Neuronal activity produces transient ionic currents that may be detectable using magnetic resonance imaging (MRI). We examined the feasibility of MRI-based detection of neuronal currents using computer simulations based on the laminar cortex model (LCM). Instead of simulating the activity of single neurons, we decomposed neuronal activity to action potentials (AP) and postsynaptic potentials (PSP). The geometries of dendrites and axons were generated dynamically to account for diverse neuronal morphologies. Magnetic fields associated with APs and PSPs were calculated during spontaneous and stimulated cortical activity, from which the neuronal current induced MRI signal was determined. We found that the MRI signal magnitude change (< 0.1 ppm) is below currently detectable levels but that the signal phase change is likely to be detectable. Furthermore, neuronal MRI signals are sensitive to temporal and spatial variations in neuronal activity but independent of the intensity of neuronal activation. Synchronised neuronal activity produces large phase changes (in the order of 0.1 mrad). However, signal phase oscillates with neuronal activity. Consequently, MRI scans need to be synchronised with neuronal oscillations to maximise the likelihood of detecting signal phase changes due to neuronal currents. These findings inform the design of MRI experiments to detect neuronal currents.