A geometry aware framework enhances noninvasive mapping of whole human brain dynamics

Abstract: Non-invasive electrophysiology lacks methods that accurately reconstruct whole-brain spatiotemporal dynamics while incorporating individual cortical geometry, leaving current electroencephalography and magnetoencephalography source imaging limited by simplistic or biologically implausible priors. Here, we show that embedding participant-specific Geometric Basis Functions (GBFs), eigenmodes derived from each individual's cortical surface, provides a powerful anatomic constraint that resolves the inverse problem and improves reconstruction fidelity. The method reconstructs neural sources as linear combinations of geometric basis functions, thereby aligning source estimates with the geometric organization of neural dynamics. We validate GBF across the Meta-Source Benchmark, task-evoked data, resting-state networks, intracranial stimulation, and epilepsy data. The results demonstrate that GBF yields high localization accuracy and captures fast spatiotemporal dynamics consistent with anatomical pathways. These findings suggest that both spontaneous and evoked whole-brain activity can be described by hundreds of geometric modes, providing a compact yet accurate representation of neural sources. By linking cortical geometry to electrophysiological dynamics, GBF offers a versatile source imaging tool for both scientific and clinical applications.

• The paper presents a novel framework that uses participant-specific Laplace-Beltrami eigenmodes as geometric basis functions to tightly link EEG/MEG source imaging with individual cortical anatomy.
• It demonstrates significant improvements in localization error, correlation, and overall fidelity by capturing ~87% of cortical variance with the first 200–300 GBFs compared to traditional inverse methods.
• The approach enhances practical applications by providing robust, anatomically consistent mapping for both task-related dynamics and clinical scenarios like epileptogenic zone localization.

Geometry-Aware EEG/MEG Source Imaging: The Geometric Basis Function Framework

Introduction

Electroencephalography (EEG) and magnetoencephalography (MEG) source imaging (ESI) are fundamentally limited by the ill-posedness of the electromagnetic inverse problem, resulting in source reconstructions that are often spatially diffuse and biologically implausible. Conventional ESI methods, relying on generic priors like minimum norm or smoothness constraints, lack subject-specific anatomical constraints and are unable to account for the idiosyncratic geometry of the cortical surface. This limitation hinders both basic neuroscience and clinical applications, as precise tracking of brain dynamics demands high spatiotemporal fidelity and anatomical interpretability.

This paper introduces a geometry-aware framework for ESI by leveraging participant-specific Geometric Basis Functions (GBFs)—the Laplace-Beltrami eigenmodes derived from an individual's cortical surface mesh. By embedding GBFs as spatial priors, the framework tightly couples the reconstruction of neural dynamics to subject anatomy, resolving key ambiguities in the inverse problem and significantly improving reconstruction fidelity.

Methodological Overview

The GBF framework begins with segmentation of individual T1-weighted MRI scans and reconstruction of the cortical surface mesh. The intrinsic geometry of this manifold is then characterized by solving the Laplace-Beltrami eigenvalue problem, yielding an orthonormal basis set of eigenmodes spanning multiple spatial scales. Neural activity is modeled as a linear combination of these geometric basis functions, such that the source estimate $x(t)$ is expressed as $x(t) = \sum_i f_i(t) v_i$, with $v_i$ denoting geometric modes and $f_i(t)$ their temporal coefficients.

The forward model links source-space dynamics to the sensor domain via the lead-field matrix, and inversion is regularized using a logarithmic spectral prior that favors low-frequency spatial modes—reflecting empirically established biophysical interpretability of cortical oscillations. The resulting closed-form maximum a posteriori (MAP) estimator is computationally efficient and effectively conditions the inverse problem.

Quantitative Benchmarking

A novel and comprehensive Meta-Source Benchmark is constructed to rigorously evaluate GBF and competing ESI methods. Unlike traditional simulations, this benchmark employs spatially distributed source patterns derived from meta-analytic fMRI activation maps annotated with cognitive terms, projected to surface space and paired with realistic sensor-level topographies. This approach enables validation against biologically grounded, semantically meaningful spatial configurations.

GBF is evaluated alongside MNE, wMNE, sLORETA, eLORETA, dSPM, and beamformer-based methods under diverse noise conditions (Gaussian and empirical EEG-derived noise, SNR variation). Across all metrics—NRMSE, localization error, Pearson correlation, cosine similarity, and AUC—GBF substantially outperforms alternatives, with statistically significant improvements across nearly all cortical parcels. The low reconstruction error persists even under severe noise, though performance degrades in deep/ventral regions, consistent with biophysical sensitivity profiles and known limitations of noninvasive surface recordings. The principal source of error arises from basis truncation and inverse ill-posedness, with the first 200–300 GBFs capturing ~87% of the explainable cortical variance.

