Thought Chart: tracking the thought with manifold learning during emotion regulation.

The Nash embedding theorem demonstrates that any compact manifold can be isometrically embedded in a Euclidean space. Assuming the complex brain states form a high-dimensional manifold in a topological space, we propose a manifold learning framework, termed Thought Chart, to reconstruct and visualize the manifold in a low-dimensional space. Furthermore, it serves as a data-driven approach to discover the underlying dynamics when the brain is engaged in a series of emotion and cognitive regulation tasks. EEG-based temporal dynamic functional connectomes are created based on 20 psychiatrically healthy participants' EEG recordings during resting state and an emotion regulation task. Graph dissimilarity space embedding was applied to all the dynamic EEG connectomes. In order to visualize the learned manifold in a lower dimensional space, local neighborhood information is reconstructed via k-nearest neighbor-based nonlinear dimensionality reduction (NDR) and epsilon distance-based NDR. We showed that two neighborhood constructing approaches of NDR embed the manifold in a two-dimensional space, which we named Thought Chart. In Thought Chart, different task conditions represent distinct trajectories. Properties such as the distribution or average length in the 2-D space may serve as useful parameters to explore the underlying cognitive load and emotion processing during the complex task. In sum, this framework is a novel data-driven approach to the learning and visualization of underlying neurophysiological dynamics of complex functional brain data.

The significance of negative correlations in brain connectivity.

Understanding the modularity of functional magnetic resonance imaging (fMRI)-derived brain networks or "connectomes" can inform the study of brain function organization. However, fMRI connectomes additionally involve negative edges, which may not be optimally accounted for by existing approaches to modularity that variably threshold, binarize, or arbitrarily weight these connections. Consequently, many existing Q maximization-based modularity algorithms yield variable modular structures. Here, we present an alternative complementary approach that exploits how frequent the blood-oxygen-level-dependent (BOLD) signal correlation between two nodes is negative. We validated this novel probability-based modularity approach on two independent publicly-available resting-state connectome data sets (the Human Connectome Project [HCP] and the 1,000 functional connectomes) and demonstrated that negative correlations alone are sufficient in understanding resting-state modularity. In fact, this approach (a) permits a dual formulation, leading to equivalent solutions regardless of whether one considers positive or negative edges; (b) is theoretically linked to the Ising model defined on the connectome, thus yielding modularity result that maximizes data likelihood. Additionally, we were able to detect novel and consistent sex differences in modularity in both data sets. As data sets like HCP become widely available for analysis by the neuroscience community at large, alternative and perhaps more advantageous computational tools to understand the neurobiological information of negative edges in fMRI connectomes are increasingly important.

Cognitive and connectome properties detectable through individual differences in graphomotor organization.

We investigated whether graphomotor organization during a digitized Clock Drawing Test (dCDT) would be associated with cognitive and/or brain structural differences detected with a tractography-derived structural connectome of the brain. 72 non-demented/non-depressed adults were categorized based on whether or not they used 'anchor' digits (i.e., 12, 3, 6, 9) before any other digits while completing dCDT instructions to "draw the face of a clock with all the numbers and set the hands to 10 after 11". 'Anchorers' were compared to 'non-anchorers' across dCDT, additional cognitive measures and connectome-based metrics. In the context of grossly intact clock drawings, anchorers required fewer strokes to complete the dCDT and outperformed non-anchorers on executive functioning and learning/memory/recognition tasks. Anchorers had higher local efficiency for the left medial orbitofrontal and transverse temporal cortices as well as the right rostral anterior cingulate and superior frontal gyrus versus non-anchorers suggesting better regional integration within local networks involving these regions; select aspects of which correlated with cognition. Results also revealed that anchorers' exhibited a higher degree of modular integration among heteromodal regions of the ventral visual processing stream versus non-anchorers. Thus, an easily observable graphomotor distinction was associated with 1) better performance in specific cognitive domains, 2) higher local efficiency suggesting better regional integration, and 3) more sophisticated modular integration involving the ventral ('what') visuospatial processing stream. Taken together, these results enhance our knowledge of the brain-behavior relationships underlying unprompted graphomotor organization during dCDT.

