Highlighting the structure-function relationship of the brain with the Ising model and graph theory

Energy of functional brain states correlates with cognition in adolescent-onset schizophrenia and healthy persons

Adolescent-onset schizophrenia (AOS) is rare, under-studied, and associated with more severe cognitive impairments and poorer outcomes than adult-onset schizophrenia. Neuroimaging has shown altered regional activations (first-order effects) and functional connectivity (second-order effects) in AOS compared to controls. The pairwise maximum entropy model (MEM) integrates first- and second-order factors into a single quantity called energy, which is inversely related to probability of occurrence of brain activity patterns. We take a combinatorial approach to study multiple brain-wide MEMs of task-associated components; hundreds of independent MEMs for various sub-systems are fit to 7 Tesla functional MRI scans. Acquisitions were collected from 23 AOS individuals and 53 healthy controls while performing the Penn Conditional Exclusion Test (PCET) for executive function, which is known to be impaired in AOS. Accuracy of PCET performance was significantly reduced among AOS compared to controls. A majority of the models showed significant negative correlation between PCET scores and the total energy attained over the fMRI. Across all instantiations, the AOS group was associated with significantly more frequent occurrence of states of higher energy, assessed with a mixed effects model. An example MEM instance was investigated further using energy landscapes, which visualize high and low energy states on a low-dimensional plane, and trajectory analysis, which quantify the evolution of brain states throughout this landscape. Both supported patient-control differences in the energy profiles. Severity of psychopathology was correlated positively with energy. The MEM's integrated representation of energy in task-associated systems can help characterize pathophysiology of AOS, cognitive impairments, and psychopathology.

Criticality in Alzheimer's and healthy brains: insights from phase-ordering

Criticality, observed during second-order phase transitions, is an emergent phenomenon. The brain operates near criticality where complex systems exhibit high correlations. As a system approaches criticality, it develops "domain"-like regions with competing phases and increased spatio-temporal correlations that diverge. The dynamics of these domains depend on the system's proximity to criticality. This study explores the differences in the proximity to criticality of Alzheimer's-afflicted and cognitively normal brains through the use of a spin-lattice model derived from resting-state fMRI data and investigates the type of criticality found in the human brain - whether it is of the Ising class or something more complex. The temporal correlations in both groups display a stretched exponential nature, indicating closer alignment with the criticality of the spin-glass class rather than the Ising class. Longer relaxation times observed in cognitively normal subjects suggest increased proximity to the phase boundary. The weak distinction observed in the spatial characteristics related to proximity to criticality might once more point to a spin-glass scenario, necessitating nuanced order parameters to distinguish between phase-ordering in Alzheimer's and cognitively normal brains.

Noise cleaning the precision matrix of short time series

We present a comparison between various algorithms of inference of covariance and precision matrices in small data sets of real vectors of the typical length and dimension of human brain activity time series retrieved by functional magnetic resonance imaging (fMRI). Assuming a Gaussian model underlying the neural activity, the problem consists of denoising the empirically observed matrices to obtain a better estimator of the (unknown) true precision and covariance matrices. We consider several standard noise-cleaning algorithms and compare them on two types of data sets. The first type consists of synthetic time series sampled from a generative Gaussian model of which we can vary the fraction of dimensions per sample q and the strength of off-diagonal correlations. The second type consists of time series of fMRI brain activity of human subjects at rest. The reliability of each algorithm is assessed in terms of test-set likelihood and, in the case of synthetic data, of the distance from the true precision matrix. We observe that the so-called optimal rotationally invariant estimator, based on random matrix theory, leads to a significantly lower distance from the true precision matrix in synthetic data and higher test likelihood in natural fMRI data. We propose a variant of the optimal rotationally invariant estimator in which one of its parameters is optimzed by cross-validation. In the severe undersampling regime (large q) typical of fMRI series, it outperforms all the other estimators. We furthermore propose a simple algorithm based on an iterative likelihood gradient ascent, leading to very accurate estimations in weakly correlated synthetic data sets.

