Tracing the evolution of multi-scale functional networks in a mouse model of depression using persistent brain network homology

Parvalbumin Regulates GAD Expression through Calcium Ion Concentration to Affect the Balance of Glu-GABA and Improve KA-Induced Status Epilepticus in PV-Cre Transgenic Mice

Aims: the study aimed to (i) use adeno-associated virus technology to modulate parvalbumin (PV) gene expression, both through overexpression and silencing, within the hippocampus of male mice and (ii) assess the impact of PV on the metabolic pathway of glutamate and γ-aminobutyric acid (GABA). Methods: a status epilepticus (SE) mouse model was established by injecting kainic acid into the hippocampus of transgenic mice. When the seizures of mice reached SE, the mice were killed at that time point and 30 min after the onset of SE. Hippocampal tissues were extracted and the mRNA and protein levels of PV and the 65 kDa (GAD65) and 67 kDa (GAD67) isoforms of glutamate decarboxylase were assessed using real-time quantitative polymerase chain reaction and Western blot, respectively. The concentrations of glutamate and GABA were detected with high-performance liquid chromatography (HPLC), and the intracellular calcium concentration was detected using flow cytometry. Results: we demonstrate that the expression of PV is associated with GAD65 and GAD67 and that PV regulates the levels of GAD65 and GAD67. PV was correlated with calcium concentration and GAD expression. Interestingly, PV overexpression resulted in a reduction in calcium ion concentration, upregulation of GAD65 and GAD67, elevation of GABA concentration, reduction in glutamate concentration, and an extension of seizure latency. Conversely, PV silencing induced the opposite effects. Conclusion: parvalbumin may affect the expression of GAD65 and GAD67 by regulating calcium ion concentration, thereby affecting the metabolic pathways associated with glutamate and GABA. In turn, this contributes to the regulation of seizure activity.

Topological state-space estimation of functional human brain networks

We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure topological differences, enabling the clustering of brain networks into distinct topological states. This technique outperforms the commonly used k-means clustering in identifying brain network state spaces by effectively incorporating the temporal dynamics of the data without the need for explicit model specification. We further investigate the genetic underpinnings of these topological features using a twin study design, examining the heritability of such state changes. Our findings suggest that the topology of brain networks, particularly in their dynamic state changes, may hold significant hidden genetic information.

Altered topological structure of the brain white matter in maltreated children through topological data analysis

Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in the global topology of the brain white matter structural covariance network among children. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging and diffusion tensor imaging. We develop a novel framework for statistical inference based on the Wasserstein distance to assess the significance of the observed topological differences. Using these methods in comparing maltreated children with a typically developing control group, we find that maltreatment may increase homogeneity in white matter structures and thus induce higher correlations in the structural covariance; this is reflected in the topological profile. Our findings strongly suggest that TDA can be a valuable framework to model altered topological structures of the brain. The MATLAB codes and processed data used in this study can be found at https://github.com/laplcebeltrami/maltreated.

Method for persistent topological features extraction of schizophrenia patients' electroencephalography signal based on persistent homology

With the development of network science and graph theory, brain network research has unique advantages in explaining those mental diseases, the neural mechanism of which is unclear. Additionally, it can provide a new perspective in revealing the pathophysiological mechanism of brain diseases from the system level. The selection of threshold plays an important role in brain networks construction. There are no generally accepted criteria for determining the proper threshold. Therefore, based on the topological data analysis of persistent homology theory, this study developed a multi-scale brain network modeling analysis method, which enables us to quantify various persistent topological features at different scales in a coherent manner. In this method, the Vietoris-Rips filtering algorithm is used to extract dynamic persistent topological features by gradually increasing the threshold in the range of full-scale distances. Subsequently, the persistent topological features are visualized using barcodes and persistence diagrams. Finally, the stability of persistent topological features is analyzed by calculating the Bottleneck distances and Wasserstein distances between the persistence diagrams. Experimental results show that compared with the existing methods, this method can extract the topological features of brain networks more accurately and improves the accuracy of diagnostic and classification. This work not only lays a foundation for exploring the higher-order topology of brain functional networks in schizophrenia patients, but also enhances the modeling ability of complex brain systems to better understand, analyze, and predict their dynamic behaviors.

