Spherical harmonics based model of electric field effects on neocortical neurons

Abstract

Abstract Transcranial electrical stimulation (tES) techniques generate electric fields in the brain whose effects on single neurons can be approximated from the cable equation as a membrane potential perturbation that is proportional to the membrane length constant (lambda). This is referred to as the lambda-E model and is a simple mechanistic approach that assumes that the membrane perturbation can be modeled as the dot product of a vector parallel to the orthodromic direction of cortical neurons with the electric field, multiplied by lambda. We propose a more general way to represent the model of the membrane perturbation as a function of the magnitude and angular orientation of the E-field, using a spherical harmonics expansion that can capture the dependence of the perturbation on electric field direction. In this representation, the lambda-E model corresponds to the first-order degree (l=1) term of the expansion. This approach can represent the three-dimensional response of a specific cell part, obtained experimentally. Here we employ it using synthetic data from realistic neocortical cell models in a DC field in the tDCS regime, fitting the coefficients for the membrane responses. We use realistic reconstructions of the somatosensory cortex from the Blue Brain Project to simulate the response of different pyramidal cells and interneurons to electric fields of 1 V/m as a function of the orientation of the field with respect to the cell using the NEURON simulation environment. We report membrane perturbation values comparable to those in the literature, extend it to different cell types, and provide the spherical harmonic coefficient profile for each neuron. Finally, we provide an azimuth-independent version of the model providing an averaged response that only depends on the electric field vector and the cortical surface. We believe this method can improve the accuracy and detail of real life simulation-based stimulation. Keywords: Electric field coupling, Multicompartment models, tES, NEURON