Complex valued equivalent-current dipole fits for MEG responses

Complex numbers appear naturally in biological systems in the context of the Fourier transform. In particular, physiological magnetic field data from whole head magneto-encephalography (MEG) is complex after a Fourier transform. The whole-head MEG Steady State Response (SSR) to a stationary modulated stimulus results in a complex magnetic field for each MEG channel, from the frequency corresponding to that of the stimulus modulation. This complex data set is used to estimate the neural current sources generating the magnetic field, naturally leading to complex current sources. We show that standard inverse methods of estimating the current sources, such as the single equivalent-current dipole, generalize to complex sources in a useful and straightforward manner. The usage and utility of the complex magnetic field and the complex neural current source are demonstrated using examples from auditory SSR experiments.