Exploring Deep Magnetoencephalography via Thalamo‐Cortical Sleep Spindles

ABSTRACT

Subcortical brain regions like the thalamus are integral to numerous sensory and cognitive functions. Magnetoencephalography (MEG) enables the study of widespread brain networks with high temporal resolution, but the degree to which deep sources like the thalamus can be resolved remains unclear. Functional connectivity methods may enhance differentiation, yet few studies have extended them beyond the cortex. We investigated the possibility of resolving deep sources via connectivity patterns during thalamo‐cortical sleep spindles to leverage their well‐characterized circuitry, and during spindle‐free periods of non‐rapid eye movement sleep to explore neural recordings that lack such high‐amplitude bursts of activity. MEG and electroencephalography (EEG) were recorded in 19 participants during a 2‐h nap. Spindle and non‐spindle periods were identified, and connectivity was assessed using coherence and imaginary coherence within a spindle‐related network. Graph theory was also applied to identify network hubs. As expected, functional connectivity increased during spindles within a distributed thalamo‐cortical‐hippocampal network. Cortical connectivity patterns allowed differentiation among small thalamic nuclei, but metric choice and contrast use influenced topography and distance effects. Graph theory revealed distinct cortical, thalamic, and hippocampal contributions to fast (13–16 Hz) and slow (10–13 Hz) sigma‐band connectivity. These findings demonstrate that MEG functional connectivity can resolve deep brain networks during NREM sleep and during spindles, and demonstrate how it can be used to study the functional roles of subcortical regions non‐invasively in healthy humans. By clarifying methodological influences, we aim to guide future research design and interpretation.

Results from functional connectivity analyses of MEG data (left) show that many thalamic nuclei can be distinguished via functional connectivity (right). However, results depend on the metric and contrast of choice, and the distance between regions.

Summary.

• Patterns of functional connectivity with the cortex can be used to resolve thalamic nuclei in magnetoencephalography data.

• Coherence and imaginary coherence are differently affected by the distance between regions of interest.

• Graph theory tools can provide insights into temporally resolved, whole‐brain connectivity patterns, including subcortical sources.

• These techniques may facilitate studies on the functional roles of thalamic nuclei, such as during sleep spindles.

1. Introduction

Subcortical structures, particularly the thalamus, are increasingly recognized not merely as relays to the cortex, but as integral components of the neural circuits that support cognition and experience‐dependent plasticity (Dehghani and Wimmer 2019; Ward 2013; Mölle and Born 2011). For example, recent data emphasize the thalamus' integrative roles in learning and memory, and in flexible adaptation, which possibly underlie more general roles in shaping mental representations (Wolff and Vann 2019). Recent studies in animal models have also revealed surprising levels of plasticity in deep brain structures including the thalamus, which challenge the traditional view that cortical areas are the primary sites of experience‐dependent change. For instance, experience‐dependent shifts in thalamic feature selectivity have been observed even in adult animals, suggesting that the thalamus plays a more active role in neuroplasticity than previously appreciated (Sonoda et al. 2025). To date, the study of temporally resolved neural activity in deep subcortical structures such as the thalamus in healthy humans has been limited by methodological constraints, resulting in limited knowledge of how the many non‐sensory thalamic nuclei are involved in cognition (Ward 2013). As a result, much of human neuroscience has remained cortex‐focused, potentially overlooking critical dynamics within corticothalamic and broader corticosubcortical circuits.

Noninvasive neuroimaging methods such as electroencephalography (EEG) and magnetoencephalography (MEG) allow researchers to study brain networks and functions in a temporally resolved manner. MEG, in particular, also has good spatial resolution (Baillet 2017), which allows the characterization of patterns of neural activity throughout the cortex. While MEG has traditionally been viewed as best suited to recording activity from superficial cortical regions, a growing body of work over the past two decades has demonstrated its capacity to detect signals from deep brain structures (Piastra et al. 2021; López‐Madrona et al. 2022; Pizzo et al. 2019), including the hippocampus, amygdala, cerebellum, and thalamus (Attal et al. 2009; Attal and Schwartz 2013; Roux et al. 2013; Bénar et al. 2021; Pu et al. 2018; Ruzich et al. 2019). These studies, combining realistic simulations and empirical data, including comparisons with intracranial recordings, have shown that deep sources (including the thalamus) are resolvable under appropriate conditions, demonstrating MEG's potential as a tool to study neural circuitry in the brain as a whole, especially when using sensitive study designs and advanced source modeling. However, the limits of MEG's deep sensitivity remain incompletely defined, particularly at the level of finer spatial resolution. In the case of the thalamus, which lacks the consistent laminar structure of cortex and whose subnuclei are compact and spatially proximal, it remains an open question whether MEG‐based analyses can meaningfully resolve differential activity or connectivity patterns across its subregions.

This situation results in part from the ill‐posed inverse problem of source reconstruction. Activity at numerous dipoles in the brain (i.e., > 30,000) are reconstructed from data recorded from relatively few sensors, which means that multiple neural configurations can give rise to similar patterns of activity at the sensor level (Baillet 2017). The magnetic fields generated by neural currents can overlap at MEG sensors, resulting in signals that contain contributions from multiple brain sources, making them difficult to accurately localize. Additionally, source reconstruction methods can assign estimated activity to incorrect brain locations, a phenomenon known as “crosstalk” or “point spread” (Liu et al. 1998; Baillet 2017), which is a property of the inverse estimation method. Signals in subcortical regions can be particularly affected by these factors, due to their geometry and distance from the sensors, further compounded by the inherently weaker MEG signals from subcortical regions (Liu et al. 1998), which can lead to poor spatial specificity and increased crosstalk (Colclough et al. 2016). These conditions can potentially lead to spurious connectivity between regions, as activity from one cortical area may be incorrectly attributed to nearby subcortical structures. However, the observation that signals generated in subcortical regions might be subject to more spread than those in cortex does not imply the absence of useful data.

In addition to the literature demonstrating MEG's ability to resolve deep structures, some literature emphasizes how functional connectivity analyses can contribute to detecting and separating signals from deep sources. Functional connectivity analyses measure the communication between different parts of the brain through relationships between their neurophysiological signals. Notably, in their review of the literature of MEG's ability to measure signals from the human cerebellum, Andersen et al. (2020) challenge the assumption that MEG is fundamentally limited to cortical signals and highlight that long‐range functional connectivity (e.g., coherence between cerebellum‐thalamus‐cortex) can serve as a robust means of detecting deep brain activity, even when signal strength is low or when spatial resolution is limited. Functional connectivity methods applied in MEG source space have successfully detected thalamic activity and thalamo‐cortical circuits (Müller et al. 2019; David et al. 2011; Roux et al. 2013; Muthuraman et al. 2014). Graph theory tools can also supplement functional connectivity by describing network properties and uncovering hidden structures in neural communications (Bullmore and Sporns 2009). Functional connectivity, sometimes combined with graph theory, is being increasingly used to understand brain function at multiple spatial and temporal scales simultaneously (He et al. 2011; Greenblatt et al. 2012; Sadaghiani et al. 2022; Avena‐Koenigsberger et al. 2018; Betzel 2023).

However, despite these promising findings, functional connectivity in EEG/MEG has overwhelmingly been applied to source reconstructions of the cortical surface. Comparatively little work has examined subcortical sources, due to methodological uncertainties. Neural tissues in subcortical regions generally do not share the cortex's laminar organization, meaning that a volume‐source model may be more appropriate than a surface model when reconstructing them (Coffey et al. 2016). Surface models, commonly used for cortical sources, assume that neural activity arises from dipoles with orientations constrained to the folded cortical sheet, which is a valid assumption for the cortex, where pyramidal neurons are aligned perpendicular to the cortical surface. However, subcortical structures like the thalamus lack this consistent laminar structure, and their neuronal populations are more heterogeneously oriented. Volume‐source models allow for unconstrained dipole orientation and distribution throughout the brain volume, making them more appropriate for modeling neural activity in deep structures with complex microarchitecture (Baillet et al. 2002; Wendel et al. 2009). These models are less frequently used and introduce some additional analytic complexity due to the three‐dimensional nature of their signals. Furthermore, the above‐mentioned issues regarding source reconstruction and signal spread can yield spurious and inflated connectivity values among deep sources (Colclough et al. 2016).