Brain Connectivity Signature Extractions from TMS Invoked EEGs

(1) Background: The correlations between brain connectivity abnormality and psychiatric disorders have been continuously investigated and progressively recognized. Brain connectivity signatures are becoming exceedingly useful for identifying patients, monitoring mental health disorders, and treatment. By using electroencephalography (EEG)-based cortical source localization along with energy landscape analysis techniques, we can statistically analyze transcranial magnetic stimulation (TMS)-invoked EEG signals, for obtaining connectivity among different brain regions at a high spatiotemporal resolution. (2) Methods: In this study, we analyze EEG-based source localized alpha wave activity in response to TMS administered to three locations, namely, the left motor cortex (49 subjects), left prefrontal cortex (27 subjects), and the posterior cerebellum, or vermis (27 subjects) by using energy landscape analysis techniques to uncover connectivity signatures. We then perform two sample t-tests and use the (5 × 10^-5) Bonferroni corrected p-valued cases for reporting six reliably stable signatures. (3) Results: Vermis stimulation invoked the highest number of connectivity signatures and the left motor cortex stimulation invoked a sensorimotor network state. In total, six out of 29 reliable, stable connectivity signatures are found and discussed. (4) Conclusions: We extend previous findings to localized cortical connectivity signatures for medical applications that serve as a baseline for future dense electrode studies.

Three-State Opinion Model on Complex Topologies

We investigate opinion diffusion on complex networks and the interplay between the existence of neutral opinion states and non-trivial network structures. For this purpose, we apply a three-state opinion model based on magnetic-like interactions to modular complex networks, both synthetic and real networks extracted from Twitter. The model allows for tuning the contribution of neutral agents using a neutrality parameter. We also consider social agitation, encoded as a temperature, that accounts for random opinion changes that are beyond the agent neighborhood opinion state. Using this model, we study which topological features influence the formation of consensus, bipartidism, or fragmentation of opinions in three parties, and how the neutrality parameter and the temperature interplay with the network structure.

Quantitative multimodal imaging in traumatic brain injuries producing impaired cognition

PURPOSE OF REVIEW

Cognitive impairments are a devastating long-term consequence following traumatic brain injury (TBI). This review provides an update on the quantitative mutimodal neuroimaging studies that attempt to elucidate the mechanism(s) underlying cognitive impairments and their recovery following TBI.

RECENT FINDINGS

Recent studies have linked individual specific behavioural impairments and their changes over time to physiological activity and structural changes using EEG, PET and MRI. Multimodal studies that combine measures of physiological activity with knowledge of neuroanatomical and connectivity damage have also illuminated the multifactorial function-structure relationships that underlie impairment and recovery following TBI.

SUMMARY

The combined use of multiple neuroimaging modalities, with focus on individual longitudinal studies, has the potential to accurately classify impairments, enhance sensitivity of prognoses, inform targets for interventions and precisely track spontaneous and intervention-driven recovery.

Modeling an auditory stimulated brain under altered states of consciousness using the generalized Ising model

Propofol is a short-acting medication that results in decreased levels of consciousness and is used for general anesthesia. Although it is the most commonly used anesthetic in the world, much remains unknown about the mechanisms by which it induces a loss of consciousness. Characterizing anesthesia-induced alterations to brain network activity might provide a powerful framework for understanding the neural mechanisms of unconsciousness. The aim of this work was to model brain activity in healthy brains during various stages of consciousness, as induced by propofol, in the auditory paradigm. We used the generalized Ising model (GIM) to fit the empirical fMRI data of healthy subjects while they listened to an audio clip from a movie. The external stimulus (audio clip) is believed to be at least partially driving a synchronization process of the brain activity and provides a similar conscious experience in different subjects. In order to observe the common synchronization among the subjects, a novel technique called the inter subject correlation (ISC) was implemented. We showed that the GIM-modified to incorporate the naturalistic external field-was able to fit the empirical task fMRI data in the awake state, in mild sedation, in deep sedation, and in recovery, at a temperature T* which is well above the critical temperature. To our knowledge this is the first study that captures human brain activity in response to real-life external stimuli at different levels of conscious awareness using mathematical modeling. This study might be helpful in the future to assess the level of consciousness of patients with disorders of consciousness and help in regaining their consciousness.