Aberrated Multidimensional EEG Characteristics in Patients with Generalized Anxiety Disorder: A Machine-Learning Based Analysis Framework

Although increasing evidences support the notion that psychiatric disorders are associated with abnormal communication between brain regions, scattered studies have investigated brain electrophysiological disconnectivity of patients with generalized anxiety disorder (GAD). To this end, this study intends to develop an analysis framework for automatic GAD detection through incorporating multidimensional EEG feature extraction and machine learning techniques. Specifically, resting-state EEG signals with a duration of 10 min were obtained from 45 patients with GAD and 36 healthy controls (HC). Then, an analysis framework of multidimensional EEG characteristics (including univariate power spectral density (PSD) and fuzzy entropy (FE), and multivariate functional connectivity (FC), which can decode the EEG information from three different dimensions) were introduced for extracting aberrated multidimensional EEG features via statistical inter-group comparisons. These aberrated features were subsequently fused and fed into three previously validated machine learning methods to evaluate classification performance for automatic patient detection. We showed that patients exhibited a significant increase in beta rhythm and decrease in alpha1 rhythm of PSD, together with the reduced long-range FC between frontal and other brain areas in all frequency bands. Moreover, these aberrated features contributed to a very good classification performance with 97.83 ± 0.40% of accuracy, 97.55 ± 0.31% of sensitivity, 97.78 ± 0.36% of specificity, and 97.95 ± 0.17% of F1. These findings corroborate previous hypothesis of disconnectivity in psychiatric disorders and further shed light on distribution patterns of aberrant spatio-spectral EEG characteristics, which may lead to potential application of automatic diagnosis of GAD.

Persistent Homology-Based Topological Analysis on the Gestalt Patterns during Human Brain Cognition Process

The neuropsychological characteristics inside the brain are still not sufficiently understood in previous Gestalt psychological analyses. In particular, the extraction and analysis of human brain consciousness information itself have not received enough attention for the time being. In this paper, we aim to investigate the features of EEG signals from different conscious thoughts. Specifically, we try to extract the physiologically meaningful features of the brain responding to different contours and shapes in images in Gestalt cognitive tests by combining persistent homology analysis with electroencephalogram (EEG). The experimental results show that more brain regions in the frontal lobe are involved when the subject perceives the random and disordered combination of images compared to the ordered Gestalt images. Meanwhile, the persistence entropy of EEG data evoked by random sequence diagram (RSD) is significantly different from that evoked by the ordered Gestalt (GST) images in several frequency bands, which indicate that the human cognition of the shape and contour of images can be separated to some extent through topological analysis. This implies the feasibility to digitize the neural signals while preserving the whole and local features of the original signals, which are further verified by our extensive experiments. In general, this paper evaluates and quantifies cognitively related neural correlates by persistent homology features of EEG signals, which provides an approach to realizing the digitization of neural signals. Preliminary verification of the analyzability of human consciousness signals provides reliable research ideas and directions for the realization of feature extraction and analysis of human brain consciousness cognition.

Changes in laboratory mice after observation of deceased conspecifics: a pilot suicidality study in animals

PURPOSE

Suicidality can be a serious feature of psychiatric symptoms in encephalitis. Investigating the psychiatric behavior associated with suicidality in animal models of encephalitis is important; thus, determining whether normal laboratory animals are aware of death is necessary.

METHODS

To examine the behavioral and brain activity changes associated with death of conspecifics, laboratory mice were exposed to a cadaveric mouse or an anesthetized mouse. Behavioral tasks associated with anxiety and locomotion were conducted after repeated exposure. Neural activity in the medial prefrontal cortex during the cadaver exploration was investigated using electroencephalographic recordings.

RESULTS

During repeated exposure, mice in the cadaver group showed a gradual decrease in time exploring the cadaver, which was not observed in mice in the anesthesia group. The cadaver group also exhibited increased levels of anxiety in the light/dark transition and elevated plus maze tasks and displayed increased locomotor activity in the open field test. In an electrophysiological study, different brain oscillations were observed when mice were exposed to a cadaveric mouse and an anesthetized mouse. Enhanced delta-band activity and reduced theta- and alpha-band activities were observed during cadaver exploration.

