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Sparsity Enables Estimation of both Subcortical and Cortical Activity from MEG and EEG
Pavitra Krishnaswamy, Gabriel Obregon-Henao, Jyrki Ahveninen, Sheraz Khan, Behtash Babadi, Juan Eugenio Iglesias, Matti S. Hamalainen, Patrick L. Purdon
TL;DR
Estimating subcortical electrophysiological activity in humans remains difficult: deep signals are weaker than cortical signals, and cortical activity can mimic deep-source fields. This paper uses sparse cortical representations in an inverse approach to estimate simultaneous cortical and subcortical activity. The reported algorithm performs better than alternatives for subcortical structures and similarly to existing approaches for cortical structures.
Problem
Human deep-brain electrophysiology is difficult to characterize, and M/EEG estimation is challenged by weaker deep signals and cortical fields that can mimic subcortical sources.
Source: INTRODUCTION · pp. 1–2Method
The paper analyzes sparse cortical and subcortical source patterns and uses a sparse-subset pursuit procedure to estimate sources from M/EEG data.
Source: INTRODUCTION · p. 2, Inverse Algorithm · p. 6Results
The algorithm performs better than alternatives for subcortical structures and similarly to existing approaches for cortical structures.
Source: DISCUSSION · p. 9Takeaways & Limitations
Sparse subdivisions of cortical and subcortical structures yield distinguishable field patterns, supporting their use in source estimation.
Source: DISCUSSION · p. 9The approach’s feasibility depends on field-pattern overlap and measurement signal-to-noise ratio, under the assumption that only a limited number of cortical sites are active.
Source: INTRODUCTION · p. 2
Abstract
from arXiv · showhide
Subcortical structures play a critical role in brain function. However, options for assessing electrophysiological activity in these structures are limited. Electromagnetic fields generated by neuronal activity in subcortical structures can be recorded non-invasively using magnetoencephalography (MEG) and electroencephalography (EEG). However, these subcortical signals are much weaker than those due to cortical activity. In addition, we show here that it is difficult to resolve subcortical sources, because distributed cortical activity can explain the MEG and EEG patterns due to deep sources. We then demonstrate that if the cortical activity can be assumed to be spatially sparse, both cortical and subcortical sources can be resolved with M/EEG. Building on this insight, we develop a novel hierarchical sparse inverse solution for M/EEG. We assess the performance of this algorithm on realistic simulations and auditory evoked response data and show that thalamic and brainstem sources can be correctly estimated in the presence of cortical activity. Our analysis and method suggest new opportunities and offer practical tools for characterizing electrophysiological activity in the subcortical structures of the human brain.
INTRODUCTION
Human deep-brain electrophysiology is difficult to characterize, and whether M/EEG can resolve subcortical currents remains open. The paper examines whether sparse cortical activity can help distinguish and estimate simultaneous cortical and subcortical sources.
INTRODUCTION
- Improved human tools for characterizing subcortical activity could support analysis of its interactions with other brain areas and its relation to perception, cognition, behavior, and disorders.The paper motivates this need with subcortical roles in sensory processing, sleep, arousal, movement, memory, emotion, and learning.Source: INTRODUCTION · p. 1
- Deep-brain dynamics are difficult to characterize in humans: invasive recordings are clinically limited, while fMRI cannot capture fast signals or oscillations.M/EEG offers non-invasive, millisecond-scale measurements, but its ability to estimate deep currents is unresolved.Source: INTRODUCTION · p. 1
- Deep sources produce weaker M/EEG signals than cortical sources, and cortical currents can potentially mimic deep-source measurements.This ambiguity complicates estimating subcortical activity during simultaneous cortical activity.Source: INTRODUCTION · pp. 1–2
- The authors propose that restricting active cortical sources to a sparse subset may permit recovery of both cortical and subcortical locations and time courses.Feasibility depends on field-pattern overlap and measurement signal-to-noise ratio.Source: INTRODUCTION · p. 2
- The paper analyzes cortical and subcortical M/EEG field patterns, introduces a hierarchical sparse inverse method, and evaluates it on simulated and experimental data.The evaluation includes data containing both cortical and subcortical activity.Source: INTRODUCTION · p. 2
A. Patches on Cortical Surface
The paper represents cortical and subcortical activity in a distributed source space and introduces a sparse estimation approach for characterizing both. Its example field patterns contrast focal cortical fields with more distributed subcortical fields.
