A Review of Forward Numerical Methods for Electroencephalography (EEG) Data

Authors

  • S. F. Ali Department of Physics, University of Karachi, Karachi, Pakistan. Government Degree College, Gulshan-e-Iqbal, Block 7, Karachi, Pakistan. https://orcid.org/0000-0002-2637-2772
  • N. Anjum Government Aisha Bawani College, Karachi, Pakistan. Department of Physics, University of Karachi, Karachi, Pakistan
  • I. A. Siddiqui Department of Physics, University of Karachi, Karachi, Pakistan

DOI:

https://doi.org/10.71330/thenucleus.2026.1515

Abstract

Despite its temporal resolution and relatively low cost, electroencephalography (EEG) is one of the most popular methods for investigating brain dynamics because it is noninvasive. Nonetheless, the interpretation of EEG signals essentially relies on the solution of the forward problem, accounting weakly for the electrical activity produced in the brain and how it diffuses, thus arousing scalp potentials. Over the past few years, the development of computational neuroscience and numerical modeling has resulted in increasingly complex forward models using realistic head geometries, anisotropic tissue conductivities, and fine numerical solvers. This review provides an in-depth discussion of the latest forward numerical techniques applied in the analysis of EEG data, including Boundary Element Methods (BEM), Finite Element Methods (FEM), Finite Difference Methods (FDM), and hybrid-computational methods. Other strategies for head modeling, recent computer advances, and the importance of software structures for EEG modeling are also discussed in this review. In addition, it highlights existing issues, such as ambiguity with respect to conductivity, intersubject variability, and computational cost. Finally, new advances in physics-inspired and data-driven modeling techniques are addressed, and the evolution towards more realistic and explainable EEG forward answers is discussed. The review finds that although there have been tremendous advances, the discipline still requires better integration of anatomical realism, numerical stability, and computational efficiency. This review comprises recent advances in AI-supported forward modeling, physics-guided computational methods, and subject-specific conductivity estimation techniques published between 2020 and 2026, none of which have been summarized in any of the prior reviews on EEG forward modeling, which have mostly focused on numerical solutions only. Moreover, it compares classical and emerging numerical methods and presents their advantages and disadvantages, particularly in terms of their applicability to current neuroimaging and brain-computer interface systems.

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23-06-2026

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[1]
S. F. Ali, N. Anjum, and I. A. Siddiqui, “A Review of Forward Numerical Methods for Electroencephalography (EEG) Data”, The Nucleus, vol. 63, no. 1, pp. 39–46, Jun. 2026.

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Vol. 63 No. 1 (2026)

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