Defibrillation of the heart is widespread and well-established procedure for resuscitation of cardiac arrest victims 1. The most accessible approach for electrical cardiac therapy is via external electrodes, placed on selected locations on the surface of the thorax. The electrodes have large contact area (70–120 cm²) 2 and provide high and supposedly uniform current density distribution in the heart, needed for excitation of most myocardial cells, thus forcing them to return to normal rhythm. Many authors have investigated optimal electrode positions and sizes via two-dimensional (2D) 34 and three-dimensional (3D) 567 finite-element method (FEM) models, with the aim of obtaining uniform current distribution in the heart. The uniformity is evaluated by the ratio of the maximum current (which could result in myocardial damage) and the threshold current needed for defibrillation. For example Camacho et al. 5 found values of 2 to 4.7 for the anterior electrode position. Panescu et al. 6 reported that about 25% of the myocardium volume could be subjected to current densities more than 4 times higher than the threshold density.

Another aspect of the problem is the predominance of high current density along the perimeter of large size electrodes applied on human skin. In defibrillation and electrosurgery it can lead to unwanted damage and even severe skin burns 89101112 or electroporation 13, under the electrode perimeter area. In transthoracic pacing, it results in strong excitation of sensory nerve endings and provokes skeletal muscle contractions and pain 1415.

To reduce these adverse effects, Wiley and Webster 8 suggested concentric segmented electrodes with higher resistance in the periphery, by the use of external resistors adjusted to equalise the currents in the separate segments. A similar approach has been considered in more detail by Kim and co-workers 14. They have proposed covering the electrode metal with resistive gel of increasing resistivity toward the periphery, according to a specific relation with respect to the electrode radius. An implementation following such a design was tested on patients undergoing atrial cardioversion 16. The skin damage after defibrillation was assessed by skin biopsy in selected points under the electrodes. The results showed less damage with the use of the modified electrodes compared to the standard ones. However, the authors noted that after separation of the cases where high energies and currents were applied, no difference was found in the skin damage data. This result was not explained. It might be due to breakdown of the higher resistivity electrode layer, or to the overall increase of the current density. Also, the skin resistivity and reaction to increased current density and temperature may very probably be nonlinear.

Another problem is related to skin irritation, resulting from long-term application of the electrodes, when a protective wearable defibrillator-monitor is used 17. In such cases certain specific electrode designs were developed, providing openings for improvement of skin aeration or "breathing" 18.

The aim of the present work is to assess the current density distribution under electrodes of different structure, including shape, size, interfacing layer thickness and specific conductivity.

The problem can be reduced to the solution of the pseudo-elliptic differential equation of Laplace type, provided the effects of quasi-stationarity are neglected.

The solution can be obtained for the scalar electrical potential V in an electrically conductive domain consisting of layers of different specific resistivity ρ. The equation is solved subject to the following boundary conditions:

- Dirichlet boundary conditions imposed on the surface SE_i in contact with the i^th electrode at potential V_i:

- Neumann boundary conditions state that the normal component of the derivative of the potential is zero in the remaining boundary plane (SB), not in contact with the electrodes:

The current density distribution is defined by the potential gradient and the specific conductivity σ of the different regions:

J(x,y,z) = σ (-gradV(x,y,z)),     (4)

here .

In this case, the propagation of the low frequency electromagnetic field is virtually free of the feedback action from eddy currents, as the human tissue is weakly conductive. Therefore, the skin effect can be neglected.

In this study, the finite element method (FEM) was used to estimate the current density distribution in a partially homogeneous conductive medium. It consists of homogeneous layers (Fig. 1a), simulating the electrode metal, the electrode-skin interface and part of a human body. All structures are modeled as purely resistive, as it has been shown that in defibrillation there was no phase difference between applied voltage and current passed through the thorax 1920.