CONCLUSION

The present study results showed that experiences involving dead conspecifics strongly affect mouse behavior and brain activity. These findings may be helpful in treating patients with psychiatric symptoms and aid in understanding the concept of death recognition/awareness in laboratory animals.

Promises and pitfalls of topological data analysis for brain connectivity analysis

Developing sensitive and reliable methods to distinguish normal and abnormal brain states is a key neuroscientific challenge. Topological Data Analysis, despite its relative novelty, already generated many promising applications, including in neuroscience. We conjecture its prominent tool of persistent homology may benefit from going beyond analysing structural and functional connectivity to effective connectivity graphs capturing the direct causal interactions or information flows. Therefore, we assess the potential of persistent homology to directed brain network analysis by testing its discriminatory power in two distinctive examples of disease-related brain connectivity alterations: epilepsy and schizophrenia. We estimate connectivity from functional magnetic resonance imaging and electrophysiology data, employ Persistent Homology and quantify its ability to distinguish healthy from diseased brain states by applying a support vector machine to features quantifying persistent homology structure. We show how this novel approach compares to classification using standard undirected approaches and original connectivity matrices. In the schizophrenia classification, topological data analysis generally performs close to random, while classifications from raw connectivity perform substantially better; potentially due to topographical, rather than topological, specificity of the differences. In the easier task of seizure discrimination from scalp electroencephalography data, classification based on persistent homology features generally reached comparable performance to using raw connectivity, albeit with typically smaller accuracies obtained for the directed (effective) connectivity compared to the undirected (functional) connectivity. Specific applications for topological data analysis may open when direct comparison of connectivity matrices is unsuitable - such as for intracranial electrophysiology with individual number and location of measurements. While standard homology performed overall better than directed homology, this could be due to notorious technical problems of accurate effective connectivity estimation.

Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

Multi-dimensional persistent feature analysis identifies connectivity patterns of resting-state brain networks in Alzheimer's disease

OBJECTIVE

The characterization of functional brain network is crucial to understanding the neural mechanisms associated with Alzheimer's disease (AD) and mild cognitive impairment (MCI). Some studies have shown that graph theoretical analysis could reveal changes of the disease-related brain networks by thresholding edge weights. But the choice of threshold depends on ambiguous cognitive conditions, which leads to the lack of interpretability. Recently, persistent homology (PH) was proposed to record the persistence of topological features of networks across every possible thresholds, reporting a higher sensitivity than graph theoretical features in detecting network-level biomarkers of AD. However, most research on PH focused on 0-dimensional features (persistence of connected components) reflecting the intrinsic topology of the brain network, rather than 1-dimensional features (persistence of cycles) with an interesting neurobiological communication pattern. Our aim is to explore the multi-dimensional persistent features of brain networks in the AD and MCI patients, and further to capture valuable brain connectivity patterns.

APPROACH

We characterized the change rate of the connected component numbers across graph filtration using the functional derivative curves, and examined the persistence landscapes that vectorize the persistence of cycle structures. After that, the multi-dimensional persistent features were validated in disease identification using a K-nearest neighbor algorithm. Furthermore, a connectivity pattern mining framework was designed to capture the disease-specific brain structures.

MAIN RESULTS

We found that the multi-dimensional persistent features can identify statistical group differences, quantify subject-level distances, and yield disease-specific connectivity patterns. Relatively high classification accuracies were received when compared with graph theoretical features.

SIGNIFICANCE

This work represents a conceptual bridge linking complex brain network analysis and computational topology. Our results can be beneficial for providing a complementary objective opinion to the clinical diagnosis of neurodegenerative diseases.

Exact topological inference of the resting-state brain networks in twins

A cycle in a brain network is a subset of a connected component with redundant additional connections. If there are many cycles in a connected component, the connected component is more densely connected. Whereas the number of connected components represents the integration of the brain network, the number of cycles represents how strong the integration is. However, it is unclear how to perform statistical inference on the number of cycles in the brain network. In this study, we present a new statistical inference framework for determining the significance of the number of cycles through the Kolmogorov-Smirnov (KS) distance, which was recently introduced to measure the similarity between networks across different filtration values by using the zeroth Betti number. In this paper, we show how to extend the method to the first Betti number, which measures the number of cycles. The performance analysis was conducted using the random network simulations with ground truths. By using a twin imaging study, which provides biological ground truth, the methods are applied in determining if the number of cycles is a statistically significant heritable network feature in the resting-state functional connectivity in 217 twins obtained from the Human Connectome Project. The MATLAB codes as well as the connectivity matrices used in generating results are provided at http://www.stat.wisc.edu/∼mchung/TDA.

