Hierarchical modularity in human brain functional networks

The idea that complex systems have a hierarchical modular organization originates in the early 1960s and has recently attracted fresh support from quantitative studies of large scale, real-life networks. Here we investigate the hierarchical modular (or "modules-within-modules") decomposition of human brain functional networks, measured using functional magnetic resonance imaging (fMRI) in 18 healthy volunteers under no-task or resting conditions. We used a customized template to extract networks with more than 1800 regional nodes, and we applied a fast algorithm to identify nested modular structure at several hierarchical levels. We used mutual information, 0 < I < 1, to estimate the similarity of community structure of networks in different subjects, and to identify the individual network that is most representative of the group. Results show that human brain functional networks have a hierarchical modular organization with a fair degree of similarity between subjects, I=0.63. The largest 5 modules at the highest level of the hierarchy were medial occipital, lateral occipital, central, parieto-frontal and fronto-temporal systems; occipital modules demonstrated less sub-modular organization than modules comprising regions of multimodal association cortex. Connector nodes and hubs, with a key role in inter-modular connectivity, were also concentrated in association cortical areas. We conclude that methods are available for hierarchical modular decomposition of large numbers of high resolution brain functional networks using computationally expedient algorithms. This could enable future investigations of Simon's original hypothesis that hierarchy or near-decomposability of physical symbol systems is a critical design feature for their fast adaptivity to changing environmental conditions

Modular and Hierarchically Modular Organization of Brain Networks

Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data

Understanding Stroke in the Connected Human Brain

Although structural damage from stroke is focal, remote dysfunction can occur in regions of the brain distant from the area of damage. Lesions in both gray and white matter can disrupt the flow of information in areas connected to or by the area of infarct. This is because the brain is not an assortment of specialized parts but an assembly of distributed networks that interact to support cognitive function. Functional connectivity analyses using resting functional magnetic resonance imaging (fMRI) have shown us that the cortex is organized into distributed brain networks. The primary goal of this work is to characterize the effects of stroke on distributed brain systems and to use this information to better understand neural correlates of deficit and recovery following stroke. We measured resting functional connectivity, lesion topography, and behavior in multiple domains (attention, visual memory, verbal memory, language, motor, and visual) in a cohort of 132 stroke patients. Patients were followed longitudinally with full behavioral and imaging batteries acquired at 2 weeks, 3 months, and 1 year post-stroke. Thirty age- and demographic- matched controls were scanned twice at an interval of three months. In chapter 1, we explore a central question motivating this work: how is behavior represented in the brain? We review progressing prospective – from basic functional localization to newer theories connecting inter-related brain networks to cognitive operations. In so doing, we attempt to build a foundation that motivates the hypotheses and experimental approaches explored in this work. Chapters 2 and 3 serve primarily to validate approaches and considerations for using resting fMRI to measure functional connectivity in stroke patients. In chapter 2, we investigate hemodynamic lags after stroke. ‘Hemodynamic lag’ is a local delay in the blood oxygen level dependent (BOLD) response to neural activity, measured using cross-correlation of local fMRI signal with some reference brain signal. This work tests assumptions of the BOLD response to neural activity after stroke, but also provides novel and clinically relevant insight into perilesional disruption to hemodynamics. Significant lags are observed in 30% of stroke patients sub-acutely and 10% of patients at one-year. Hemodynamic lag corresponds to gross aberrancy in functional connectivity measures, performance deficits and local and global perfusion deficits. Yet, relationships between functional connectivity and behavior reviewed in chapter 1 persist after hemodynamic delays is corrected for. Chapter 3 provides a more extended discussion of approaches and considerations for using resting fMRI to measure functional connectivity in stroke patients. Like chapter 1, the goal is to motivate experimental approaches taken in later chapters. But here, more technical challenges relating to brain co-registration, neurovascular coupling, and clinical population selection are considered. In chapter 4, we uncover the relationships between local damage, network wide functional disconnection, and neurological deficit. We find that visual memory and verbal memory are better predicted by connectivity, whereas visual and motor deficits are better predicted by lesion topography. Attention and language deficits are well predicted by both. We identify a general pattern of physiological network dysfunction consisting of decrease of inter-hemispheric integration and decrease in intra-hemispheric segregation, which strongly related to behavioral impairment in multiple domains. In chapter 5, we explore a case study of abulia – severe apathy. This work ties together principles of local damage, network disruption, and network-related deficit and demonstrates how they can be useful in understanding and developing targeted treatments (such as transcranial magnetic stimulation) for individual stroke patients. In chapter 6, we explore longitudinal changes in functional connectivity that parallel recovery. We find that the topology and boundaries of cortical regions remains unchanged across recovery, empirically validating our parcel-wise connectivity approach. In contrast, we find that the modularity of brain systems i.e. the degree of integration within and segregation between networks, is significantly reduced after a stroke, but partially recovered over time. Importantly, the return of modular network structure parallels recovery of language and attention, but not motor function. This work establishes the importance of normalization of large-scale modular brain systems in stroke recovery. In chapter 7, we discuss some fundamental revisions of past lesion-deficit frameworks necessitated by recent findings. Firstly, anatomical priors of structural and functional connections are needed to explain why certain lesions across distant locations should share behavioral consequences. Secondly, functional priors of connectomics are needed to explain how local injury can produce widespread disruption to brain connectivity and behavior that have been observed

