Multiscale and Multiphysics neuron and E-field solvers
Background. Commonly used cable equation-based approaches for determining the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or “whole” finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling, however, they do not scale.
Objective. Our objective is to create bidomain or "whole" solvers that scale enabling their use for analyzing large populations of neurons that ephaptically couple and include the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.
Approach. We introduce a boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane induced E-fields.
Main Results. Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is made computationally tractable, and the relative placement of devices and cells can be varied without the need to generate a new mesh.
Significance. Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.
Ongoing work. Ongoing efforts are improving the meshing of cell boundaries (e.g. to have realistically shaped soma and include dendritic spines), adding more membrane mechanisms to model fully realistic neurons, and applying novel compression techniques to speed-up the compuation of the bidomain boundary element method.