Semi-Metric Topology of the Human Connectome: Sensitivity and Specificity to Autism and Major Depressive Disorder

The ultrametric backbone is the union of all minimum spanning forests

Minimum spanning trees and forests are powerful sparsification techniques that remove cycles from weighted graphs to minimize total edge weight while preserving node reachability, with applications in computer science, network science, and graph theory. Despite their utility and ubiquity, they have several limitations, including that they are only defined for undirected networks, they significantly alter dynamics on networks, and they do not generally preserve important network features such as shortest distances, shortest path distribution, and community structure. In contrast, distance backbones, which are subgraphs formed by all edges that obey a generalized triangle inequality, are well defined in directed and undirected graphs and preserve those and other important network features. The backbone of a graph is defined with respect to a specified path-length operator that aggregates weights along a path to define its length, thereby associating a cost to indirect connections. The backbone is the union of all shortest paths between each pair of nodes according to the specified operator. One such operator, the max function, computes the length of a path as the largest weight of the edges that compose it (a weakest link criterion). It is the only operator that yields an algebraic structure for computing shortest paths that is consistent with De Morgan's laws. Applying this operator yields the ultrametric backbone of a graph in that (semi-triangular) edges whose weights are larger than the length of an indirect path connecting the same nodes (i.e. those that break the generalized triangle inequality based on max as a path-length operator) are removed. We show that the ultrametric backbone is the union of minimum spanning forests in undirected graphs and provides a new generalization of minimum spanning trees to directed graphs that, unlike minimum equivalent graphs and minimum spanning arborescences, preserves all max - min shortest paths and De Morgan's law consistency.

Genetic risk for schizophrenia is associated with increased proportion of indirect connections in brain networks revealed by a semi-metric analysis: evidence from population sample stratified for polygenic risk

Research studies based on tractography have revealed a prominent reduction of asymmetry in some key white-matter tracts in schizophrenia (SCZ). However, we know little about the influence of common genetic risk factors for SCZ on the efficiency of routing on structural brain networks (SBNs). Here, we use a novel recall-by-genotype approach, where we sample young adults from a population-based cohort (ALSPAC:N genotyped = 8,365) based on their burden of common SCZ risk alleles as defined by polygenic risk score (PRS). We compared 181 individuals at extremes of low (N = 91) or high (N = 90) SCZ-PRS under a robust diffusion MRI-based graph theoretical SBN framework. We applied a semi-metric analysis revealing higher SMR values for the high SCZ-PRS group compared with the low SCZ-PRS group in the left hemisphere. Furthermore, a hemispheric asymmetry index showed a higher leftward preponderance of indirect connections for the high SCZ-PRS group compared with the low SCZ-PRS group (PFDR < 0.05). These findings might indicate less efficient structural connectivity in the higher genetic risk group. This is the first study in a population-based sample that reveals differences in the efficiency of SBNs associated with common genetic risk variants for SCZ.

Mapping intrinsic functional network topological architecture in major depression disorder after electroconvulsive therapy

Disrupted topological organization of functional brain networks has been well documented in major depressive disorder (MDD). However, there is no report about how electroconvulsive therapy (ECT), a rapid way for depression remission, affects whole-brain functional network topological architecture to improve clinical symptoms in individuals with MDD. In this study, resting-state functional magnetic resonance imaging (rs-fMRI) data were collected for twenty-four MDD patients before and after receiving ECT and 25 gender-, age- and education-matched healthy controls (HC). The functional brain network for each subject was mapped using Brainnetome Atlas and graph-theory was applied to measure topological properties for both binary and weighted network. The results showed that ECT can significantly increase shortest path length and decrease global efficiency in MDD patients. In addition, significant alterations in nodal degree, nodal efficiency as well as between nodal functional connectivity strength were found in MDD patients after ECT. The network nodes showing changed degree, efficiency and connectivity were primarily distributed in default mode network (DMN), fronto-parietal network (FPN), and limbic system. Our findings demonstrates that ECT improves depressive symptoms by reorganizing disrupted network topological architecture in MDD patients and highlights the important role of functional reorganization of DMN, FPN, and limbic network contributing to depression remission.

