  Magnetic field sensing, with its recent advances, is emerging as a viable
alternative to measure functional activity of single neurons in the brain by
sensing action potential associated magnetic fields (APMFs). Measurement of
APMFs of large axons of worms have been possible due to their size. In the
mammalian brain, axon sizes, their numbers and routes, restricts using such
functional imaging methods. With segmented model of mammalian pyramidal
neurons, we show that the APMF of intra-axonal currents in the axon hillock are
two orders of magnitude larger than other neuronal locations. Expected
2-dimensional vector magnetic field maps of naturalistic spiking activity of a
volume of neurons via widefield diamond-nitrogen-vacancy-center-magnetometry
(DNVM) were simulated. A dictionary based matching pursuit type algorithm
applied to the data using the axon-hillock's APMF signature allowed
spatiotemporal reconstruction of APs in the volume of brain tissue at single
cell resolution. Enhancement of APMF signals coupled with NVMM advances thus
can potentially replace current functional brain mapping techniques.
