# Edition Wissenschaft

Edition No. 6 April 1996

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Computation of the Input Impedance of Pacemakers
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The increasing use of procedures in industry, medicine and communication technology utilizing electromagnetic fields with frequencies up to several GHz makes it necessary to investigate the influence of such fields on implanted pacemakers of persons located also in the nearfield of the sources. The nearfield condition is especially fulfilled if mobile telephones working in the C, D or E-net are used. Until now only a few investigations has been made dealing with the influence of external fields on pacemakers with frequencies higher than 30 MHz. The present contribution with the title “Computation of the Input Impedance of Pacemakers” deals with the development and application of a procedure allowing the computation of the input impedance of an implanted pacemaker as well as the disturbing voltage generated by the external field sources. A realistic modelling of both the human body and the pacemaker leads to a very complicated boundary value problem. In order to circumvent this problem, the model is simplified in the following manner:

The human body is substituted by a model constisting of a sequence of planar layers describing the skin, fat and lung tissue, specified by its complex dielectrical constants. Because the pacemaker housing is very thin as compared to the wavelength, it can be replaced by a planar plate consisting of a high conductive material oriented parallel to the layer interfaces. In order to get a uniform description, the round electrode with isolation is substituted by a planar isolated strip with arbitrary conductivity. The mobile telephone is replaced by a planar strip dipole excited by a delta gap voltage source. Subsequently an integral equation for the current density can be formulated with the help of the Green function of the dielectric layers describing the human body. This Green function can be formulated analytically in the so called spectral domain. The electromagnetic influence of the isolation can be considered with the help of a polarisation current density substituting the isolation layer. In order to solve for the current distribution, the Method of Moments is applied transforming the integral equation into a linear algebraic system of equations. For this goal the surface current on pacemaker housing, electrode and exciting dipole are described by subdomain basis functions on rectangular segmentations. In a further step coupling integrals must be evaluated, which are a measure of the electromagnetic interactions of the basis functions. This evaluation is performed by a mixed space domain and spectral domain approach. Very important in this context is the accurate computation of coupling intergrals associated with isolated electrode bends. The width of the planar isolated electrode is determined in such a way that the electromagnetic behavior of the planar electrode is identical with the round isolated electrode by a comparison of the coupling integrals of both models. This model can also be verified by comparing it with a model based on a isolation layer with infinite lateral dimensions.

The input impedance Z_{s} of the pacemaker is determined by exciting the pacemaker with a delta gap voltage source at its input clamps whereas the disturbing voltage is determined by the computation of the short circuit current in the input clamps influenced by the strip dipole outside. The numerical investigation of the input impedance Z_{s} exhibits a very low dependence of the exact orientation of the electrode due to the strong losses of the surrounding tissue. Also due to this fact, a monotone behavior of the input impedance can generally be observed, only in the frequency range below 500 MHz stronger fluctuations occur due to standing waves on the electrode.

The investigation of the disturbing voltage exhibits a strong increase in the
region up to 500 MHz. This effect can be explained by the introduction
of image sources replacing the layer structure in the nearfield. Up to
a frequency of 1500 MHz the disturbing voltage shows a quite complicated
behavior due to standing waves in the layer structure. For frequencies
over 1500 MHz a monotone decrease can be observed because the losses of
the tissue are dominant in this frequency region. Furthermore the distance
dependence of the disturbing voltage was investigated.