[Paper Review] Zeffiro user interface for electromagnetic brain imaging: a GPU accelerated FEM tool for forward and inverse computations in Matlab

Qin He, Atena Rezaei+1 more|arXiv (Cornell University)|Nov 19, 2018

Advanced MRI Techniques and ApplicationsMedicine32 references3 citations

TL;DR

Zeffiro is an open-source, GPU-accelerated MATLAB interface for electromagnetic brain imaging that enables fast finite element method (FEM)-based forward and inverse computations for EEG, MEG, and linearized EIT. It leverages GPU acceleration to significantly reduce computation time in mesh generation and lead field matrix assembly, and implements hierarchical Bayesian model (HBM)-based inverse solvers with validated performance on real and synthetic data.

ABSTRACT

This article introduces the Zeffiro interface (ZI) version 2.2 for brain imaging. ZI aims to provide a simple, accessible and multimodal open source platform for finite element method (FEM) based and graphics processing unit (GPU) accelerated forward and inverse computations in the Matlab environment. It allows one to (1) generate a given multi-compartment head model, (2) to evaluate a lead field matrix as well as (3) to invert and analyze a given set of measurements. GPU acceleration is applied in each of the processing stages (1)-(3). In its current configuration, ZI includes forward solvers for electro-/magnetoencephalography (EEG) and linearized electrical impedance tomography (EIT) as well as a set of inverse solvers based on the hierarchical Bayesian model (HBM). We report the results of EEG and EIT inversion tests performed with real and synthetic data, respectively, and demonstrate numerically how the inversion parameters affect the EEG inversion outcome in HBM. The GPU acceleration was found to be essential in the generation of the FE mesh and the LF matrix in order to achieve a reasonable computing time. The code package can be extended in the future based on the directions given in this article.

Motivation & Objective

• To provide an accessible, open-source platform for FEM-based electromagnetic brain imaging in MATLAB.
• To accelerate computationally intensive FEM processes—especially mesh generation and lead field matrix computation—using GPU acceleration.
• To integrate forward solvers for EEG/MEG and linearized EIT with inverse solvers based on the hierarchical Bayesian model (HBM).
• To enable users to perform multimodal brain imaging with real and synthetic data, supporting both forward modeling and inverse source localization.
• To design a modular, extensible framework that allows future extension to other FEM-based forward models.

Proposed method

• Employs the finite element method (FEM) to model the head as a multi-compartment domain with realistic tissue conductivity distributions.
• Uses a weak form of the PDE ∇·(σ∇u) = ∇·Jᵖ to model electric potential fields, with Jᵖ representing neural current sources in EEG/MEG.
• Applies GPU acceleration to speed up FEM assembly, particularly for mesh generation and lead field matrix computation.
• Derives the lead field matrix L from the solution of linear systems involving the stiffness matrix A and boundary matrix B, using the transfer matrix T = A⁻¹B.
• Implements the hierarchical Bayesian model (HBM) for inverse problems, using an iterative alternating sequential (IAS) algorithm to estimate source locations and hyperparameters.
• For linearized EIT, derives the lead field via differentiation of the system matrix A with respect to conductivity elements, yielding L with entries ∂yk/∂sm.

Experimental results

Research questions

• RQ1 How can GPU acceleration be effectively applied to reduce computation time in FEM-based forward modeling for EEG and EIT?

Key findings

• GPU acceleration was essential for achieving reasonable computation times in FEM mesh generation and lead field matrix assembly, particularly for high-resolution models.
• The Zeffiro interface successfully enabled fast and accurate forward and inverse computations for both EEG and EIT using real and synthetic data.
• The hierarchical Bayesian model (HBM) with IAS inversion provided stable and interpretable source localization results, with convergence observed over iterative updates of hyperparameters.
• The framework demonstrated numerical robustness in showing how inversion parameters—such as hyperprior settings—affected the spatial resolution and localization accuracy in EEG source reconstruction.
• The modular design of Zeffiro allows for future extension to other FEM-based forward models beyond EEG, MEG, and EIT.