Brain network efficiency and topology depend on the fiber tracking method: 11 tractography algorithms compared in 536 subjects

As connectivity analyses become more popular, claims are often made about how the brain's anatomical networks depend on age, sex, or disease. It is unclear how results depend on tractography methods used to compute fiber networks. We applied 11 tractography methods to high angular resolution diffusion images of the brain (4-Tesla 105-gradient HARDI) from 536 healthy young adults. We parcellated 70 cortical regions, yielding 70×70 connectivity matrices, encoding fiber density. We computed popular graph theory metrics, including network efficiency, and characteristic path lengths. Both metrics were robust to the number of spherical harmonics used to model diffusion (4th-8th order). Age effects were detected only for networks computed with the probabilistic Hough transform method, which excludes smaller fibers. Sex and total brain volume affected networks measured with deterministic, tensor-based fiber tracking but not with the Hough method. Each tractography method includes different fibers, which affects inferences made about the reconstructed networks.

Heritability of brain network topology in 853 twins and siblings

Anatomical brain networks change throughout life and with diseases. Genetic analysis of these networks may help identify processes giving rise to heritable brain disorders, but we do not yet know which network measures are promising for genetic analyses. Many factors affect the downstream results, such as the tractography algorithm used to define structural connectivity. We tested nine different tractography algorithms and four normalization methods to compute brain networks for 853 young healthy adults (twins and their siblings). We fitted genetic structural equation models to all nine network measures, after a normalization step to increase network consistency across tractography algorithms. Probabilistic tractography algorithms with global optimization (such as Probtrackx and Hough) yielded higher heritability statistics than 'greedy' algorithms (such as FACT) which process small neighborhoods at each step. Some global network measures (probtrackx-derived GLOB and ST) showed significant genetic effects, making them attractive targets for genome-wide association studies.

Functional brain network efficiency predicts intelligence

The neuronal causes of individual differences in mental abilities such as intelligence are complex and profoundly important. Understanding these abilities has the potential to facilitate their enhancement. The purpose of this study was to identify the functional brain network characteristics and their relation to psychometric intelligence. In particular, we examined whether the functional network exhibits efficient small-world network attributes (high clustering and short path length) and whether these small-world network parameters are associated with intellectual performance. High-density resting state electroencephalography (EEG) was recorded in 74 healthy subjects to analyze graph-theoretical functional network characteristics at an intracortical level. Ravens advanced progressive matrices were used to assess intelligence. We found that the clustering coefficient and path length of the functional network are strongly related to intelligence. Thus, the more intelligent the subjects are the more the functional brain network resembles a small-world network. We further identified the parietal cortex as a main hub of this resting state network as indicated by increased degree centrality that is associated with higher intelligence. Taken together, this is the first study that substantiates the neural efficiency hypothesis as well as the Parieto-Frontal Integration Theory (P-FIT) of intelligence in the context of functional brain network characteristics. These theories are currently the most established intelligence theories in neuroscience. Our findings revealed robust evidence of an efficiently organized resting state functional brain network for highly productive cognitions.

What do brain network interactions tell about cognitive processes? How to seek causality?

Optimal adjustment of brain networks allows the biased processing of information in response to the demand of environments and is therefore prerequisite for adaptive behaviour. It is widely shown that a biased state of networks is associated with a particular cognitive process. However, those associations were identified by backward categorization of trials and cannot provide a causal association with cognitive processes. This problem still remains a big obstacle to advance the state of our field in particular human cognitive neuroscience. In my talk, I will present two approaches to address the causal relationships between brain network interactions and behaviour. Firstly, we combined connectivity analysis of fMRI data and a machine leaning method to predict inter-individual differences of behaviour and responsiveness to environmental demands. The connectivity-based classification approach outperforms local activation-based classification analysis, suggesting that interactions in brain networks carry information of instantaneous cognitive processes. Secondly, we have recently established a brand new method combining transcranial alternating current stimulation (tACS), transcranial magnetic stimulation (TMS), and EEG. We use the method to measure signal transmission between brain areas while introducing extrinsic oscillatory brain activity and to study causal association between oscillatory activity and behaviour. We show that phase-matched oscillatory activity creates the phase-dependent modulation of signal transmission between brain areas, while phase-shifted oscillatory activity blunts the phase-dependent modulation. The results suggest that phase coherence between brain areas plays a cardinal role in signal transmission in the brain networks. In sum, I argue that causal approaches will provide more concreate backbones to cognitive neuroscience.

