Approach to the use of the fluctuation index for the classification of diseases based on the wavelet-package decomposition in the electromyography Текст научной статьи по специальности «Медицинские технологии»

ТЕХНИЧЕСКИЕ НАУКИ

ПОДХОД К ИСПОЛЬЗОВАНИЮ ФЛУКТУАЦИОННОГО ИНДЕКСА ДЛЯ КЛАССИФИКАЦИИ ЗАБОЛЕВАНИЙ НА ОСНОВЕ ВЕЙВЛЕТ-ПАКЕТНОГО РАЗЛОЖЕНИЯ В ЭЛЕКТРОМИОГРАФИИ Исмайылова К.Ш. Email: Ismayilova17111@scientifictext.ru

Исмайылова Камала Ширин кызы - кандидат технических наук, доцент,

кафедра приборостроительной инженерии, Азербайджанский государственный университет нефти и индустрии, г. Баку, Азербайджанская Республика

Аннотация: разработана процедура вычисления флуктуационного индекса нервно -мышечной системы на основе вейвлет-пакетного разложения биоэлектрических сигналов, полученных при регистрации стимуляционной электромиограммы мышечных волокон в норме и в патологиях карпального туннельного синдрома, кубитального туннельного синдрома и полиневропатии. Показана возможность классифиции различных видов заболеваний нервно-мышечной системы по значению флуктационного индекса, поскольку графики функций dn> естественным образом разделяются и упорядочиваются.

Ключевые слова: вейвлет-пакетное разложение, стимуляционная электромиограмма, флуктационный индекс, степень хаотичности.

APPROACH TO THE USE OF THE FLUCTUATION INDEX FOR THE CLASSIFICATION OF DISEASES BASED ON THE WAVELET-PACKAGE DECOMPOSITION IN THE ELECTROMYOGRAPHY Ismayilova K.Sh.

Ismayilova Kamala Shirin - PhD on Engineering, Associate Professor, DEPARTAMENT OF INSTRUMENTATION ENGENEERING, AZERBAIJAN STATE OIL AND INDUSTRY UNIVERSITY, BAKU, REPUBLIC OF AZERBAIJAN

Abstract: based on the wavelet package decomposition of bioelectrical signals obtained during the registration of the stimulation electromyogram of muscle fiber, there was developed a procedure of calculation of the fluctuation index of the neuromuscular system in norm and in pathologies carpal tunnel syndrome, cubital tunnel syndrome and polyneuropathy. There was shown the possibility of classification of different kinds of neuromuscular diseases based on the value of the fluctuation index, as dn> function charts are divided and ordered naturally.

Keywords: wavelet-package decomposition, stimulation electromyogram, fluctuation index, chaotic state degree.

UDC: 616.74

Dynamic state of biologic systems leads to the fact that majority of biomedical signals are accidental and non steady by nature. It means that characteristics of signals such as mean value, dispersion and power spectrum density change in time. Therefore, signals of diagnostic systems shall be analyzed within long periods of time including different states of the system, and the results shall be assessed in terms of respective states [1, 2].

Unlike the Fourier transformation using smoothing windows, it is good temporal locality of wavelets that gives required means for the increase of spectral compoints frequencies necessary for the revelation of short-time local features of signals. To ensure effective designing of wavelets it is necessary to have clear idea about the advantages and disadvantages of basic functions of wavelets using different classifying signs; settlement of problems of diagnosis of the state, choice of wavelets according to their types and features seems effective.

Traditional stochastic and spectral methods used in the analysis of electromyograms do not often identify the position or dynamics of the applied system. Development of analysis methods of complex systems in information processing and compatibility of the used automated systems makes it possible to find new opportunities in the issues of diagnostics of bioelectric signals [3, 4].

Wavelet transformation in the analysis of signals has unique capabilities of recognition of local characteristics of complex and unsteady systems. It depends of the division of localized basic functions in the time and frequency space of temporary signal realization. Wavelets make it possible to identify not only frequency characteristics of the arbitrary signal, but also to fix the time their display [5, 6].

For EMG signals of the considered set of diseases (carpal tunnel syndrome, cubital tunnel syndrome and demyelinating polyneuropathy) examples of different levels of wavelet decomposition not wrenching the resolution ability of the signal are given.

