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Abstract

Across all domains of brain stimulation (neuromodulation), conventional analysis of neuron activation involves two discrete steps: i) prediction of macroscopic electric field, ignoring presence of cells and; ii) prediction of cell activation from tissue electric fields. The first step assumes that current flow is not distorted by the dense tortuous network of cell structures. The deficiencies of this assumption have long been recognized, but - except for trivial geometries - ignored, because it presented intractable computation hurdles. This study introduces a novel approach for analyzing electric fields within a microscopically realistic brain volume. Our pipeline overcomes the technical intractability that prevented such analysis while also showing significant implications for brain stimulation. Contrary to the standard finite element method (FEM), we suggest using a nested iterative boundary element method (BEM) coupled with the fast multipole method (FMM). This approach allows for solving problems with multiple length scales more efficiently. A target application is a subvolume of the L2/3 P36 mouse primary visual cortex containing approximately 400 detailed densely packed neuronal cells at a resolution of 100 nm, which is obtained from scanning electron microscopy data. Our immediate result is a reduction of the stimulation field strength necessary for neuron activation by a factor of 0.85-0.55 (by 15%-45%) as compared to macroscopic predictions. This is in line with modern experimental data stating that existing macroscopic theories substantially overestimate electric field levels necessary for brain stimulation.