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Neurons generate magnetic fields which can be recorded with macroscopictechniques such as magneto-encephalography. The theory that accounts for thegenesis of neuronal magnetic fields involves dendritic cable structures inhomogeneous resistive extracellular media. Here, we generalize this model byconsidering dendritic cables in extracellular media with arbitrarily complexelectric properties. This method is based on a multi-scale mean-field theorywhere the neuron is considered in interaction with a "mean" extracellularmedium (characterized by a specific impedance). We first show that, asexpected, the generalized cable equation and the standard cable generatemagnetic fields that mostly depend on the axial current in the cable, with amoderate contribution of extracellular currents. Less expected, we also showthat the nature of the extracellular and intracellular media influence theaxial current, and thus also influence neuronal magnetic fields. We illustratethese properties by numerical simulations and suggest experiments to test thesefindings.

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