Serotonergic psychedelics LSD & psilocybin increase the fractal dimension of cortical brain activity in spatial and temporal domains

Psychedelic drugs, such as psilocybin and LSD, represent unique tools for researchers investigating the neural origins of consciousness. Currently, the most compelling theories of how psychedelics exert their effects is by increasing the complexity of brain activity and moving the system towards a critical point between order and disorder, creating more dynamic and complex patterns of neural activity. While the concept of criticality is of central importance to this theory, few of the published studies on psychedelics investigate it directly, testing instead related measures such as algorithmic complexity or Shannon entropy. We propose using the fractal dimension of functional activity in the brain as a measure of complexity since findings from physics suggest that as a system organizes towards criticality, it tends to take on a fractal structure. We tested two different measures of fractal dimension, one spatial and one temporal, using fMRI data from volunteers under the influence of both LSD and psilocybin. The first was the fractal dimension of cortical functional connectivity networks and the second was the fractal dimension of BOLD time-series. In addition to the fractal measures, we used a well-established, non-fractal measure of signal complexity and show that they behave similarly. We were able to show that both psychedelic drugs significantly increased the fractal dimension of functional connectivity networks, and that LSD significantly increased the fractal dimension of BOLD signals, with psilocybin showing a non-significant trend in the same direction. With both LSD and psilocybin, we were able to localize changes in the fractal dimension of BOLD signals to brain areas assigned to the dorsal-attenion network. These results show that psychedelic drugs increase the fractal dimension of activity in the brain and we see this as an indicator that the changes in consciousness triggered by psychedelics are associated with evolution towards a critical zone.

Individual differences in local functional brain connectivity affect TMS effects on behavior

Behavioral effects of transcranial magnetic stimulation (TMS) often show substantial differences between subjects. One factor that might contribute to these inter-individual differences is the interaction of current brain states with the effects of local brain network perturbation. The aim of the current study was to identify brain regions whose connectivity before and following right parietal perturbation affects individual behavioral effects during a visuospatial target detection task. 20 subjects participated in an fMRI experiment where their brain hemodynamic response was measured during resting state, and then during a visuospatial target detection task following 1 Hz rTMS and sham stimulation. To select a parsimonious set of associated brain regions, an elastic net analysis was used in combination with a whole-brain voxel-wise functional connectivity analysis. TMS-induced changes in accuracy were significantly correlated with the pattern of functional connectivity during the task state following TMS. The functional connectivity of the left superior temporal, angular, and precentral gyri was identified as key explanatory variable for the individual behavioral TMS effects. Our results suggest that the brain must reach an appropriate state in which right parietal TMS can induce improvements in visual target detection. The ability to reach this state appears to vary between individuals.

Modeling functional resting-state brain networks through neural message passing on the human connectome

In this work, we propose a natural model for information flow in the brain through a neural message-passing dynamics on a structural network of macroscopic regions, such as the human connectome (HC). In our model, each brain region is assumed to have a binary behavior (active or not), the strengths of interactions among them are encoded in the anatomical connectivity matrix defined by the HC, and the dynamics of the system is defined by the Belief Propagation (BP) algorithm, working near the critical point of the network. We show that in the absence of direct external stimuli the BP algorithm converges to a spatial map of activations that is similar to the Default Mode Network (DMN) of the brain, which has been defined from the analysis of functional MRI data. Moreover, we use Susceptibility Propagation (SP) to compute the matrix of long-range correlations between the different regions and show that the modules defined by a clustering of this matrix resemble several Resting State Networks (RSN) determined experimentally. Both results suggest that the functional DMN and RSNs can be seen as simple consequences of the anatomical structure of the brain and a neural message-passing dynamics between macroscopic regions. With the new model, we explore predictions on how functional maps change when the anatomical brain network suffers structural alterations, like in Alzheimer's disease and in lesions of the Corpus Callosum. The implications and novel interpretations suggested by the model, as well as the role of criticality, are discussed.

