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1.  A Computational Model Incorporating Neural Stem Cell Dynamics Reproduces Glioma Incidence across the Lifespan in the Human Population 
PLoS ONE  2014;9(11):e111219.
Glioma is the most common form of primary brain tumor. Demographically, the risk of occurrence increases until old age. Here we present a novel computational model to reproduce the probability of glioma incidence across the lifespan. Previous mathematical models explaining glioma incidence are framed in a rather abstract way, and do not directly relate to empirical findings. To decrease this gap between theory and experimental observations, we incorporate recent data on cellular and molecular factors underlying gliomagenesis. Since evidence implicates the adult neural stem cell as the likely cell-of-origin of glioma, we have incorporated empirically-determined estimates of neural stem cell number, cell division rate, mutation rate and oncogenic potential into our model. We demonstrate that our model yields results which match actual demographic data in the human population. In particular, this model accounts for the observed peak incidence of glioma at approximately 80 years of age, without the need to assert differential susceptibility throughout the population. Overall, our model supports the hypothesis that glioma is caused by randomly-occurring oncogenic mutations within the neural stem cell population. Based on this model, we assess the influence of the (experimentally indicated) decrease in the number of neural stem cells and increase of cell division rate during aging. Our model provides multiple testable predictions, and suggests that different temporal sequences of oncogenic mutations can lead to tumorigenesis. Finally, we conclude that four or five oncogenic mutations are sufficient for the formation of glioma.
doi:10.1371/journal.pone.0111219
PMCID: PMC4237327  PMID: 25409511
4.  Spreading dynamics on spatially constrained complex brain networks 
The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics and has been widely undertaken. Typically, however, networks employed in theoretical studies bear little relation to the spatial embedding or connectivity of the neural networks that they attempt to replicate. Here, we employ detailed neuroimaging data to define a network whose spatial embedding represents accurately the folded structure of the cortical surface of a rat brain and investigate the propagation of activity over this network under simple spreading and connectivity rules. By comparison with standard network models with the same coarse statistics, we show that the cortical geometry influences profoundly the speed of propagation of activation through the network. Our conclusions are of high relevance to the theoretical modelling of epileptic seizure events and indicate that such studies which omit physiological network structure risk simplifying the dynamics in a potentially significant way.
doi:10.1098/rsif.2013.0016
PMCID: PMC3627122  PMID: 23407574
spreading dynamics; network science; neuroscience; epilepsy; connectome
5.  fMRI resting state networks and their association with cognitive fluctuations in dementia with Lewy bodies 
NeuroImage : Clinical  2014;4:558-565.
Cognitive fluctuations are a core symptom in dementia with Lewy bodies (DLB) and may relate to pathological alterations in distributed brain networks. To test this we analysed resting state fMRI changes in a cohort of fluctuating DLB patients (n = 16) compared with age matched controls (n = 17) with the aim of finding functional connectivity (FC) differences between these two groups and whether these associate with cognitive fluctuations in DLB. Resting state networks (RSNs) were estimated using independent component analysis and FC between the RSN maps and the entirety of the brain was assessed using dual regression. The default mode network (DMN) appeared unaffected in DLB compared to controls but significant cluster differences between DLB and controls were found for the left fronto-parietal, temporal, and sensory–motor networks. Desynchronization of a number of cortical and subcortical areas related to the left fronto-parietal network was associated with the severity and frequency of cognitive fluctuations. Our findings provide empirical evidence for the potential role of attention–executive networks in the aetiology of this core symptom in DLB.
Highlights
•We report resting state network (RSN) alterations in dementia with Lewy bodies (DLB).•The default mode network was intact in DLB compared to healthy controls (HC).•Fronto-parietal, temporal, and sensory–motor RSNs showed differences (DLB < HC).•The left fronto-parietal network (FPN) correlated with cognitive fluctuations in DLB.•The FPN therefore may be a potential marker for cognitive fluctuations in DLB.
doi:10.1016/j.nicl.2014.03.013
PMCID: PMC3984441  PMID: 24818081
Cognitive fluctuations; Visual hallucinations; Resting state network; Lewy bodies; Dementia
6.  Adolescent Brain Maturation and Cortical Folding: Evidence for Reductions in Gyrification 
PLoS ONE  2014;9(1):e84914.
