IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 4, APRIL 2006 1395 A Comparison of Two Models of Electrodes for ECT Simulations Robert Szmurlo, Bartosz Sawicki, Jacek Starzyn ´ski, and Stanislaw Wincenciak Institute of Theory of Electrical Engineering, Measurement, and Information Systems, Warsaw University of Technology, 00-662 Warsaw, Poland This paper discusses some numerical aspects of the simulation of electroconvulsive therapy (ECT). A realistic finite-element model of the human head is used to discuss two approaches to modeling the electrodes applied to human head skin. The first approach models the electrode by a mixed-boundary condition, while the second one uses additional subdomain imitating electrode-to-skin contact for that purpose [three-dimensional (3-D) model]. An algorithm of grid modification used to add an external subdomain modeling the electrode contact resistance is presented. The authors examine the influence of the electrode model on the convergence speed of the iterative solver. The authors state that the 3-D model is better conditioned, and, thus, it converges faster. I. INTRODUCTION D URING electroconvulsive therapy, electric currents are passed through the head between two electrodes placed on the patient’s skin. The electrical path of the ECT stim- ulus includes the ECT output device, the patients stimulus cable, electrodes, scalp, skull, CSF (cerebrospinal fluid), and brain tissue. The time variation of the stimulus is usually a square pulse of 1- to 1.5-ms width, repeated with frequency of 20–150 Hz. The Fourier spectrum of the stimulus can be limited to 20 kHz. The numerical model of ECT of the human head is based on a relatively simple Laplace equation, but the internal structure of the investigated domain is very complicated. The numerical simulations of ECT with realistic models of the human head [2], [6] have confirmed that, during ECT, the extreme values of the electric field (and current density) appear near the electrodes. This observation allows one to suggest that the model of the stimulating electrodes will have a significant influence on the simulation results. The goal of this paper is to discuss two different models of the electrodes and their in- fluence on the complexity of the problem and on the results of simulation. The universal model of the metallic electrode, which can be applied externally to the existing FEM model of the head, will be presented. Two models were used in tests. The first one, called VH here, was created from data from the Visible Human Database [3]. The FE grid of it consists of 674 807 tetrahedral elements and 119 290 nodes. The second model based on the MRI database from the University of Nothingham [9], called NG here, has 2 681 047 tetrahedra and 469 255 nodes. In this model, the re- gions of brain are much more detailed. II. MODELS OF ELECTRODES A combination of human skin, metal electrodes, and elec- trode jelly seems to be relatively simple. Unfortunately, deeper investigations unveil that, in fact, this sandwich (see Fig. 2) is a little bit complicated. We can distinguish the following layers: Digital Object Identifier 10.1109/TMAG.2006.871580 electrode—the round metal plate; electrode jelly—the special gel used to reduce contact resistance between the skin and the electrode; epidermis—the external part of the skin, a very thin, isolating layer; dermis—the main part of skin, low conducting. Several observations are based on the analysis of Fig. 2. • The electrode and the jelly are very good conductors, and we can assume that electrical potential is constant there. There is no need to simulate them, but it is enough to set the proper Dirichlet boundary condition on the contact surface shown with the thick line in Fig. 2. • It is difficult to simulate exactly the shape of the jelly. It can vary very much depending on the amount of gel applied. It will be assumed here that a small amount of the gel is applied, and, thus, it has the same shape as the electrode (usually circular). • The electrode is applied with some force , necessary to assure good contact with the skin. As the result of this force, some deformation of the skin is observed. We sim- ulate this deformation by flattening the skin surface under electrodes. • A model of the epidermis is the hardest problem. This lifeless part of body is protecting soft tissues from ex- ternal conditions, such as temperature, physical contact with other objects, and it also gives good protection against an external electric field. The epidermis should be modeled as a very thin layer of isolator, but its low thickness makes generation of the finite-element mesh very difficult. Thus, the authors decided to model only this part of epidermis, which is just under the electrode. • The dermis is the main part of skin. Its thickness is com- parable to other parts of head, so it is simply included with the other soft tissues of skin in our head model (as shown in Fig. 1). A. Basic Mathematical Model of ECT The displacement currents can be neglected for a given fre- quency range (20 kHz) and, thus, to obtain the field distribution, the following Laplace equation has to be solved: (1) 0018-9464/$20.00 © 2006 IEEE