Longitudinal increases in structural connectome segregation and functional connectome integration are associated with better recovery after mild TBI

Traumatic brain injury damages white matter pathways that connect brain regions, disrupting transmission of electrochemical signals and causing cognitive and emotional dysfunction. Connectome-level mechanisms for how the brain compensates for injury have not been fully characterized. Here, we collected serial MRI-based structural and functional connectome metrics and neuropsychological scores in 26 mild traumatic brain injury subjects (29.4 ± 8.0 years, 20 males) at 1 and 6 months postinjury. We quantified the relationship between functional and structural connectomes using network diffusion (ND) model propagation time, a measure that can be interpreted as how much of the structural connectome is being utilized for the spread of functional activation, as captured via the functional connectome. Overall cognition showed significant improvement from 1 to 6 months (t25 = -2.15, p = .04). None of the structural or functional global connectome metrics was significantly different between 1 and 6 months, or when compared to 34 age- and gender-matched controls (28.6 ± 8.8 years, 25 males). We predicted longitudinal changes in overall cognition from changes in global connectome measures using a partial least squares regression model (cross-validated R2 = .27). We observe that increased ND model propagation time, increased structural connectome segregation, and increased functional connectome integration were related to better cognitive recovery. We interpret these findings as suggesting two connectome-based postinjury recovery mechanisms: one of neuroplasticity that increases functional connectome integration and one of remote white matter degeneration that increases structural connectome segregation. We hypothesize that our inherently multimodal measure of ND model propagation time captures the interplay between these two mechanisms.

Anticorrelations between Active Brain Regions: An Agent-Based Model Simulation Study

Anticorrelations among brain areas observed in fMRI acquisitions under resting state are not endowed with a well-defined set of characters. Some evidence points to a possible physiological role for them, and simulation models showed that it is appropriate to explore such an issue. A large-scale brain representation was considered, implementing an agent-based brain-inspired model (ABBM) incorporating the SER (susceptible-excited-refractory) cyclic mechanism of state change. The experimental data used for validation included 30 selected functional images of healthy controls from the 1000 Functional Connectomes Classic collection. To study how different fractions of positive and negative connectivities could modulate the model efficiency, the correlation coefficient was systematically used to check the goodness-of-fit of empirical data by simulations under different combinations of parameters. The results show that a small fraction of positive connectivity is necessary to match at best the empirical data. Similarly, a goodness-of-fit improvement was observed upon addition of negative links to an initial pattern of only-positive connections, indicating a significant information intrinsic to negative links. As a general conclusion, anticorrelations showed that it is crucial to improve the performance of our simulation and, since these cannot be assimilated to noise, should be always considered in order to refine any brain functional model.

Neuroanatomical profiles of bilingual children

The goal of the present study was to examine differences in cortical thickness, cortical surface area, and subcortical volume between bilingual children who are highly proficient in two languages (i.e., English and Spanish) and bilingual children who are mainly proficient in one of the languages (i.e., Spanish). All children (N = 49) learned Spanish as a native language (L1) at home and English as a second language (L2) at school. Proficiency of both languages was assessed using the standardized Woodcock Language Proficiency Battery. Five-minute high-resolution anatomical scans were acquired with a 3-Tesla scanner. The degree of discrepancy between L1 and L2 proficiency was used to classify the children into two groups: children with balanced proficiency and children with unbalanced proficiency. The groups were comparable on language history, parental education, and other variables except English proficiency. Values of cortical thickness and surface area of the transverse STG, IFG-pars opercularis, and MFG, as well as subcortical volume of the caudate and putamen, were extracted from FreeSurfer. Results showed that children with balanced bilingualism had thinner cortices of the left STG, left IFG, left MFG and a larger bilateral putamen, whereas unbalanced bilinguals showed thicker cortices of the same regions and a smaller putamen. Additionally, unbalanced bilinguals with stronger foreign accents in the L2 showed reduced surface areas of the MFG and STS bilaterally. The results suggest that balanced/unbalanced bilingualism is reflected in different neuroanatomical characteristics that arise from biological and/or environmental factors.