Measuring embeddedness: Hierarchical scale-dependent information exchange efficiency of the human brain connectome.

This article presents a novel approach for understanding information exchange efficiency and its decay across hierarchies of modularity, from local to global, of the structural human brain connectome. Magnetic resonance imaging techniques have allowed us to study the human brain connectivity as a graph, which can then be analyzed using a graph-theoretical approach. Collectively termed brain connectomics, these sophisticated mathematical techniques have revealed that the brain connectome, like many networks, is highly modular and brain regions can thus be organized into communities or modules. Here, using tractography-informed structural connectomes from 46 normal healthy human subjects, we constructed the hierarchical modularity of the structural connectome using bifurcating dendrograms. Moving from fine to coarse (i.e., local to global) up the connectome's hierarchy, we computed the rate of decay of a new metric that hierarchically preferentially weighs the information exchange between two nodes in the same module. By computing "embeddedness"-the ratio between nodal efficiency and this decay rate, one could thus probe the relative scale-invariant information exchange efficiency of the human brain. Results suggest that regions that exhibit high embeddedness are those that comprise the limbic system, the default mode network, and the subcortical nuclei. This supports the presence of near-decomposability overall yet relative embeddedness in select areas of the brain. The areas we identified as highly embedded are varied in function but are arguably linked in the evolutionary role they play in memory, emotion and behavior.

The intrinsic geometry of the human brain connectome.

This paper describes novel methods for constructing the intrinsic geometry of the human brain connectome using dimensionality-reduction techniques. We posit that the high-dimensional, complex geometry that represents this intrinsic topology can be mathematically embedded into lower dimensions using coupling patterns encoded in the corresponding brain connectivity graphs. We tested both linear and nonlinear dimensionality-reduction techniques using the diffusion-weighted structural connectome data acquired from a sample of healthy subjects. Results supported the nonlinearity of brain connectivity data, as linear reduction techniques such as the multidimensional scaling yielded inferior lower-dimensional embeddings. To further validate our results, we demonstrated that for tractography-derived structural connectome more influential regions such as rich-club members of the brain are more centrally mapped or embedded. Further, abnormal brain connectivity can be visually understood by inspecting the altered geometry of these three-dimensional (3D) embeddings that represent the topology of the human brain, as illustrated using simulated lesion studies of both targeted and random removal. Last, in order to visualize brain's intrinsic topology we have developed software that is compatible with virtual reality technologies, thus allowing researchers to collaboratively and interactively explore and manipulate brain connectome data.

Brain connectivity in late-life depression and aging revealed by network analysis.

OBJECTIVE: To use novel methods to examine age associations across an integrated brain network in healthy older adults (HOA) and individuals with late-life depression (LLD). Graph theory metrics describe the organizational configuration of both the global network and specified brain regions. METHODS: Cross-sectional data were acquired. Graph theory was used to explore diffusion tensor imaging-derived white matter networks. Forty-eight HOA and 28 adults with LLD were recruited from the community. Global and local metrics in prefrontal, cingulate, and temporal regions were calculated. Group differences and associations with age were explored. RESULTS: Group differences were noted in local metrics of the right prefrontal and temporal regions, but no significant differences were observed on global metrics. Local (not global) metrics were associated with age differently across groups. For HOA, local metrics across all regions correlated with age, whereas in adults with LLD, correlations were only observed within temporal regions. In keeping with hypothesized regions impacted by LLD, stronger hubs in right temporal regions were observed among HOA, whereas LLD individuals were characterized by robust hubs in frontal regions. CONCLUSION: We demonstrate widespread age-related changes in local network properties among HOA with different and more restricted local changes in LLD. Although a preliminary analysis, different patterns of correlations in local networks coupled with equivalent global metrics may reflect altered local structural brain networks in patients with LLD.

Altered structural brain connectome in young adult fragile X premutation carriers.

