A SYSTEM FOR THE COMPUTER VISUALIZATION...

In current research into the processes of propagation of excitation over the heart, together with traditional electrophysiological methods an ever increasing role is being played by autowave approaches based on the close analogy the myocardium and other active media of a biological, chemical and physical nature [1]. In such approaches the myocardium is represented by a three-dimensional active medium with energy sources distributed over it. The propagation of excitation over the heart, which serves as the trigger mechanism of mechanical contraction, is regarded as an autowave which keeps its form, amplitude, velocity and other parameters constant thanks to the non -linearity of the medium and which pumps energy from distributed sources. Special points in the heart (pacemakers, ectopic foci and sites of the emergence of additional conduction pathways) are interpreted as autowave sources.

An experimental investigation of the propagation of excitation in the heart is now based on computer visualization (electrophysiological mapping) [2]. This method used the computational power of a computer for rapid digital recording of the electrocardiosignals (electrograms) simultaneously at many points of the myocardium and the restoration, on the basis of them, of the course of propagation of the wave. The result of visualization is a map of the spread of the wave in the form of a set of isochrones corresponding to the successive positions of the wavefront.

An experimental investigation of autowave patterns in the heart involves special procedural complexities. These difficulties are largely due to the specific features of the ectopic excitation sources, such properties of them as wavelength, unsteadiness, the close dependence of the conditions of reproduction on the state of the myocardium and the short time of existence. A study of the patterns of excitation of the myocardium requires the solution of a number of problems, in particular, a considerable increase in the accuracy of the recording of the electrophysiological data, the development of methods for observing unstable, spontaneously evolving processes, and improvements in the visual representation of wave patterns.

The aim of the present research was to develop a method for the computer visualization of the autowave patterns on the surface of the heart tissue. We developed an algorithmic system and software for exploring the evolution of autowave patterns, making it possible to provide an adequate representation of the spread of excitation with complex trajectories and to distinguish the most important details of the behaviour of the excitation sources.

THE COMPUTER VISUALIZATION SYSTEM

From experience using the Volna apparatus constructed in the Institute of Biological Physics [3], we devised a new system for the computer visualization of the of the propagation of excitation waves in the myocardium. Part of the system realising the user interface, processing and storage of experimental data operates in the Smalltalk/V 286 program of Digitalk. The subroutines for servicing the equipment are written in Assembler language for an IBM PC. The system was designed using the Grady Booch methodology [4]. The system is constructed on the basis of the graphic multiwindow user interface [5]. It offers the following options.

In conducting the experiment it is possible to record simultaneously signals from 64 electrodes (32 electrodes each for the endocardium and the epicardium of the preparation). The sampling frequency for each electrode is 1 kHz. It is possible to use 64, 128 or 256 electrodes without updating the system. During the experiment the system continuously forms a base sequence of stimulation pulses on the stimulating electrode. The experimenter can arbitrarily fix their amplitude, period and duration. For data recording the system generates independent sequences of test (out-of-turn) pulses over one or two electrodes. Eim pulses are used to initiate tachyarrythmia. For each sequence the experimenter can indicate the number of pulses in it, the initial duration, amplitude and the period of the pulses and also the gains in amplitude and period.

The signals recorded during the course of the experiment are inspected in the windows of the electrograms (Fig. 1). An arbitrary number of such waves may be simultaneously opened. Processing of the electrograms consists in fixing tags marking the instants of activation. The program allows this operation to be performed automatically or manually. On the basis of the data on the position of the tags, maps of the spread of excitation are automatically plotted (Fig. 2). The operator may indicate the time interval between the isochrones.

To analyse the electrical activity of the preparation as a whole the system may compute and visualize the function E(t) (Fig.3). The pseudoECG E(t) is calculated by the program from the formula

                    s cosQ D S _N
            E(t) = ------------------ S [ Uek_i(t) - K₂ Uep_i(t) ]
                      4p s _ex r_L^{2
     i=1}

where
s is the conductivity of the tissue,

Q is the angle between the normal to the surface of the preparation and the direction to the point at which the pseudoECG is calculated,

D S is the area of the elementary portion,

s_ex is the conductivity of the extracellular medium,

r_L is the distance between the surface of the preparation and the point at which the which the pseudoECG is calculated,

U_{ek_i}(t)and U_{ep_i}(t) are the voltages at the instant of time t on the ith electrode of the matrix of the endocardium and epicardium, respectively, and

K₂ is a coefficient allowing for the different input resistance of the electrodes of the endocardium and epicardium. To inspect E(t), a special window is introduced (Fig. 4). The electrograms, the pseudoECG, and the maps plotted by the system may be printed out. In addition, it is possible to convert them to a form suitable for processing in other graphic packages, such as Harvard Graphics and SigmaPlot (see the caption to Fig.3).