Energy landscape analysis of neuroimaging data

Computational neuroscience models have been used for understanding neural dynamics in the brain and how they may be altered when physiological or other conditions change. We review and develop a data-driven approach to neuroimaging data called the energy landscape analysis. The methods are rooted in statistical physics theory, in particular the Ising model, also known as the (pairwise) maximum entropy model and Boltzmann machine. The methods have been applied to fitting electrophysiological data in neuroscience for a decade, but their use in neuroimaging data is still in its infancy. We first review the methods and discuss some algorithms and technical aspects. Then, we apply the methods to functional magnetic resonance imaging data recorded from healthy individuals to inspect the relationship between the accuracy of fitting, the size of the brain system to be analysed and the data length.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Brain connectome modularity in weight-restored anorexia nervosa and body dysmorphic disorder

BACKGROUND

Anorexia nervosa (AN) and body dysmorphic disorder (BDD) frequently co-occur, and have several overlapping phenomenological features. Little is known about their shared neurobiology. The aim of the study was to compare modular organization of brain structural connectivity.

METHOD

We acquired diffusion-weighted magnetic resonance imaging data on unmedicated individuals with BDD (n = 29), weight-restored AN (n = 24) and healthy controls (HC) (n = 31). We constructed connectivity matrices using whole-brain white matter tractography, and compared modular structures across groups.

RESULTS

AN showed abnormal modularity involving frontal, basal ganglia and posterior cingulate nodes. There was a trend in BDD for similar abnormalities, but no significant differences compared with AN. In AN, poor insight correlated with longer path length in right caudal anterior cingulate and right posterior cingulate.

CONCLUSIONS

Abnormal network organization patterns in AN, partially shared with BDD, may have implications for understanding integration between reward and habit/ritual formation, as well as conflict monitoring/error detection.

The application of a mathematical model linking structural and functional connectomes in severe brain injury

Following severe injuries that result in disorders of consciousness, recovery can occur over many months or years post-injury. While post-injury synaptogenesis, axonal sprouting and functional reorganization are known to occur, the network-level processes underlying recovery are poorly understood. Here, we test a network-level functional rerouting hypothesis in recovery of patients with disorders of consciousness following severe brain injury. This hypothesis states that the brain recovers from injury by restoring normal functional connections via alternate structural pathways that circumvent impaired white matter connections. The so-called network diffusion model, which relates an individual's structural and functional connectomes by assuming that functional activation diffuses along structural pathways, is used here to capture this functional rerouting. We jointly examined functional and structural connectomes extracted from MRIs of 12 healthy and 16 brain-injured subjects. Connectome properties were quantified via graph theoretic measures and network diffusion model parameters. While a few graph metrics showed groupwise differences, they did not correlate with patients' level of consciousness as measured by the Coma Recovery Scale — Revised. There was, however, a strong and significant partial Pearson's correlation (accounting for age and years post-injury) between level of consciousness and network diffusion model propagation time (r = 0.76, p < 0.05, corrected), i.e. the time functional activation spends traversing the structural network. We concluded that functional rerouting via alternate (and less efficient) pathways leads to increases in network diffusion model propagation time. Simulations of injury and recovery in healthy connectomes confirmed these results. This work establishes the feasibility for using the network diffusion model to capture network-level mechanisms in recovery of consciousness after severe brain injury.

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A “functional rerouting” hypothesis in recovery from brain injury is tested.

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The connectome-based network diffusion model measures functional rerouting.

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Recovery in severe brain injury correlates with a network diffusion model parameter.

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Simulation in healthy connectomes independently validates the results in patients.