The distance backbone of complex networks

Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that includes all possible measures of path length for weighted graphs. The result, without breaking the graph into smaller components, is a distance backbone subgraph sufficient to compute all shortest paths. This is important for understanding the dynamics of spread and communication phenomena in real-world networks. The general methodology we formally derive yields a principled graph reduction technique and provides a finer characterization of the triangular geometry of all edges-those that contribute to shortest paths and those that do not but are involved in other network phenomena. We demonstrate that the distance backbone is very small in large networks across domains ranging from air traffic to the human brain connectome, revealing that network robustness to attacks and failures seems to stem from surprisingly vast amounts of redundancy.

Detection of Emotional Sensitivity Using fNIRS Based Dynamic Functional Connectivity

In this study, we proposed an analytical framework to identify dynamic task-based functional connectivity (FC) features as new biomarkers of emotional sensitivity in nursing students, by using a combination of unsupervised and supervised machine learning techniques. The dynamic FC was measured by functional Near-Infrared Spectroscopy (fNIRS), and computed using a sliding window correlation (SWC) analysis. A k -means clustering technique was applied to derive four recurring connectivity states. The states were characterized by both graph theory and semi-metric analysis. Occurrence probability and state transition were extracted as dynamic FC network features, and a Random Forest (RF) classifier was implemented to detect emotional sensitivity. The proposed method was trialled on 39 nursing students and 19 registered nurses during decision-making, where we assumed registered nurses have developed strategies to cope with emotional sensitivity. Emotional stimuli were selected from International Affective Digitized Sound System (IADS) database. Experiment results showed that registered nurses demonstrated single dominant connectivity state of task-relevance, while nursing students displayed in two states and had higher level of task-irrelevant state connectivity. The results also showed that students were more susceptive to emotional stimuli, and the derived dynamic FC features provided a stronger discriminating power than heart rate variability (accuracy of 81.65% vs 71.03%) as biomarkers of emotional sensitivity. This work forms the first study to demonstrate the stability of fNIRS based dynamic FC states as a biomarker. In conclusion, the results support that the state distribution of dynamic FC could help reveal the differentiating factors between the nursing students and registered nurses during decision making, and it is anticipated that the biomarkers might be used as indicators when developing professional training related to emotional sensitivity.

Single-participant structural similarity matrices lead to greater accuracy in classification of participants than function in autism in MRI

BACKGROUND

Autism has previously been characterized by both structural and functional differences in brain connectivity. However, while the literature on single-subject derivations of functional connectivity is extensively developed, similar methods of structural connectivity or similarity derivation from T1 MRI are less studied.

METHODS

We introduce a technique of deriving symmetric similarity matrices from regional histograms of grey matter volumes estimated from T1-weighted MRIs. We then validated the technique by inputting the similarity matrices into a convolutional neural network (CNN) to classify between participants with autism and age-, motion-, and intracranial-volume-matched controls from six different databases (29,288 total connectomes, mean age = 30.72, range 0.42-78.00, including 1555 subjects with autism). We compared this method to similar classifications of the same participants using fMRI connectivity matrices as well as univariate estimates of grey matter volumes. We further applied graph-theoretical metrics on output class activation maps to identify areas of the matrices that the CNN preferentially used to make the classification, focusing particularly on hubs.

LIMITATIONS

While this study used a large sample size, the majority of data was from a young age group; furthermore, to make a viable machine learning study, we treated autism, a highly heterogeneous condition, as a binary label. Thus, these results are not necessarily generalizable to all subtypes and age groups in autism.

RESULTS

Our models gave AUROCs of 0.7298 (69.71% accuracy) when classifying by only structural similarity, 0.6964 (67.72% accuracy) when classifying by only functional connectivity, and 0.7037 (66.43% accuracy) when classifying by univariate grey matter volumes. Combining structural similarity and functional connectivity gave an AUROC of 0.7354 (69.40% accuracy). Analysis of classification performance across age revealed the greatest accuracy in adolescents, in which most data were present. Graph analysis of class activation maps revealed no distinguishable network patterns for functional inputs, but did reveal localized differences between groups in bilateral Heschl's gyrus and upper vermis for structural similarity.