A. Patches on Cortical Surface
- The full source space combines cortical surface patches with subcortical volume subdivisions and hippocampal surface patches.The cortical patches are 650 mm2; subcortical subdivisions range from 175–1800 mm3, and hippocampal patches are 47 mm2.Source: Figure 1 · p. 2
- Example MEG fields are more focal for a cortical patch and more distributed for a brainstem subdivision.The examples are noiseless field patterns from frontotemporal cortex and brainstem.Source: Figure 1 · p. 2
- The paper introduces a sparse estimation algorithm to characterize cortical and subcortical activity and evaluates it on simulated and experimental M/EEG data.The data contain both cortical and subcortical activity.Source: A. Patches on Cortical Surface · p. 2
THEORY
The theory models measured M/EEG fields as arising from neural current dipoles. It expresses the fields using a gain matrix, source amplitudes, and measurement noise.
THEORY
- Neural currents, modeled as an ensemble of current dipoles, generate the measured M/EEG fields.The model represents the fields as Y = GX + V.Source: THEORY · p. 2
- The gain matrix G is determined by the quasistatic approximation of Maxwell’s equations.G relates source currents to measured fields in the model.Source: THEORY · p. 2
- In the model, X contains current-dipole source amplitudes, V is noise, and N, M, and T count sensors, sources, and measured time points.The dimensions are Y_N×T = G_N×M X_M×T + V_N×T.Source: THEORY · p. 2
B. Subcortical Field Pattern
A deep-source field can be closely reproduced by currents spread across the full cortical source space, creating ambiguity. The authors find that sparse cortical activity can make cortical and subcortical field patterns distinguishable.
B. Subcortical Field Pattern
- The distributed source space groups cortical and subcortical dipoles into patches or volume subdivisions, with gain matrices and source currents defined for each division.The full space combines neocortical and hippocampal surfaces with subcortical regions.Source: B. Subcortical Field Pattern · p. 3
- A cortical minimum-norm fit reproduces a simulated VPL thalamic MEG field with 98.5% goodness-of-fit using small currents spread across several cortical patches.The fitted cortical field pattern is nearly indistinguishable from the subcortical pattern.Source: Figure 2 · p. 2, B. Subcortical Field Pattern · p. 3
- With the full cortical source space, subcortical currents cannot be unambiguously estimated because cortical and subcortical gain patterns overlap.The maximum principal angle between any subcortical gain matrix and the cortical gain matrix was 1.5×10^-13 degrees.Source: B. Subcortical Field Pattern · p. 3
- For sparse cortical and subcortical divisions, median principal angles are 42.3° between subcortical and cortical configurations and 62.7° between mutually exclusive cortical configurations.Subcortical and cortical field patterns with principal angles as low as 45° are reported as clearly distinguishable.Source: B. Subcortical Field Pattern · p. 3
- Spatial sparsity constraints can distinguish cortical and subcortical field patterns, motivating an inverse algorithm for simultaneous activity localization.The analysis is described as a conservative scenario and reports similar trends in more general cases.Source: B. Subcortical Field Pattern · p. 3
INVERSE ALGORITHM
Hierarchical sparsity combines cortical pruning with subcortical source selection to estimate both source types. In simulations, the resulting estimates were mostly near-diagonal, with median spatial dispersion and dipole localization error of 0.737 cm.
INVERSE ALGORITHM
- In the median-nerve example, cortical and subcortical MEG field patterns remained spatially distinct even at a principal angle of 30°.The figure reports stronger distinctions for principal angles greater than 45°.Source: Figure 3 · p. 4
- For the distributed cortical and subcortical source space, MNE had median spatial dispersion of 4.23 cm and median dipole localization error of 1.89 cm.Cortical localization error was approximately 0.5 cm, compared with 2–3 cm for subcortical sources, which spread toward the cortex.Source: INVERSE ALGORITHM · p. 4
- Median spatial dispersion and dipole localization error were both 0.737 cm with hierarchical subspace pursuit, a substantial improvement over solutions without sparsity constraints.The empirical resolution matrix was near-diagonal for most cortical and subcortical sources.Source: Figure 4 · p. 5, INVERSE ALGORITHM · p. 6
- With sparse cortical regions but all subcortical divisions, MNE reduced subcortical spread to cortex, but median spatial dispersion remained 2.10 cm and dipole localization error was 0.805 cm.Subcortical estimates still spread across the subcortical source space.Source: INVERSE ALGORITHM · pp. 4–5
Inverse Algorithm
- The algorithm applies subspace pursuit to distributed cortex, refines cortical estimates from coarse to fine, then jointly selects cortical and subcortical sources.The final pass estimates source locations and neural-current time courses from the composite space.Source: Inverse Algorithm · p. 6
DATA EXAMPLES
The examples test hierarchical sparse estimation on a noisy somatosensory simulation and auditory evoked recordings. Estimates recover cortical and subcortical activity in both cases, including weak thalamic fields and auditory brainstem responses.