In this paper, we propose a new topological distance based on the Kolmogorov-Smirnov (KS) distance that is adapted for brain networks, and compare them against other topological network distances including the Gromov-Hausdorff (GH) distances. KS-distance is recently introduced to measure the similarity between networks across different filtration values by using the zeroth Betti number, which measures the number of connected components. In this paper, we show how to extend the method to the first Betti number, which measures the number of cycles. The performance analysis was conducted using random network simulations with ground truths. Using a twin imaging study, which provides biological ground truth (of network differences), we demonstrate that the KS distances on the zeroth and first Betti numbers have the ability to determine heritability.

A concise and persistent feature to study brain resting-state network dynamics: Findings from the Alzheimer's Disease Neuroimaging Initiative

Alzheimer's disease (AD) is the most common type of dementia in the elderly with no effective treatment currently. Recent studies of noninvasive neuroimaging, resting-state functional magnetic resonance imaging (rs-fMRI) with graph theoretical analysis have shown that patients with AD and mild cognitive impairment (MCI) exhibit disrupted topological organization in large-scale brain networks. In previous work, it is a common practice to threshold such networks. However, it is not only difficult to make a principled choice of threshold values, but also worse is the discard of potential important information. To address this issue, we propose a threshold-free feature by integrating a prior persistent homology-based topological feature (the zeroth Betti number) and a newly defined connected component aggregation cost feature to model brain networks over all possible scales. We show that the induced topological feature (Integrated Persistent Feature) follows a monotonically decreasing convergence function and further propose to use its slope as a concise and persistent brain network topological measure. We apply this measure to study rs-fMRI data from the Alzheimer's Disease Neuroimaging Initiative and compare our approach with five other widely used graph measures across five parcellation schemes ranging from 90 to 1,024 region-of-interests. The experimental results demonstrate that the proposed network measure shows more statistical power and stronger robustness in group difference studies in that the absolute values of the proposed measure of AD are lower than MCI and much lower than normal controls, providing empirical evidence for decreased functional integration in AD dementia and MCI.

Topological Data Analysis of Single-Trial Electroencephalographic Signals

Epilepsy is a neurological disorder that can negatively affect the visual, audial and motor functions of the human brain. Statistical analysis of neurophysiological recordings, such as electroencephalogram (EEG), facilitates the understanding and diagnosis of epileptic seizures. Standard statistical methods, however, do not account for topological features embedded in EEG signals. In the current study, we propose a persistent homology (PH) procedure to analyze single-trial EEG signals. The procedure denoises signals with a weighted Fourier series (WFS), and tests for topological difference between the denoised signals with a permutation test based on their PH features persistence landscapes (PL). Simulation studies show that the test effectively identifies topological difference and invariance between two signals. In an application to a single-trial multichannel seizure EEG dataset, our proposed PH procedure was able to identify the left temporal region to consistently show topological invariance, suggesting that the PH features of the Fourier decomposition during seizure is similar to the process before seizure. This finding is important because it could not be identified from a mere visual inspection of the EEG data and was in fact missed by earlier analyses of the same dataset.

Connectivity in fMRI: Blind Spots and Breakthroughs

In recent years, driven by scientific and clinical concerns, there has been an increased interest in the analysis of functional brain networks. The goal of these analyses is to better understand how brain regions interact, how this depends upon experimental conditions and behavioral measures and how anomalies (disease) can be recognized. In this paper, we provide, first, a brief review of some of the main existing methods of functional brain network analysis. But rather than compare them, as a traditional review would do, instead, we draw attention to their significant limitations and blind spots. Then, second, relevant experts, sketch a number of emerging methods, which can break through these limitations. In particular we discuss five such methods. The first two, stochastic block models and exponential random graph models, provide an inferential basis for network analysis lacking in the exploratory graph analysis methods. The other three addresses: network comparison via persistent homology, time-varying connectivity that distinguishes sample fluctuations from neural fluctuations, and network system identification that draws inferential strength from temporal autocorrelation.

