The unique determination of the primary current by MEG and EEG

In this paper, we use a more realistic head model with ovoid geometry for approximation of a human head. By inverting the Geselowitz equation, some analytic results on the inverse MEG problem are presented in homogenous ovoid geometry. On one hand, some information about the components of primary current is shown by the decomposition of primary current in different coordinates in the case of a special MEG sensor position. On the other hand, in the general case, using decomposition of the primary current in spherical coordinates, we show that two scalar functions which specify the tangential part of the primary current can be uniquely determined with the assumption that two scalar functions are conjugate and harmonic in terms of two variables. Hence, the tangential part of the current can be completely known from the two scalar functions. Moreover, we obtain the unique determination of the primary current by combining MEG with EEG.