Cornelis J. Stam

Consistent resting-state networks across healthy subjects

Functional MRI (fMRI) can be applied to study the functional connectivity of the human brain. It has been suggested that fluctuations in the blood oxygenation level-dependent (BOLD) signal during rest reflect the neuronal baseline activity of the brain, representing the state of the human brain in the absence of goal-directed neuronal action and external input, and that these slow fluctuations correspond to functionally relevant resting-state networks. Several studies on resting fMRI have been conducted, reporting an apparent similarity between the identified patterns. The spatial consistency of these resting patterns, however, has not yet been evaluated and quantified. In this study, we apply a data analysis approach called tensor probabilistic independent component analysis to resting-state fMRI data to find coherencies that are consistent across subjects and sessions. We characterize and quantify the consistency of these effects by using a bootstrapping approach, and we estimate the BOLD amplitude modulation as well as the voxel-wise cross-subject variation. The analysis found 10 patterns with potential functional relevance, consisting of regions known to be involved in motor function, visual processing, executive functioning, auditory processing, memory, and the so-called default-mode network, each with BOLD signal changes up to 3%. In general, areas with a high mean percentage BOLD signal are consistent and show the least variation around the mean. These findings show that the baseline activity of the brain is consistent across subjects exhibiting significant temporal dynamics, with percentage BOLD signal change comparable with the signal changes found in task-related experiments.

Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources

To address the problem of volume conduction and active reference electrodes in the assessment of functional connectivity, we propose a novel measure to quantify phase synchronization, the phase lag index (PLI), and compare its performance to the well‐known phase coherence (PC), and to the imaginary component of coherency (IC).

Efficiency of Functional Brain Networks and Intellectual Performance

Our brain is a complex network in which information is continuously processed and transported between spatially distributed but functionally linked regions. Recent studies have shown that the functional connections of the brain network are organized in a highly efficient small-world manner, indicating a high level of local neighborhood clustering, together with the existence of more long-distance connections that ensure a high level of global communication efficiency within the overall network. Such an efficient network architecture of our functional brain raises the question of a possible association between how efficiently the regions of our brain are functionally connected and our level of intelligence. Examining the overall organization of the brain network using graph analysis, we show a strong negative association between the normalized characteristic path length λ of the resting-state brain network and intelligence quotient (IQ). This suggests that human intellectual performance is likely to be related to how efficiently our brain integrates information between multiple brain regions. Most pronounced effects between normalized path length and IQ were found in frontal and parietal regions. Our findings indicate a strong positive association between the global efficiency of functional brain networks and intellectual performance.

Altered resting state networks in mild cognitive impairment and mild Alzheimer's disease : An fMRI study

Activity and reactivity of the default mode network in the brain was studied using functional magnetic resonance imaging (fMRI) in 28 nondemented individuals with mild cognitive impairment (MCI), 18 patients with mild Alzheimers disease (AD), and 41 healthy elderly controls (HC). The default mode network was interrogated by means of decreases in brain activity, termed deactivations, during a visual encoding task and during a nonspatial working memory task. Deactivation was found in the default mode network involving the anterior frontal, precuneus, and posterior cingulate cortex. MCI patients showed less deactivation than HC, but more than AD. The most pronounced differences between MCI, HC, and AD occurred in the very early phase of deactivation, reflecting the reactivity and adaptation of the network. The default mode network response in the anterior frontal cortex significantly distinguished MCI from both HC (in the medial frontal) and AD (in the anterior cingulate cortex). The response in the precuneus could only distinguish between patients and HC, not between MCI and AD. These findings may be consistent with the notion that MCI is a transitional state between healthy aging and dementia and with the proposed early changes in MCI in the posterior cingulate cortex and precuneus. These findings suggest that altered activity in the default mode network may act as an early marker for AD pathology. Hum Brain Mapp, 2005.

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

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.

Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain.

The brain is a complex dynamic system of functionally connected regions. Graph theory has been successfully used to describe the organization of such dynamic systems. Recent resting-state fMRI studies have suggested that inter-regional functional connectivity shows a small-world topology, indicating an organization of the brain in highly clustered sub-networks, combined with a high level of global connectivity. In addition, a few studies have investigated a possible scale-free topology of the human brain, but the results of these studies have been inconclusive. These studies have mainly focused on inter-regional connectivity, representing the brain as a network of brain regions, requiring an arbitrary definition of such regions. However, using a voxel-wise approach allows for the model-free examination of both inter-regional as well as intra-regional connectivity and might reveal new information on network organization. Especially, a voxel-based study could give information about a possible scale-free organization of functional connectivity in the human brain. Resting-state 3 Tesla fMRI recordings of 28 healthy subjects were acquired and individual connectivity graphs were formed out of all cortical and sub-cortical voxels with connections reflecting inter-voxel functional connectivity. Graph characteristics from these connectivity networks were computed. The clustering-coefficient of these networks turned out to be much higher than the clustering-coefficient of comparable random graphs, together with a short average path length, indicating a small-world organization. Furthermore, the connectivity distribution of the number of inter-voxel connections followed a power-law scaling with an exponent close to 2, suggesting a scale-free network topology. Our findings suggest a combined small-world and scale-free organization of the functionally connected human brain. The results are interpreted as evidence for a highly efficient organization of the functionally connected brain, in which voxels are mostly connected with their direct neighbors forming clustered sub-networks, which are held together by a small number of highly connected hub-voxels that ensure a high level of overall connectivity.

Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets

The study of complex systems consisting of many interacting subsystems requires the use of analytical tools which can detect statistical dependencies between time series recorded from these subsystems. Typical examples are the electroencephalogram (EEG) and magnetoencephalogram (MEG) which may involve the simultaneous recording of 150 or more time series. Coherency, which is often used to study such data, is only sensitive to linear and symmetric interdependencies and cannot deal with non-stationarity. Recently, several algorithms based upon the concept of generalized synchronization have been introduced to overcome some of the limitations of coherency estimates (e.g. [Physica D 134 (1999) 419; Brain Res. 792 (1998) 24]). However, these methods are biased by the degrees of freedom of the interacting subsystems [Physica D 134 (1999) 419; Physica D 148 (2001) 147]. We propose a novel measure for generalized synchronization in multivariate data sets which avoids this bias and can deal with non-stationary dynamics.

Aberrant Frontal and Temporal Complex Network Structure in Schizophrenia: A Graph Theoretical Analysis

Brain regions are not independent. They are interconnected by white matter tracts, together forming one integrative complex network. The topology of this network is crucial for efficient information integration between brain regions. Here, we demonstrate that schizophrenia involves an aberrant topology of the structural infrastructure of the brain network. Using graph theoretical analysis, complex structural brain networks of 40 schizophrenia patients and 40 human healthy controls were examined. Diffusion tensor imaging was used to reconstruct the white matter connections of the brain network, with the strength of the connections defined as the level of myelination of the tracts as measured through means of magnetization transfer ratio magnetic resonance imaging. Patients displayed a preserved overall small-world network organization, but focusing on specific brain regions and their capacity to communicate with other regions of the brain revealed significantly longer node-specific path lengths (higher L) of frontal and temporal regions, especially of bilateral inferior/superior frontal cortex and temporal pole regions. These findings suggest that schizophrenia impacts global network connectivity of frontal and temporal brain regions. Furthermore, frontal hubs of patients showed a significant reduction of betweenness centrality, suggesting a less central hub role of these regions in the overall network structure. Together, our findings suggest that schizophrenia patients have a less strongly globally integrated structural brain network with a reduced central role for key frontal hubs, resulting in a limited structural capacity to integrate information across brain regions.

The application of graph theoretical analysis to complex networks in the brain

Considering the brain as a complex network of interacting dynamical systems offers new insights into higher level brain processes such as memory, planning, and abstract reasoning as well as various types of brain pathophysiology. This viewpoint provides the opportunity to apply new insights in network sciences, such as the discovery of small world and scale free networks, to data on anatomical and functional connectivity in the brain. In this review we start with some background knowledge on the history and recent advances in network theories in general. We emphasize the correlation between the structural properties of networks and the dynamics of these networks. We subsequently demonstrate through evidence from computational studies, in vivo experiments, and functional MRI, EEG and MEG studies in humans, that both the functional and anatomical connectivity of the healthy brain have many features of a small world network, but only to a limited extent of a scale free network. The small world structure of neural networks is hypothesized to reflect an optimal configuration associated with rapid synchronization and information transfer, minimal wiring costs, resilience to certain types of damage, as well as a balance between local processing and global integration. Eventually, we review the current knowledge on the effects of focal and diffuse brain disease on neural network characteristics, and demonstrate increasing evidence that both cognitive and psychiatric disturbances, as well as risk of epileptic seizures, are correlated with (changes in) functional network architectural features.

Loss of 'Small-World' Networks in Alzheimer's Disease: Graph Analysis of fMRI Resting-State Functional Connectivity

Background Local network connectivity disruptions in Alzheimers disease patients have been found using graph analysis in BOLD fMRI. Other studies using MEG and cortical thickness measures, however, show more global long distance connectivity changes, both in functional and structural imaging data. The form and role of functional connectivity changes thus remains ambiguous. The current study shows more conclusive data on connectivity changes in early AD using graph analysis on resting-state condition fMRI data. Methodology/Principal Findings 18 mild AD patients and 21 healthy age-matched control subjects without memory complaints were investigated in resting-state condition with MRI at 1.5 Tesla. Functional coupling between brain regions was calculated on the basis of pair-wise synchronizations between regional time-series. Local (cluster coefficient) and global (path length) network measures were quantitatively defined. Compared to controls, the characteristic path length of AD functional networks is closer to the theoretical values of random networks, while no significant differences were found in cluster coefficient. The whole-brain average synchronization does not differ between Alzheimer and healthy control groups. Post-hoc analysis of the regional synchronization reveals increased AD synchronization involving the frontal cortices and generalized decreases located at the parietal and occipital regions. This effectively translates in a global reduction of functional long-distance links between frontal and caudal brain regions. Conclusions/Significance We present evidence of AD-induced changes in global brain functional connectivity specifically affecting long-distance connectivity. This finding is highly relevant for it supports the anterior-posterior disconnection theory and its role in AD. Our results can be interpreted as reflecting the randomization of the brain functional networks in AD, further suggesting a loss of global information integration in disease.