# Custom Edge-Element FEM Solver and its Application to Eddy-Current Simulation of Realistic 2M-Element Human Brain Phantom

## TL;DR

This paper introduces a custom edge-element FEM solver for efficient and stable eddy-current simulations in large, realistic human brain models, avoiding complex coil meshing and reducing computational load.

## Contribution

A novel edge-element FEM solver based on weakly coupled theory that improves efficiency and stability for large-scale eddy-current simulations in biological tissues.

## Key findings

- Successfully simulated a 2 million element human brain model.
- Reduced computational complexity by separating background field and scalar potential.
- Eliminated need to mesh excitation coil, increasing efficiency.

## Abstract

Extensive research papers of three-dimensional computational techniques are widely used for the investigation of human brain pathophysiology. Eddy current analyzing could provide an indication of conductivity change within a biological body. A significant obstacle to current trend analyses is the development of a numerically stable and efficiency-finite element scheme that performs well at low frequency and does not require a large number of degrees of freedom. Here, a custom finite element method (FEM) solver based on edge elements is proposed using the weakly coupled theory, which separates the solution into two steps. First, the background field (the magnetic vector potential on each edge) is calculated and stored. Then, the electric scalar potential on each node is obtained by FEM based on Galerkin formulations. Consequently, the electric field and eddy current distribution in the object can be obtained. This solver is more efficient than typical commercial solvers since it reduces the vector eddy current equation to a scalar one, and reduces the meshing domain to just the eddy current region. It can therefore tackle complex eddy current calculations for models with much larger numbers of elements, such as those encountered in eddy current computation in biological tissues. An example is presented with a realistic human brain mesh of 2 million elements. In addition, with this solver, the equivalent magnetic field induced from the excitation coil is applied, and therefore there is no need to mesh the excitation coil. In combination, these significantly increase the efficiency of the solver.

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Source: https://tomesphere.com/paper/1906.01513