CONCLUSION

This study provides a simple means of feature extraction for inputting large numbers of structural MRIs into machine learning models. Our methods revealed a unique emphasis of the deep learning model on the structure of the bilateral Heschl's gyrus when characterizing autism.

fNIRS-based functional connectivity estimation using semi-metric analysis to study decision making by nursing students and registered nurses

This study aims to investigate the generalizability of the semi-metric analysis of the functional connectivity (FC) for functional near-infrared spectroscopy (fNIRS) by applying it to detect the dichotomy in differential FC under affective and neutral emotional states in nursing students and registered nurses during decision making. The proposed method employs wavelet transform coherence to construct FC networks and explores semi-metric analysis to extract network redundancy features, which has not been considered in conventional fNIRS-based FC analyses. The trials of the proposed method were performed on 19 nursing students and 19 registered nurses via a decision-making task under different emotional states induced by affective and neutral emotional stimuli. The cognitive activities were recorded using fNIRS, and the emotional stimuli were adopted from the International Affective Digitized Sound System (IADS). The induction of emotional effects was validated by heart rate variability (HRV) analysis. The experimental results by the proposed method showed significant difference (FDR-adjusted p = 0.004) in the nursing students’ cognitive FC network under the two different emotional conditions, and the semi-metric percentage (SMP) of the right prefrontal cortex (PFC) was found to be significantly higher than the left PFC (FDR-adjusted p = 0.036). The benchmark method (a typical weighted graph theory analysis) gave no significant results. In essence, the results support that the semi-metric analysis can be generalized and extended to fNIRS-based functional connectivity estimation.

Ensemble Deep Learning on Large, Mixed-Site fMRI Datasets in Autism and Other Tasks

Deep learning models for MRI classification face two recurring problems: they are typically limited by low sample size, and are abstracted by their own complexity (the “black box problem”). In this paper, we train a convolutional neural network (CNN) with the largest multi-source, functional MRI (fMRI) connectomic dataset ever compiled, consisting of 43,858 datapoints. We apply this model to a cross-sectional comparison of autism spectrum disorder (ASD) versus typically developing (TD) controls that has proved difficult to characterize with inferential statistics. To contextualize these findings, we additionally perform classifications of gender and task versus rest. Employing class-balancing to build a training set, we trained [Formula: see text] modified CNNs in an ensemble model to classify fMRI connectivity matrices with overall AUROCs of 0.6774, 0.7680, and 0.9222 for ASD versus TD, gender, and task versus rest, respectively. Additionally, we aim to address the black box problem in this context using two visualization methods. First, class activation maps show which functional connections of the brain our models focus on when performing classification. Second, by analyzing maximal activations of the hidden layers, we were also able to explore how the model organizes a large and mixed-center dataset, finding that it dedicates specific areas of its hidden layers to processing different covariates of data (depending on the independent variable analyzed), and other areas to mix data from different sources. Our study finds that deep learning models that distinguish ASD from TD controls focus broadly on temporal and cerebellar connections, with a particularly high focus on the right caudate nucleus and paracentral sulcus.

Enhancement of indirect functional connections with shortest path length in the adult autistic brain

Autism is a neurodevelopmental condition characterized by atypical brain functional organization. Here we investigated the intrinsic indirect (semi-metric) connectivity of the functional connectome associated with autism. Resting-state functional magnetic resonance imaging scans were acquired from 65 neurotypical adults (33 males/32 females) and 61 autistic adults (30 males/31 females). From functional connectivity networks, semi-metric percentages (SMPs) were calculated to assess the proportion of indirect shortest functional pathways at global, hemisphere, network, and node levels. Group comparisons were then conducted to ascertain differences between autism and neurotypical control groups. Finally, the strength and length of edges were examined to explore the patterns of semi-metric connections associated with autism. Compared with neurotypical controls, autistic adults displayed significantly higher SMP at all spatial scales, similar to prior observations in adolescents. Differences were primarily in weaker, longer-distance edges in the majority between networks. However, no significant diagnosis-by-sex interaction effects were observed on global SMP. These findings suggest increased indirect functional connectivity in the autistic brain is persistent from adolescence to adulthood and is indicative of reduced functional network integration.

