[Paper Review] Validation of EEG forward modeling approaches in the presence of anisotropy in the source space

Florian Drechsler, Johannes Vorwerk+3 more|arXiv (Cornell University)|Jan 1, 2022

Advanced MRI Techniques and Applications1 citations

TL;DR

This study validates three finite element method (FEM) approaches—subtraction, Venant, and partial integration—for EEG forward modeling in the presence of cortical conductivity anisotropy. It demonstrates that anisotropy significantly affects potential computation, especially in developing brains, and identifies the Venant FEM approach as optimal due to its balance of accuracy, computational efficiency, and robustness to mesh resolution.

ABSTRACT

The quality of the inverse approach in electroencephalography (EEG) source analysis is - among other things - depending on the accuracy of the forward modeling approach, i.e., the simulation of the electric potential for a known dipole source in the brain. Here, we use multilayer sphere modeling scenarios to investigate the performance of three different finite element method (FEM) based EEG forward approaches - subtraction, Venant and partial integration - in the presence of tissue conductivity anisotropy in the source space. In our studies, the effect of anisotropy on the potential is related to model errors when ignoring anisotropy and to numerical errors, convergence behavior and computational speed of the different FEM approaches. Three different source space anisotropy models that best represent adult, child and premature baby volume conduction scenarios, are used. Major findings of the study include (1) source space conductivity anisotropy has a significant effect on electric potential computation: The effect increases with increasing anisotropy ratio; (2) with numerical errors far below anisotropy effects, all three FEM approaches are able to model source space anisotropy accordingly, with the Venant approach offering the best compromise between accuracy and computational speed; (3) FE meshes have to be fine enough in the subdomain between the source and the sensors that capture its main activity. We conclude that, especially for the analysis of cortical development, but also for more general applications using EEG source analysis techniques, source space conductivity anisotropy should be modeled and the FEM Venant approach is an appropriate method.

Motivation & Objective

• . To evaluate the performance of three FEM-based EEG forward modeling approaches—subtraction, Venant, and partial integration—under tissue conductivity anisotropy in the source space.
• . To quantify the impact of source space anisotropy on EEG potential computation and assess model errors when anisotropy is ignored.
• . To investigate the influence of numerical errors, mesh resolution, and convergence behavior on the accuracy of forward modeling in anisotropic head models.
• . To determine the optimal FEM approach for modeling cortical anisotropy, particularly in pediatric and developmental EEG applications.
• . To establish guidelines for mesh refinement in regions between the source and the most active EEG sensors to ensure computational accuracy and efficiency.

Proposed method

• . The study employs multilayer sphere models to simulate adult, child, and premature baby head volume conductors with realistic anisotropy ratios.
• . Three distinct anisotropy models are used: a 1.41:1 ratio for adults, and lower ratios for children and premature infants, based on DT-MRI data and effective medium theory.
• . The three FEM approaches—subtraction, Venant, and partial integration—are implemented and compared using high-resolution finite element meshes.
• . Model accuracy is assessed via relative error (RE) between anisotropic and isotropic simulations, with convergence behavior analyzed across multiple mesh refinements.
• . The study evaluates mesh sensitivity by refining elements around the source and between source and sensors, using both global and local refinement strategies.
• . The Venant method is evaluated for its numerical stability, computational speed, and ability to handle singularities in anisotropic media without requiring special treatment of the source neighborhood.

Experimental results

Research questions

• RQ1 . How does cortical conductivity anisotropy affect the accuracy of EEG forward modeling, and how does this effect scale with increasing anisotropy ratios?
• RQ2 . How do the three FEM-based forward modeling approaches—subtraction, Venant, and partial integration—perform in terms of numerical accuracy, convergence, and computational cost when modeling anisotropic source space?
• RQ3 . What is the impact of mesh resolution and refinement strategy—particularly around the source and between source and sensors—on the accuracy of forward modeling in anisotropic media?
• RQ4 . Does the homogeneity condition required by the subtraction method remain viable in anisotropic grey matter, and how does it affect numerical error?
• RQ5 . Which FEM approach offers the best trade-off between accuracy, computational efficiency, and robustness for modeling anisotropic source space conductivity in developmental EEG studies?

Key findings

• . Source space conductivity anisotropy has a significant effect on EEG potential computation, with the effect increasing proportionally with the anisotropy ratio.
• . The Venant FEM approach achieves the best balance between accuracy and computational speed, outperforming subtraction and partial integration in both numerical stability and efficiency.
• . Numerical errors across all three FEM methods are substantially smaller than the model errors introduced by ignoring anisotropy, confirming that accurate anisotropy modeling is essential.
• . Mesh refinement is most critical in the region between the source and the EEG sensors capturing the main activity, while coarser meshes suffice in distant brain regions.
• . The subtraction method is highly sensitive to the homogeneity condition around the source, and its performance degrades when conductivity tensors are adapted in refined zones, unlike the Venant and partial integration methods.
• . The study confirms FE convergence for all three methods at high mesh resolutions, with relative errors far below the anisotropy-induced model errors, validating the robustness of the FEM approaches.