Generalized cable formalism to calculate the magnetic field of single neurons and neuronal populations

Abstract: Neurons generate magnetic fields which can be recorded with macroscopic techniques such as magneto-encephalography. The theory that accounts for the genesis of neuronal magnetic fields involves dendritic cable structures in homogeneous resistive extracellular media. Here, we generalize this model by considering dendritic cables in extracellular media with arbitrarily complex electric properties. This method is based on a multi-scale mean-field theory where the neuron is considered in interaction with a "mean" extracellular medium (characterized by a specific impedance). We first show that, as expected, the generalized cable equation and the standard cable generate magnetic fields that mostly depend on the axial current in the cable, with a moderate contribution of extracellular currents. Less expected, we also show that the nature of the extracellular and intracellular media influence the axial current, and thus also influence neuronal magnetic fields. We illustrate these properties by numerical simulations and suggest experiments to test these findings.