Depression comorbidity in epileptic rats is related to brain glucose hypometabolism and hypersynchronicity in the metabolic network architecture

OBJECTIVE

Temporal lobe epilepsy (TLE) is one of the most common types of epilepsy syndromes in the world. Depression is an important comorbidity of epilepsy, which has been reported in patients with TLE and in different experimental models of epilepsy. However, there is no established consensus on which brain regions are associated with the manifestation of depression in epilepsy. Here, we investigated the alterations in cerebral glucose metabolism and the metabolic network in the pilocarpine-induced rat model of epilepsy and correlated it with depressive behavior during the chronic phase of epilepsy.

METHODS

Fluorodeoxyglucose (¹⁸ F-FDG) was used to investigate the cerebral metabolism, and a cross-correlation matrix was used to examine the metabolic network in chronically epileptic rats using micro-positron emission tomography (microPET) imaging. An experimental model of epilepsy was induced by pilocarpine injection (320 mg/kg, ip). Forced swim test (FST), sucrose preference test (SPT), and eating-related depression test (ERDT) were used to evaluate depression-like behavior.

RESULTS

Our results show an association between epilepsy and depression comorbidity based on changes in both cerebral glucose metabolism and the functional metabolic network. In addition, we have identified a significant correlation between brain glucose hypometabolism and depressive-like behavior in chronically epileptic rats. Furthermore, we found that the epileptic depressed group presents a hypersynchronous brain metabolic network in relation to the epileptic nondepressed group.

SIGNIFICANCE

This study revealed relevant alterations in glucose metabolism and the metabolic network among the brain regions of interest for both epilepsy and depression pathologies. Thus it seems that depression in epileptic animals is associated with a more diffuse hypometabolism and altered metabolic network architecture and plays an important role in chronic epilepsy.

Tracking the Reorganization of Module Structure in Time-Varying Weighted Brain Functional Connectivity Networks

Identification of module structure in brain functional networks is a promising way to obtain novel insights into neural information processing, as modules correspond to delineated brain regions in which interactions are strongly increased. Tracking of network modules in time-varying brain functional networks is not yet commonly considered in neuroscience despite its potential for gaining an understanding of the time evolution of functional interaction patterns and associated changing degrees of functional segregation and integration. We introduce a general computational framework for extracting consensus partitions from defined time windows in sequences of weighted directed edge-complete networks and show how the temporal reorganization of the module structure can be tracked and visualized. Part of the framework is a new approach for computing edge weight thresholds for individual networks based on multiobjective optimization of module structure quality criteria as well as an approach for matching modules across time steps. By testing our framework using synthetic network sequences and applying it to brain functional networks computed from electroencephalographic recordings of healthy subjects that were exposed to a major balance perturbation, we demonstrate the framework’s potential for gaining meaningful insights into dynamic brain function in the form of evolving network modules. The precise chronology of the neural processing inferred with our framework and its interpretation helps to improve the currently incomplete understanding of the cortical contribution for the compensation of such balance perturbations.

Gating of memory encoding of time-delayed cross-frequency MEG networks revealed by graph filtration based on persistent homology

To explain gating of memory encoding, magnetoencephalography (MEG) was analyzed over multi-regional network of negative correlations between alpha band power during cue (cue-alpha) and gamma band power during item presentation (item-gamma) in Remember (R) and No-remember (NR) condition. Persistent homology with graph filtration on alpha-gamma correlation disclosed topological invariants to explain memory gating. Instruction compliance (R-hits minus NR-hits) was significantly related to negative coupling between the left superior occipital (cue-alpha) and the left dorsolateral superior frontal gyri (item-gamma) on permutation test, where the coupling was stronger in R than NR. In good memory performers (R-hits minus false alarm), the coupling was stronger in R than NR between the right posterior cingulate (cue-alpha) and the left fusiform gyri (item-gamma). Gating of memory encoding was dictated by inter-regional negative alpha-gamma coupling. Our graph filtration over MEG network revealed these inter-regional time-delayed cross-frequency connectivity serve gating of memory encoding.

