Estimation of current density distribution under electrodes for external defibrillation
 Vessela Tz Krasteva^{1}Email author and
 Sava P Papazov^{1}
DOI: 10.1186/1475925X17
© Krasteva and Papazov; licensee BioMed Central Ltd. 2002
Received: 4 October 2002
Accepted: 16 December 2002
Published: 16 December 2002
Abstract
Background
Transthoracic defibrillation is the most common lifesaving technique for the restoration of the heart rhythm of cardiac arrest victims. The procedure requires adequate application of large electrodes on the patient chest, to ensure lowresistance electrical contact. The current density distribution under the electrodes is nonuniform, leading to muscle contraction and pain, or risks of burning. The recent introduction of automatic external defibrillators and even wearable defibrillators, presents new demanding requirements for the structure of electrodes.
Method and Results
Using the pseudoelliptic differential equation of Laplace type with appropriate boundary conditions and applying finite element method modeling, electrodes of various shapes and structure were studied. The nonuniformity of the current density distribution was shown to be moderately improved by adding a low resistivity layer between the metal and tissue and by a ring around the electrode perimeter. The inclusion of openings in longterm wearable electrodes additionally disturbs the current density profile. However, a number of smallsize perforations may result in acceptable current density distribution.
Conclusion
The current density distribution nonuniformity of circular electrodes is about 30% less than that of squareshaped electrodes. The use of an interface layer of intermediate resistivity, comparable to that of the underlying tissues, and a highresistivity perimeter ring, can further improve the distribution. The inclusion of skin aeration openings disturbs the current paths, but an appropriate selection of number and size provides a reasonable compromise.
Background
Defibrillation of the heart is widespread and wellestablished 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 cm^{2}) [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 twodimensional (2D) [3, 4] and threedimensional (3D) [5–7] finiteelement 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 [8–12] 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 [14, 15].
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 coworkers [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 longterm application of the electrodes, when a protective wearable defibrillatormonitor 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.
Method
The problem can be reduced to the solution of the pseudoelliptic differential equation of Laplace type, provided the effects of quasistationarity are neglected.

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)
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.
Using software for FEM modelling and 3Dcomputer graphics (parts of ANSYS 5.7 and MATLAB 5.2), a simplified 3D finite element model with over 50,000 eightnode tetrahedron elements was developed (Fig. 1b). Since the measurements were taken 0.5 mm under the electrodeskin 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 interelectrode 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 cm^{2} 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 interelectrode 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) lowresistivity (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.
Results
Standard electrode configurations
Circular electrode analysis
Comparative results for two electrodes with different radii.
Electrode Radius [cm]  Interfacing layer (5 mm thickness)  J_{max}/J_{min} [Am^{2}]  K=J_{max}/J_{min}  

ρ [Ωm]  R [Ω ]  
5  20  1.25  1780/570  3.12 
2.5  4  1.25  2450/800  3.06 
5  80  5.1  1490/550  2.71 
2.5  20  5.1  2150/780  2.76 
Various electrode configurations
Discussion
Commonly used rectangular electrodes (area ~80 cm^{2}) exhibit high nonuniformity of the current density distribution at the electrodeskin interface. The profile across the corners shows a nonuniformity coefficient of 4.6 (Fig. 2a). The standard circular electrode with the same area yields 32% lower nonuniformity (Fig. 2b).
Smaller electrodes produce higher current density, with slightly lower nonuniformity (Fig. 3). However, the electrode radius cannot be less than 4.7 cm for the minimum area of 70 cm^{2}, recommended for efficient defibrillation.
The resistance of the electrodeskin interfacing layer is a major determinant of the maximum current density in the distribution profile. Two electrodes with different radii show equal nonuniformity, assessed by the coefficient K= J_{max}/J_{min}, if the underelectrode 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 nonuniformity, 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 [14, 21]. 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 nonuniformity coefficient dropped to K = 2.71 (1570/580 A/m^{2}). 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 nonuniformity, as the current density under the vents drops strongly. However, the distribution nonuniformity becomes negligible with increased distance from the electrode surface, as evident in Fig. 6. The bellshaped 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.
Conclusion
The current density distribution nonuniformity of circular electrodes is about 30% smaller than that of squareshaped electrodes. The use of an interface layer of intermediate resistivity, comparable to that of the underlying tissues can further improve the distribution. A highresistivity 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.
Declarations
Acknowledgements
The authors would like to express their deep gratitude to Prof. I. Daskalov for the scientific guidance and help in the biomedical engineering aspect of the study. The authors thank the Technical University of Sofia for granting the use of the FEM software.
Authors’ Affiliations
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