DISCUSSION

The main improvement over the previous version of the Volna apparatus is the use of an integrated medium based on a multiwindow interface enabling one to combine into one program such functions of the system as control of the conduct of the experiment, processing, presentation and storage of data. One of the deficiencies of the previous system was the limitation on the duration of the recorded electrograms (not more than 4-s use of 64 electrodes at a sampling frequency of 1 kHz).

In the new system this deficiency is eliminated and the recording time is determined only by the computer memory capacity. In addition, the set of regimes for generating the stimulation pulses of the preparation on data recording is greatly extended. The data processing of the experiments conducted using the system made it possible to demonstrate the link between the pseudoECG characteristic of polymorphous arrhythmias (Fig.4) and complex changes with time in the wave patterns recorded simultaneously from the epicardium and endocardium (Fig. 5). In some cases these changes were in the form of drift of the ectopic source of excitation. Figure 6 shows the drift of the core of the reverberator recorded in one experiment. The modified version of the Volna apparatus greatly extends the possibilities of the experiment with the aim of seeking new approaches to exploring the mechanisms of disturbance of cardiac rhythm.

This research was supported financially by the Soros International Foundation and the Russian Foundation for basic Research.

REFERENCES

ILLUSTRATIONS

Fig.1. Electrograms simultaneously recorded at the sites of extracellular electrodes. Two windows are shown differing in the number of electrograms. The segments denote the tags of the instants of activation of the myocardium under the corresponding electrode. Each window may contain any number of electrograms, which is set by the position of the vertical band denoted by hatching on the right of each window. The time interval for which the electrograms are drawn may also be set by the position of the horizontal band denoted by hatching under each window. In the course of work with the window in its upper part, information may be gleaned on the channel number, the instant of time and the first derivative of the signal in time at the point indicated by the user.

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Fig.2. Map of the propagation of excitation over the surface of heart tissue. The windows of the map of the propagation of the excitation wave present above the window of the electrograms is shown. The map in the left half of the window corresponds to the endocardium and in the right half to the epicardium. The lines on the map (isochrones) correspond to the position of the excitation wave front at different instants of time. For each isochrone the instant of time corresponding to it is indicated (the numbers in the rectangles). The points denote the positions of the recording electrodes, and the numerals below them denote the electrode numbers. The numbers above the points correspond to the instants when the excitation wave passes (in ms) under the corresponding electrodes. In constructing the isochrones we used the method of linear interpolation followed by approximation by splines. In the upper part of the window, the window number in the series of the total number of windows in the given experiment is indicated.
The time interval of recording in ms is also indicated.

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Fig.3. PseudoECG. The graph is plotted from the SigmaPlot 2.01 Program of Jardel Scientific.

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Fig.4. PseudoECG window. An example of a window containing the pseudoECG constructed by the program is shown. During work with the window, in its upper part the instant of time and value of the pseudoECG at the point indicated by the user is shown.

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Fig.5. Wave pattern recorded simultaneously on the endo- and epicardial surface of the preparation of the wall of the right ventricle. The wave pattern numbers with the markings endo or epi are indicated on the left of the image the corresponding surfaces of the preparation. The relative instants (for each wave) of activation in ms are indicated next to the corresponding isochrones. The arrows denote the directions in which excitation was carried out. The broken arrows show the conduction of excitation from one surface of the preparation to another. The transition regions are shaded. Next to them are shown the absolute values of the instant of the transition in ms. The functionally non-exited regions are blackened.

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Fig.6. Drift of the nucleus of the vortex on the endocardium. The points denote the positions of the recording electrodes. The position of the electrodes coincides with that on the right side of the map in Fig.2. The ellipses and lines denote the positions of the nucleus. The sequence of position of the nucleus is nominally denoted by the numbers in the squares. The rate of drift changes with time.

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A SYSTEM FOR THE COMPUTER VISUALIZATION OF THE PROPAGATION OF EXCITATION WAVES IN THE MYOCARDIUM

THE COMPUTER VISUALIZATION SYSTEM

DISCUSSION

REFERENCES

ILLUSTRATIONS