  Magnetic fields associated with currents flowing in tissue can be measured
non-invasively by means of zero-field-encoded ultra-low-field magnetic
resonance imaging (ULF MRI) enabling current density imaging (CDI) and possibly
conductivity mapping of human head tissues. Since currents applied to a human
are limited by safety regulations and only a small fraction of the current
passes through the relatively high-resistive skull, a sufficient
signal-to-noise ratio (SNR) may be difficult to obtain when using this method.
In this work, we study the relationship between the image SNR and the SNR of
the field reconstructions from zero-field-encoded data. We evaluate these
results for two existing ULF MRI scanners, one ultra-sensitive single-channel
system and one whole-head multi-channel system, by simulating sequences
necessary for current-density reconstruction. We also derive realistic
current-density and magnetic-field estimates from finite-element-method
simulations based on a three-compartment head model. We found that existing
ULF-MRI systems reach sufficient SNR to detect intra-cranial current
distributions with statistical uncertainty below 10%. However, they also reveal
that image artifacts influence the reconstruction quality. Further, our
simulations indicate that current-density reconstruction in the scalp requires
a resolution less than 5 mm and demonstrate that the necessary sensitivity
coverage can be accomplished by multi-channel devices.