Fragile X premutation carriers (fXPC) are characterized by 55-200 CGG trinucleotide repeats in the 5' untranslated region on the Xq27.3 site of the X chromosome. Clinically, they are associated with the fragile X-Associated Tremor/Ataxia Syndrome, a late-onset neurodegenerative disorder with diffuse white matter neuropathology. Here, we conducted first-ever graph theoretical network analyses in fXPCs using 30-direction diffusion-weighted magnetic resonance images acquired from 42 healthy controls aged 18-44 years (HC; 22 male and 20 female) and 46 fXPCs (16 male and 30 female). Globally, we found no differences between the fXPCs and HCs within each gender for all global graph theoretical measures. In male fXPCs, global efficiency was significantly negatively associated with the number of CGG repeats. For nodal measures, significant group differences were found between male fXPCs and male HCs in the right fusiform and the right ventral diencephalon (for nodal efficiency), and in the left hippocampus [for nodal clustering coefficient (CC)]. In female fXPCs, CC in the left superior parietal cortex correlated with counting performance in an enumeration task.

Investigating brain community structure abnormalities in bipolar disorder using path length associated community estimation.

In this article, we present path length associated community estimation (PLACE), a comprehensive framework for studying node-level community structure. Instead of the well-known Q modularity metric, PLACE utilizes a novel metric, Ψ(PL), which measures the difference between intercommunity versus intracommunity path lengths. We compared community structures in human healthy brain networks generated using these two metrics and argued that Ψ(PL) may have theoretical advantages. PLACE consists of the following: (1) extracting community structure using top-down hierarchical binary trees, where a branch at each bifurcation denotes a collection of nodes that form a community at that level, (2) constructing and assessing mean group community structure, and (3) detecting node-level changes in community between groups. We applied PLACE and investigated the structural brain networks obtained from a sample of 25 euthymic bipolar I subjects versus 25 gender- and age-matched healthy controls. Results showed community structural differences in posterior default mode network regions, with the bipolar group exhibiting left-right decoupling.

White matter microstructure in body dysmorphic disorder and its clinical correlates.

Body dysmorphic disorder (BDD) is characterized by an often-delusional preoccupation with misperceived defects of appearance, causing significant distress and disability. Although previous studies have found functional abnormalities in visual processing, frontostriatal, and limbic systems, no study to date has investigated the microstructure of white matter connecting these systems in BDD. Participants comprised 14 medication-free individuals with BDD and 16 healthy controls who were scanned using diffusion-weighted magnetic resonance imaging (MRI). We utilized probabilistic tractography to reconstruct tracts of interest, and tract-based spatial statistics to investigate whole brain white matter. To estimate white matter microstructure, we used fractional anisotropy (FA), mean diffusivity (MD), and linear and planar anisotropy (c(l) and c(p)). We correlated diffusion measures with clinical measures of symptom severity and poor insight/delusionality. Poor insight negatively correlated with FA and c(l) and positively correlated with MD in the inferior longitudinal fasciculus (ILF) and the forceps major (FM). FA and c(l) were lower in the ILF and the inferior fronto-occipital fasciculus and higher in the FM in the BDD group, but differences were nonsignificant. This is the first diffusion-weighted MR investigation of white matter in BDD. Results suggest a relationship between impairments in insight, a clinically important phenotype, and fiber disorganization in tracts connecting visual with emotion/memory processing systems.

White matter tract integrity of anterior limb of internal capsule in major depression and type 2 diabetes.

A number of studies have shown an association between diabetes and depression. However, the underlying mechanisms are still unclear. Previous findings indicate a role for the prefrontal cortex and subcortical gray matter regions in type 2 diabetes and major depressive disorder (MDD). The purpose of this study was to examine the white matter integrity in the fibers that are part of the anterior limb of internal capsule (ALIC) in MDD and diabetic subjects using diffusion tensor imaging tractography. We studied 4 groups of subjects including 1) 42 healthy controls (HC), 2) 28 MDD subjects (MD), 3) 24 patients diagnosed with type 2 diabetes without depression (DC), and 4) 22 patients diagnosed with diabetes and depression (DD). Results revealed significantly decreased fractional anisotropy (FA; P=.021) and a trend towards significant increase in radial diffusivity (RD; P=.078) of the right ALIC in depressed subjects (MD+DD) compared to non-depressed subjects (HC+DC). While there were no significant diabetes effects or interactions between depression and diabetes, subjects with high depression ratings and high hemoglobin A1c levels had the lowest mean FA values in the right ALIC. In addition, we found a significant negative correlation between FA of the left ALIC with hemoglobin A1c in diabetic subjects (DC+DD; P=.016). Our study demonstrated novel findings of white matter abnormalities of the ALIC in depression and diabetes. These findings have implications for clinical manifestations of depression and diabetes as well as their pathophysiology.

