlas of practical electrocardiography/ Y.М. Bala, А.V. Nikitin, V.B. Fuki. – Voronezh: Publishing house of Voronezhskiy University.
– 1983. – 176 p.