Generalizability Across Experimental Paradigms

Applying GBF inversion to empirical EEG data from visual, auditory, somatosensory, and motor paradigms, the reconstructed cortical activation maps exhibit precise spatial localization. Task-evoked components (ERPs/ERDs) are reliably aligned with canonical neuroanatomy: visual cortex for visual stimulation, bilateral auditory cortices for auditory paradigms, contralateral somatosensory or motor cortex for median nerve stimulation and voluntary movement, respectively. Comparisons to Neurosynth-derived reference maps and other inverse methods demonstrate sharper, more focal, and anatomically consistent localization with GBF. Temporal dynamics are preserved, with clear task-locked peaks and accurate stimulus alignment.

Recovery of Functional Connectivity and Propagation Patterns

An essential criterion for neurophysiologically valid source imaging is the recovery of large-scale functional networks. Using resting-state MEG data from the HCP repository and referencing against group-level iEEG connectomes (n=110), GBF-based MEG-derived "virtual iEEG" functional connectivity matrices demonstrate maximal spatial correspondence (Pearson's $r \approx 0.20$–$0.45$ by band) with in vivo iEEG networks, outperforming all alternative inverse solutions, particularly in non-$\theta$ bands. Edge-level analyses and bootstrap-driven null models confirm these effects across lobes and hemispheres. As expected, cross-modal (MEG-fMRI) correlations are numerically weaker than within-modality comparisons, reflecting neurovascular coupling and cross-modal integration challenges.

GBF's capacity for reconstructing fast spatiotemporal propagation was evaluated using simultaneous intracranial electrical stimulation (iES) and high-density scalp EEG. The framework accurately localizes stimulation sites (sub-centimeter error), with localization error robust across stimulation depths and consistently lower than all conventional inverse methods. Phase-gradient optical flow analysis enables the identification of distributed propagation trajectories (N1/N2 components), mapping directed millisecond-scale wavefronts from the stimulation locus to remote cortical hubs—findings congruent with ground-truth recordings and CCEP studies.

Clinical Application to Epileptogenic Zone Localization

Localizing the epileptogenic zone (EZ) in drug-resistant focal epilepsy is a critical semiology for presurgical decision-making. GBF-based analysis of interictal discharges in high-density EEG, validated against individualized resection masks derived from pre-/post-op MRI, yields minimal localization error compared to MNE, dSPM, sLORETA, and eLORETA, with improved (significant) anatomical alignment to surgical ground truth. Application to low- and high-density clinical datasets further demonstrates the ability of GBF to identify seizure-onset zones (SOZ) closer to clinician-annotated regions, with frequency-domain Granger causality revealing plausible propagation hierarchies within pathological networks.

Implications and Future Directions

The GBF framework represents a key methodological advance for noninvasive electrophysiology, offering participant-specific, geometry-constrained source imaging that bridges the anatomical and functional architecture of the brain. By leveraging cortical eigenmodes, it supports both focal and distributed dynamics analysis while maintaining computational tractability and inherent interpretability.

Several directions are highlighted for future work:

• Subcortical Extension: Preliminary feasibility for subcortical source reconstruction is demonstrated; further validation in deep structures (e.g., thalamus, hippocampus) is warranted.
• Spatiotemporal Priors: Incorporating temporally structured or state-space priors could further enhance dynamic tracking fidelity and real-time applications.
• Integration with Deep Learning: GBFs are proposed as compact geometric tokens for multimodal foundation models and geometry regularized neural architectures.
• Clinical Robustness: Expansion to larger, more diverse populations and explicit handling of lesioned/malformed cortex will generalize applicability, especially in neurodevelopmental disorders and structural pathologies.

Conclusion

This geometry-aware ESI framework, based on Laplace-Beltrami-derived GBFs, delivers substantial improvements in spatial accuracy, functional interpretability, and generalizability for EEG/MEG source imaging. It robustly aligns neural dynamics with intrinsic cortical geometry, facilitates cross-modal and clinical validation, and establishes a principled foundation for both scientific inquiry and translational neuroengineering applications. The approach opens new opportunities for anatomically constrained analysis of large-scale neural waves, network dynamics, stimulation propagation, and the clinical management of focal brain pathologies.