Modeling direct effects of neural current on MRI

We investigate the effect of the magnetic field generated by neural activity on the magnitude and phase of the MRI signal in terms of a phenomenological parameter with the dimensions of length; it involves the product of the strength and duration of these currents. We obtain an analytic approximation to the MRI signal when the neuromagnetically induced phase is small inside the MRI voxel. The phase shift is the average of the MRI phase over the voxel, and therefore first order in that phase; and the reduction in the signal magnitude is one half the square of the standard deviation of the MRI phase, which is second order. The analytic approximation is compared with numerical simulations. For weak currents the agreement is excellent, and the magnitude change is generally much smaller than the phase shift. Using MEG data as a weak constraint on the current strength we find that for a net dipole moment of 10 nAm, a typical value for an evoked response, the reduction in the magnitude of the MRI signal is two parts in 10(5), and the maximum value of the overall phase shift is approximately 4 x 10(-3), obtained when the MRI voxel is displaced 2/3 the size of the neuronal activity. We also show signal changes over a large range of values of the net dipole moment. We compare these results with others in the literature. Our model overestimates the effect on the MRI signal.