The Local Subtraction Approach for EEG and MEG Forward Modeling
Malte B. Höltershinken, Pia Lange, Tim Erdbrügger, Yvonne Buschermöhle, Fabrice Wallois, Alena Buyx, Sampsa Pursiainen, Johannes Vorwerk, Christian Engwer, Carsten Hermann Wolters · SIAM Journal on Scientific Computing · 2025
Abstract. In FEM-based electroencephalography (EEG) and magnetoencephalography (MEG) source analysis, the subtraction approach has been proposed to simulate sensor measurements generated by neural activity. While this approach possesses a rigorous foundation and produces accurate results, its major downside is that it is computationally prohibitively expensive in practical applications. To overcome this, we developed a new approach, called the local subtraction approach. This approach is designed to preserve the mathematical foundation of the subtraction approach, while also leading to sparse right-hand sides in the FEM formulation, making it efficiently computable. We achieve this by introducing a cut-off into the subtraction, restricting its influence to the immediate neighborhood of the source. We perform validation in multilayer sphere models where analytical solutions exist. There, we demonstrate that the local subtraction approach is vastly more efficient than the subtraction approach. Moreover, we find that for the EEG forward problem, the local subtraction approach is less dependent on the global structure of the FEM mesh when compared to the subtraction approach. Additionally, we show the local subtraction approach to rival, and in many cases even surpass, the other investigated approaches in terms of accuracy. For the MEG forward problem, we show the local subtraction approach and the subtraction approach to produce highly accurate approximations of the volume currents close to the source. The local subtraction approach thus reduces the computational cost of the subtraction approach to an extent that makes it usable in practical applications without sacrificing the rigorousness and accuracy the subtraction approach is known for. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://zenodo.org/records/12575669 and in the supplemental material ( SISC_Localized_Subtraction_Supplementary.pdf [ 740KB]). [Formula: see text]