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Related Experiment Video

Updated: Jul 12, 2026

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
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Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

Published on: June 21, 2022

Charge based boundary element method with residual driven adaptive mesh refinement for high resolution electrical

Derek A Drumm1, Gregory M Noetscher2, Hannes Oppermann3

  • 1Department of Electrical & Computer Engineering, Worcester Polytechnic Institute, Worcester, MA, USA. dadrumm@wpi.edu.

Scientific Reports
|July 9, 2026
PubMed
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This summary is machine-generated.

This study introduces adaptive mesh refinement for accurate modeling of brain stimulation and EEG. The method ensures stable and precise simulations for transcranial electrical stimulation (TES) and electroencephalography (EEG) in realistic head models.

Area of Science:

  • Computational neuroscience
  • Biomedical engineering
  • Numerical methods

Background:

  • Accurate forward modeling for transcranial electrical stimulation (TES), electroconvulsive therapy (ECT), and electroencephalography (EEG) is crucial.
  • Numerical singularities in charge density near electrodes and tissue interfaces pose a significant challenge.

Purpose of the Study:

  • To present an adaptive mesh refinement (AMR) strategy for the charge-based boundary element method (BEM) accelerated by the fast multiple method (BEM-FMM).
  • To address electrode and interface singularities in forward modeling.
  • To improve the numerical stability and accuracy of TES and EEG simulations.

Main Methods:

  • Developed an AMR strategy for BEM-FMM incorporating electrode and interface singularities.

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  • Derived a novel error estimator considering local and nonlocal contributions of the single-layer potential operator.
  • Constructed a refinement criterion based on charge solution differences across AMR iterations.
  • Evaluated the approach on spherical and subject-specific head models (SimNIBS and Sim4Life segmentations) using voltage and true-current electrode formulations.

    • Main Results:

    • Achieved relative residual errors below 0.1% for SimNIBS and 1% for Sim4Life models on white matter and deep hippocampal targets.
    • Demonstrated convergence of electric fields with the proposed AMR strategy.
    • Validated the method on both simplified and complex, realistic head geometries.

    Conclusions:

    • The residual-based AMR applied to BEM-FMM provides numerically stable and accurate forward solutions for TES and EEG.
    • This approach effectively resolves singularities, enhancing the reliability of computational models for brain stimulation and electrophysiology.