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Comparing brain networks of different size and connectivity density using graph theory.

ABSTRACT: Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others.

SUBMITTER: van Wijk BC

PROVIDER: S-EPMC2965659 | biostudies-other | 2010

REPOSITORIES: biostudies-other

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Comparing brain networks of different size and connectivity density using graph theory.

van Wijk Bernadette C M BC Stam Cornelis J CJ Daffertshofer Andreas A

PloS one 20101028 10

Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with diffe ...[more]

PMID: 21060892

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Project description:Recent advances in large datasets analysis offer new insights to modern biology allowing system-level investigation of pathologies. Here we describe a novel computational method that exploits the ever-growing amount of "omics" data to shed light on Alzheimer's and Parkinson's diseases. Neurological disorders exhibit a huge number of molecular alterations due to a complex interplay between genetic and environmental factors. Classical reductionist approaches are focused on a few elements, providing a narrow overview of the etiopathogenic complexity of multifactorial diseases. On the other hand, high-throughput technologies allow the evaluation of many components of biological systems and their behaviors. Analysis of Parkinson's Disease (PD) and Alzheimer's Disease (AD) from a network perspective can highlight proteins or pathways common but differently represented that can be discriminating between the two pathological conditions, thus highlight similarities and differences.In this work we propose a strategy that exploits network community structure identified with a state-of-the-art network community discovery algorithm called InfoMap, which takes advantage of information theory principles. We used two similarity measurements to quantify functional and topological similarities between the two pathologies. We built a Similarity Matrix to highlight similar communities and we analyzed statistically significant GO terms found in clustered areas of the matrix and in network communities. Our strategy allowed us to identify common known and unknown processes including DNA repair, RNA metabolism and glucose metabolism not detected with simple GO enrichment analysis. In particular, we were able to capture the connection between mitochondrial dysfunction and metabolism (glucose and glutamate/glutamine).This approach allows the identification of communities present in both pathologies which highlight common biological processes. Conversely, the identification of communities without any counterpart can be used to investigate processes that are characteristic of only one of the two pathologies. In general, the same strategy can be applied to compare any pair of biological networks.

Project description:Bipolar disorder is often misdiagnosed as major depressive disorder, which leads to inadequate treatment. Depressed individuals versus healthy control subjects, show increased expectation of negative outcomes. Due to increased impulsivity and risk for mania, however, depressed individuals with bipolar disorder may differ from those with major depressive disorder in neural mechanisms underlying anticipation processes. Graph theory methods for neuroimaging data analysis allow the identification of connectivity between multiple brain regions without prior model specification, and may help to identify neurobiological markers differentiating these disorders, thereby facilitating development of better therapeutic interventions. This study aimed to compare brain connectivity among regions involved in win/loss anticipation in depressed individuals with bipolar disorder (BDD) versus depressed individuals with major depressive disorder (MDD) versus healthy control subjects using graph theory methods. The study was conducted at the University of Pittsburgh Medical Center and included 31 BDD, 39 MDD, and 36 healthy control subjects. Participants were scanned while performing a number guessing reward task that included the periods of win and loss anticipation. We first identified the anticipatory network across all 106 participants by contrasting brain activation during all anticipation periods (win anticipation + loss anticipation) versus baseline, and win anticipation versus loss anticipation. Brain connectivity within the identified network was determined using the Independent Multiple sample Greedy Equivalence Search (IMaGES) and Linear non-Gaussian Orientation, Fixed Structure (LOFS) algorithms. Density of connections (the number of connections in the network), path length, and the global connectivity direction ('top-down' versus 'bottom-up') were compared across groups (BDD/MDD/healthy control subjects) and conditions (win/loss anticipation). These analyses showed that loss anticipation was characterized by denser top-down fronto-striatal and fronto-parietal connectivity in healthy control subjects, by bottom-up striatal-frontal connectivity in MDD, and by sparse connectivity lacking fronto-striatal connections in BDD. Win anticipation was characterized by dense connectivity of medial frontal with striatal and lateral frontal cortical regions in BDD, by sparser bottom-up striatum-medial frontal cortex connectivity in MDD, and by sparse connectivity in healthy control subjects. In summary, this is the first study to demonstrate that BDD and MDD with comparable levels of current depression differed from each other and healthy control subjects in density of connections, connectivity path length, and connectivity direction as a function of win or loss anticipation. These findings suggest that different neurobiological mechanisms may underlie aberrant anticipation processes in BDD and MDD, and that distinct therapeutic strategies may be required for these individuals to improve coping strategies during expectation of positive and negative outcomes.

Dataset Information

Comparing brain networks of different size and connectivity density using graph theory.

Publications

Comparing brain networks of different size and connectivity density using graph theory.

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