One partial solution to the latter problem is to use connectivity metrics which correct for signal spread by removing instantaneous activity (characterized by zero phase‐lag connectivity between two sources). For instance, imaginary coherence (ICOH) computes the similarity between two signals based on spectral amplitude and phase, but removes the real part of coherence (COH) and retains only the imaginary part which ensures that only activity which has a temporal delay between the two regions is retained in the calculation of connectivity (Nolte et al. 2004; Bowyer 2016). Using such corrected metrics in connectivity analyses rests on the assumption that signals measured at the same time in different brain regions are not physiologically meaningful. As axonal conduction between brain regions should cause some delay, signals that are temporally synchronized are assumed to be artifacts of signal spread (i.e., activity from the same source being attributed different spatial locations). However, some literature suggests that true zero‐phase lag activity is biologically possible; for example, phase‐locking loops have been reported in which neuronal ensembles in distant regions synchronize their activity to allow long‐range information exchange (Gollo et al. 2010; Vicente et al. 2008). Therefore, it is likely that removing zero‐phase lag connectivity may not only remove spurious connectivity patterns, but also remove signals of experimental interest. A better understanding of how exclusion of the zero‐phase component affects measurements, as well as how connectivity measures relate to brain activity in and between deep sources and the cortex is needed to support design and analysis choices in MEG cognitive neuroscience research (Van Diessen et al. 2015; Bastos and Schoffelen 2016; Marzetti et al. 2019).

One option to assess the ability for MEG to probe deep sources using functional connectivity and to investigate the effects of design choices such as removing zero‐lag information is to validate analytic techniques on a biological test case with relatively well‐known physiology that includes both cortical and subcortical structures. Exploring circuits involving the thalamus in particular would be of broad scientific relevance, as it has a complex architecture and is involved in numerous cognitive processes from perception to attention to emotional processing and memory (Schiff 2008; Ward 2013; Saalmann and Kastner 2015; Wolff and Vann 2019). It is also an important brain region in many forms of psycho and neuro‐pathology (Cronenwett and Csernansky 2010; Biesbroek et al. 2024), yet it has scarcely been studied in the context of non‐invasive functional connectivity (but see David et al. (2011); Roux et al. (2013); Müller et al. (2019)).

We propose that the thalamo‐cortical sleep spindle is a useful candidate for evaluating applications of functional connectivity metrics in MEG deep sources. Sleep spindles are transient waxing and waning thalamo‐cortical oscillations that occur during non‐rapid eye movement (NREM) sleep stages 2 and 3 (NREM2, NREM3). They are relatively high‐amplitude signals which occur in a defined frequency range (~10‐16 Hz), and their generation, topographical distribution and other properties are relatively well understood (see Box 1 for a summary of spindle physiology relevant for interpreting the connectivity analyses in this work, and Fernandez and Lüthi (2020) for a comprehensive review of sleep spindles). Critically, spindles are generated through interactions between both cortical and deep thalamic sources, and different spindle types (e.g., fast vs. slow) show distinct frequency characteristics and spatial distributions across the cortex. The thalamus itself is organized into anatomically and functionally distinct nuclei with varying patterns of connectivity to different cortical regions, making spindles a promising case for evaluating whether MEG‐based functional connectivity can resolve nucleus‐specific contributions within deep thalamo‐cortical circuits. Beyond their methodological utility, spindles are also of high importance to cognitive neuroscience, as they are involved in sleep‐dependent memory consolidation (Mölle and Born 2011; Boutin and Doyon 2020), are correlated with cognitive ability (Fang et al. 2017; Ujma 2021), as well as cognitive decline in older adulthood (Clawson et al. 2016), and are implicated in various neuro‐degenerative diseases and pathologies (Weng et al. 2020; Neylan and Walsh 2022; Herrera and Tarokh 2024), making validating new means of investigating them of high interest to the research community.

BOX 1. Overview of Spindle Physiology.

Sleep spindles are generated when thalamo‐cortical neurons fire in excitatory rebound burst discharges in response to inhibitory bursts from the thalamic reticular nucleus (a thin sheet of cells surrounding the entire thalamus) (Fernandez and Lüthi 2020). Spindles begin as predominantly local events, recruiting only some thalamic nuclei and projecting focally to middle cortical layers (Andrillon et al. 2011; Bastuji et al. 2020). Cortical regions receiving spindle inputs then project back down to the same thalamic nucleus, but also branch out to innervate nuclei immediately adjacent to the one from which inputs were originally received (Figure A below). Spindles can then spread in this way across the thalamus and cortex, into widespread synchronized events; these are the spindles most often detected in dorsal EEG derivations. Spindles are often classified into fast (13–16 Hz) and slow (10–13 Hz) spindles. Fast spindles span mostly centro‐parietal areas and are involved in offline declarative and motor memory consolidation (Cairney et al. 2018; Petzka et al. 2022; Barakat et al. 2011), whereas slow spindles are found largely over frontal areas (Mölle et al. 2011), and their roles are less clearly defined (Figure B below). Additionally, spindles occur within a broader context of nested oscillations, where slower hippocampal rhythms can modulate thalamo‐cortical spindle activity, creating hierarchical coupling across multiple frequency bands and brain regions (Figure C) (Staresina et al. 2015).

The purpose of this work is to investigate the extent to which MEG functional connectivity can tease apart small proximal sources deep in the brain. More specifically, we explore whether MEG can differentiate thalamic subregions based on their functional connectivity with the cortex. Rather than attempting precise localization of thalamic activity per se, we evaluate whether different thalamic nuclei exhibit distinguishable cortical connectivity profiles across both spontaneous NREM epochs and during sleep spindles. Our approach assumes that if MEG can capture structured variation in thalamic‐cortical connectivity—such that connectivity patterns are more self‐similar across datasets than between nuclei—then functional differentiation of thalamic subregions may be possible, even if the underlying source estimates contain noise or cross‐talk. While MEG‐based detection of deep sources is supported by growing literature, substantial uncertainty remains, particularly in the absence of direct ground‐truth validation. Our goal is therefore to assess the viability and limitations of functional connectivity as a means of probing deep networks, using sleep spindles as a physiological window into dynamic thalamo‐cortical coupling.

We recorded EEG and MEG data in 19 healthy young adults during a daytime nap and examined connectivity in cortical and subcortical sources during NREM sleep with and without sleep spindles. We perform a neural fingerprinting analysis to assess whether patterns of communication with the cortex can be used to consistently distinguish thalamic nuclei from one another. Additionally, we consider whether comparable thalamic resolution can be achieved when spindles are not present during baseline NREM epochs, increasing the generalizability of the methods results beyond the study of sleep spindles. We explore factors that influence analytic outcomes, such as choice of connectivity metric (i.e., COH versus ICOH), the use of a contrast (i.e., the difference in connectivity during a neural event vs. in its absence), and distance between ROIs. We also explore how graph theory partitions can supplement connectivity to distinguish between small, proximal nuclei in the thalamus. Finally, we discuss the implications and possibilities afforded by our approach for future research.

2. Materials and Methods

2.1. Participants

Nineteen neurologically healthy young adults were recruited. All participants were right‐handed and had no history of neurological or sleep disorders (mean age: 21.65 years; SD = 2.84; 13 female). The sample size was determined as being in line with previous work looking at behavioural or neurophysiological changes associated with a motor learning task (Boutin et al. 2018; Pinsard et al. 2019), which was a parallel motivation for collecting the present dataset (the results of the behavioural task are not relevant for the current work and are not presented herein). Informed consent was obtained, all experimental procedures were approved by the Montreal Neurological Institute (MNI) Research Ethics Board and Concordia University's Human Research Ethics Committee, and participants were compensated for their time.

2.2. Procedure

Upon arrival at the lab, informed consent was obtained. Subjects changed into comfortable sleeping clothes and were prepared for EEG (as in Jourde et al. (2024)). Head shape and the location of head position indicator coils were digitized (Polhemus Isotrak, Polhemus Inc., VT, USA) for co‐registration of MEG with a standard anatomical T1‐weighted magnetic resonance image (MRI). Participants entered the magnetically shielded MEG chamber and positioned themselves in the supine recording position to become familiar with the environment. Researchers confirmed that there was no electromagnetic interference from their clothing or body with the MEG sensors. A 5 min resting‐state scan was first recorded with simultaneous EEG and MEG. Participants then performed a basic motor sequence learning task with their left hand (as in Walker et al. (2003)) to address research questions for a different study. Another 5 min resting‐state scan was taken after the learning session. The lights were then dimmed and participants had a 2.5‐h nap opportunity while MEG‐EEG was recorded. Standard T1‐weighted anatomical data (176 slices, FOV = 256 × 256, TR/TE/TI: 2300/2.98/900 m s, voxel size = 1 mm isotropic) were also acquired in a subsequent appointment using a MPRAGE pulse sequence on a 3 T Siemens MRI scanner for purposes of modeling neural sources.

2.3. MEG Data Collection and Pre‐Processing

Two hundred and seventy channels of MEG (axial gradiometers), five channels of EEG data (C3, C4, Cz, M1 and M2; 10–20 system Homan et al. (1987)), electrooculogram (EOG) and electrocardiogram (ECG), and one audio channel were simultaneously acquired using a CTF MEG System and its in‐built EEG system (Omega 275, CTF Systems Inc.). Eye blink and heartbeat artifacts were detected and removed from the MEG signal using the Brainstorm software (Tadel et al. 2011). Data were sampled at 2400 Hz, band‐pass filtered (0.1–55 Hz), down‐sampled (200 Hz), and 30 s epochs were sleep‐scored according to standard criteria (AASM; Berry et al. 2012).

Sleep spindles were detected in NREM2 and NREM3 sleep stages at the Cz electrode in EEG, referenced to the right mastoid, because spindles are known to peak over centro‐parietal regions near Cz (Cox et al. 2017). We used a standard offline detection algorithm (Lacourse et al. 2019), which defines spindles according to absolute and relative sigma band power (10–16 Hz), as well as the correlation and covariance between the original EEG signal and sigma band‐passed signal (absolute sigma = 0.8; relative sigma = 1.0; covariance = 1.0; correlation = 0.4). In this algorithm, a spindle is detected when the sigma‐band envelope exceeds a fixed absolute power threshold (absolute sigma) and is also elevated relative to the surrounding baseline (relative sigma). To improve specificity, additional thresholds are applied to the covariance and correlation between the original EEG and sigma‐filtered signal, which help to ensure that detected events exhibit the expected waveform morphology of true spindles (please see Lacourse et al. (2019) for additional details). T1 MRI images were segmented with Freesurfer software (Fischl et al. 2002; Fischl 2012) and were used along with head position information to compute overlapping spheres volume‐based forward head models. These models describe how electrical currents within the brain would be detected by the sensors. Before each recording session, we computed a noise covariance matrix from 2 min empty room recordings. Using the forward model and noise covariance matrix, we then computed minimum norm estimate (MNE) unconstrained volume source models (source grid = 5 mm, depth weighting = 0.7) which attempt to spatially reconstruct the sources of signals detected by the sensors by estimating activity based on the spatial constraints of each subject's head model. Finally, we extracted time series from the mean of each region of interest (ROI) in 1.7 s time windows from the start of sleep spindles. Because we model the brain as a volume, each time series extracted from a region of interest yields a 3‐dimensional signal.

2.4. Regions of Interest

ROIs included 15 thalamic nuclei and 10 cortical regions per hemisphere, including portions of the subiculum in the hippocampal formation. Cortical regions were selected in order to sample a distribution of cortical areas spanning from parietal to frontal regions, where spindles are known to occur. Regions were selected from the HCP‐MMP1 atlas, which delineates 180 cerebral regions per hemisphere based on architecture, function, connectivity, and topography derived from multi‐modal MRI images from the Human Connectome Project (Glasser et al. 2016). All thalamic nuclei were defined according to the AAL3v1 (Rolls et al. 2020). Seed coordinates with the highest probability of belonging to a given region were identified using the software FSL (Jenkinson et al. 2012), and each ROI was subsequently expanded to roughly match other ROIs in volume. Average volume of ROIs was 0.54 cm³ for cortical regions (SD = 0.26 cm³) and 0.23 cm³ for thalamic regions (SD = 0.23 cm³). The anterior and posterior subiculum (aSUB, pSUB) were defined in a similar way using a 3 T MRI human hippocampal subfield atlas (Winterburn et al. 2013). We included the subiculum in the network since it constitutes the primary output of the hippocampus with important projections to frontal cortical and thalamic regions and has been shown to be involved in offline memory reprocessing (Andrade et al. 2011). Finally, the hand knob (HK) was identified for each subject individually based on their T1 MRI. This was motivated by the fact that participants performed a motor sequence learning task prior to sleep for the purposes of another study, and spindles have been shown to be more present in brain regions that were used before sleep (Johnson et al. 2012; Fogel et al. 2017). Although we did not look at behaviour in the present work, we included regions that are likely to generate spindle activity. Figure 1 below represents all ROIs considered in our network.

FIGURE 1.

Regions of interests and abbreviations. (A) Schematic representation of cortical, hippocampal and thalamic ROIs considered in the network. Colours of nuclei in the thalamus are matched to cortical regions to illustrate general anatomical relationships (note that structural relationships were not used as validation criteria in the present analyses). For example, the ventral‐posterior‐lateral (VPL) nucleus projects primarily to sensory regions in centro‐parietal lobes. Note that the pulvinar (light grey) has not been colour coded here as it projects broadly across the cortex, with important connections to parietal and occipital lobes. (B, C) Names and abbreviations for all cortical and thalamic ROIs. The subiculum is included in cortical ROIs.

2.5. Functional Connectivity Analyses

For functional connectivity analyses, we computed coherence (COH) and imaginary coherence (ICOH) on all pairs of time‐series extracted from our ROIs. COH is a connectivity metric that measures the similarity between two signals based on both phase and spectral amplitude. ICOH is similar but removes any zero‐phase lag activity between the two signals to ensure that connectivity is not inflated by signal leakage (Nolte et al. 2004). Spindle epochs were defined as 1.7 s time windows from the start of a spindle detection, on account of the fact that the average spindle length was 1.5 s. Clear epochs are defined as 1.7 s time windows of NREM2 or NREM3 sleep with no spindle present. To tease apart proximal signals in the thalamus and to partially mitigate signal leakage issues, we computed a difference matrix representing the change in connectivity from clear to spindle epochs between all regions (Spindles—Clear). We refer to this difference matrix as the Contrast condition. This approach emphasizes task‐locked changes in connectivity by isolating modulations specific to spindle events rather than relying on absolute connectivity levels. Both spindle and non‐spindle epochs share the same biophysical constraints (e.g., tissue conductivity, head geometry, and forward model). Therefore, while connectivity changes between conditions, some signal leakage artifacts remain constant and are subtracted out through the use of a contrast (He et al. 2020). Both Contrast and Spindle conditions provide complementary information, and subsequent results will specify whether analyses were performed on Clear, Spindle, or Contrast conditions.

2.6. Dimension Reduction

Because our unconstrained source models treat the brain as a volume, signals extracted from ROIs produce three time‐series, representing the 3 axes, or dimensions of the complex signal coming from a particular source. This complicates data analysis as compared with the uni‐dimensional signals that are generated using surface‐based cortical approaches. To simplify connectivity analyses, we use a dimension reduction approach which involves running connectivity metrics on all possible pairs of signal dimensions between two ROIs, yielding a 3 × 3 connectivity matrix for each pair of regions (see Figure 2A for an illustration). We then select the maximum connectivity across all 9 combinations, thus reducing the matrix to a single value. This process is grounded in empirical tests which demonstrated that retaining the maximum value across coherence spectra yields robust connectivity estimates (see Brainstorm's corticomuscular coherence tutorial, online). For each subject, we run this dimension reduction process on every spindle and clear epoch individually, and for both COH and ICOH separately.

FIGURE 2.

Dimension reduction technique and thalamic differentiation methods. (A) Dimension reduction. 3‐Dimensional signals are extracted from ROIs, representing the x, y and z components of the signal. Connectivity is computed between every possible pair of signals between two ROIs, yielding 9 connectivity values for each pair of ROIs. The maximum connectivity value is retained and other values are discarded. (B) Thalamic differentiation. The goal is to tease apart the behaviour of small proximal nuclei in the thalamus. Thalamic nuclei are differentiated by comparing patterns of cortical connectivity between each nucleus, across two datasets. Connectivity is computed between each thalamic nucleus and all 10 cortical regions in each dataset. These 10 values are correlated with those of every other nucleus across dataset, yielding a 15 × 15 asymmetrical correlation matrix. If a given nucleus is most highly correlated with itself across datasets, it is successfully differentiated.

2.7. Thalamic Differentiation Analyses

We conducted a neural fingerprinting analysis to determine whether we could meaningfully parse signals from small and proximal thalamic nuclei using MEG connectivity. Neural fingerprinting analyses usually seek to differentiate individual participants from each other based on features from their brain data (i.e., spectral information, connectivity, see Finn et al. (2015); da Silva Castanheira et al. (2021)). These features are used to compute a group correlation matrix between participants, across separate datasets. A differentiation test then seeks to identify participants by observing the index of the matrix featuring the largest correlation across datasets. A correct differentiation consists of an instance in which the neural features of a given subject in the first dataset are most highly correlated with the neural features of that same participant in the second dataset (Fraschini et al. 2014; Kong et al. 2019; La Rocca et al. 2014; da Silva Castanheira et al. 2021).

In our case, we apply the same logic, but to thalamic nuclei instead of participants (see Figure 2B for an illustration). The nuclei become our “participants”, and we attempt to differentiate them based on their cortical connectivity features. First, we randomly split both Spindle and Clear epochs into two datasets. In each dataset, we compute the cortical connectivity features of each thalamic nucleus (10 cortical ROIs for each of the 15 thalamic nuclei). We then correlate these features among thalamic nuclei, and across both datasets, yielding a 15 × 15 asymmetrical correlation matrix representing the similarity of cortical connectivity patterns between each thalamic nucleus across datasets. Rows correspond to dataset 1, and columns to dataset 2; the diagonal of the matrix therefore corresponds to self‐correlations for each thalamic nucleus across both datasets. From this correlation matrix, we perform differentiation tests for both Spindle and Clear conditions. If the cortical connectivity features of a given nucleus in dataset 1 are most highly correlated with those of that same nucleus in dataset 2, the differentiation is successful.

To further quantify our differentiation capacity, we also compute a differentiation index score, as used in da Silva Castanheira et al. (2021), and originally adapted from Amico and Goñi (2018), which quantifies the reliability of differentiation of thalamic nuclei from each other. The metric defines Dself as the z score of a thalamic nucleus's self‐correlation between dataset 1 and dataset 2, relative to that nucleus's correlations with all other nuclei (see da Silva Castanheira et al. (2021) for details). Higher Dself values indicate a nucleus that is more easily distinguishable, while lower scores suggest greater difficulty in differentiating that nucleus from others. We used permutation statistics to test whether differentiation scores were significantly higher than randomly permuted connectivity matrices. Permutation tests were first performed by shuffling connectivity matrices before recomputing the differentiation index in each permutation, to test whether nuclei are differentiable compared to random connectivity with the same topology. Next, we recomputed permutation tests by shuffling the labels of thalamic nuclei on the already computed differentiation index scores, to test whether some nuclei are significantly more differentiable than others. To test for differences between metrics in differentiation ability, we also performed t‐tests between the Dself scores of COH and ICOH. For each metric, we took the average Dself scores across thalamic nuclei in each participant. We then ran t‐tests across participants between COH and ICOH, in both the Spindle, Clear, and Contrast conditions. P‐values are corrected for False Discovery Rate using a Benjamini–Hochberg correction (alpha = 0.05) throughout (Thissen et al. 2002).

Note that his differentiation analysis does not aim to establish the precise spatial accuracy of thalamic source estimates, nor to decide upon the validity and meaningfulness of deep source signals. Rather, we ask whether cortical connectivity patterns assigned to different thalamic nuclei are distinguishable and consistent across datasets. If so, this suggests that MEG‐based functional connectivity, even if influenced by source leakage, contains enough structured variance to differentiate subregions based on their cortical interactions. This approach therefore offers a test of functional resolvability, rather than anatomical validation.

2.8. Distance Correlations

We examined the association between functional connectivity and the distance between ROIs for both COH and ICOH, aiming to gain a deeper understanding of how incorporating zero‐phase lag activity influences the network. Distance between ROIs was obtained by calculating the Euclidean distance between the centroids of each ROI, on the basis of a standard anatomical brain template (i.e., MNI152). Centroids were defined as the geometric center or the average spatial coordinate of all the voxels within that ROI.

2.9. Graph Theory Analysis

To test whether the expected topographical differences between fast and slow spindle activity (see Box 1) can be detected in the thalamus and cortex using MEG functional connectivity, we implemented a graph theory metric known as the core/periphery partition. The goal of this analysis was to determine whether known topographical differences between fast and slow spindle activity could be recovered in a data‐driven manner using graph theory, and whether corresponding differences could be discerned in thalamic contributions. This analysis serves as a convergent validation approach—if physiologically meaningful patterns emerge without explicit constraints, it provides additional evidence that the extracted signals reflect genuine neural activity rather than purely artifactual connectivity.

The core/periphery partition is an algorithm that splits the network into two groups, the core and periphery groups, in a way that maximizes the number/weight of within‐core group edges and minimizes the number/weight of within‐periphery group edges. This yields an estimate of the most important central hubs driving connectivity within the network (Elliott et al. 2020; Yanchenko and Sengupta 2023). All metrics are taken and implemented from the MATLAB Brain Connectivity Toolbox (Rubinov and Sporns 2010). For this analysis, we opted to examine functional connectivity core‐periphery partitions on fast (13–16 Hz) and slow (10–13 Hz) sigma band frequencies separately. The goal was to see if known topographical differences in fast/slow spindle activity would replicate in the cortex, and if corresponding differences could be discerned in the thalamus. While the offline spindle detection algorithm used to identify epochs containing spindles in this work (Lacourse et al. 2019) did not differentiate between fast and slow spindles, evidence suggests that Cz‐detected EEG spindles may reflect more global as opposed to local spindles, which synchronize widespread areas of cortex and evolve from faster, centro‐parietal events to slower, frontal events (Andrillon et al. 2011; Fernandez and Lüthi 2020). Therefore, we reasoned that MEG activity surrounding EEG‐detected spindles at Cz may still capture both fast and slow sigma activity. We computed fast and slow sigma connectivity matrices by averaging COH and ICOH spectra across these respective frequency bands. To filter out noisy connections and increase sensitivity, we then applied a threshold to our connectivity matrices, retaining only the 20% strongest connections in the network (Garrison et al. 2015). Core‐periphery partitions were computed on the resulting connectivity matrices in the Contrast condition (Spindles—Clear), for both COH and ICOH, and for both fast and slow sigma bands. Here we are exclusively interested in the Contrast condition since we want to examine the connectivity changes associated with spindles specifically. To assess the robustness and consistency of these partitions, we computed the core‐ness score (q) for each partition, which quantifies how well the network conforms to a core‐periphery structure, and the Jaccard similarity index (J), which measures the consistency of the observed core group relative to core groups derived from a random permuted distribution.

3. Results

3.1. Thalamo‐Cortical and Thalamo–Thalamo Functional Connectivity Increases During Spindles

To confirm that we are able to resolve expected connectivity increases during sleep spindles, we statistically evaluated the average connectivity between each thalamic nucleus and all cortical regions as a measure of the overall connectivity between thalamus and cortex during spindle and clear epochs. We found greater thalamo‐cortical connectivity during spindles (COH: M = 0.53, SD = 0.02, ICOH: M = 0.48, SD = 0.01) compared to clear epochs (COH: M = 0.51, SD = 0.01, ICOH: M = 0.47, SD = 0.003) using both COH t(18) = 13.2, p < 0.001, and ICOH t(18) = 14.47, p < 0.001. This result indicates that we are able to resolve expected connectivity increases between cortical and subcortical contributors to spindle activity during spindles. Next, we evaluated average connectivity between thalamic nuclei. Connectivity increased significantly during spindles compared to clear epochs when using ICOH (Spindles: M = 0.47, SD = 0.007, Clear: M = 0.46, SD = 0.004) t(18) = 9.7, p < 0.001, but not when using COH (Spindles: M = 0.76, SD = 0.03, Clear: M = 0.76, SD = 0.03) t(18) = −0.04, p = 0.48. These results indicate that within these deep, proximal regions, functional connectivity metrics which include or exclude zero‐lag information yield different results. Results are displayed in Figure 3.

FIGURE 3.

Functional connectivity changes during spindles. (A) Connectivity increases during spindles compared to clear epochs across thalamo‐cortical pairs using both COH and ICOH. (B) Within the thalamus, connectivity also increases among thalamic nuclei when using ICOH, but not COH.

To further explore whether the ICOH increases during spindles observed in the thalamus was driven by specific thalamic nuclei, we computed the average connectivity between each thalamic nucleus and the rest of the thalamus during both Spindles and Clear and ran paired sample t‐tests on each nucleus individually, to see if some nuclei were driving the average connectivity increase over and above others. All thalamic nuclei displayed significant increases in connectivity during spindles compared to clear epochs in both right and left hemispheres (all p values < 0.001). These results could suggest a relatively uniform increase in spindle band connectivity across the thalamus using ICOH. An alternative explanation could be that thalamic nuclei may be too small and proximal to resolve differences between them in their connectivity increase with the cortex. This motivated the subsequent thalamic differentiation analyses, which sought to tease apart the connectivity profiles of thalamic nuclei through their connectivity patterns with the cortex.

3.2. Thalamic Nuclei Can Be Differentiated via Their Cortical Connectivity Patterns

Having established that connectivity increases across the network during spindles compared to clear, we sought to test the extent to which proximal signals in the thalamus can be differentiated through their connectivity with the cortex, using a fingerprinting analysis. We further computed differentiation index scores to quantify how differentiable each nucleus is based on its cortical connectivity patterns. Figure 4A shows results of permutation tests on differentiation index scores, examining whether thalamic nuclei are differentiable compared to random connectivity with the same topology.

FIGURE 4.

Thalamic differentiation results. (A) Permutation statistics results on differentiation scores, testing whether thalamic nuclei are significantly differentiable from each other relative to a permuted distribution of random thalamo‐cortical connectivity. Regions highlighted in red are statistically significant. Using COH, all nuclei are differentiable during both spindles and clear epochs. Using ICOH, most nuclei are also differentiable across these conditions. When considering connectivity changes (Contrast condition), only some nuclei are differentiable using COH, and none are differentiable using ICOH. (B) Permutation statistics results, testing whether some thalamic nuclei are significantly more differentiable than others (relative to each other). Using COH, the AV and LP nuclei are significantly more differentiable than the rest of the thalamus for both Spindle and Clear conditions. (C) T‐test results on differentiation scores between COH and ICOH. The thalamus is significantly more differentiable using COH compared to ICOH, across all conditions. COH = coherence, ICOH = imaginary coherence, see Figure 1 for ROI abbreviations.

Using COH, differentiation scores from all nuclei were statistically significant (all p values < 0.01) across Clear and Spindle conditions. Using ICOH, most nuclei remained significant, with exceptions in some medio‐dorsal, lateral and anterior regions. In the Contrast condition, some nuclei were significantly differentiable using COH, but none were significant using ICOH. Exact p values can be found in supplementary methods. Importantly, the number and pattern of significantly differentiable nuclei was comparable between Spindle and Clear conditions, suggesting that thalamic resolution via cortical connectivity is not uniquely dependent on spindle activity.

Next, we recomputed permutation tests by shuffling the labels of thalamic nuclei on the already computed differentiation index scores to test whether some nuclei are significantly more differentiable than others (Figure 4B). The anteroventral (AV) and lateral posterior (LP) nuclei emerged as significantly more differentiable than the rest of the thalamus using COH in both Clear and Spindle conditions (LP: p = 0, AV: p = 0.0015).

To test for differences between metrics in differentiability, we ran t‐tests on differentiation scores between COH and ICOH, for Clear, Spindles and Contrast conditions separately. The thalamus was significantly more differentiable when using COH compared to ICOH across all conditions (Clear: t(17) = 6.87, p < 0.001, Spindles: t(17) = 7.47, p < 0.001, Contrast: t(17) = 7.54, p < 0.001) (Figure 4C).

To further investigate differences between COH and ICOH, we ran correlations between COH and ICOH values for the thalamic connectivity of every cortical region for Clear, Spindle and Contrast conditions, yielding 10 correlations per condition. We then computed one‐sample t‐tests to determine whether average correlations between COH and ICOH were significantly different from 0. These tests confirmed that COH and ICOH tend in opposite directions across thalamo‐cortical networks during Clear (left: M = −0.77, SD = 0.33, t(10) = −7.31, p < 0.001; right: M = −0.63, SD = 0.44, t(10) = −4.59, p = 0.004), and Spindle conditions (left: M = −0.56, SD = 0.56, t(10) = −3.12, p = 0.015; right: M = −0.62, SD = 0.52, t(10) = −3.77, p = 0.007). However, in the Contrast condition (Spindles—Clear), COH and ICOH were positively related (left: M = 0.55, SD = 0.53, t(10) = 3.63, p = 0.008; right: M = 0.39, SD = 0.31, t(10) = 3.96, p = 0.007). Figure 5 shows the relationship between COH and ICOH thalamo‐cortical connectivity across conditions. This highlights the limits of our approach: while both metrics afford differentiability, they are tracking distinct features of the data, and we cannot unambiguously say whether the features used to differentiate thalamic nuclei are entirely genuine or spurious. However, these results also suggest that using a contrast (Spindles—Clear) resolves opposite trends between COH and ICOH, making it an effective way to isolate connectivity changes associated with a phenomenon of interest, using both kinds of metrics.

FIGURE 5.

Thalamo‐cortical connectivity patterns between COH and ICOH. Plots show connectivity between thalamic nuclei and a sample cortical region (OFC) for COH (green) and ICOH (blue), for Clear (A), Spindles (B) and Contrast conditions (C). The OFC is shown as an illustrative example. T‐tests on average correlations between COH and ICOH for every cortical region confirmed a significant negative relationship between the two metrics during clear and spindle epochs. When using a contrast, COH and ICOH become positively correlated. Note that relative ordering of nuclei on the x‐axes is arbitrary. Connecting lines are used to visually highlight changes in the pattern of relationships across conditions. (D) shows average COH–ICOH correlations within subjects, across all ROIs, for each condition.

Overall, these results suggest that proximal nuclei in the thalamus can be differentiated based on their cortical connectivity patterns. However, the choice of connectivity metric substantially impacts network topology, with COH and ICOH displaying opposite patterns of connectivity between the cortex and thalamus. Overall, COH also allows greater differentiation than ICOH. This may suggest that structured zero‐phase lag activity contributes to thalamo‐cortical pattern differentiation. It is unclear whether and how much zero‐phase lag activity between the thalamus and cortex is genuine or spurious, but these results suggest zero‐phase lag activity is not entirely meaningless and merely attributable to signal leakage. We emphasize that these results should not be taken as definitive evidence of anatomical specificity. Instead, they indicate that MEG‐based connectivity estimates reflect structured variation across thalamic areas, some of which may reflect physiological differences, and some of which may arise from modeling artifacts or shared cortical projections.

3.3. COH Versus ICOH as a Function of Distance Between ROIs

To better understand the effects of (potentially spurious) zero‐phase lag activity on connectivity metrics, we tested the relationship between connectivity and distance between ROIs across the network, for both COH and ICOH. Figure 6 displays connectivity between all pairs of nodes as a function of distance between ROIS, for both connectivity metrics. Functional connectivity was highly correlated with distance between ROIs, during both spindles (COH: r = −0.91, ICOH: r = 0.71, p < 0.001) and clear epochs (COH: r = −0.91, ICOH: r = 0.70, p < 0.001). COH and ICOH displayed opposite relationships with distance. At short distances, COH was negatively correlated while ICOH was positively correlated. When distance between ROIs surpassed about 6 cm, COH and ICOH values converge. To statistically evaluate the differences and convergence of connectivity across COH and ICOH, we ran paired t‐tests between both metrics for every pair of connectivity values. Figure 6 displays FDR‐corrected t‐tests results in the bottom subplot. Results confirm that COH and ICOH values are significantly different for distances below 6 cm, but mostly converge beyond this threshold. This pattern of results held true for the left hemisphere (see Supporting Information). When analyzing the Contrast condition however, this relationship with distance is attenuated for ICOH (r = 0.42) and is reversed for COH (r = 0.79). Curiously, COH connectivity change displays a strong positive correlation with distance, contrasting with the strong negative association observed during spindles and clear epochs. Overall, these results suggest that the use of a contrast and of corrected metrics is an effective way of controlling for the potential spurious effects of distance on connectivity, especially when distance between ROIs are below approximately 6 cm.

FIGURE 6.

Functional connectivity as a function of distance between ROIs. Green and blue points represent COH and ICOH, respectively, with best‐fit lines and goodness‐of‐fit measures plotted for each metric. Vertical dotted lines separate thalamus–thalamus (< 2.8 cm), thalamo‐cortical (< 8.26 cm), and cortico‐cortical (> 8.26 cm) distances. The subplots show log‐scaled p‐values of FDR‐corrected t‐tests comparing COH and ICOH at each distance, with significant results (p < 0.001) above the red dotted line. In Clear and Spindle conditions (A, B), COH decreases with distance, while ICOH increases, converging around 6 cm, as indicated by rising p‐values. In the Contrast condition, COH is positively related to distance, while ICOH's relationship to distance weakens. Note that the Contrast condition represents connectivity change (Spindles—Clear). Thus, negative values represent instances in which within‐thalamus connections were stronger during Clear compared to Spindles. Right hemisphere results are shown here, but left hemisphere results were nearly identical, and can be found in Supporting Information.

3.4. Graph Theory Analyses

Based on our demonstrated ability to distinguish connectivity in deep, small, and proximal MEG volume sources, we reasoned that meaningful information could be extracted from these deep networks using graph theory. Therefore, we sought to elucidate the contributions of specific thalamic nuclei during spindles with graph theory using a core‐periphery partition analysis, which splits the network into a highly connected hub and a minimally connected hub.

Core‐periphery partition results are displayed in Figure 7. The resulting partition appears to be both theoretically and anatomically plausible, based on the known topographical differences between fast and slow spindle activity (Box 1). In both COH and ICOH, fast sigma connectivity core hubs are clustered in centro‐parietal areas, whereas slow sigma connectivity core hubs cluster in frontal areas (see Figure 7). In the thalamus, only the left VPL was included in the fast sigma core group, and no nuclei were part of the slow sigma core group when using COH. For ICOH, however, the fast sigma core group partition displayed more specificity in the thalamus, including the bilateral pulvinar, LP and MGN, the left VPL and AV, as well as the right LGN. The slow sigma core group for ICOH also included the IL and Re nuclei in the thalamus. Interestingly, using ICOH, the slow sigma core group also included the right pSUB and the left aSUB, which have been found to functionally and structurally connect with the RE nucleus in the thalamus and the ACC in the frontal lobes (Angulo‐Garcia et al. 2020; Lin et al. 2020; Griffin 2021).

FIGURE 7.

Core‐periphery partition results. Orange regions represent the maximally‐connected core group, whereas blue regions represent the minimally‐connected periphery group. Partitions were computed separately for (A) COH and (B) ICOH, on fast (13–16 Hz) and slow (10–13 Hz) spindle band Contrast data, and for left and right hemispheres.

To assess the robustness and consistency of these partitions, we computed the core‐ness score (q), and the Jaccard similarity index (J) for each partition. For fast sigma, the average core‐ness score was q = 0.72, and the average Jaccard similarity index was J = 0.56 across hemispheres and conditions. For slow sigma, the average core‐ness score was q = 0.71, and the average Jaccard similarity index was J = 0.54. All comparisons reached statistical significance compared to the permuted distribution (p < 0.001), confirming that the observed core‐periphery organization is not random but reflects a structured, non‐arbitrary partition of the network.

The core‐periphery analysis provides a graph‐theoretical summary of network organization during spindles, highlighting regions that exhibit important connectivity increases. While some specificity in the thalamus emerges, we caution against over‐interpreting these findings as being anatomically specific, given the potential influence of proximity‐based signal spread and the lack of “ground truth” validation. Rather, we interpret these results as another tentative clue that is suggestive of MEG's ability to resolve connectivity dynamics in deep sources like the thalamus.

4. Discussion

In this study, we explored the possibilities of using functional connectivity metrics on MEG data to resolve small proximal deep sources in the brain, using NREM sleep and thalamocortical sleep spindles as a biologically and scientifically relevant test case. We found that (1) COH and ICOH detect expected connectivity increases across a broad thalamo‐cortico‐hippocampal network during spindles compared to NREM2 sleep epochs with no spindles present (Figure 3). (2) Connectivity also increases between thalamic nuclei during spindles, but only using ICOH. (3) Deep proximal volume sources in the thalamus can be reliably statistically differentiated through their cortical connectivity patterns, though COH and ICOH show opposite trends in these patterns. (4) The relationship between connectivity and distance between ROIs is affected by inclusion (COH) or exclusion (ICOH) of zero‐lag information (Figure 6), and (5) Graph theory analyses on fast and slow spindle networks reveal theoretically and anatomically plausible core connectivity hubs in both cortical and thalamic sources (Figure 7).

We begin here by discussing our findings pertaining to the goal of distinguishing between small proximal thalamic nuclei using MEG functional connectivity. Next, we consider the insights that our connectivity findings provide into the thalamo‐cortical contributions to the functional circuits and physiology underlying sleep spindles. We then explore the implications of our method and findings to future research, and finally, we address the limitations of our study.

4.1. Functional Connectivity Metrics Are Sensitive to Thalamo‐Cortical Activity in MEG Volume Models

One of the main goals of this study was to elucidate the extent to which small proximal sources deep in the brain can be measured and differentiated through their connectivity profiles. By establishing that such sources can in fact be teased apart, we provide preliminary evidence supporting the validity of source‐localized MEG functional connectivity (using volume models) as a method to evaluate the network activity of subcortical regions, notably in the thalamus, which is a deep, central structure. However, these findings should be interpreted as an exploratory step rather than a definitive demonstration of anatomical resolution, given remaining uncertainty regarding potential signal leakage artifacts, and the lack of access to any “ground truth” to validate our data. However, we believe that taken together, our findings strongly suggest that our observed connectivity patterns are not spurious.

As a first step, we found higher connectivity across the entire thalamo‐cortical‐hippocampal network during spindles compared to clear for both COH and ICOH, reflecting a widespread increase in spindle band connectivity, regardless of the inclusion of zero‐phase lag activity or not. However, within the thalamus, only ICOH displayed a significant increase among thalamic nuclei during spindles; COH failed to distinguish connectivity changes between small proximal regions of the thalamus. Possible reasons for this include signal spread artifacts that obscure genuine connectivity changes or ceiling effects due to high baseline COH values among thalamic nuclei that may already be acting in concert. Alternatively, it could be that only time‐lagged connectivity increases among thalamic nuclei during spindles. ICOH (which captures only time‐lagged activity) is poised to detect this increase, whereas COH (which is sensitive to both time‐lagged and instantaneous connectivity) may fail to discern it due to zero‐phase lag activity diluting the signal. The physiological mechanisms underlying spindle generation may be such that thalamic nuclei synchronize in a time‐lagged manner during spindles, since descending cortico‐thalamic projections innervate nuclei adjacent to the ones from which input was originally received, thus spreading across the thalamus in a functionally related, but time‐lagged manner (see Fernandez and Lüthi (2020) and Box 1). We speculate some combination of these three factors is likely.

While absolute connectivity values and variance were relatively low and stable across conditions, we note that this may reflect both the narrow frequency band of interest and the relatively homogeneous neural state (N2/N3 sleep). Previous studies using imaginary coherence with somewhat similar analyses report a wide range of values depending on task, frequency, and preprocessing approach. Given that few studies have applied source‐level connectivity metrics during sleep, particularly within deep structures, our findings offer a benchmark for future comparisons.

4.1.1. Thalamic Differentiation Analyses

Based on these findings of increased connectivity, we sought to further characterize the separability of thalamic nuclei through their connectivity patterns with the cortex. We performed a neural differentiation analysis in which thalamic nuclei's cortical connectivity patterns were correlated with each other across datasets. Across Clear and Spindle conditions, all thalamic nuclei were significantly differentiable using COH, whereas most nuclei were significantly differentiable using ICOH. In the Contrast condition, several nuclei were also differentiable, but only using COH. These results suggest that thalamic nuclei can be effectively distinguished based on their cortical connectivity patterns in the sigma band, during both Spindles and Clear conditions, and to a lesser extent, when considering connectivity change (Contrast). This further indicates that deep source resolution is not contingent on the presence of high‐amplitude rhythmic events such as spindles, since nuclei were equally differentiable during Clear epochs. When considering thalamic differentiability relative to each other, only the AV and LP nuclei were significantly more differentiable compared to the rest of the thalamus, using COH, across Spindle and Clear conditions (see Figure 4). This further demonstrates specificity among nuclei in their differentiability, with the AV and LP nuclei standing out from others, and future studies could further characterize these differences to better understand their precise role in sleep and spindle mechanisms and potentially memory consolidation (Jankowski et al. 2013; Barnett et al. 2021; Roy et al. 2022).

Another insight from these thalamic differentiation analyses is that some nuclei cannot be differentiated from each other based on their cortical connectivity. This observation indicates either that these nuclei were too small and close together to detect meaningful differences in their connectivity profiles, or that they were simply behaving in the same fashion (which is plausible according to the nature of spindle circuitry, see Box 1). Either way, this type of result can inform us on the limits of an experimental paradigm and can guide subsequent analyses. For instance, if several small adjacent nuclei, or subdivisions of larger nuclei, are all highly connected and cannot be differentiated based on their cortical connectivity patterns, one could proceed by collapsing the regions together into one larger cluster to improve statistical sensitivity. Using these kinds of differentiation analyses could therefore be a useful preliminary step in future research to define ROIs, in some research contexts.

We next tested for differences between COH and ICOH in their ability to differentiate thalamic nuclei. COH afforded significantly greater differentiation of thalamic nuclei than did ICOH, across all conditions. These results suggest that zero phase‐lagged connectivity (included in COH) between thalamus and cortex is more variable among thalamic nuclei, compared to when considering strictly non‐zero phase‐lagged connectivity (ICOH). We further argue that the fact that connectivity change (Contrast condition) allows differentiation of thalamic nuclei using COH, but not ICOH, supports the idea that connectivity during spindles may reflect, in part, a genuine increase in instantaneous zero‐phase lag connectivity between thalamus and cortex, on the basis that spurious signal leakage (captured in COH) would be unlikely to contribute to differentiating between activity connected with specific nuclei. The corresponding increase in ICOH during spindles compared to Clear is more homogeneous across the thalamus, which explains why thalamic nuclei are more difficult to statistically differentiate when using this metric.

Further differences between COH and ICOH were observed in their opposing patterns of thalamic connectivity to individual cortical regions. Indeed, for both Spindle and Clear conditions, the most connected nuclei to a given cortical region using COH were often also the least connected nuclei to that same cortical region when using ICOH, and analyses confirmed that thalamic patterns of COH and ICOH were significantly negatively correlated across the cortex (Figure 5). This result indicates that while thalamic nuclei can be statistically distinguished from each other based on their cortical connectivity features, the actual pattern and direction of this discrimination are substantially impacted by metric choice, likely because of differences in the inclusion of zero‐phase lag information. This highlights the limits of our approach: while both metrics afford differentiability, they are tracking distinct features of the data, and we cannot unambiguously say whether the features used to differentiate thalamic nuclei are entirely genuine or spurious. Gaining a better understanding of the meaningfulness of zero‐phase lag activity across the network is crucial since metric selection would lead to quite different conclusions concerning circuit properties, and these opposite patterns of connectivity can considerably alter the outcome of graph theoretical metrics which weigh both absolute and relative connectivity strength of nodes to describe different topological features of the network (Della Penna et al. 2019; Avena‐Koenigsberger et al. 2018; Minati et al. 2013). However, in the Contrast condition (Spindles—Clear), this opposite relationship was abolished and thalamic patterns of COH and ICOH were now positively correlated across the cortex. This suggests that using a contrast (if appropriate to the research application) restores agreement between COH and ICOH by removing activity that is common to both conditions, and supports our claim that contrasting conditions helps partially alleviate leakage‐related effects.

4.1.2. The Effects of Distance on Connectivity Metrics

Differences in results arise from metrics that vary in their inclusion of zero‐phase lag activity. As our focus is on distinguishing signals from nearby sources, we examined how COH and ICOH change with ROI distance. In the Spindle and Clear conditions, COH increased while ICOH decreased with distance, converging at 6 cm. This suggests that distance helps explain the COH–ICOH discrepancy, with COH in proximal deep connections (e.g., thalamo‐thalamic) largely reflecting zero‐phase lag activity.

In the Contrast condition, COH increased with distance, while ICOH's association with distance weakened. This may result from ceiling effects, as proximal thalamic regions already show high COH during spindles and clear epochs, reducing sensitivity to small local increases in COH. As ROI distance grows, ceiling effects diminish, amplifying COH changes. Overall, using a contrast minimized COH–ICOH differences, mitigating the impact of distance on functional connectivity.

Based on these results, combined with our findings that ICOH but not COH increases among thalamic nuclei during spindles, we recommend using ICOH to measure connectivity either between deep regions (i.e., within the thalamus) or between deep regions and cortical regions (i.e., within thalamo‐cortical loops) that are less than approximately 6 cm distance from each other, to avoid spurious connectivity from signal spread and ceiling effects, although being cognizant that doing so necessarily loses potentially meaningful connections between regions. The minimum distance between cortical regions considered in these analyses was 8.3 cm, meaning that we cannot comment on the applicability of this suggestion to cortico‐cortical connectivity analyses at this time. It is likely that COH and ICOH would show fewer differences in their relationship to distance for proximal sources at the cortical surface, given that these are closer to the sensors.

4.1.3. On Using a Contrast

When using a contrast in study designs, it is important to consider the qualitative differences between this condition versus directly observing connectivity in the signal of interest. In our case, the Contrast condition isolates specific connectivity changes associated with sleep spindles, partially alleviating the effects of signal spread and distance artifacts by subtracting out influences common to both conditions. It is possible that some residual spurious connectivity could remain in the Contrast condition, for example if sources of spatial leakage scale with signal power. Despite this concern, our results show that using the Contrast condition helped attenuate certain confounds commonly associated with leakage. Specifically, connectivity‐distance relationships were reduced, and agreement between phase‐insensitive (COH) and phase‐sensitive (ICOH) metrics improved across thalamo‐cortical networks, suggesting that the contrast at least partially alleviates power‐related inflation and spatial spread. It is worth noting that using a contrast also removes structural‐functional information that may be relevant in understanding network behaviour and topology, which the Spindle and Clear conditions retain. For example, if connectivity increased across all nodes in an even manner during spindles compared to clear, this would result in a perfectly homogeneous network in the Contrast condition, where all nodes behave in the exact same manner. This would obscure potentially interesting baseline topological differences across nodes that are lost when only considering connectivity change between conditions. It is therefore important to carefully consider the signal of interest and associated research questions when deciding on a suitable contrast, as well as which condition is best suited for different analyses.

4.1.4. Core‐Periphery Thalamic Specificity

Beyond merely determining changes in connectivity between specific nodes, graph theory can provide highly informative descriptions of network behaviour and topology. Indeed, small differences in connectivity between nodes can seem noisy and homogeneous, but may obscure intricate patterns of functional organization at different spatial and temporal scales across the network. Our graph theory analyses using the core‐periphery partition (Figure 7) provide a final piece of evidence that we can potentially obtain meaningful signals from thalamic sources in MEG. We found connectivity differences between fast and slow spindle activity that are in line with expectations from previous work (Box 1). Most notably, we found that specific thalamic nuclei were included in the core connectivity hubs of the network. This specificity provides further support for the idea that functional connectivity, combined with graph theory approaches, can distinguish between the connectivity profiles of small proximal nuclei in deep structures of the brain, and suggests how these analytic strategies might yield insights into spindles' roles and functions (discussed below).

4.2. Toward the Non‐Invasive Study of Whole‐Brain Circuitry

In addition to demonstrating the sensitivity of MEG signals in deeper sources, our methods also highlight the potential to provide leads and insights into neurophysiology and ultimately function, non‐invasively in intact humans. For example, the AV and LP nuclei stood out from others as regards differentiability. The AV complex forms a collection of nuclei at the front of the thalamus which reciprocally connect the hippocampal formation and the prefrontal cortex, and plays an important role in working memory (Jankowski et al. 2013; Barnett et al. 2021; Roy et al. 2022). The LP is also a higher‐order nucleus forming the rostral extension of the pulvinar. It projects broadly to cortical areas, with important connections to the parietal lobes, and plays a role in complex sensory integration and visual information processing (Patestas and Gartner 2016; Juavinett et al. 2020). Our approach could thus be leveraged to explore the roles of these nuclei in sleep and cognition.

As another potential application, in the core‐periphery analysis, we explored contributions of thalamic nuclei to generating fast and slow spindle activity. Fast spindle activity is known to be involved in memory consolidation (Muehlroth et al. 2019; Dehnavi et al. 2023), but the contributions of specific thalamic nuclei to different aspects of memory consolidation have not been characterized. Our core‐periphery findings reveal hubs of fast spindle connectivity that increase between mostly posterior thalamic clusters and centro‐parietal cortical areas during spindles, including nuclei such as the VPL, LP, and pulvinar, which are known to have different structural connections to diverse brain regions, subserving their distinct roles in cognition. For example, the VPL is a first‐order nucleus that relays sensory information from the body to the somatosensory cortex for processing (Vertes et al. 2015). Thus, this nucleus may be important for processing specifically somatosensory aspects of re‐activated memories (Fernandez and Lüthi 2020). The pulvinar is a large higher‐order nucleus involved in numerous cognitive mechanisms, with an emphasis on visual attention and processing (Froesel et al. 2021). Along with the LP, it is involved in sensory integration, visual attention, and visually guided behaviour (Patestas and Gartner 2016; Juavinett et al. 2020). These nuclei therefore might serve to integrate multi‐modal information from visual and sensory features of mnemonic content being consolidated during spindles. Future research could leverage the thalamic specificity afforded by MEG functional connectivity and graph theory to untangle the specific contributions of these nuclei to different aspects of memory consolidation and perhaps help clarify the roles of slow spindle activity, whose function is particularly unclear, and which showed different connectivity patterns to fast spindle activity. Indeed, our slow sigma core‐periphery findings showed ICOH connectivity hubs between mostly frontal cortical regions, as well as the left anterior subiculum (aSUB), right posterior subiculum (pSUB), and left nucleus reuniens (RE) within the thalamus.

The RE is a small nucleus found in the ventral mid‐line of the thalamus, which reciprocally connects the hippocampus and medial prefrontal cortex (mPFC) and has been shown to functionally orchestrate synchrony between the mPFC and the hippocampus to support memory consolidation processes (Herkenham 1978; Angulo‐Garcia et al. 2020; Lin et al. 2020; Griffin 2021). The RE nucleus seems to be critical for long‐term memory consolidation and retrieval (5–25 days post learning), but not for recently encoded memories (Mei et al. 2018; Varela and Wilson 2020; Ferraris et al. 2021; Hamilton and Dalrymple‐Alford 2023). Therefore, one interesting possibility regarding the role of slow spindles is that, while they do not appear to support overnight consolidation (in learning paradigms explored to date), they may be involved in coordinating longer‐term consolidation processes by providing windows of synaptic plasticity over temporal and frontal regions that facilitate the functional coupling of the hippocampus and mPFC via the RE to support the gradual maturation of memory traces in the mPFC and the concurrent silencing of memory traces in the hippocampus, resulting in long‐term retrieval becoming hippocampus‐independent over several days or weeks (Tonegawa et al. 2018; Ferraris et al. 2021). Few studies have investigated the role of spindles in the interplay between the hippocampus, RE, and prefrontal cortex (Varela and Wilson 2020), and none to our knowledge have done so in humans. The vast majority of investigations into midline and intralaminar nuclei come from animal models because of the difficulties in studying them in humans due to their size and location in the brain (Cassel et al. 2021). Thus, our ability to measure the connectivity of such regions using MEG volume‐source connectivity and graph theory is an important advancement to their study in humans.

4.3. Limitations and Future Work

This study has several limitations. First, we did not use regions of interest with full cortical and subcortical coverage but rather selected a subset of regions to be included in our network analyses based on prior spindle literature. This choice offers better statistical sensitivity, is less computationally demanding, and is appropriate for exploring functional connectivity in established networks.

Second, we explored only a small subset of common parameter choices in MEG analyses. Processing steps that may influence functional connectivity measures include data pre‐processing steps, the selection of ROIs and ROI sizes, source localization methods (Hauk et al. 2022; Tait et al. 2021), connectivity metric choice (Colclough et al. 2016), epoch length (Fraschini et al. 2016), dimension reduction techniques (Brkić et al. 2023), and the choice of an appropriate threshold on connectivity matrices (Garrison et al. 2015; Adamovich et al. 2022). More research is needed to systematically investigate all the different methodological options available to researchers wishing to conduct MEG functional connectivity analyses, and ultimately establish standardized pipelines and best practices.

Third, a limitation of our approach is the potential influence of crosstalk, whereby source reconstruction methods may assign cortical activity to subcortical locations (Liu et al. 1998). This is particularly relevant for deep sources like thalamic nuclei, where signal strength is inherently lower. However, our analyses reveal structured rather than random patterns of connectivity, and we have presented multiple lines of converging evidence suggesting that our findings are not artifactual. Future work using simultaneous intracranial recordings or simulation studies could further validate the extent of genuine versus spurious connectivity in thalamic source estimates.

Finally, the present work focuses on methodology and physiology, but does not address the relationships of physiology to behaviour, which is ultimately of interest to many researchers in cognitive neuroscience and neurology. Nevertheless, a better understanding of these methods and their capabilities is a necessary first step that will facilitate future work relating brain circuits and behaviour.

Taking advantage of recent methods development in other areas, this work may be extended in the future in several ways. Graph theory may prove to be an invaluable tool for assessing the implication of deep subcortical structures in widespread brain networks associated with various behaviours and cognitive processes, especially when the networks or signals under scrutiny are subtle and noisy. Supplementing functional connectivity with graph theory tools can afford richer qualitative and quantitative descriptions of network characteristics (Avena‐Koenigsberger et al. 2018), and can uncover hidden neural patterns (Betzel 2023).

Dynamic functional connectivity (i.e., connectivity that evolves over time), which allows for the characterization of transient networks, can reflect the temporal scale upon which cognition occurs (Baker et al. 2014). While some studies have begun to investigate how electrophysiological connectivity evolves over time, none to our knowledge have done so beyond the cortical surface (O'Neill et al. 2017, 2018). Further combining these approaches with other analytic tools such as cross‐frequency and phase‐amplitude coupling analyses, as well as with experimental manipulations like targeted memory reactivation and closed‐loop auditory stimulation (Ngo et al. 2013), will allow researchers to study causal relationships in whole‐brain phenomena at multiple spatial and temporal scales simultaneously (Roux et al. 2013).

We hope future research will leverage these tools in combination with MEG functional connectivity to explore the activity and neural dynamics of the brain as a whole. The ability to measure the network activity of different sub‐divisions of the thalamus in a non‐invasive and temporally precise manner, as demonstrated here, can offer a unique window into a plethora of brain processes and neuropsychiatric diseases (Cronenwett and Csernansky 2010; Biesbroek et al. 2024).

5. Conclusions

This study investigated the ability for MEG functional connectivity to differentiate between deep sources in the brain, using thalamo‐cortical sleep spindles as a biological test case. Taken together, our results support the viability of MEG functional connectivity as a window into deep thalamo‐cortical dynamics, while also highlighting the methodological challenges and interpretive uncertainties that accompany efforts to resolve fine‐grained subcortical structures using noninvasive neuroimaging methods. Our findings demonstrate that MEG functional connectivity analyses can distinguish variation in connectivity patterns between small deep sources in the thalamus during NREM sleep with and without spindles, suggesting generalizability of the methods to other brain states, and therefore have great potential for studying the intricate dynamics of (deep) brain activity in a non‐invasive, spatially resolved, and temporally precise manner—areas that have been relatively neglected in the study of human cognition to date (Dehghani and Wimmer 2019; Ward 2013; Wolff and Vann 2019). We further show that study design, metric choice, and distance between ROIs can considerably alter results obtained from these sorts of analyses, highlighting the potential impact of genuine and spurious zero‐phase lag correlation between regions on connectivity. Finally, we explored a graph theoretical core‐periphery partition algorithm to segment the network into highly connected core groups and minimally connected periphery groups, revealing specificity in the thalamo‐cortical and hippocampal contributions to fast and slow sigma band connectivity during spindles. These results provide promising leads into the thalamic specificity involved in fast and slow sleep spindle mechanisms, providing a foundation for further investigation into their role in cognition and memory consolidation in healthy and impaired function (Ward 2013), and demonstrating how neurophysiological research may benefit from brain‐wide volume‐source localized investigations. Deep source connectivity approaches can be applied to a wide range of other circuits and research questions, given careful attention to research design choices such as the use of metrics and contrasts and taking advantage of techniques that make full use of the richness and complexity of MEG data (Sadaghiani et al. 2022).

Author Contributions

Gregory F. Rattray: conceptualization, methodology, software, formal analysis, writing – original draft, writing – review and editing, visualization. Hugo R. Jourde: conceptualization, methodology, data curation, software, investigation, writing – review and editing, visualization. Sylvain Baillet: conceptualization, methodology, writing – review and editing. Emily B. J. Coffey: conceptualization, methodology, data curation, resources, writing – review and editing, visualization, supervision, project administration, funding acquisition.

Disclosure

The authors have nothing to report.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Data S1: Supporting Information.

Rattray, G. F. , Jourde H. R., Baillet S., and Coffey E. B. J.. 2025. “Exploring Deep Magnetoencephalography via Thalamo‐Cortical Sleep Spindles.” Human Brain Mapping 46, no. 14: e70354. 10.1002/hbm.70354.

Data Availability Statement

Anonymized, pre‐processed MEG functional connectivity data that were used for the main analyses are freely available on Open Science Framework https://osf.io/g7fce/?view_only=94e2d04d7d3e40b6895a13f7381e6c25. Raw data may be available upon reasonable request, pending ethical approval.