On the electrodynamics of neural networks

We present a microscopic approach for the coupling of cortical activity, as resulting from proper dipole currents of pyramidal neurons, to the electromagnetic field in extracellular fluid in presence of diffusion and Ohmic conduction. Starting from a full-fledged three-compartment model of a single pyramidal neuron, including shunting and dendritic propagation, we derive an observation model for dendritic dipole currents in extracellular space and thereby for the dendritic field potential that contributes to the local field potential of a neural population. Under reasonable simplifications, we then derive a leaky integrate-and-fire model for the dynamics of a neural network, which facilitates comparison with existing neural network and observation models. In particular, we compare our results with a related model by means of numerical simulations. Performing a continuum limit, neural activity becomes represented by a neural field equation, while an observation model for electric field potentials is obtained from the interaction of cortical dipole currents with charge density in non-resistive extracellular space as described by the Nernst-Planck equation. Our work consistently satisfies the widespread dipole assumption discussed in the neuroscientific literature. Peter beim Graben Bernstein Center for Computational Neuroscience Berlin, Department of German Studies and Linguistics, Humboldt-Universität zu Berlin, Germany · Serafim Rodrigues Centre for Robotics and Neural Systems, School of Computing and Mathematics, University of Plymouth, United Kingdom 1 ar X iv :1 31 0. 18 01 v1 [ qbi o. N C ] 7 O ct 2 01 3 2 Peter beim Graben and Serafim Rodrigues