When carrying out wavelet-package decomposition of the EMG signal we'll change the resolution scale of frequencies through the replacement of resolution level j with m=J-j (J - is the largest level of resolution), with the m=0 value corresponding to the j=J level, and the root of the tree of signal decomposition will locate at the m=0 level. Wavelet-package coefficients corresponding to the m frequency band and k (0<k<2m-1) frequency subband shall be denoted through Zmn(i).Each x(n)(tj), i=(n-1) N,..., nN-1 n-segment (fragment) of the N length of the EMG-signal in each freaquencysubband will correspond to 2m+k (k=0,1...1,2m-1) of sequences of wavelet-package coefficient of of the N/2m length

N

Îioi i = (n-1) + k-Nn -!)• N + (k +1)

N

2

2

m

-1

(1)

Let us calculate mean powers of wavelet coefficients J Z(n) (i) I, in the feubband of the

1 m,kv

m frequency band:

P(n) = I

i,eA(n), m,k

( )2/

N 2m

where A(n), m,k

N

(2)

N

(n-1)• N + k•jm,(n-1)N + (k +1) m

-1

is the

segment of the frequency axis, which corresponds to the ra=2m+k frequency of x(n)(ti) signal at i e A(n)=[(n-1 )N,nN-1 ].

We would like to show the possibility to use signs (2) for the determination of the entropy of the behavior of the system of muscular fibers shown in the EMG of rest of the

examined patient by using the fluctuation index.

(n) (n)

For this purpose, setting j:=m andw^.-,' := P\ , , we'll insert mean values by k subbands of the value

< w(n) >= 2~J1 w(n) (3)

jk k=0 Jk

For standardized coefficients

z^ = w(n)l < W^ > (4) jk jk jk ()

equation in implemented

z(n = 2~J 2Jf\ = 1 (5)

Jk k=0 Jk

To carry out quantitative assessment of the fluctuation based on the k of sequence

(n)

element [z^ }, one shall determine

K(n) =< z(n In z(n >= 2~j j z(n ln z(n (6) j jk jk k=0 jk jk

Setting p(^) := 2 j • z(^) and taking into considerationthe equation

jk ' jk

2 k1 №=i (7)

k=0 jk

Shannon entropy may be determined as

S (n) = -j-1 ln j k=0 jk jk

(8)

Connected with K(n) by the ration

j

S(n) = j ln2 - K(n) (9) j j

Let us insert the factorial moment

Cp\M) =<(z(n>)p >= 2-j2j\z(n))p (10) P jk k=0 jk where dependence on j is expressed through the M=2J value. From the expression (6) we obtain

dC(pi) = 2jY (z(n))p ■ ln z(n) (11) dp p k jk jk where with p=1 we find

^C Pn)| 1 = K(n) (12) dp p 'p=1 /

dp p 'p=1 j If C(n) (M) has scaling feature

Cpn\M) * M^ (13) then by using expressions (10) and (12), we'll obtain

K(n) M = v{n) j In 2, (14)

where

u(n) = d W(n)\ (15)

1 dp^p \p=1 ()

Fluctuation index a(n) is determined in the following manner

j(n)=1-|(n) (16)

From (14) and (16) we'll obtain

CT(n)=

1 .c(n)

• ^ (17)

j ln2 J

Consequently, increase ofo(n) leads to the increase of Sjn) entropy.

The figure gives the dependence of the fluctuation index a(n) on the number n of fragments with m=4.

0.25

0.2

0.15

0.1

0.05

*

» t

\

1

* \ i

\ \ /

» / ■■

\ \ \ \\ / . t ? /■* »

„ x 'A /, / /*

\\\ ;// * /.* ■ /

1 2 3 4

—♦— Polyneuropathy

Cubital tunnel syndrome —— Carpal tunnel syndrome —*—Norm

m

Fig. 1. Dependence of the fluctuation index on the number n offragments with m=4

The figure shows that on every fragment n inequalities are implemented

¿en j j

Here increase of the resolution ability m of the wavelet-package decomposition increases the degree of separation of thevalues of the fluctuation index for considered diseases.

Thus, fluctuation index j(n), calculated by the formula (16) is an informative sign characterizing the degree of the chaotic state of the studied neuromuscular system. Based on the value of the indicator it is also possible to classify different kinds of neuromuscular diseases, as function graphsj(n)are divided and ordered naturally. For a certain studied set of diseases the biggest valuej(n) is reached for the most pathologic diseases.

References / Список литературы

1. Rangayyan R.M. Biomedical Signal Analisys. IEEE and Wiley. New York. NY, 2002.

2. Hwa R.C. Scaling exponent of multiplicity fluctuation in phase transition// Phys.Rev. D47. P. 2773-2781.

3. Henneberg K.A. Principles of electromyography in The Biomedical Engineering Handbook. Bronzino J. Ed. Boca Raton. Fl: CRC Press, 1995. P. 191-200.

4. Coifman R.R., Wickerhauser M.V. Entropy-based algorithms for best basis selection. // IEEE Trans. on Inform. Theory, 1992. V. 38. № 2. P. 713-718.

5. Ecmann J.P., Ruelle D. Ergodic theory of chaos and strange attractors // Rev. Mod. Phys., 1985. V. 57. № 3, P. 617-656.