Model of extended curved current source

In studying the relation between the electric and the magnetic field produced by the current sources of different forms there is a challenging question: Which are possible current distributions in the brain and/or the heart that require either magnetic or electric measurements to obtain the relevant information? A feasible example of a current source, which can be detected only by the magnetic measurements, is a vortical or curved current distribution.

Here we approximated an extended curved current source with a model assuming a shape of a circular arc and a constant current along the arc. Nine parameters, six for the origin, the radius, the length and the starting angle of the arc, two for the orientation of the arc plane and one for the current amplitude determine the model. The current is approximated by uniformly distributed current dipoles positioned tangentially along the arc. With this model we simulated various magnetic isofield maps and electric isopotential maps in different volume conductor models (sphere and realistic torso). We applied Levenberg-Marquardt least square procedure to find parameters of the arc source. The influence of measurement noise on the stability of the inverse problem solution was studied. For comparison, we have also included in the inverse procedure three other simple models (current dipole, magnetic dipole and extended linear source).

Our study shows that the proposed model of a curved current source can be successfully applied in the localization procedure particularly in cases where the magnetic isofield map indicates the presence of possible vortex currents. On the other hand, the curved current source cannot be identified by the electric measurements since the electric field generated by the curved current source is equivalent to the field of the straight linear source connecting the starting and the ending point of the source.