Structural changes after videogame practice related to a brain network associated with intelligence

Here gray and white matter changes after four weeks of videogame practice were analyzed using optimized voxel-based morphometry (VBM), cortical surface and cortical thickness indices, and white matter integrity computed from several projection, commissural, and association tracts relevant to cognition. Beginning with a sample of one hundred young females, twenty right handed participants were recruited for the study and assigned to a practice or a control group carefully matched by their general cognitive ability scores. After the first scan, the practice group played ‘Professor Layton and The Pandora's Box’ 4 h per week during four weeks. A second scan was obtained at the end of practice and intelligence was measured again. Image analyses revealed gray and white matter changes in the practice group. Gray matter changes theoretically relevant for intelligence were observed for the practice group mainly in frontal clusters (Brodmann areas 9 and 10) and also in smaller parietal and temporal regions. White matter findings were focused in the hippocampal cingulum and the inferior longitudinal fasciculus. These gray and white matter changes presumably induced by practice did not interact with intelligence tests' scores.

Hierarchical topological network analysis of anatomical human brain connectivity and differences related to sex and kinship

Modern non-invasive brain imaging technologies, such as diffusion weighted magnetic resonance imaging (DWI), enable the mapping of neural fiber tracts in the white matter, providing a basis to reconstruct a detailed map of brain structural connectivity networks. Brain connectivity networks differ from random networks in their topology, which can be measured using small worldness, modularity, and high-degree nodes (hubs). Still, little is known about how individual differences in structural brain network properties relate to age, sex, or genetic differences. Recently, some groups have reported brain network biomarkers that enable differentiation among individuals, pairs of individuals, and groups of individuals. In addition to studying new topological features, here we provide a unifying general method to investigate topological brain networks and connectivity differences between individuals, pairs of individuals, and groups of individuals at several levels of the data hierarchy, while appropriately controlling false discovery rate (FDR) errors. We apply our new method to a large dataset of high quality brain connectivity networks obtained from High Angular Resolution Diffusion Imaging (HARDI) tractography in 303 young adult twins, siblings, and unrelated people. Our proposed approach can accurately classify brain connectivity networks based on sex (93% accuracy) and kinship (88.5% accuracy). We find statistically significant differences associated with sex and kinship both in the brain connectivity networks and in derived topological metrics, such as the clustering coefficient and the communicability matrix.

Validation of network communicability metrics for the analysis of brain structural networks.

Computational network analysis provides new methods to analyze the brain's structural organization based on diffusion imaging tractography data. Networks are characterized by global and local metrics that have recently given promising insights into diagnosis and the further understanding of psychiatric and neurologic disorders. Most of these metrics are based on the idea that information in a network flows along the shortest paths. In contrast to this notion, communicability is a broader measure of connectivity which assumes that information could flow along all possible paths between two nodes. In our work, the features of network metrics related to communicability were explored for the first time in the healthy structural brain network. In addition, the sensitivity of such metrics was analysed using simulated lesions to specific nodes and network connections. Results showed advantages of communicability over conventional metrics in detecting densely connected nodes as well as subsets of nodes vulnerable to lesions. In addition, communicability centrality was shown to be widely affected by the lesions and the changes were negatively correlated with the distance from lesion site. In summary, our analysis suggests that communicability metrics that may provide an insight into the integrative properties of the structural brain network and that these metrics may be useful for the analysis of brain networks in the presence of lesions. Nevertheless, the interpretation of communicability is not straightforward; hence these metrics should be used as a supplement to the more standard connectivity network metrics.

