We describe a mathematical algorithm to obtain an image of a two-dimensional current distribution from measurements of its magnetic field. The spatial resolution of this image is determined by the signal-to-noise ratio of the magnetometer data and the distance between the magnetometer and the plane of the current distribution. In many cases, the quality of the image can be improved more by decreasing the current-to-magnetometer distance than by decreasing the noise in the magnetometer.

A model is presented to explain the physics of nerve stimulation by electromagnetic induction. Maxwell's equations predict the induced electric field distribution that is produced when a capacitor is discharged through a stimulating coil. A nonlinear Hodgkin-Huxley cable model describes the response of the nerve fiber to this induced electric field. Once the coil's position, orientation, and shape are given and the resistance, capacitance, and initial voltage of the stimulating circuit are specified, this model predicts the resulting transmembrane potential of the fiber as a function of distance and time. It is shown that the nerve fiber is stimulated by the gradient of the component of the induced electric field that is parallel to the fiber, which hyperpolarizes or depolarizes the membrane and may stimulate an action potential. Finally, it predicts complicated dynamics such as action potential annihilation and dispersion.

Electrical conductivities in the bidomain model of cardiac tissue are expressed as functions of four parameters. These expressions allow simulations to be performed using nominal, equal, and reciprocal anisotropy without introducing undesired effects, such as length constant variations. Relative values of the bidomain conductivities are estimated to be: /spl sigma//sub iL/=1, /spl sigma//sub iT/=0.1, /spl sigma//sub eL/=1, and /spl sigma//sub eT/=0.4.