A model study of the effects of extracellular shocks on cardiac tissue

M. Al  Akkad,    E Vigmond, and L.J. Leon
Dept. of Electrical and Computer Engineering, University of Calgary,
2500 University Drive NW. Calgary, Alberta, CANADA T2N 1N4

Abstract: A finite element bidomain model of cardiac tissue and use it to examine the effects of stimulation using strong electric shocks is described. It was found that monophasic shocks require less energy to bring tissue in the far field to threshold. Just-threshold biphasic shocks stimulate a much larger region than do just-threshold monophasic shocks. This larger area of influence may be one reason why biphasic shocks are more effective at defibrillating than monophasic shocks.

INTRODUCTION

Although electrical defibrillation has been in clinical use for more than 50 years, the exact mechanism by which a strong electrical shock defibrillates the heart remains somewhat of a mystery. In this paper we describe a mathematical/computer model to study this problem.

METHODS

The underlying model used in this study was the anisotropic  bidomain model[1]. In the bidomain model cardiac tissue is assumed to be made up of an intracellular medium and an extracellular  medium occupying the same space. The potential distribution in the intracellular domain, _i, is assumed to satisfy Poisson’s equation, as is the potential in the extracellular domain, _e. The two media are also assumed to be connected electrically through a Hodgkin-Huxley[2] type membrane. The bidiomain equations can thus  be written as follows:

                                                       (1)

                                          (2)

                                                (3)

where , I_m  is the transmembrane current density, and are the intracellular and extracellular conductivity tensors respectively, ß is the surface to volume ratio of the cardiac cells, I_e is an extracellular current stimulus, C_m is the capacitance per unit area, V_m is the transmembrane voltage which is defined as _i- , and I_ion is the ionic current, in this case described by the Beeler-Reuter model as modified by Drouhard and Roberge [2] . The model was implemented using the  Finite Element Method. All software was written in our laboratory using C. The bidomain modeling software is extremely flexible allowing a different conductivity tensor at each node. This allows for the inclusion of variations in fiber direction as well as  regions with higher or lower  extracellular and intracellular conductivity value. The model preparation used in this study consisted of 300x200 nodes representing   a  sheet of cardiac tissue length 3 cm and witdth 2 cm (see Figure 1). An obstacle region of dimensions 0.1x1.6 cm² was inserted in the middle of the tissue. Within the obstacle region, the intracellular conductivities were reduced to 25% of that of the rest of the tissue. The middle point of the top edge of the preparation was grounded to be the reference point.  An anode and a cathode electrode were placed in the extracellular medium on the long axis of the sheet 0.3 cm from either end. The electrodes were small square regions with a cross-section of 0.1x1 cm².  Two different waveforms were applied through the stimulating pair, an 8 millisecond monophasic and an 8 millisecond biphasic.

Figure 1.  The model preparation showing placement of both Anode and Cathodes. All measurements are in cm.

The extracellular conductivity values throughout the tissue are: 0.236 S/m (transverse) and 0.625 S/m (longitudinal). The intracellular conductivities within the obstacle region were: 0.00475 S/m (transverse) and 0.0435 S/m (longitudinal) while those of the bulk of the tissue are: 0.019 S/m (transverse) and 0.174 S/m..

RESULTS

In this study we examined the effects of waveform shape on the stimulation process. We considered two cases: 1) a monophasic waveform of 8 milliseconds in durations and 2) a biphasic waveform 4 milliseconds for each polarity. The minimum current to stimulate in the far field region was found. In all cases stimulation occurred at the boundary of the obstacle region.

In the case of the monophasic shock a current of 855 microA/cm² was required. In the case of the biphasic shock a stimulus current of 1155 microA/cm² was needed.

It is interesting to compare the voltage profiles 1.4  milliseconds after the break of the shock. Although it required less current to bring tissue in the far field to threshold, using a monophasic shock, a just-superthreshold biphasic shock had a far more significant effect. This is illustrated clearly in Fig.1. The top panel shows the transmembrane potential distribution

Figure 2. Top Panel: Transmembrane Potential Distribution along the central axis of the sheet at 1.4 ms after the break of an eight millisecond monophasic shock.  Bottom Panel: Transmembrane Potential Distribution along the central axis of the sheet at 1.4 ms after the break of an eight millisecond biphasic shock.

along the central axis of the sheet, 1.4 milliseconds after the break of the shock. The tissue just under the cathode is depolarized to almost 200 mV, with one small region at the boundary of the obstacle region depolarized. In comparison the bottom panel of Fig. 2 shows the transmembrane potential distribution along the same line following a just threshold biphasic shock. In this case, the maximum voltage in the preparation is roughly 125 mV. More importantly, virtually the whole horizontal line has been stimulated. Activity propagated from both electrodes, and from both edges of the obstacle region towards the center of the sheet.

DISCUSSION

In this paper we describe a finite element bidomain model of cardiac tissue and use it to examine the effects of stimulation using strong electric shocks. We found that although monophasic shocks require less energy to bring tissue in the far field to threshold, just-threshold biphasic shocks stimulate a much larger region. This larger area of influence may be one reason why biphasic shocks are more effective at defibrillating than monophasic shocks. A second interesting observation is that monophasic shocks cause a much higher depolarization (and hyperpolarization) than do biphasics. This could possibly lead to more significant electroporation effects.

Acknowledgments:  Work supported by the NSERC and startup grants from the University of Calgary.

REFERENCES

Number references consecutively in square brackets in the order of their first citation in the text [1]. Do not use any footnotes.  List all references in a reference section at the end of the paper in the style indicated below:

[1] Henriquez CS, Simulating   the electrical behavior of cardiac tissue using the bidomain model. Critical Reviews in Biomedical Engineering. 21(1):1-77, 1993

[3] J. P. Drouhard and F. A. Roberge, Revised formulation of the Hodgkin-Huxley representation of the sodium current in cardiac cells</i>," Computers and Biomedical Research, vol. 20, pp. 333--350, 1987