Development of brain structural connectivity between ages 12 and 30: A 4-Tesla diffusion imaging study in 439 adolescents and adults

Understanding how the brain matures in healthy individuals is critical for evaluating deviations from normal development in psychiatric and neurodevelopmental disorders. The brain's anatomical networks are profoundly re-modeled between childhood and adulthood, and diffusion tractography offers unprecedented power to reconstruct these networks and neural pathways in vivo. Here we tracked changes in structural connectivity and network efficiency in 439 right-handed individuals aged 12 to 30 (211 female/126 male adults, mean age=23.6, SD=2.19; 31 female/24 male 12 year olds, mean age=12.3, SD=0.18; and 25 female/22 male 16 year olds, mean age=16.2, SD=0.37). All participants were scanned with high angular resolution diffusion imaging (HARDI) at 4 T. After we performed whole brain tractography, 70 cortical gyral-based regions of interest were extracted from each participant's co-registered anatomical scans. The proportion of fiber connections between all pairs of cortical regions, or nodes, was found to create symmetric fiber density matrices, reflecting the structural brain network. From those 70 × 70 matrices we computed graph theory metrics characterizing structural connectivity. Several key global and nodal metrics changed across development, showing increased network integration, with some connections pruned and others strengthened. The increases and decreases in fiber density, however, were not distributed proportionally across the brain. The frontal cortex had a disproportionate number of decreases in fiber density while the temporal cortex had a disproportionate number of increases in fiber density. This large-scale analysis of the developing structural connectome offers a foundation to develop statistical criteria for aberrant brain connectivity as the human brain matures.

Human brain networks of auditory attention and working memory

This thesis examines brain networks involved in auditory attention and auditory working memory using measures of task performance, brain activity, and neuroanatomical connectivity. Auditory orienting and maintenance of attention were compared with visual orienting and maintenance of attention, and top-down controlled attention was compared to bottom-up triggered attention in audition. Moreover, the effects of cognitive load on performance and brain activity were studied using an auditory working memory task. Corbetta and Shulman s (2002) model of visual attention suggests that what is known as the dorsal attention system (intraparietal sulcus/superior parietal lobule, IPS/SPL and frontal eye field, FEF) is involved in the control of top-down controlled attention, whereas what is known as the ventral attention system (temporo-parietal junction, TPJ and areas of the inferior/middle frontal gyrus, IFG/MFG) is involved in bottom-up triggered attention. The present results show that top-down controlled auditory attention also activates IPS/SPL and FEF. Furthermore, in audition, TPJ and IFG/MFG were activated not only by bottom-up triggered attention, but also by top-down controlled attention. In addition, the posterior cerebellum and thalamus were activated by top-down controlled attention shifts and the ventromedial prefrontal cortex (VMPFC) was activated by to-be-ignored, but attention-catching salient changes in auditory input streams. VMPFC may be involved in the evaluation of environmental events causing the bottom-up triggered engagement of attention. Auditory working memory activated a brain network that largely overlapped with the one activated by top-down controlled attention. The present results also provide further evidence of the role of the cerebellum in cognitive processing: During auditory working memory tasks, both activity in the posterior cerebellum (the crus I/II) and reaction speed increased when the cognitive load increased. Based on the present results and earlier theories on the role of the cerebellum in cognitive processing, the function of the posterior cerebellum in cognitive tasks may be related to the optimization of response speed.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Network Similarity Measures and Automatic Construction of Graph Models using Genetic Programming

A complex network is an abstract representation of an intricate system of interrelated elements where the patterns of connection hold significant meaning. One particular complex network is a social network whereby the vertices represent people and edges denote their daily interactions. Understanding social network dynamics can be vital to the mitigation of disease spread as these networks model the interactions, and thus avenues of spread, between individuals. To better understand complex networks, algorithms which generate graphs exhibiting observed properties of real-world networks, known as graph models, are often constructed. While various efforts to aid with the construction of graph models have been proposed using statistical and probabilistic methods, genetic programming (GP) has only recently been considered. However, determining that a graph model of a complex network accurately describes the target network(s) is not a trivial task as the graph models are often stochastic in nature and the notion of similarity is dependent upon the expected behavior of the network. This thesis examines a number of well-known network properties to determine which measures best allowed networks generated by different graph models, and thus the models themselves, to be distinguished. A proposed meta-analysis procedure was used to demonstrate how these network measures interact when used together as classifiers to determine network, and thus model, (dis)similarity. The analytical results form the basis of the fitness evaluation for a GP system used to automatically construct graph models for complex networks. The GP-based automatic inference system was used to reproduce existing, well-known graph models as well as a real-world network. Results indicated that the automatically inferred models exemplified functional similarity when compared to their respective target networks. This approach also showed promise when used to infer a model for a mammalian brain network.