Structure-Function Network Mapping and Its Assessment via Persistent Homology

Understanding the relationship between brain structure and function is a fundamental problem in network neuroscience. This work deals with the general method of structure-function mapping at the whole-brain level. We formulate the problem as a topological mapping of structure-function connectivity via matrix function, and find a stable solution by exploiting a regularization procedure to cope with large matrices. We introduce a novel measure of network similarity based on persistent homology for assessing the quality of the network mapping, which enables a detailed comparison of network topological changes across all possible thresholds, rather than just at a single, arbitrary threshold that may not be optimal. We demonstrate that our approach can uncover the direct and indirect structural paths for predicting functional connectivity, and our network similarity measure outperforms other currently available methods. We systematically validate our approach with (1) a comparison of regularized vs. non-regularized procedures, (2) a null model of the degree-preserving random rewired structural matrix, (3) different network types (binary vs. weighted matrices), and (4) different brain parcellation schemes (low vs. high resolutions). Finally, we evaluate the scalability of our method with relatively large matrices (2514x2514) of structural and functional connectivity obtained from 12 healthy human subjects measured non-invasively while at rest. Our results reveal a nonlinear structure-function relationship, suggesting that the resting-state functional connectivity depends on direct structural connections, as well as relatively parsimonious indirect connections via polysynaptic pathways.

Low β2 Main Peak Frequency in the Electroencephalogram Signs Vulnerability to Depression

Objective: After an intense and repeated stress some rats become vulnerable to depression. This state is characterized by persistent low serum BDNF concentration. Our objective was to determine whether electrophysiological markers can sign vulnerability to depression. Methods: Forty-three Sprague Dawley rats were recorded with supradural electrodes above hippocampus and connected to wireless EEG transmitters. Twenty-nine animals experienced four daily social defeats (SD) followed by 1 month recovery. After SD, 14 rats had persistent low serum BDNF level and were considered as vulnerable (V) while the 15 others were considered as non-vulnerable (NV). EEG signals were analyzed during active waking before SD (Baseline), just after SD (Post-Stress) and 1 month after SD (Recovery). Results: We found that V animals are characterized by higher high θ and α spectral relative powers and lower β2 main peak frequency before SD. These differences are maintained at Post-Stress and Recovery for α spectral relative powers and β2 main peak frequency. Using ROC analysis, we show that low β2 main peak frequency assessed during Baseline is a good predictor of the future state of vulnerability to depression. Conclusion: Given the straightforwardness of EEG recordings, these results open the way to prospective studies in humans aiming to identify population at-risk for depression.

Two's company, three (or more) is a simplex : Algebraic-topological tools for understanding higher-order structure in neural data

The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying assumption: that the quintessential unit of interest in a brain is a dyad – two nodes (neurons or brain regions) connected by an edge. While rarely mentioned, this fundamental assumption inherently limits the types of neural structure and function that graphs can be used to model. Here, we describe a generalization of graphs that overcomes these limitations, thereby offering a broad range of new possibilities in terms of modeling and measuring neural phenomena. Specifically, we explore the use of simplicial complexes: a structure developed in the field of mathematics known as algebraic topology, of increasing applicability to real data due to a rapidly growing computational toolset. We review the underlying mathematical formalism as well as the budding literature applying simplicial complexes to neural data, from electrophysiological recordings in animal models to hemodynamic fluctuations in humans. Based on the exceptional flexibility of the tools and recent ground-breaking insights into neural function, we posit that this framework has the potential to eclipse graph theory in unraveling the fundamental mysteries of cognition.

A Multivariate Granger Causality Concept towards Full Brain Functional Connectivity

Detecting changes of spatially high-resolution functional connectivity patterns in the brain is crucial for improving the fundamental understanding of brain function in both health and disease, yet still poses one of the biggest challenges in computational neuroscience. Currently, classical multivariate Granger Causality analyses of directed interactions between single process components in coupled systems are commonly restricted to spatially low- dimensional data, which requires a pre-selection or aggregation of time series as a preprocessing step. In this paper we propose a new fully multivariate Granger Causality approach with embedded dimension reduction that makes it possible to obtain a representation of functional connectivity for spatially high-dimensional data. The resulting functional connectivity networks may consist of several thousand vertices and thus contain more detailed information compared to connectivity networks obtained from approaches based on particular regions of interest. Our large scale Granger Causality approach is applied to synthetic and resting state fMRI data with a focus on how well network community structure, which represents a functional segmentation of the network, is preserved. It is demonstrated that a number of different community detection algorithms, which utilize a variety of algorithmic strategies and exploit topological features differently, reveal meaningful information on the underlying network module structure.