Abnormal brain network organization in body dysmorphic disorder.

Body dysmorphic disorder (BDD) is characterized by preoccupation with misperceived defects of appearance, causing significant distress and disability. Previous studies suggest abnormalities in information processing characterized by greater local relative to global processing. The purpose of this study was to probe whole-brain and regional white matter network organization in BDD, and to relate this to specific metrics of symptomatology. We acquired diffusion-weighted 34-direction MR images from 14 unmedicated participants with DSM-IV BDD and 16 healthy controls, from which we conducted whole-brain deterministic diffusion tensor imaging tractography. We then constructed white matter structural connectivity matrices to derive whole-brain and regional graph theory metrics, which we compared between groups. Within the BDD group, we additionally correlated these metrics with scores on psychometric measures of BDD symptom severity as well as poor insight/delusionality. The BDD group showed higher whole-brain mean clustering coefficient than controls. Global efficiency negatively correlated with BDD symptom severity. The BDD group demonstrated greater edge betweenness centrality for connections between the anterior temporal lobe and the occipital cortex, and between bilateral occipital poles. This represents the first brain network analysis in BDD. Results suggest disturbances in whole brain structural topological organization in BDD, in addition to correlations between clinical symptoms and network organization. There is also evidence of abnormal connectivity between regions involved in lower-order visual processing and higher-order visual and emotional processing, as well as interhemispheric visual information transfer. These findings may relate to disturbances in information processing found in previous studies.

Impaired inter-hemispheric integration in bipolar disorder revealed with brain network analyses.

BACKGROUND: This represents the first graph theory-based brain network analysis study in bipolar disorder, a chronic and disabling psychiatric disorder characterized by severe mood swings. Many imaging studies have investigated white matter in bipolar disorder, with results suggesting abnormal white matter structural integrity, particularly in the fronto-limbic and callosal systems. However, many inconsistencies remain in the literature, and no study to date has conducted brain network analyses with a graph-theoretic approach. METHODS: We acquired 64-direction diffusion-weighted magnetic resonance imaging on 25 euthymic bipolar I disorder subjects and 24 gender- and age-equivalent healthy subjects. White matter integrity measures including fractional anisotropy and mean diffusivity were compared in the whole brain. Additionally, structural connectivity matrices based on whole-brain deterministic tractography were constructed, followed by the computation of both global and local brain network measures. We also designed novel metrics to further probe inter-hemispheric integration. RESULTS: Network analyses revealed that the bipolar brain networks exhibited significantly longer characteristic path length, lower clustering coefficient, and lower global efficiency relative to those of control subjects. Further analyses revealed impaired inter-hemispheric but relatively preserved intra-hemispheric integration. These findings were supported by whole-brain white matter analyses that revealed significantly lower integrity in the corpus callosum in bipolar subjects. There were also abnormalities in nodal network measures in structures within the limbic system, especially the left hippocampus, the left lateral orbitofrontal cortex, and the bilateral isthmus cingulate. CONCLUSIONS: These results suggest abnormalities in structural network organization in bipolar disorder, particularly in inter-hemispheric integration and within the limbic system.

Constructing the resting state structural connectome.