Structural white matter alterations in male adults with high functioning autism spectrum disorder and concurrent depressive symptoms; a diffusion tensor imaging study

BACKGROUND

Autism spectrum disorder (ASD), a prevalent developmental condition, is associated with comorbid mood disorders, most importantly depression. Here, we explored the underlying association between brain white matter microstructural integrity, assessed by diffusion tensor imaging (DTI), and depressive symptoms, in male adults with high-functioning ASD.

METHOD

To assess our main purpose, Autism Brain Imaging Data Exchange II dataset was used to acquire brain diffusion imaging from 26 adult male patients with ASD ranging from 18 to 62 years of age, and 26 age and gender-matched typically developed control subjects. Participants were evaluated for depressive symptoms manifestation by the Beck Depression Index (BDI). DWI images were preprocessed and analyzed for DTI scalers in the "ExploreDTI" toolbox. Adjusted linear regression models were used. Association between normalized BDI score and its interaction with diagnosis, as predictors, and measures of fractional anisotropy (FA) and mean diffusivity (MD) of regions of interest according to Mori atlas was assessed.

RESULT

Significant lower microstructural integrity of white matter was found in association with higher BDI scores in ASD group, mainly in regions of anterior limb of internal capsule (ALIC) and corona radiata. Also, a statistically significant positive interaction between BDI and ASD was seen in FA of left ALIC.

DISCUSSION

Considering similar regional brain white matter involvement with the imaging studies of depression in the typically developed population, we propose that these alterations of white matter tracts in depressive symptoms of adult ASD subjects might be, at least, similar to depression in typically developed population.

Normative pathways in the functional connectome

Functional connectivity is frequently derived from fMRI data to reduce a complex image of the brain to a graph, or "functional connectome". Often shortest-path algorithms are used to characterize and compare functional connectomes. Previous work on the identification and measurement of semi-metric (shortest circuitous) pathways in the functional connectome has discovered cross-sectional differences in major depressive disorder (MDD), autism spectrum disorder (ASD), and Alzheimer's disease. However, while measurements of shortest path length have been analyzed in functional connectomes, less work has been done to investigate the composition of the pathways themselves, or whether the edges composing pathways differ between individuals. Developments in this area would help us understand how pathways might be organized in mental disorders, and if a consistent pattern can be found. Furthermore, studies in structural brain connectivity and other real-world graphs suggest that shortest pathways may not be as important in functional connectivity studies as previously assumed. In light of this, we present a novel measurement of the consistency of pathways across functional connectomes, and an algorithm for improvement by selecting the most frequently occurring "normative pathways" from the k shortest paths, instead of just the shortest path. We also look at this algorithm's effect on various graph measurements, using randomized matrix simulations to support the efficacy of this method and demonstrate our algorithm on the resting-state fMRI (rs-fMRI) of a group of 34 adolescent control participants. Additionally, a comparison of normative pathways is made with a group of 82 age-matched participants, diagnosed with MDD, and in doing so we find the normative pathways that are most disrupted. Our results, which are carried out with estimates of connectivity derived from correlation, partial correlation, and normalized mutual information connectomes, suggest disruption to the default mode, affective, and ventral attention networks. Normative pathways, especially with partial correlation, make greater use of critical anatomical pathways through the striatum, cingulum, and the cerebellum. In summary, MDD is characterized by a disruption of normative pathways of the ventral attention network, increases in alternative pathways in the frontoparietal network in MDD, and a mixture of both in the default mode network. Additionally, within- and between-groups findings depend on the estimate of connectivity.

Functional network dysconnectivity as a biomarker of treatment resistance in schizophrenia