Topological persistence vineyard for dynamic functional brain connectivity during resting and gaming stages

BACKGROUND

Recent studies have shown the dynamic functional connectivity (FC) of the brain. Accordingly, new challenges have arisen for analyzing and interpreting this rich information.

NEW METHOD

We identified the patterns of coherent FC using a novel method in computational topology called the persistence vineyard. It has been developed to track the characteristic change of the network topology under data perturbations in a threshold-free manner.

RESULTS

We showed the relevance of this new approach by examining the dynamic FC in the resting and gaming stages of 26 healthy subjects. Our proposed method revealed stage and band-specific FC states that were topologically robust.

COMPARISON WITH EXISTING METHODS

While principal component analysis (PCA) estimated similar patterns to our FC states, it produced spurious connectivity due to its orthogonality assumption. Temporal variations of local and global network properties were examined with graph measures. However, unlike the persistence vineyard approach, their results were affected by the network density and its unknown topology.

CONCLUSIONS

Unlike the existing methods, the persistence vineyard provided a more reliable and robust way to estimate FC states. Their extracted network topology changes showed patterns consistent with those of previous studies. Therefore, it may be a potentially powerful tool for studying the dynamic brain network.

Gamma oscillation in functional brain networks is involved in the spontaneous remission of depressive behavior induced by chronic restraint stress in mice

BACKGROUND

Depression is one of the most prevalent mood disorders, and is known to be associated with abnormal functional connectivity in neural networks of the brain. Interestingly, a significant proportion of patients with depression experience spontaneous remission without any treatment. However, the relationship between electroencephalographic (EEG) functional connectivity and the spontaneous remission in depression remains poorly understood. Here, we investigated regional and network brain activity using EEG signals from a chronic restraint stress (CRS)-induced mouse model of depression. After 1 (CRS1W) or 3 weeks (CRS3W) following the cessation of a 4-week-long CRS, mice were subjected to depression-associated behavioral tasks. EEG signals were obtained from eight cortical regions (frontal, somatosensory, parietal, and visual cortices in each hemisphere).

RESULTS

The CRS1W group exhibited behavioral dysfunctions in the open field and forced swim tasks, whereas the CRS3W group displayed normal levels of behaviors in those tasks. In a linear correlation analysis, the CRS1W group exhibited increased correlation coefficient values at all frequency bands (delta, 1.5-4; theta, 4-8; alpha, 8-12; beta, 12-30; gamma, 30-80 Hz) compared with the control group. However, the differences in delta- and gamma-frequency bands between the control and CRS1W groups were no longer observed in the CRS3W group. Persistent brain network homology revealed significantly different functional connectivity between the control and CRS1W groups, and it demonstrated a huge restoration of the decreased distances in the gamma-frequency band for the CRS3W group. Moreover, the CRS3W group displayed a similar strength of connectivity among somatosensory and frontal cortices as the control group.

CONCLUSION

A mouse model of CRS-induced depression showed spontaneous behavioral remission of depressive behavior. Using persistent brain network homology analysis of EEG signals from eight cortical regions, we found that restoration of gamma activity at the network level is associated with behavioral remission.

Rhythmical Photic Stimulation at Alpha Frequencies Produces Antidepressant-Like Effects in a Mouse Model of Depression

Current therapies for depression consist primarily of pharmacological agents, including antidepressants, and/or psychiatric counseling, such as psychotherapy. However, light therapy has recently begun to be considered as an effective tool for the treatment of the neuropsychiatric behaviors and symptoms of a variety of brain disorders or diseases, including depression. One methodology employed in light therapy involves flickering photic stimulation within a specific frequency range. The present study investigated whether flickering and flashing photic stimulation with light emitting diodes (LEDs) could improve depression-like behaviors in a corticosterone (CORT)-induced mouse model of depression. Additionally, the effects of the flickering and flashing lights on depressive behavior were compared with those of fluoxetine. Rhythmical flickering photic stimulation at alpha frequencies from 9–11 Hz clearly improved performance on behavioral tasks assessing anxiety, locomotor activity, social interaction, and despair. In contrast, fluoxetine treatment did not strongly improve behavioral performance during the same period compared with flickering photic stimulation. The present findings demonstrated that LED-derived flickering photic stimulation more rapidly improved behavioral outcomes in a CORT-induced mouse model of depression compared with fluoxetine. Thus, the present study suggests that rhythmical photic stimulation at alpha frequencies may aid in the improvement of the quality of life of patients with depression.

