A model of finite electrodes in layered biological media: Hybrid image series and moment method scheme

The low-frequency electromagnetic field interaction with layered biological tissue is investigated for electrode array excitation. The problem may be reduced into a system of P (number of electrodes) Fredholm integral equations of the first kind for the electrodes' current distribution. We have shown that the kernel (Green's function) of each integral equation can be expressed by image series. This leads to a most effective inversion of the integral equation system via the moment method, since the moment matrix elements can be expressed explicitly by image series. The outlined procedure is simple to implement and allows estimation of the distributions of low-frequency potential, current, field and power within the multilayer tissue. It may serve as a simplified first-order prototype model for realistic biomedical problems where the dependence on the number of electrodes, tissue layers and their electrical properties must be accounted for. The model has been utilized for the calculation of the electrode array impedance matrix, potential fields, intra-muscular current distributions and isometric recruitment curves (IRC). The simulation results indicate that the IRCs are insensitive to the electrodes' size, however, the inclusion of the bone/fascia layer significantly increases the IRC slope. Furthermore, the simulation scheme, which can be readily implemented for the classification, calibration, verification and interpretation of reported numerical and experimental biomedical data, is also applicable in other problem areas such as geophysical prospecting and electrode grounding in power systems.