Geometric Basis Functions (GBF) framework for noninvasive whole human brain dynamics mapping using participant-specific eigenmodes derived from cortical geometry. Use when working with EEG/MEG source imaging, brain dynamics reconstruction, neuroimaging inverse problems, or cortical geometry-based neural activity mapping. Enables high-fidelity spatiotemporal reconstruction of neural sources using geometric constraints.
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Geometric Basis Functions (GBF) framework for noninvasive whole human brain dynamics mapping using participant-specific eigenmodes derived from cortical geometry. Use when working with EEG/MEG source imaging, brain dynamics reconstruction, neuroimaging inverse problems, or cortical geometry-based neural activity mapping. Enables high-fidelity spatiotemporal reconstruction of neural sources using geometric constraints.
Geometric Basis Functions (GBF) methodology for noninvasive mapping of whole human brain dynamics using participant-specific cortical geometry eigenmodes.
Overview
The GBF framework addresses the fundamental limitation of EEG/MEG source imaging: low-dimensional, indirect observations of high-dimensional neural dynamics. By embedding participant-specific geometric basis functions (eigenmodes derived from each individual's cortical surface), GBF provides powerful anatomical constraints that resolve the inverse problem and improve reconstruction fidelity.
Core Innovation
Traditional EEG/MEG source imaging relies on simplistic or biologically implausible priors. GBF reconstructs neural sources as linear combinations of geometric basis functions, aligning source estimates with the geometric organization of neural dynamics.
Key Capabilities
Participant-Specific Modeling: Uses each individual's cortical surface geometry
High Localization Accuracy: Validated across multiple benchmarks and datasets
Fast Spatiotemporal Dynamics: Captures dynamics consistent with anatomical pathways
Compact Representation: Describes whole-brain activity with hundreds of geometric modes
Versatile Applications: Scientific research and clinical applications
Theoretical Foundation
Geometric Basis Functions
GBFs are eigenmodes derived from the Laplace-Beltrami operator on each participant's cortical surface mesh:
Δφ_k = -λ_k φ_k
Where:
Δ is the Laplace-Beltrami operator on the cortical surface
φ_k are the eigenfunctions (geometric basis functions)
λ_k are the corresponding eigenvalues
Forward Model
The EEG/MEG forward model relates neural sources to sensor measurements:
Y = LX + ε
Where:
Y is the sensor data (channels × timepoints)
L is the leadfield matrix (channels × sources)
X is the neural source activity (sources × timepoints)
ε is noise
GBF Source Representation
Neural sources are represented as linear combinations of GBFs:
X = Φα
Where:
Φ is the GBF matrix (sources × modes)
α are the GBF coefficients (modes × timepoints)
Inverse Solution
The inverse problem becomes estimating GBF coefficients:
α̂ = argmin_α ||Y - LΦα||²_F + λR(α)
Where R(α) is a regularization term (e.g., L2 norm).
Wang, S., Lou, K., Wei, C., et al. (2026). A geometry aware framework enhances noninvasive mapping of whole human brain dynamics. arXiv:2604.25592 [q-bio.NC].
Related Methods
Laplace-Beltrami eigenfunctions for cortical surface analysis
Minimum norm estimation (MNE) for EEG/MEG source imaging