In-depth behavioral characterization of the corticosterone mouse model and the critical involvement of housing conditions

Depression and anxiety are disabling and highly prevalent psychiatric disorders. To better understand the neurobiological basis of mood and anxiety disorders, relevant animal models are needed. The corticosterone mouse model is frequently used to study depression. Chronic stress and accompanying glucocorticoid elevation causes pathological changes in the central nervous system, which are related to psychiatric symptoms. Exogenous administration of corticosterone is therefore often used to induce depressive-like behavior in mice and in some cases also features of anxiety-like behavior are shown. However, a thorough characterization of this model has never been conducted and housing conditions of the used subjects often differ between the implemented protocols. We chronically administered a subcutaneous corticosterone bolus injection to single- and group-housed mice, and we subsequently evaluated the face validity of this model by performing a battery of behavioral tests (forced swim test, mouse-tail suspension test, saccharin intake test, novelty-suppressed feeding test, elevated plus maze, light/dark paradigm and open field test). Our results show that corticosterone treatment has a substantial overall effect on depressive-like behavior. Increases in anxiety-like behavior on the other hand are mainly seen in single housed animals, independent of treatment. The current study therefore does not only show a detailed behavioral characterization of the corticosterone mouse model, but furthermore also elucidates the critical influence of housing conditions on the behavioral outcome in this model.

Are Structural Changes Induced by Lithium in the HIV Brain Accompanied by Changes in Functional Connectivity?

Lithium therapy has been shown to affect imaging measures of brain function and microstructure in human immunodeficiency virus (HIV)-infected subjects with cognitive impairment. The aim of this proof-of-concept study was to explore whether changes in brain microstructure also entail changes in functional connectivity. Functional MRI data of seven cognitively impaired HIV infected individuals enrolled in an open-label lithium study were included in the connectivity analysis. Seven regions of interest (ROI) were defined based on previously observed lithium induced microstructural changes measured by Diffusion Tensor Imaging. Generalized partial directed coherence (gPDC), based on time-variant multivariate autoregressive models, was used to quantify the degree of connectivity between the selected ROIs. Statistical analyses using a linear mixed model showed significant differences in the average node strength between pre and post lithium therapy conditions. Specifically, we found that lithium treatment in this population induced changes suggestive of increased strength in functional connectivity. Therefore, by exploiting the information about the strength of functional interactions provided by gPDC we can quantify the connectivity changes observed in relation to a given intervention. Furthermore, in conditions where the intervention is associated with clinical changes, we suggest that this methodology could enable an interpretation of such changes in the context of disease or treatment induced modulations in functional networks.

Ultrasound stimulation inhibits recurrent seizures and improves behavioral outcome in an experimental model of mesial temporal lobe epilepsy

Current therapies for epilepsy consist mostly of pharmacological agents or invasive surgery. Recently, ultrasound (US) stimulation has been considered a promising tool for the noninvasive treatment of brain diseases, including epilepsy. However, in temporal lobe epilepsy (TLE), a common form of epilepsy, neurophysiological and functional outcomes following US stimulation are not well defined. To address this, we developed a paradigm of transcranial pulsed US stimulation to efficiently suppress seizure activity in the initial/acute period in a kainate (KA)-induced mouse model of mesial TLE. Pulsed US stimulation inhibited acute seizure activity and either delayed the onset of or suppressed status epilepticus (SE). Kainate-treated mice that had received US stimulation in the initial period exhibited fewer spontaneous recurrent seizures (SRSs) and improved performance in behavioral tasks assessing sociability and depression in the chronic period of epilepsy. Our results demonstrate that US stimulation in the acute period of epilepsy can inhibit SRSs and improve behavioral outcomes in a mouse model of mesial TLE. The present study suggests that noninvasive transcranial pulsed US stimulation may be feasible as an adjuvant therapy in patients with epilepsy. This article is part of a Special Issue entitled "Status Epilepticus".