Somatosensory Evoked Simulations
- In the somatosensory simulation, estimated cortical and thalamic locations and time courses closely match ground truth, including the phasic on/off thalamic pattern without cortical leakage.A weak, relatively constant stray estimate appears in the right thalamus.Source: Figure 5 · p. 7, DATA EXAMPLES · pp. 7–8
- The simulated thalamic fields fall below the noise floor despite cortical activity, making recovery a test of phasic, temporally overlapping sources under low signal strength.The simulation used additive Gaussian noise at an SNR of approximately 7 dB.Source: DATA EXAMPLES · p. 7
Auditory Evoked Response Experiments
- The auditory estimates localize middle-latency activity to auditory cortex and early-latency activity primarily to the inferior colliculus, with time courses consistent with Na-Pa and Wave V peaks.The early-latency recordings had relatively low-SNR Wave V peaks.Source: Figure 6 · p. 8, DATA EXAMPLES · p. 9
Somatosensory Evoked Simulations
- The algorithm significantly outperforms methods without sparsity and hierarchy, and both principles are necessary to accurately resolve thalamic source locations and time courses.Hierarchical sparsity also helps recover the true regional distribution of mean source activity.Source: DATA EXAMPLES · p. 8
DISCUSSION
The discussion argues that sparse cortical and subcortical activity can be distinguished despite fundamental ambiguity in M/EEG source estimation. It presents hierarchical subspace pursuit as a practical approach and identifies potential extensions for more extended cortical activity.
DISCUSSION
- When cortical and subcortical source distributions are sparse, their field patterns can be distinguished and the otherwise ambiguous resolution problem becomes tractable.The authors note that this condition is relevant in many neuroscience investigations.Source: DISCUSSION · p. 9
- The hierarchical algorithm estimates sparse cortical and subcortical sources and performs better than alternatives for subcortical structures, with similar performance for cortical structures.The approach is reported to resolve simultaneous sources even when their activities overlap in time and under low-SNR conditions.Source: DISCUSSION · p. 9
- The method automatically finds source constellations, unlike fitting multiple dipolar sources, which usually requires tailored and often interactively guided strategies.It represents subcortical activity with distributed dipoles within anatomical subdivisions rather than isolated current dipoles.Source: DISCUSSION · p. 9
- Distributed sparse representations and dynamical sparsity constraints are suggested as possible extensions for estimating subcortical sources when cortical activity is more extended.Source: DISCUSSION · p. 9
- The authors report demonstrating the algorithm on realistic simulations and experimental data and present it as a practical tool for estimating simultaneous cortical and subcortical activity.Source: DISCUSSION · p. 9
METHODS
The methods construct MRI-based cortical and subcortical source spaces, derive whitened forward models, and analyze field-pattern distinguishability. A hierarchical sparse inverse procedure is then applied to simulated and recorded M/EEG data.
Acquisition
- MRI and M/EEG were acquired from five healthy subjects, while auditory evoked responses were recorded in two healthy subjects using simultaneous MEG and EEG.The auditory protocol used binaural broadband click trains and collected more than 10,000 epochs for averaging.Source: METHODS · pp. 9, 11
Source Space Construction
- MRI segmentation defined cortical surfaces and subcortical volumes, which were represented by cortical patches and subcortical subdivisions grouped to homogenize signal strengths.The source space included thalamus, putamen, caudate, brainstem, and amygdala.Source: METHODS · p. 10
Forward Solutions
- MRI-based forward solutions were whitened using observation-noise covariance estimates, and gain matrices were scaled for regional current strengths and reduced to capture over 95% of spectral energy.Source: METHODS · p. 10
Analysis of Forward Solutions
- The field-pattern analysis fit subcortical fields with cortical sources using regularized minimum norm, then quantified fit and compared possible regional patterns using principal angles.The angle analysis considered subsets of gain-matrix eigenmodes for each region.Source: METHODS · p. 10
Analysis of Resolution Matrices
- Resolution matrices were used to evaluate minimum-norm and subspace-pursuit solutions with spatial dispersion and dipole localization error measures.Spatial dispersion measures source spread, while localization error measures the distance between division centroids.Source: METHODS · p. 10
Source Estimation Algorithm
- At each hierarchy level, a modified subspace-pursuit algorithm selects sparse source subsets using a minimum-norm proxy and an adaptive mutual-coherence threshold.The relaxed thresholds varied approximately from 0.75 to 0.90 across hierarchy levels.Source: METHODS · pp. 10–11
Simulations and Recordings
- Somatosensory simulations combined thalamic and cortical responses with Gaussian noise, while recorded M/EEG data were filtered into brainstem and middle-latency auditory response bands before source estimation.The simulation used approximately 7 dB SNR; recorded data were whitened using noise covariance estimates from baseline recordings.Source: METHODS · p. 11