BACKGROUND: Many recent studies have separately investigated functional and white matter (WM) based structural connectivity, yet their relationship remains less understood. In this paper, we proposed the functional-by-structural hierarchical (FSH) mapping to integrate multimodal connectome data from resting state fMRI (rsfMRI) and the whole brain tractography-derived connectome. METHODS: FSH first observes that the level of resting-state functional correlation between any two regions in general decreases as the graph distance of the corresponding structural connectivity matrix between them increases. As not all white matter tracts are actively in use (i.e., "utilized") during resting state, FSH thus models the rsfMRI correlation as an exponential decay function of the graph distance of the rsfMRI-informed structural connectivity or rsSC. rsSC is mathematically computed by multiplying entry-by-entry the tractography-derived structural connectivity matrix with a binary white matter "utilization matrix" U. U thus encodes whether any specific WM tract is being utilized during rsFMRI, and is estimated using simulated annealing. We applied this technique and investigated the hierarchical modular structure of rsSC from 7 depressed subjects and 7 age/gender matched controls. RESULTS: No significant group differences were detected in the modular structures of either the resting state functional connectome or the whole brain tractography-derived connectome. By contrast, FSH results revealed significantly different patterns of association in the bilateral posterior cingulate cortex and right precuneus, with the depressed group exhibiting stronger associations among regions instrumental in self-referential operations. DISCUSSION: The results of this study support that enhanced sensitivity can be obtained by integrating multimodal imaging data using FSH, a novel computational technique that may increase power to detect group differences in brain connectomes.

Multi-resolutional brain network filtering and analysis via wavelets on non-Euclidean space.

Advances in resting state fMRI and diffusion weighted imaging (DWI) have led to much interest in studies that evaluate hypotheses focused on how brain connectivity networks show variations across clinically disparate groups. However, various sources of error (e.g., tractography errors, magnetic field distortion, and motion artifacts) leak into the data, and make downstream statistical analysis problematic. In small sample size studies, such noise have an unfortunate effect that the differential signal may not be identifiable and so the null hypothesis cannot be rejected. Traditionally, smoothing is often used to filter out noise. But the construction of convolving with a Gaussian kernel is not well understood on arbitrarily connected graphs. Furthermore, there are no direct analogues of scale-space theory for graphs--ones which allow to view the signal at multiple resolutions. We provide rigorous frameworks for performing 'multi-resolutional' analysis on brain connectivity graphs. These are based on the recent theory of non-Euclidean wavelets. We provide strong evidence, on brain connectivity data from a network analysis study (structural connectivity differences in adult euthymic bipolar subjects), that the proposed algorithm allows identifying statistically significant network variations, which are clinically meaningful, where classical statistical tests, if applied directly, fail.

A framework for quantifying node-level community structure group differences in brain connectivity networks.

We propose a framework for quantifying node-level community structures between groups using anatomical brain networks derived from DTI-tractography. To construct communities, we computed hierarchical binary trees by maximizing two metrics: the well-known modularity metric (Q), and a novel metric that measures the difference between inter-community and intra-community path lengths. Changes in community structures on the nodal level were assessed between generated trees and a statistical framework was developed to detect local differences between two groups of community structures. We applied this framework to a sample of 42 subjects with major depression and 47 healthy controls. Results showed that several nodes (including the bilateral precuneus, which have been linked to self-awareness) within the default mode network exhibited significant differences between groups. These findings are consistent with those reported in previous literature, suggesting a higher degree of ruminative self-reflections in depression.

Hierarchical structural mapping for globally optimized estimation of functional networks.

In this study, we propose a framework to map functional MRI (fMRI) activation signals using DTI-tractography. This framework, which we term functional by structural hierarchical (FSH) mapping, models the regional origin of fMRI brain activation to construct "N-step reachable structural maps". Linear combinations of these N-step reachable maps are then used to predict the observed fMRI signals. Additionally, we constructed a utilization matrix, which numerically estimates whether the inclusion of a specific structural connection better predicts fMRI, using simulated annealing. We applied this framework to a visual fMRI task in a sample of body dysmorphic disorder (BDD) subjects and comparable healthy controls. Group differences were inferred by comparing the observed utilization differences against 10,000 permutations under the null hypothesis. Results revealed that BDD subjects under-utilized several key local connections in the visual system, which may help explain previously reported fMRI findings and further elucidate the underlying pathophysiology of BDD.