Modeling Pyramidal Neurons Using Bidomain BEM and Hierarchical Matrix Approximation

Electromagnetic brain stimulation uses electrodes or coils to induce electric fields (E-fields) in the brain and affect its activity. Our understanding of the precise effects of the device-induced E-fields on neural activity is limited. In this paper, we present a novel bidomain boundary integral equation-based method that enables the modeling of fully coupled E-fields from both neurons and stimulation devices. This boundary element approach is accelerated using fast direct solvers to allow for the analysis of realistic scenarios. We present examples, indicating the ability of our solver to analyze rat L2/3 pyramidal neurons derived from the Blue Brain Project. A comprehensive analysis shows that this method can be easily extended to model a group of neurons that were previously computationally intractable.