An analytic solution is derived for the magnetic field generated by current sources located in a piecewise homogeneous volume conductor. A linear discretization approach is used, whereby the surface potential is assumed to be a piecewise linear function over each tessellated surface defining the regions of differing conductivity. The magnetic field is shown to be a linear combination of vector functions which are strictly dependent on the geometry of the problem, the surface tesselation, and the observation point.

A comprehensive review of factors affecting the accuracy of the boundary element method (BEM) for calculating surface potentials is presented. A relative-error statistic is developed which is only sensitive to calculation errors that could affect the inverse solution for source position, and insensitive to errors that only affect the solution for source strength. The factors considered in this paper are: numerical approximations intrinsic to the BEM, such as constant-potential versus linear-potential basis functions and sharp-edged versus smooth-surfaced volumes; aspects of the volume conductor including the volume shape, density of surface elements, and element shape; source position and orientation; and effects of "refinements" in the numerical methods. The effects of these factors are considered in both smooth-shaped (spheres and spheroids) and sharp-edged (cubes) volume conductors. This represents the first attempt to assess the effects of many of these factors pertaining to the numerical methods commonly used in fields such as electrocardiography (ECG) and electroencephalography (EEG). Strategies for obtaining the most accurate solutions are presented.

The changes in the contractile properties induced by a 30-Hz phasic stimulation paradigm were measured and compared with the changes induced by a 10-Hz continuous stimulation paradigm. The study was performed on the tibialis anterior muscles of cats with one paradigm applied to one hindlimb muscle and the other to the contralateral limb. Both hindlimb muscles received the same number of stimuli in a day, making the average stimulation frequency 10 Hz. Two periods of daily stimulation were studied, 8 and 24 h/day. Muscles stimulated at 30 Hz produced greater overall tetanic tension and, during a prolonged stimulation test, exerted a greater mean tension than muscles stimulated at 10 Hz (50 and 32% increase for animals stimulated for 8 and 24 h/day, respectively). Muscle mass was least reduced and fewer pathological abnormalities were observed in the muscles stimulated at 30 Hz. There were no apparent differences in the histochemistry or biochemistry between muscles stimulated at 10 and 30 Hz, which could account for these differences in muscle properties. These results indicate the 30-Hz paradigm may be better suited than 10 Hz continuous stimulation for applications requiring sustained muscle tension such as correction of scoliosis or muscle conditioning for motor prostheses.

The effect of the surface boundary between free space and a conducting medium on the excitation properties of neurons by magnetic fields are analyzed. The electric field and the spatial derivative of the induced field generated by a coil mounted both parallel and perpendicular to the surface of a semi-infinite conducting medium were calculated using the method of images. An imaginary axon is located in the same relative position from the coil in both configurations and the excitation properties are compared. The calculations are expressed in terms of the activating function for the electrical stimulation of axons. The calculations indicate that the activating function for magnetic stimulation is biphasic as opposed to triphasic for electrical stimulation. The large spatial extent of the magnetically induced electric field compared to the electric field generated by point source electrode suggests a different mode of excitation for neuronal structures in the CNS. The field distribution have been verified experimentally and are important for the understanding of the mechanisms of magnetic stimulation of neural tissue.

The electric fields and current densities induced by a magnetic field have been calculated using the concept of mutual inductance. The spatial derivative of the electrical field generated by a coil located below and parallel to a semi-infinite conducting medium have been evaluated along lines parallel to the coil. The results have been verified experimentally and are important for the understanding of the mechanisms of peripheral axonal excitation.