Social perception gaze patterns, symptom severity and resting brain function measured using Arterial Spin Labelling

Autistic spectrum disorder (ASD) is characterised by qualitative alterations in reciprocal social interactions. Some recent studies show alterations in gaze patterns during social perception and rest-functional abnormalities in the ‘social brain network’. This study investigated: i) social perception gaze patterns in children with ASD and controls, ii) the relationship between autism clinical severity and social perception gaze patterns, iii) the relationship between resting cerebral blood flow (rCBF) and social perception gaze patterns. Methods: Nine children with ASD and 9 children with typical development were studied. Eye-tracking was used to detect gaze patterns during presentation of stimuli depicting social scenes. Autism clinical severity was established using the Autism Diagnostic Interview Revised (ADI-R). Arterial spin labelling MRI was used to quantify rCBF. Results: The ASD group looked less at social regions and more at non-social regions than controls. No significant correlation was found between ASD clinical severity and social perception gaze patterns. In the ASD group, gaze behaviour was related to rCBF in the temporal lobe regions at trend level. Positive correlations were found between temporal rCBF and gaze to the face region, while negative correlations were found between temporal rCBF and gaze to non-social regions. Conclusions: These preliminary results suggest that social perception gaze patterns are altered in children with ASD, and could be related to temporal rCBF.

Dynamic Changes in the Mental Rotation Network Revealed by Pattern Recognition Analysis of fMRI Data

We investigated the temporal dynamics and changes in connectivity in the mental rotation network through the application of spatio-temporal support vector machines (SVMs). The spatio-temporal SVM [Mourao-Miranda, J., Friston, K. J., et al. (2007). Dynamic discrimination analysis: A spatial-temporal SVM. Neuroimage, 36, 88-99] is a pattern recognition approach that is suitable for investigating dynamic changes in the brain network during a complex mental task. It does not require a model describing each component of the task and the precise shape of the BOLD impulse response. By defining a time window including a cognitive event, one can use spatio-temporal fMRI observations from two cognitive states to train the SVM. During the training, the SVM finds the discriminating pattern between the two states and produces a discriminating weight vector encompassing both voxels and time (i.e., spatio-temporal maps). We showed that by applying spatio-temporal SVM to an event-related mental rotation experiment, it is possible to discriminate between different degrees of angular disparity (0 degrees vs. 20 degrees, 0 degrees vs. 60 degrees, and 0 degrees vs. 100 degrees), and the discrimination accuracy is correlated with the difference in angular disparity between the conditions. For the comparison with highest accuracy (08 vs. 1008), we evaluated how the most discriminating areas (visual regions, parietal regions, supplementary, and premotor areas) change their behavior over time. The frontal premotor regions became highly discriminating earlier than the superior parietal cortex. There seems to be a parcellation of the parietal regions with an earlier discrimination of the inferior parietal lobe in the mental rotation in relation to the superior parietal. The SVM also identified a network of regions that had a decrease in BOLD responses during the 100 degrees condition in relation to the 0 degrees condition (posterior cingulate, frontal, and superior temporal gyrus). This network was also highly discriminating between the two conditions. In addition, we investigated changes in functional connectivity between the most discriminating areas identified by the spatio-temporal SVM. We observed an increase in functional connectivity between almost all areas activated during the 100 degrees condition (bilateral inferior and superior parietal lobe, bilateral premotor area, and SMA) but not between the areas that showed a decrease in BOLD response during the 100 degrees condition.

Repeatability analysis of global and local metrics of brain structural networks

Computational network analysis provides new methods to analyze the human connectome. Brain structural networks can be characterized by global and local metrics that recently gave promising insights for diagnosis and further understanding of neurological, psychiatric and neurodegenerative disorders. In order to ensure the validity of results in clinical settings the precision and repeatability of the networks and the associated metrics must be evaluated. In the present study, nineteen healthy subjects underwent two consecutive measurements enabling us to test reproducibility of the brain network and its global and local metrics. As it is known that the network topology depends on the network density, the effects of setting a common density threshold for all networks were also assessed. Results showed good to excellent repeatability for global metrics, while for local metrics it was more variable and some metrics were found to have locally poor repeatability. Moreover, between subjects differences were slightly inflated when the density was not fixed. At the global level, these findings confirm previous results on the validity of global network metrics as clinical biomarkers. However, the new results in our work indicate that the remaining variability at the local level as well as the effect of methodological characteristics on the network topology should be considered in the analysis of brain structural networks and especially in networks comparisons.