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Simultaneous EEG Monitoring During Transcranial Direct Current Stimulation
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EEG for Current With Two-Dimensional Support.

George Dassios, Athanassios S Fokas, Parham Hashemzadeh

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    Summary
    This summary is machine-generated.

    This study simplifies calculating neuronal current density from scalp EEG by developing a formula using only the "visible" current components. This improves the stability and reduces ambiguity in inverse solutions for electroencephalography (EEG).

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    Area of Science:

    • Biophysics
    • Neuroscience
    • Computational Electromagnetics

    Background:

    • The inverse problem of determining neuronal current density from electroencephalography (EEG) signals is inherently ill-posed due to non-unique source-to-potential mappings.
    • Existing methods face challenges in accurately localizing current sources within the brain.

    Purpose of the Study:

    • To develop an explicit formula for scalp EEG potentials derived from current sources constrained to the cortical surface.
    • To reduce the ambiguity in inverse solutions by focusing on current components that directly influence EEG measurements.

    Main Methods:

    • Utilized the quasi-static form of Maxwell's equations to derive a new formula for scalp EEG.
    • Incorporated auxiliary functions dependent on the complex topology and conductivity of biological tissues (cerebrum, cerebrospinal fluid, bone, scalp).
    • Characterized the
    • visible
    • current component, comprising normal and tangential elements.

    Main Results:

    • Derived expressions for scalp potential applicable to general nested topologies, including spherical and ellipsoidal surfaces.
    • Validated the formula by showing agreement with a 3-D formulation for a thin current shell in the cerebrum.
    • Demonstrated that the
    • visible
    • current can be explicitly defined.

    Conclusions:

    • The developed formula effectively isolates the current components relevant to EEG, thereby restricting the source space.
    • This restriction significantly reduces ambiguity in inverse solutions, leading to more stable and reliable EEG source localization.
    • Auxiliary functions can be computed efficiently, facilitating practical application of the method.