Hybrid PET/MR Imaging and Brain Connectivity

In recent years, brain connectivity is gaining ever-increasing interest from the interdisciplinary research community. The study of brain connectivity is characterized by a multifaceted approach providing both structural and functional evidence of the relationship between cerebral regions at different scales. Although magnetic resonance (MR) is the most established imaging modality for investigating connectivity in vivo, the recent advent of hybrid positron emission tomography (PET)/MR scanners paved the way for more comprehensive investigation of brain organization and physiology. Due to the high sensitivity and biochemical specificity of radiotracers, combining MR with PET imaging may enrich our ability to investigate connectivity by introducing the concept of metabolic connectivity and cometomics and promoting new insights on the physiological and molecular bases underlying high-level neural organization. This review aims to describe and summarize the main methods of analysis of brain connectivity employed in MR imaging and nuclear medicine. Moreover, it will discuss practical aspects and state-of-the-art techniques for exploiting hybrid PET/MR imaging to investigate the relationship of physiological processes and brain connectivity.

Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model

Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point.

Brain connectivity and prediction of relapse after cognitive-behavioral therapy in obsessive-compulsive disorder

BACKGROUND

Intensive cognitive-behavioral therapy (CBT) can effectively reduce symptoms in obsessive-compulsive disorder (OCD). However, many relapse after treatment. Few studies have investigated biological markers predictive of follow-up clinical status. The objective was to determine if brain network connectivity patterns prior to intensive CBT predict worsening of clinical symptoms during follow-up.

METHODS

We acquired resting-state functional magnetic resonance imaging data from 17 adults with OCD prior to and following 4 weeks of intensive CBT. Functional connectivity data were analyzed to yield graph-theory metrics. We examined the relationship between pre-treatment connectome properties and OCD clinical symptoms before and after treatment and during a 12-month follow-up period.

RESULTS

Mean OCD symptom decrease was 40.4 ± 16.4% pre- to post-treatment (64.7% responded; 58.8% remitted), but 35.3% experienced clinically significant worsening during follow-up. From pre- to post-treatment, small-worldness and clustering coefficient significantly increased. Decreases in modularity correlated with decreases in OCD symptoms. Higher pre-treatment small-world connectivity was significantly associated with worsening of OCD symptoms during the follow-up period. Psychometric and neurocognitive measures pre- and post-treatment were not significant predictors.

CONCLUSION

This is the first graph-theory connectivity study of the effects of CBT in OCD, and the first to test associations with follow-up clinical status. Results show functional network efficiency as a biomarker of CBT response and relapse in OCD. CBT increases network efficiency as it alleviates symptoms in most patients, but those entering therapy with already high network efficiency are at greater risk of relapse. Results have potential clinical implications for treatment selection.

Spin-glass model predicts metastable brain states that diminish in anesthesia

Patterns of resting state connectivity change dynamically and may represent modes of cognitive information processing. The diversity of connectivity patterns (global brain states) reflects the information capacity of the brain and determines the state of consciousness. In this work, computer simulation was used to explore the repertoire of global brain states as a function of cortical activation level. We implemented a modified spin glass model to describe UP/DOWN state transitions of neuronal populations at a mesoscopic scale based on resting state BOLD fMRI data. Resting state fMRI was recorded in 20 participants and mapped to 10,000 cortical regions (sites) defined on a group-aligned cortical surface map. Each site represented the population activity of a ~20 mm(2) area of the cortex. Cross-correlation matrices of the mapped BOLD time courses of the set of sites were calculated and averaged across subjects. In the model, each cortical site was allowed to interact with the 16 other sites that had the highest pair-wise correlation values. All sites stochastically transitioned between UP and DOWN states under the net influence of their 16 pairs. The probability of local state transitions was controlled by a single parameter T corresponding to the level of global cortical activation. To estimate the number of distinct global states, first we ran 10,000 simulations at T = 0. Simulations were started from random configurations that converged to one of several distinct patterns. Using hierarchical clustering, at 99% similarity, close to 300 distinct states were found. At intermediate T, metastable state configurations were formed suggesting critical behavior with a sharp increase in the number of metastable states at an optimal T. Both reduced activation (anesthesia, sleep) and increased activation (hyper-activation) moved the system away from equilibrium, presumably incompatible with conscious mentation. During equilibrium, the diversity of large-scale brain states was maximum, compatible with maximum information capacity-a presumed condition of consciousness.