Brain connectivity analysis: a short survey

This short survey the reviews recent literature on brain connectivity studies. It encompasses all forms of static and dynamic connectivity whether anatomical, functional, or effective. The last decade has seen an ever increasing number of studies devoted to deduce functional or effective connectivity, mostly from functional neuroimaging experiments. Resting state conditions have become a dominant experimental paradigm, and a number of resting state networks, among them the prominent default mode network, have been identified. Graphical models represent a convenient vehicle to formalize experimental findings and to closely and quantitatively characterize the various networks identified. Underlying these abstract concepts are anatomical networks, the so-called connectome, which can be investigated by functional imaging techniques as well. Future studies have to bridge the gap between anatomical neuronal connections and related functional or effective connectivities

The Overlapping Community Structure of Structural Brain Network in Young Healthy Individuals

Community structure is a universal and significant feature of many complex networks in biology, society, and economics. Community structure has also been revealed in human brain structural and functional networks in previous studies. However, communities overlap and share many edges and nodes. Uncovering the overlapping community structure of complex networks remains largely unknown in human brain networks. Here, using regional gray matter volume, we investigated the structural brain network among 90 brain regions (according to a predefined anatomical atlas) in 462 young, healthy individuals. Overlapped nodes between communities were defined by assuming that nodes (brain regions) can belong to more than one community. We demonstrated that 90 brain regions were organized into 5 overlapping communities associated with several well-known brain systems, such as the auditory/language, visuospatial, emotion, decision-making, social, control of action, memory/learning, and visual systems. The overlapped nodes were mostly involved in an inferior-posterior pattern and were primarily related to auditory and visual perception. The overlapped nodes were mainly attributed to brain regions with higher node degrees and nodal efficiency and played a pivotal role in the flow of informa- tion through the structural brain network. Our results revealed fuzzy boundaries between communities by identifying overlapped nodes and provided new insights into the understanding of the relationship between the structure and function of the human brain. This study provides the first report of the overlapping community structure of the structural network of the human brain

Clustering and Community Detection in Directed Networks: A Survey

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on the edges, making the semantics of the edges non symmetric. An interesting feature that real networks present is the clustering or community structure property, under which the graph topology is organized into modules commonly called communities or clusters. The essence here is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. Revealing the underlying community structure of directed complex networks has become a crucial and interdisciplinary topic with a plethora of applications. Therefore, naturally there is a recent wealth of research production in the area of mining directed graphs - with clustering being the primary method and tool for community detection and evaluation. The goal of this paper is to offer an in-depth review of the methods presented so far for clustering directed networks along with the relevant necessary methodological background and also related applications. The survey commences by offering a concise review of the fundamental concepts and methodological base on which graph clustering algorithms capitalize on. Then we present the relevant work along two orthogonal classifications. The first one is mostly concerned with the methodological principles of the clustering algorithms, while the second one approaches the methods from the viewpoint regarding the properties of a good cluster in a directed network. Further, we present methods and metrics for evaluating graph clustering results, demonstrate interesting application domains and provide promising future research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear