Hippocampus-parietal cortex circuits are thought to play a crucial role in memory and attention, but their neural basis remains poorly understood. We employed intracranial intracranial electroencephalography (iEEG) to investigate the neurophysiological underpinning of these circuits across three memory tasks spanning verbal and spatial domains. We uncovered a consistent pattern of higher causal directed connectivity from the hippocampus to both lateral parietal cortex (supramarginal and angular gyrus) and medial parietal cortex (posterior cingulate cortex) in the delta-theta band during memory encoding and recall. This connectivity was independent of activation or suppression states in the hippocampus or parietal cortex. Crucially, directed connectivity from the supramarginal gyrus to the hippocampus was enhanced in participants with higher memory recall, highlighting its behavioral significance. Our findings align with the attention-to-memory model, which posits that attention directs cognitive resources toward pertinent information during memory formation. The robustness of these results was demonstrated through Bayesian replication analysis of the memory encoding and recall periods across the three tasks. Our study sheds light on the neural basis of casual signaling within hippocampus-parietal circuits, broadening our understanding of their critical roles in human cognition.

Hippocampus-parietal cortex circuits are thought to play a crucial role in memory and attention, but their neural basis remains poorly understood. We employed intracranial EEG from 96 participants (51 females) to investigate the neurophysiological underpinning of these circuits across three memory tasks spanning verbal and spatial domains. We uncovered a consistent pattern of higher causal directed connectivity from the hippocampus to both lateral parietal cortex (supramarginal and angular gyrus) and medial parietal cortex (posterior cingulate cortex) in the delta-theta band during memory encoding and recall. This connectivity was independent of activation or suppression states in the hippocampus or parietal cortex. Crucially, directed connectivity from the supramarginal gyrus to the hippocampus was enhanced in participants with higher memory recall, highlighting its behavioral significance. Our findings align with the attention-to-memory model, which posits that attention directs cognitive resources toward pertinent information during memory formation. The robustness of these results was demonstrated through Bayesian replication analysis of the memory encoding and recall periods across the three tasks. Our study sheds light on the neural basis of casual signaling within hippocampus-parietal circuits, broadening our understanding of their critical roles in human cognition.

A fundamental challenge in neuroscience is explaining how widespread brain regions flexibly interact to support behaviors. We hypothesize that traveling waves of oscillations are a key mechanism of neural coordination, such that they propagate across the cortex in distinctive patterns that control how different regions interact. To test this hypothesis, we used direct brain recordings from humans performing multiple memory experiments and an analytical framework that flexibly measures the propagation patterns of traveling waves. We found that traveling waves propagated along the cortex in not only plane waves, but also spirals, sources and sinks, and more complex patterns. The propagation patterns of traveling waves correlated with novel aspects of behavior, with specific wave shapes reflecting particular cognitive processes and even individual remembered items. Our findings suggest that large-scale cortical patterns of traveling waves reveal the spatial organization of cognitive processes in the brain and may be relevant for neural decoding.### Competing Interest StatementThe authors have declared no competing interest.

Dynamic interactions between large-scale brain networks underpin human cognitive processes, but their electrophysiological mechanisms remain elusive. The triple network model, encompassing the salience network (SN), default mode network (DMN), and frontoparietal network (FPN), provides a framework for understanding these interactions. We analyzed intracranial electroencephalography (EEG) recordings from 177 participants across four diverse episodic memory experiments, each involving encoding as well as recall phases. Phase transfer entropy analysis revealed consistently higher directed information flow from the anterior insula (AI), a key SN node, to both DMN and FPN nodes. This directed influence was significantly stronger during memory tasks compared to resting state, highlighting the AI’s task-specific role in coordinating large-scale network interactions. This pattern persisted across externally driven memory encoding and internally governed free recall. Control analyses using the inferior frontal gyrus (IFG) showed an inverse pattern, with DMN and FPN exerting higher influence on IFG, underscoring the AI’s unique role. We observed task-specific suppression of high-gamma power in the posterior cingulate cortex/precuneus node of the DMN during memory encoding, but not recall. Crucially, these results were replicated across all four experiments spanning verbal and spatial memory domains with high Bayes replication factors. Our findings advance understanding of how coordinated neural network interactions support memory processes, highlighting the AI’s critical role in orchestrating large-scale brain network dynamics during both memory encoding and retrieval. By elucidating the electrophysiological basis of triple network interactions in episodic memory, our study provides insights into neural circuit dynamics underlying memory function and offer a framework for investigating network disruptions in memory-related disorders.

Dynamic interactions between large-scale brain networks are thought to underpin human cognitive processes such as episodic memory formation, but their underlying electrophysiological dynamics are not known. The triple network model, highlighting the salience, default mode, and frontoparietal networks, are fundamental to this process. To unravel the electrophysiological mechanisms underlying these interactions, we utilized intracranial EEG from 177 participants across four memory experiments. Findings revealed directed information flow from the anterior insula node of the salience network to the default mode and frontoparietal networks, regardless of the nature of the tasks - whether they involved externally driven stimuli during encoding or internally governed processes during free recall. Moreover, this pattern of information transmission was observed irrespective of the activation or suppression states of network nodes. Crucially, results were replicated across four different memory experiments. Our study advances understanding of how coordinated neural network interactions underpin cognitive operations.

Electrical stimulation of the medial temporal lobe (MTL) has the potential to uncover causal circuit mechanisms underlying memory function. However, little is known about how MTL stimulation alters information flow with frontoparietal cortical regions implicated in episodic memory. We used intracranial EEG recordings from humans (14 participants, 10 females) to investigate how MTL stimulation alters directed information flow between MTL and PFC and between MTL and posterior parietal cortex (PPC). Participants performed a verbal episodic memory task during which they were presented with words and asked to recall them after a delay of ∼20 s; 50 Hz stimulation was applied to MTL electrodes on selected trials during memory encoding. Directed information flow was examined using phase transfer entropy. Behaviorally, we observed that MTL stimulation reduced memory recall. MTL stimulation decreased top-down PFC→MTL directed information flow during both memory encoding and subsequent memory recall, revealing aftereffects more than 20 s after end of stimulation. Stimulation suppressed top-down PFC→MTL influences to a greater extent than PPC→MTL. Finally, MTL→PFC information flow on stimulation trials was significantly lower for successful, compared with unsuccessful, memory recall; in contrast, MTL→ventral PPC information flow was higher for successful, compared with unsuccessful, memory recall. Together, these results demonstrate that the effects of MTL stimulation are behaviorally, regionally, and directionally specific, that MTL stimulation selectively impairs directional signaling with PFC, and that causal MTL-ventral PPC circuits support successful memory recall. Findings provide new insights into dynamic casual circuits underling episodic memory and their modulation by MTL stimulation.SIGNIFICANCE STATEMENT The medial temporal lobe (MTL) and its interactions with prefrontal and parietal cortices (PFC and PPC) play a critical role in human memory. Dysfunctional MTL-PFC and MTL-PPC circuits are prominent in psychiatric and neurologic disorders, including Alzheimer's disease and schizophrenia. Brain stimulation has emerged as a potential mechanism for enhancing memory and cognitive functions, but the underlying neurophysiological mechanisms and dynamic causal circuitry underlying bottom-up and top-down signaling involving the MTL are unknown. Here, we use intracranial EEG recordings to investigate the effects of MTL stimulation on causal signaling in key episodic memory circuits linking the MTL with PFC and PPC. Our findings have implications for translational applications aimed at realizing the promise of brain stimulation-based treatment of memory disorders.

The brain is a complex, interconnected network and the large-scale spatiotemporal coordination of neuronal activity is vital for cognition and behavior. Prior studies have proposed that traveling waves of brain oscillations are one mechanism that helps coordinate complex neuronal processes and are crucial for cognition. Traveling waves consist of oscillations that propagate progressively across the cortex and previous studies have shown that these waves play a foundational role for learning, memory processing, and memory consolidation and a range of other behaviors across multiple species. The prevalence of traveling waves in cognition thus indicates that spatiotemporal patterns of neuronal oscillations may coordinate multiple neuronal brain networks and impact behavior. Even though there are several different approaches for analyzing traveling waves using electrophysiological recordings, computational tools targeting the analysis and visualization and understanding of traveling waves are still rare. We briefly review the literature on human intracranial electroencephalography (iEEG), which has shown that traveling waves play an important role in cognition. We then describe a statistical methodology based on circular–linear regression for the detection and analysis of traveling waves from human electrophysiological oscillations. We hope that this approach will provide a more mechanistic understanding of the coordination of neurons across space and time.

Interactions between the hippocampus and prefrontal cortex (PFC) play an essential role in both human spatial navigation and episodic memory, but the underlying causal flow of information between these regions across task domains is poorly understood. Here we use intracranial EEG recordings and spectrally resolved phase transfer entropy to investigate information flow during two different virtual spatial navigation and memory encoding/recall tasks and examine replicability of information flow patterns across spatial and verbal memory domains. Information theoretic analysis revealed a higher causal information flow from hippocampus to lateral PFC than in the reverse direction. Crucially, an asymmetric pattern of information flow was observed during memory encoding and recall periods of both spatial navigation tasks. Further analyses revealed frequency specificity of interactions characterized by greater bottom-up information flow from hippocampus to PFC in delta-theta band (0.5-8 Hz); in contrast, top-down information flow from PFC to hippocampus was stronger in beta band (12-30 Hz). Bayesian analysis revealed a high degree of replicability between the two spatial navigation tasks (Bayes factor > 5.46e+3) and across tasks spanning the spatial and verbal memory domains (Bayes factor > 7.32e+8). Our findings identify a domain-independent and replicable frequency-dependent feedback loop engaged during memory formation in the human brain.

The brain is a complex, interconnected network and the large-scale spatiotemporal coordination of neuronal activity is vital for cognition and behavior. Prior studies have proposed that traveling waves of brain oscillations are one mechanism that helps coordinate complex neuronal processes and are crucial for cognition. Traveling waves consist of oscillations that propagate progressively across the cortex and previous studies have shown that these waves play a foundational role for learning, memory processing, and memory consolidation and a range of other behaviors across multiple species. The prevalence of traveling waves in cognition thus indicates that spatiotemporal patterns of neuronal oscillations may coordinate multiple neuronal brain networks and impact behavior. Even though there are several different approaches for analyzing traveling waves using electrophysiological recordings, computational tools targeting the analysis and visualization and understanding of traveling waves are still rare. We briefly review the literature on human intracranial electroencephalography (iEEG), which has shown that traveling waves play an important role in cognition. We then describe a statistical methodology based on circular–linear regression for the detection and analysis of traveling waves from human electrophysiological oscillations. We hope that this approach will provide a more mechanistic understanding of the coordination of neurons across space and time.

The insula plays a fundamental role in a wide range of adaptive human behaviors, but its electrophysiological dynamics are poorly understood. Here, we used human intracranial electroencephalographic recordings to investigate the electrophysiological properties and hierarchical organization of spontaneous neuronal oscillations within the insula. We analyzed the neuronal oscillations of the insula directly and found that rhythms in the theta and beta frequency oscillations are widespread and spontaneously present. These oscillations are largely organized along the anterior-posterior (AP) axis of the insula. Both the left and right insula showed anterior-to-posterior decreasing gradients for the power of oscillations in the beta frequency band. The left insula also showed a posterior-to-anterior decreasing frequency gradient and an anterior-to-posterior decreasing power gradient in the theta frequency band. In addition to measuring the power of these oscillations, we also examined the phase of these signals across simultaneous recording channels and found that the insula oscillations in the theta and beta bands are traveling waves. The strength of the traveling waves in each frequency was positively correlated with the amplitude of each oscillation. However, the theta and beta traveling waves were uncoupled to each other in terms of phase and amplitude, which suggested that insular traveling waves in the theta and beta bands operate independently. Our findings provide new insights into the spatiotemporal dynamics and hierarchical organization of neuronal oscillations within the insula, which, given its rich connectivity with widespread cortical regions, indicates that oscillations and traveling waves have an important role in intrainsular and interinsular communications.

Investigations using noninvasive functional magnetic resonance imaging (fMRI) have provided significant insights into the unique functional organization and profound importance of the human default mode network (DMN), yet these methods are limited in their ability to resolve network dynamics across multiple timescales. Electrophysiological techniques are critical to address these challenges, yet few studies have explored the neurophysiological underpinnings of the DMN. Here we investigate the electrophysiological organization of the DMN in a common large-scale network framework consistent with prior fMRI studies. We used intracranial EEG (iEEG) recordings, and evaluated intra- and cross-network interactions during resting-state and its modulation during a cognitive task involving episodic memory formation. Our analysis revealed significantly greater intra-DMN phase iEEG synchronization in the slow-wave (< 4 Hz), while DMN interactions with other brain networks was higher in the beta (12–30 Hz) and gamma (30–80 Hz) bands. Crucially, slow-wave intra-DMN synchronization was observed in the task-free resting-state and during both verbal memory encoding and recall. Compared to resting-state, slow-wave intra-DMN phase synchronization was significantly higher during both memory encoding and recall. Slow-wave intra-DMN phase synchronization increased during successful memory retrieval, highlighting its behavioral relevance. Finally, analysis of nonlinear dynamic causal interactions revealed that the DMN is a causal outflow network during both memory encoding and recall. Our findings identify frequency specific neurophysiological signatures of the DMN which allow it to maintain stability and flexibility, intrinsically and during task-based cognition, provide novel insights into the electrophysiological foundations of the human DMN, and elucidate network mechanisms by which it supports cognition.

Hippocampus and prefrontal cortex (PFC) circuits are thought to play a prominent role in human episodic memory, but the precise nature, and electrophysiological basis, of directed information flow between these regions and their role in verbal memory formation has remained elusive. Here we investigate nonlinear causal interactions between hippocampus and lateral PFC using intracranial EEG recordings (26 participants, 16 females) during verbal memory encoding and recall tasks. Direction-specific information theoretic analysis revealed higher causal information flow from the hippocampus to PFC than in the reverse direction. Crucially, this pattern was observed during both memory encoding and recall, and the strength of causal interactions was significantly greater during memory task performance than resting baseline. Further analyses revealed frequency specificity of interactions with greater causal information flow from hippocampus to the PFC in the delta-theta frequency band (0.5-8 Hz); in contrast, PFC to hippocampus causal information flow were stronger in the beta band (12-30 Hz). Across all hippocampus-PFC electrode pairs, propagation delay between the source and target signals was estimated to be 17.7 ms, which is physiologically meaningful and corresponds to directional signal interactions on a timescale consistent with monosynaptic influence. Our findings identify distinct asymmetric feedforward and feedback signaling mechanisms between the hippocampus and PFC and their dissociable roles in memory recall, demonstrate that these regions preferentially use different frequency channels, and provide novel insights into the electrophysiological basis of directed information flow during episodic memory formation in the human brain. SIGNIFICANCE STATEMENT Hippocampal-PFC circuits play a critical role in episodic memory in rodents, nonhuman primates, and humans. Investigations using noninvasive fMRI techniques have provided insights into coactivation of the hippocampus and PFC during memory formation; however, the electrophysiological basis of dynamic causal hippocampal-PFC interactions in the human brain is poorly understood. Here, we use data from a large cohort of intracranial EEG recordings to investigate the neurophysiological underpinnings of asymmetric feedforward and feedback hippocampal-PFC interactions and their nonlinear causal dynamics during both episodic memory encoding and recall. Our findings provide novel insights into the electrophysiological basis of directed bottom-up and top-down information flow during episodic memory formation in the human brain.

Real-valued sparse representation methods have recently become popular for directions of arrival (DOAs) of unknown and possibly correlated signals using an array of sensors. Such a representation is useful when it is not straightforward to extend sparse representation algorithms, which are specifically designed in the real domain, to the complex domain or when the array output is represented in the sparse covariance domain. However, most existing real-valued sparse representation methods simply separate the real and imaginary parts of the signals, which are possibly complex, and treat them independently, rather than simultaneously, to impose the sparsity constraint. We use a unitary transformation-based real-valued sparse representation approach to convert the problem of estimating the DOAs from complex to the real domain for a uniform linear array. A fully automatic sparse Bayesian learning principle-based algorithm is then proposed to estimate the DOAs by simultaneously imposing the sparsity constraint on both the real and imaginary parts of the signals. This is in contrast to conventional deterministic sparse signal processing methods, which require tuning of regularization parameters, making them unsuitable to be used in practice where the ground truth is usually unknown. Since in practice, the DOAs of signals may not be exactly aligned with the predefined angular grids, we use an off-grid model to infer the off-grid DOAs. Using the singular value decomposition directly on the array output, the proposed real-valued DOA estimation can also be carried out in the same dimensional space as the original complex domain, which results in a reduction of computational complexity. Moreover, since in ocean acoustics, signals are usually wideband, we extend our proposed narrowband algorithm to the wideband case, where we estimate one spatial power spectrum by simultaneously exploiting sparsity from all frequency bins. Finally, we demonstrate the application of the proposed algorithms by analyzing both narrowband and wideband correlated multipath signals from a shallow water high-frequency (namely, HF97) ocean acoustic experiment.

Mental arithmetic involves distributed brain regions spanning parietal and temporal cortices, yet little is known about the neural dynamics of causal functional circuits that link them. Here we use high-temporal resolution (1000 Hz sampling rate) intracranial EEG from 35 participants, 362 electrodes, and 1727 electrode pairs, to investigate dynamic causal circuits linking posterior parietal cortex (PPC) with ventral temporal-occipital cortex and hippocampal regions which constitute the perceptual, visuospatial, and mnemonic building blocks of mental arithmetic. Nonlinear phase transfer entropy measures capable of capturing information flow identified dorsal PPC as a causal inflow hub during mental arithmetic, with strong causal influences from fusiform gyrus in ventral temporal-occipital cortex as well as the hippocampus. Net causal inflow into dorsal PPC was significantly higher during mental arithmetic, compared to both resting-state and verbal memory recall. Our analysis also revealed functional heterogeneity of casual signaling in the PPC, with greater net causal inflow into the dorsal PCC, compared to ventral PPC. Additionally, the strength of causal influences was significantly higher on dorsal, compared to ventral, PPC from the hippocampus, and ventral temporal-occipital cortex during mental arithmetic, when compared to both resting-state and verbal memory recall. Our findings provide novel insights into dynamic neural circuits and hubs underlying numerical problem solving and reveal neurophysiological circuit mechanisms by which both the visual number form processing and declarative memory systems dynamically engage the PPC during mental arithmetic.

The salience network (SN) plays a critical role in cognitive control and adaptive human behaviors, but its electrophysiological foundations and millisecond timescale dynamic temporal properties are poorly understood. Here, we use invasive intracranial EEG (iEEG) from multiple cohorts to investigate the neurophysiological underpinnings of the SN and identify dynamic temporal properties that distinguish it from the default mode network (DMN) and dorsolateral frontal-parietal network (FPN), two other large-scale brain networks that play important roles in human cognition. iEEG analysis of network interactions revealed that the anterior insula and anterior cingulate cortex, which together anchor the SN, had stronger intranetwork interactions with each other than cross-network interactions with the DMN and FPN. Analysis of directionality of information flow between the SN, DMN, and FPN revealed causal outflow hubs in the SN consistent with its role in fast temporal switching of network interactions. Analysis of regional iEEG temporal fluctuations revealed faster temporal dynamics and higher entropy of neural activity within the SN, compared to the DMN and FPN. Critically, these results were replicated across multiple cohorts. Our findings provide new insights into the neurophysiological basis of the SN, and more broadly, foundational mechanisms underlying the large-scale functional organization of the human brain.

It is generally understood that there is a preictal phase in the development of a seizure and this precictal period is the basis for seizure prediction attempts.The focus of this study is the preictal global spatiotemporal dynamics and its intra-patient variability.We analyzed preictal broadband brain connectivity from human electrocorticography (ECoG) recordings of 185 seizures (which included 116 clinical seizures) collected from 12 patients.ECoG electrodes record from only a part of the cortex, leaving large regions of the brain unobserved.Brain connectivity was therefore estimated using the sparse-plus-latent-regularized precision matrix (SLRPM) method, which calculates connectivity from partial correlations of the conditional statistics of the observed regions given the unobserved latent regions.Brain connectivity was quantified using eigenvector centrality (EC), from which a degree of heterogeneity was calculated for the preictal periods of all seizures in each patient.Results from the SLRPM method are compared to those from the sparse-regularized precision matrix (SRPM) and correlation methods, which do not account for the unobserved inputs when estimating brain connectivity.The degree of heterogeneity estimated by the SLRPM method is higher than those estimated by the SRPM and correlation methods for the preictal periods in most patients.These results reveal substantial heterogeneity or desynchronization among brain areas in the preictal period of human epileptic seizures.Furthermore, the SLRPM method identifies more onset channels from the preictal active electrodes compared to the SRPM and correlation methods.Finally, the correlation between the degree of heterogeneity and seizure severity of patients for SLRPM and SRPM methods were lower than that obtained from the correlation method.These results support recent findings suggesting that inhibitory neurons can have anti-seizure effects by inducing variability or heterogeneity across seizures.Understanding how this variability is linked to seizure initiation may lead to better predictions and controlling therapies.

Epilepsy is a neurological disorder characterized by the sudden occurrence of unprovoked seizures. There is extensive evidence of significantly altered brain connectivity during seizure periods in the human brain. Research on analyzing human brain functional connectivity during epileptic seizures has been limited predominantly to the use of the correlation method. However, spurious connectivity can be measured between two brain regions without having direct connection or interaction between them. Correlations can be due to the apparent interactions of the two brain regions resulting from common input from a third region, which may or may not be observed. Hence, researchers have recently proposed a sparse-plus-latent-regularized precision matrix (SLRPM) when there are unobserved or latent regions interacting with the observed regions. The SLRPM method yields partial correlations of the conditional statistics of the observed regions given the latent regions, thus identifying observed regions that are conditionally independent of both the observed and latent regions. We evaluate the performance of the methods using a spring-mass artificial network and assuming that some nodes cannot be observed, thus constituting the latent variables in the example. Several cases have been considered, including both sparse and dense connections, short-range and long-range connections, and a varying number of latent variables. The SLRPM method is then applied to estimate brain connectivity during epileptic seizures from human ECoG recordings. Seventy-four clinical seizures from five patients, all having complex partial epilepsy, were analyzed using SLRPM, and brain connectivity was quantified using modularity index, clustering coefficient, and eigenvector centrality. Furthermore, using a measure of latent inputs estimated by the SLRPM method, it was possible to automatically detect 72 of the 74 seizures with four false positives and find six seizures that were not marked manually.

In this paper, we propose novel deterministic and Bayesian methods to identify the directions-of-arrival (DOAs) of coherent multipath signals assuming that a very few number of multipath signals are present and multiple snapshots are available. For both types of methods, we exploit both sparsity and the underlying structure of coherent signal propagation. For the deterministic case, we formulate the problem of estimating the DOAs of coherent multipath signals as a biconvex optimization problem and then solve it by an alternating convex search approach. This is in contrast to the widely used sparse signal recovery convex optimization problem, which only exploits sparsity of the signal under consideration. For the Bayesian case, we propose two novel algorithms based on the mean field variational Bayesian expectation maximization approach. The first algorithm assumes that the true scenario DOAs of the multipath signals are exactly aligned with the angular grids. We next extend the on-grid model to deal with the off-grid problem, which is the second proposed Bayesian algorithm of this paper. These two Bayesian algorithms are in contrast to the widely used sparse Bayesian learning relevance vector machine algorithm, which only exploits sparsity in spatial domain. A simulation study is carried out in terms of root-mean-squared error in the DOA estimates to compare the performances of different algorithms. Finally, we demonstrate the application of the proposed off-grid Bayesian algorithm by analyzing data from the shallow water HF97 ocean acoustic experiment.

In human brain imaging studies, researchers have predominantly used the correlation method to estimate the “functional connectivity”. However, spurious correlations can be measured between two brain regions without even having direct connection or interaction between them. This high correlation can be due to the strong interactions of the two brain regions with common input from a third region which may or may not be observed. One previously proposed solution to this problem is to use a sparse-regularized inverse covariance matrix or precision matrix (SRPM) when all the regions are observed. The SRPM method yields partial correlations to measure strong direct interactions between pairs of observed regions while simultaneously removing the influence of the rest of the observed regions thus identifying observed regions that are conditionally independent. However, in most brain studies, especially in electrocorticography (ECoG), simultaneously recording all brain regions is a near impossible task using existing imaging technologies. Hence researchers have recently proposed to use a sparse-plus-latent-regularized precision matrix (SLRPM) when there are unobserved or latent regions interacting with the observed regions. The SLRPM method yields partial correlations of the conditional statistics of the observed regions given the latent regions thus identifying observed regions that are conditionally independent of both the observed and latent regions.In the first contribution of the thesis, we evaluate the performance of the SRPM and SLRPM methods using simple artificial networks. In the second contribution of the thesis, we demonstrate the application of the SRPM method for estimating brain connectivity duringstage 2 sleep spindles from human ECoG recordings from a patient with complex partial epilepsy. We only consider sleep spindles occurring in long seizure-free periods. Sleep spindles are automatically detected using delay-differential analysis (DDA), then analyzedwith SRPM and the Louvain method for community detection (LMCD). The performance of the SLRPM method is found to be similar to that of the SRPM method for this application. In the third contribution of the thesis, we demonstrate the application of the SLRPM method to estimate brain connectivity during epileptic seizures from human ECoG recordings. Seizures from 12 patients having complex partial epilepsy were analyzed using SLRPM and brain connectivity has been quantified using modularity index (MI), clustering coefficient (CC), and eigenvector centrality (EC). These applications will enhance our understanding of the global connectivity pattern of the human brain and may help us in finding better treatments in epilepsy.

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an [Formula: see text] electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present.