Технические науки\ 12. Автоматизированные системы управления на производстве

 

Savostin A.A., Ivel V.P.

The North Kazakhstan state university after M. Kozybaev, Kazakhstan

MODELING OF THE MAN’S TYPICAL ELECTROCARDIOSIGNAL

 

Annotation

In the article the problem of modelling of bioelectric activity of heart is surveyed. Principles of creation of the model which is capable to synthesise a signal which form corresponds to a typical man's electrocardiosignal are pointed out. The model allows to define morphology of PQRST cycle, to set frequency of heart beat, to take into account a deflection of an isoelectric line because of breath and to establish noise level and frequency of digitization. This model can be used for estimation of biomedical methods of handling and analysis of signals, when holding the metrological control of the cardiologic equipment etc.

 

Keywords: morphology of PQRST cycle, electrocardiosignal, modelling, electrocardiogram, bioelectric activity of heart, Matlab.

 

I. Introduction

In spite of dynamical development of diagnostic methods and pathology treatment of the cardiovascular system, one of the cores still have analysis of electrocardiosignal (ECS) by means of electrocardiogram (ECG). ECS represents a difference of potentials, changing in time according to oscillations of magnitude and direction of electric field, which arises between various points on body surface because of excitation and repolarization of heart [1]. Thus, ECS reflects the character of cardiac muscle functioning. Its registration with the subsequent extraction of the helpful information is the diagnostic problem which allows to analyze a deflection of a signal form from norm in real time and to make a continuous monitoring of a palpitation rhythm.

Instantaneously with the performance of a diagnostic problem a number of difficulties arises which is easily solved without using real ECS, fixed in clinical conditions. For example, when constructing electrocardiologic systems of recognition reference models of ECS belonging to different classes of pathologies can be demanded.   ECS model of a man is effective at an assessment of algorithms of statistical data calculation; with its help it is possible to make a comparison of various methods of a signal handling.  Synthesis of ECS can be fulfilled with arbitrary frequencies of sample and noise levels, it allows to estimate an overall performance of the cardiologic equipment. Carrying out the metrological control of apparatus and/or program parts of the modern electrocardiograph it is also efficient to use models of ECS in order to keep to accepted standards.

 

II. Problem statement

ECS imitation economizes time and eliminates the difficulties connected with invasive and non-invasive methods of a real signals registration, gives the possibility to get normal and pathological forms of ECS without using electrocardiograph, allows to receive morphological elements of the ECG practically of any voltage and duration.

Everything that was told previously makes the creation of model of the typical ECG of the man, which reflects bioelectric activity of heart, actual. It is necessary to solve a so-called inverse problem of cardiology from the bioengineering approach point of view to cardiologic researches. Its formulation can consist of two parts:

–              Model construction of known typical deflections of morphological characters of the electrocardiogram;

–              Definition of mathematical model ECG as a summarized equal in effect electrical activity (transmembrane potentials) of separate cells of a myocardium.

The sense of the second part consists in the following: electric generators of heart throughout a warm cycle are set; it is required to define electric potentials on a body surface during the same span. In a degree it has theoretical character and will not be surveyed further.

There is no single principle of soluting the first part; however, while using a reference signal of certified trials of the cardiologic equipment there is a following condition among others – presence of the list of obligatory parameters of ECG indications.

 

III. Outcomes

While modeling ECG it is necessary to secure morphological elements of a signal and to compare it with the conforming approximating functions. ECG will be surveyed as a sequence of intervals (segments) and peaks of half-waves (fields of approximating functions). While extracting the approximating functions it is necessary to consider that existing algorithms of electrocardiograms decoding are based on the concept of peaks of curves, and there is no supposition about the nature of peak of half-wave [2]. Therefore the extraction of the equation of half-wave in this case can have arbitrary character.     

Parabolas, potential functions on a certain interval, Gaussian impulses etc. can represent such equations (fig. 1).

In this case function sin(x) (cos(x)) on the interval [0; T], where T is the function period. This extraction can be explained by the following: using of fields of parabolas or sinusoids with on interval [0; T/2] as approximating functions (fig. 1, a, b) on diagram of synthesized ECS curves unnatural (abrupt) transitions between lines of next elements ECS appear (fig. 2). The similar situation is observed at linear QRS interpolation of a complex when the complex is represented in the form of broken line.

 

a)

b)

c)

d)

Figure 1 – Variants of application of various approximating functions on an example of the P-wave of the electrocardiogram:

a) b) c)

d)

 

Figure 2 – Abrupt transitions between adjoining ECS elements

 

This effect can be eliminated by means of a low-frequency filtration; however, it will lead to considerable distortions of an initial signal and essential complicating of algorithm. Use of Gaussian impulses (fig. 1, c) solves this problem, but brings the new ones connected with an infinite expansion of the function. Function application helps to avoid the specified difficulties, and also the onset of breaks between the next elements at the inexact setting of parameters. As a result all ECS half-waves will be presents in the form of function sin(x) (fig. 1, d) on the interval [0; T] of various voltage and duration (depending on duration of a morphological element di).

  The panel of such synthesised morphological elements typical in their voltage and duration for the normal human ECG [3] is shown on figure 3. Each i-th element is described by the equation like:

 

                                         (1)

 

  Here Ai is voltage element, ti is time, and di is duration (the function period). Function of a cosine (1) is even and therefore is more convenient in use.

Figure 3 – Representation of half-waves of an electrocardiogram in the form of functions cos(x)

 

For shaping of ECS elements of the set form and for observance of sequence of their following, the panel of frames enters. The beginning of each panel of frames coincides with the beginning of a current cardial cycle and sequentially moves with the beginning of the following cardial cycle. The axis of abscissas corresponds to the ECS isoelectric line, therefore the first moment of a deflection of an initial morphological element from an isoelectric line is considered to be the frame beginning in a current cardial cycle.

 

IV. Conclusion

As a result, synthesised ECS represents a moved panel of cardial cycle functions consisting of a combination of elements of the phylum (1) which frequency of following along an axis of abscissas corresponds to frequency of heart reductions.

Modelling of ECS was made with the use of standard instruments of mathematical matrix laboratory Matlab. The results of modeling are shown on figure 4.

Figure 4 – The fragment of the synthesised electrocardiogram

 

Deflection of an isoelectric line from zero because of breath can be imitated by adding to the basic signal of function

 

                                                                                             (2)

 

Where А0 is voltage, f is a respiration rate. For realness of synthesised signal to the ECS model noise, received under the law of uniform distribution is added.

In the conclusion it is necessary to notice that in the presented model of ECS generator imitation of an irregular worm rhythm is not provided because of specificity of this problem, but such possibility is present at a certain modification of algorithm.

 

Literature

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2.                Вайсман М. В., Прилуцкий Д. А., Селищев С. В. Алгоритм синтеза имитационных электрокардиосигналов для испытания цифровых электрокардиографов: Научно-технический журнал "Известия высших учебных заведений. Электроника", 2000 № 6. - с. 94-100;

3.                Струтынский А.В. Электрокардиограмма: анализ и интерпретация: Учебное пособие – М.: ООО «МЕДпресс», 1999. – 224 с.;

4.                Дьяконов В.П. MATLAB 6/6.1/6.5 + Simulink 4/5 в математике и моделировании: Полное руководство пользователя. М.: СОЛОН-Пресс. – 2003. – 567 с.