Using software for FEM modelling and 3D-computer graphics (parts of ANSYS 5.7 and MATLAB 5.2), a simplified 3D finite element model with over 50,000 eight-node tetrahedron elements was developed (Fig. 1b). Since the measurements were taken 0.5 mm under the electrode-skin interface, the geometry of the thorax was simplified and simulated as a cylindrical domain (10 cm radius; 10 cm height), with specific resistivity 20 Ωm. This value was chosen as an approximate average of very high and very low conductivities (soft tissue, blood and bone, lung air). The estimated inter-electrode resistance R ≈ ρ l/S ≈ 65Ω (l – distance between the electrodes, S – electrode surface), corresponds to the real conditions in defibrillation. The electrodes, of about 80 cm² area and 1 mm thickness, were located on the surface of the upper and lower cylinder bases. The defibrillation voltage was applied on the group of nodes forming the exterior electrode surface. The inter-electrode potential difference used in all comparative studies was set at 1000 V. This value was selected for convenience, since the relative distribution is independent of the voltage applied. The interfacing gel was simulated by a thick (0.5 – 1.5 mm) low-resistivity (20 – 60 Ωm) layer under the electrodes. Thus a varying layer resistance was represented, in a range of 1.5% to 15% of the total thoracic resistance, i.e. value from 1 to 10 Ω.

Commonly used rectangular electrodes (area ~80 cm²) exhibit high non-uniformity of the current density distribution at the electrode-skin interface. The profile across the corners shows a non-uniformity coefficient of 4.6 (Fig. 2a). The standard circular electrode with the same area yields 32% lower non-uniformity (Fig. 2b).

Smaller electrodes produce higher current density, with slightly lower non-uniformity (Fig. 3). However, the electrode radius cannot be less than 4.7 cm for the minimum area of 70 cm², recommended for efficient defibrillation.

The resistance of the electrode-skin interfacing layer is a major determinant of the maximum current density in the distribution profile. Two electrodes with different radii show equal non-uniformity, assessed by the coefficient K= J_max/J_min, if the under-electrode layer specific resistivity is chosen to provide the same electrode resistance (Table 1). This result was confirmed also for interfacing layers of different thicknesses (Fig. 5). For example, a thick layer with lower specific resistance (ρ = 20 Ωm and 1.5 mm thickness) has the same performance as a thin layer with higher ρ (ρ = 60 Ωm and 0.5 mm thickness). This result did not confirm our expectations that the thickness of the interface has a certain straightening effect on the current lines. A higher layer resistance is associated with lower non-uniformity, but it should not add more than 3–5% to the total resistance of the defibrillation current path. Many authors investigated the advantage of covering the electrode metal with resistive layers of increasing resistivity toward the periphery 1421. Such a technique seems technologically difficult and expensive for disposable electrodes. The use of a ring of higher resistivity along the electrode perimeter seems acceptable, as the resistance in the current pathway was not increased, the maximum periphery current was reduced by 12% and the non-uniformity coefficient dropped to K = 2.71 (1570/580 A/m²). The same result could be achieved with 3 times higher resistance of a uniform layer. However, the problem of technological difficulties remains open.

Various electrode structures with openings for skin "breathing" (Figs. 7,8,9,10,11), increase the effect of non-uniformity, as the current density under the vents drops strongly. However, the distribution non-uniformity becomes negligible with increased distance from the electrode surface, as evident in Fig. 6. The bell-shaped distribution in Fig. 12 is estimated for the central region of the cylindrical thorax model, 50 mm under the interfacing layer surface. Consequently, the current density distribution under various electrode structures relates to effects on the skin, rather than to the defibrillation efficiency.

The current density distribution non-uniformity of circular electrodes is about 30% smaller than that of square-shaped electrodes. The use of an interface layer of intermediate resistivity, comparable to that of the underlying tissues can further improve the distribution. A high-resistivity perimeter ring adds a further 13% improvement without increasing the total interface resistance, hence the resistance to the defibrillation current, which is an important advantage in defibrillation.

The inclusion of skin aeration openings for wearable electrodes disturbs the current paths, but an appropriate selection of number and size provides a reasonable compromise.

VTK solved the problems of adequate FEM modeling, the development of various electrode configurations, and generation and presentation of the current distribution profiles. SPP was responsible for the theoretical basis of the investigation and for the setting the main ideas in the solution analysis. Both authors read and approved the final manuscript.