Schizophrenia may develop from disruptions in functional connectivity regulated by neurotransmitters such as dopamine and acetylcholine. The modulatory effects of these neurotransmitters might explain how antipsychotics attenuate symptoms of schizophrenia and account for the variable response to antipsychotics observed in clinical practice. Based on the putative mechanisms of antipsychotics and evidence of disrupted connectivity in schizophrenia, we hypothesised that functional network connectivity, as assessed using network-based statistics, would exhibit differences between treatment response subtypes of schizophrenia and healthy controls. Resting-state functional MRI data were obtained from 17 healthy controls as well as individuals with schizophrenia who responded well to first-line atypical antipsychotics (first-line responders; FLR, n=18), had failed at least two trials of antipsychotics but responded to clozapine (treatment-resistant schizophrenia; TRS, n=18), or failed at least two trials of antipsychotics and a trial of clozapine (ultra-treatment-resistant schizophrenia; UTRS, n=16). Data were pre-processed using the Advanced Normalization Toolkit and BrainWavelet Toolbox. Network connectivity was assessed using the Network-Based Statistics toolbox in Matlab. ANOVA revealed a significant difference in functional connectivity between groups that extended between cerebellar and parietal regions to the frontal cortex (p<0.05). Post-hoc t-tests revealed weaker network connectivity in individuals with UTRS compared with healthy controls but no other differences between groups. Results demonstrated distinct differences in functional connectivity between individuals with UTRS and healthy controls. Future work must determine whether these changes occur prior to the onset of treatment and if they can be used to predict resistance to antipsychotics during first-episode psychosis.

A Winding Road: Alzheimer's Disease Increases Circuitous Functional Connectivity Pathways

Neuroimaging has been successful in characterizing the pattern of cerebral atrophy that accompanies the progression of Alzheimer's disease (AD). Examination of functional connectivity, the strength of signal synchronicity between brain regions, has gathered pace as another way of understanding changes to the brain that are associated with AD. It appears to have good sensitivity and detect effects that precede cognitive decline, and thus offers the possibility to understand the neurobiology of the disease in its earliest phases. However, functional connectivity analyzes to date generally consider only the strongest connections, with weaker links ignored. This proof-of-concept study compared patients with mild-to-moderate AD (N = 11) and matched control individuals (N = 12) based on functional connectivities derived from blood-oxygenation level dependent (BOLD) sensitive functional MRI acquired during resting wakefulness. All positive connectivities irrespective of their strength were included. Transitive closures of the resulting connectome were calculated that classified connections as either direct or indirect. Between-group differences in the proportion of indirect paths were observed. In AD, there was broadly increased indirect connectivity across greater spatial distances. Furthermore, the indirect pathways in AD had greater between-subject topological variance than controls. The prevailing characterization of AD as being a disconnection syndrome is refined by the observation that direct links between regions that are impaired are perhaps replaced by an increase in indirect functional pathways that is only detectable through inclusion of connections across the entire range of connection strengths.

Semi-metric analysis of the functional brain network: Relationship with familial risk for psychotic disorder

Background

Dysconnectivity in schizophrenia can be understood in terms of dysfunctional integration of a distributed network of brain regions. Here we propose a new methodology to analyze complex networks based on semi-metric behavior, whereby higher levels of semi-metricity may represent a higher level of redundancy and dispersed communication. It was hypothesized that individuals with (increased risk for) psychotic disorder would have more semi-metric paths compared to controls and that this would be associated with symptoms.

Methods

Resting-state functional MRI scans were obtained from 73 patients with psychotic disorder, 83 unaffected siblings and 72 controls. Semi-metric percentages (SMP) at the whole brain, hemispheric and lobar level were the dependent variables in a multilevel random regression analysis to investigate group differences. SMP was further examined in relation to symptomatology (i.e., psychotic/cognitive symptoms).

Results

At the whole brain and hemispheric level, patients had a significantly higher SMP compared to siblings and controls, with no difference between the latter. In the combined sibling and control group, individuals with high schizotypy had intermediate SMP values in the left hemisphere with respect to patients and individuals with low schizotypy. Exploratory analyses in patients revealed higher SMP in 12 out of 42 lobar divisions compared to controls, of which some were associated with worse PANSS symptomatology (i.e., positive symptoms, excitement and emotional distress) and worse cognitive performance on attention and emotion processing tasks. In the combined group of patients and controls, working memory, attention and social cognition were associated with higher SMP.

Discussion

The results are suggestive of more dispersed network communication in patients with psychotic disorder, with some evidence for trait-based network alterations in high-schizotypy individuals. Dispersed communication may contribute to the clinical phenotype in psychotic disorder. In addition, higher SMP may contribute to neuro- and social cognition, independent of psychosis risk.

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Higher SMP was observed at whole brain and hemispheric level in psychotic disorder.

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In patients, lobar SMP was associated with psychotic and cognitive symptoms.

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Trait-based SMP alterations were observed in high schizotypy individuals.