Neuronal communication in the brain involves electrochemical currents, which produce magnetic fields. Stimulus-evoked brain responses lead to changes in these fields and can be studied using magneto- and electro-encephalography (MEG/EEG). In this paper we model the spatiotemporal distribution of the magnetic field of a physiologically idealized but anatomically realistic neuron to assess the possibility of using magnetic resonance imaging (MRI) for directly mapping the neuronal currents in the human brain. Our results show that the magnetic field several centimeters from the centre of the neuron is well approximated by a dipole source, but the field close to the neuron is not, a finding particularly important for understanding the possible contrast mechanism underlying the use of MRI to detect and locate these currents. We discuss the importance of the spatiotemporal characteristics of the magnetic field in cortical tissue for evaluating and optimizing an experiment based on this mechanism and establish an upper bound for the expected MRI signal change due to stimulus-induced cortical response. Our simulations show that the expected change of the signal magnitude is 1.6% and its phase shift is 1 degrees . An unexpected finding of this work is that the cortical orientation with respect to the external magnetic field has little effect on the predicted MRI contrast. This encouraging result shows that magnetic resonance contrast directly based on the neuronal currents present in the cortex is theoretically a feasible imaging technique. MRI contrast generation based on neuronal currents depends on the dendritic architecture and we obtained high-resolution optical images of cortical tissue to discuss the spatial structure of the magnetic field in grey matter.