Evidence from anatomical and functional imaging studies have highlighted major modifications of cortical circuits during adolescence. These include reductions of gray matter (GM), increases in the myelination of cortico-cortical connections and changes in the architecture of large-scale cortical networks. It is currently unclear, however, how the ongoing developmental processes impact upon the folding of the cerebral cortex and how changes in gyrification relate to maturation of GM/WM-volume, thickness and surface area. In the current study, we acquired high-resolution (3 Tesla) magnetic resonance imaging (MRI) data from 79 healthy subjects (34 males and 45 females) between the ages of 12 and 23 years and performed whole brain analysis of cortical folding patterns with the gyrification index (GI). In addition to GI-values, we obtained estimates of cortical thickness, surface area, GM and white matter (WM) volume which permitted correlations with changes in gyrification. Our data show pronounced and widespread reductions in GI-values during adolescence in several cortical regions which include precentral, temporal and frontal areas. Decreases in gyrification overlap only partially with changes in the thickness, volume and surface of GM and were characterized overall by a linear developmental trajectory. Our data suggest that the observed reductions in GI-values represent an additional, important modification of the cerebral cortex during late brain maturation which may be related to cognitive development.
doi:10.1371/journal.pone.0084914
PMCID: PMC3893168  PMID: 24454765
7.  Resting-State Functional Connectivity in Late-Life Depression: Higher Global Connectivity and More Long Distance Connections 
Functional magnetic resonance imaging recordings in the resting-state (RS) from the human brain are characterized by spontaneous low-frequency fluctuations in the blood oxygenation level dependent signal that reveal functional connectivity (FC) via their spatial synchronicity. This RS study applied network analysis to compare FC between late-life depression (LLD) patients and control subjects. Raw cross-correlation matrices (CM) for LLD were characterized by higher FC. We analyzed the small-world (SW) and modular organization of these networks consisting of 110 nodes each as well as the connectivity patterns of individual nodes of the basal ganglia. Topological network measures showed no significant differences between groups. The composition of top hubs was similar between LLD and control subjects, however in the LLD group posterior medial-parietal regions were more highly connected compared to controls. In LLD, a number of brain regions showed connections with more distant neighbors leading to an increase of the average Euclidean distance between connected regions compared to controls. In addition, right caudate nucleus connectivity was more diffuse in LLD. In summary, LLD was associated with overall increased FC strength and changes in the average distance between connected nodes, but did not lead to global changes in SW or modular organization.
doi:10.3389/fpsyt.2012.00116
PMCID: PMC3540775  PMID: 23316175
late-life depression; aging; resting-state; functional connectivity; default mode network; network analysis; graph theory; functional magnetic resonance
8.  The potential of the human connectome as a biomarker of brain disease 
The human connectome at the level of fiber tracts between brain regions has been shown to differ in patients with brain disorders compared to healthy control groups. Nonetheless, there is a potentially large number of different network organizations for individual patients that could lead to cognitive deficits prohibiting correct diagnosis. Therefore changes that can distinguish groups might not be sufficient to diagnose the disease that an individual patient suffers from and to indicate the best treatment option for that patient. We describe the challenges introduced by the large variability of connectomes within healthy subjects and patients and outline three common strategies to use connectomes as biomarkers of brain diseases. Finally, we propose a fourth option in using models of simulated brain activity (the dynamic connectome) based on structural connectivity rather than the structure (connectome) itself as a biomarker of disease. Dynamic connectomes, in addition to currently used structural, functional, or effective connectivity, could be an important future biomarker for clinical applications.
doi:10.3389/fnhum.2013.00484
PMCID: PMC3744009  PMID: 23966935
brain connectivity; network disease; brain disorders; classification; diagnosis
9.  Critical paths in a metapopulation model of H1N1: Efficiently delaying influenza spreading through flight cancellation 
PLoS Currents  2012;4:e4f8c9a2e1fca8.
Disease spreading through human travel networks has been a topic of great interest in recent years, as witnessed during outbreaks of influenza A (H1N1) or SARS pandemics. One way to stop spreading over the airline network are travel restrictions for major airports or network hubs based on the total number of passengers of an airport. Here, we test alternative strategies using edge removal, cancelling targeted flight connections rather than restricting traffic for network hubs, for controlling spreading over the airline network. We employ a SEIR metapopulation model that takes into account the population of cities, simulates infection within cities and across the network of the top 500 airports, and tests different flight cancellation methods for limiting the course of infection. The time required to spread an infection globally, as simulated by a stochastic global spreading model was used to rank the candidate control strategies. The model includes both local spreading dynamics at the level of populations and long-range connectivity obtained from real global airline travel data. Simulated spreading in this network showed that spreading infected 37% less individuals after cancelling a quarter of flight connections between cities, as selected by betweenness centrality. The alternative strategy of closing down whole airports causing the same number of cancelled connections only reduced infections by 18%. In conclusion, selecting highly ranked single connections between cities for cancellation was more effective, resulting in fewer individuals infected with influenza, compared to shutting down whole airports. It is also a more efficient strategy, affecting fewer passengers while producing the same reduction in infections.
doi:10.1371/4f8c9a2e1fca8
PMCID: PMC3392097  PMID: 22919563
10.  Modelling human connectome development: precursors to neural circuits 
BMC Neuroscience  2011;12(Suppl 1):P163.
doi:10.1186/1471-2202-12-S1-P163
PMCID: PMC3240260
12.  Automatic Network Fingerprinting through Single-Node Motifs 
PLoS ONE  2011;6(1):e15765.
Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs—a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can be determined automatically. Such automatic routines make high-throughput studies of many networks feasible. Second, the new routines are validated in different network-series. Third, we provide an example of how the method can be used to analyse network time-series. In conclusion, we provide a robust method for systematically discovering and classifying characteristic nodes of a network. In contrast to classical motif analysis, our approach can identify individual components (here: nodes) that are specific to a network. Such special nodes, as hubs before, might be found to play critical roles in real-world networks.
doi:10.1371/journal.pone.0015765
PMCID: PMC3031529  PMID: 21297963
13.  Neural Development Features: Spatio-Temporal Development of the Caenorhabditis elegans Neuronal Network 
PLoS Computational Biology  2011;7(1):e1001044.
The nematode Caenorhabditis elegans, with information on neural connectivity, three-dimensional position and cell linage, provides a unique system for understanding the development of neural networks. Although C. elegans has been widely studied in the past, we present the first statistical study from a developmental perspective, with findings that raise interesting suggestions on the establishment of long-distance connections and network hubs. Here, we analyze the neuro-development for temporal and spatial features, using birth times of neurons and their three-dimensional positions. Comparisons of growth in C. elegans with random spatial network growth highlight two findings relevant to neural network development. First, most neurons which are linked by long-distance connections are born around the same time and early on, suggesting the possibility of early contact or interaction between connected neurons during development. Second, early-born neurons are more highly connected (tendency to form hubs) than later-born neurons. This indicates that the longer time frame available to them might underlie high connectivity. Both outcomes are not observed for random connection formation. The study finds that around one-third of electrically coupled long-range connections are late forming, raising the question of what mechanisms are involved in ensuring their accuracy, particularly in light of the extremely invariant connectivity observed in C. elegans. In conclusion, the sequence of neural network development highlights the possibility of early contact or interaction in securing long-distance and high-degree connectivity.
Author Summary
Long-distance connections are crucial for information processing in neural systems, and changes in long-distance connectivity have been shown for many brain diseases ranging from Alzheimer's to schizophrenia. How do long-distance connections develop? Traditionally, connections can be formed over long distances using guidance cues for steering axonal growth. Subsequently, other connections can follow those pioneer axons to a target location. Alternatively, two neurons can establish a connection early on, which turns into a long-distance connection as the neural system grows. However, the relative contribution of both mechanisms previously remained unclear. Here, we study long-distance connection development in the neuronal network of the roundworm C. elegans. We find that most neurons that are connected by a long-distance connection could interact and establish contact early on. This suggests that early formation could be an influential factor for establishing long-distance connectivity, with a hypothetical role in neuronal wiring accuracy. Reducing the need for axonal guidance is also likely to reduce metabolic costs during development. We also find that highly-connected neurons (hubs) are born early on, potentially giving them more time to host and establish connections. Therefore, neuron birth times can be an important developmental factor for the spatial and topological properties of neural circuits.
doi:10.1371/journal.pcbi.1001044
PMCID: PMC3017107  PMID: 21253561
14.  Integrating Temporal and Spatial Scales: Human Structural Network Motifs Across Age and Region of Interest Size 
Human brain networks can be characterized at different temporal or spatial scales given by the age of the subject or the spatial resolution of the neuroimaging method. Integration of data across scales can only be successful if the combined networks show a similar architecture. One way to compare networks is to look at spatial features, based on fiber length, and topological features of individual nodes where outlier nodes form single node motifs whose frequency yields a fingerprint of the network. Here, we observe how characteristic single node motifs change over age (12–23 years) and network size (414, 813, and 1615 nodes) for diffusion tensor imaging structural connectivity in healthy human subjects. First, we find the number and diversity of motifs in a network to be strongly correlated. Second, comparing different scales, the number and diversity of motifs varied across the temporal (subject age) and spatial (network resolution) scale: certain motifs might only occur at one spatial scale or for a certain age range. Third, regions of interest which show one motif at a lower resolution may show a range of motifs at a higher resolution which may or may not include the original motif at the lower resolution. Therefore, both the type and localization of motifs differ for different spatial resolutions. Our results also indicate that spatial resolution has a higher effect on topological measures whereas spatial measures, based on fiber lengths, remain more comparable between resolutions. Therefore, spatial resolution is crucial when comparing characteristic node fingerprints given by topological and spatial network features. As node motifs are based on topological and spatial properties of brain connectivity networks, these conclusions are also relevant to other studies using connectome analysis.
doi:10.3389/fninf.2011.00010
PMCID: PMC3143730  PMID: 21811454
network analysis; network motifs; structural connectivity; human
15.  Optimal Hierarchical Modular Topologies for Producing Limited Sustained Activation of Neural Networks 
An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable regimes of network activation, typically arising from a limited parameter range. In this range of limited sustained activity (LSA), the activity of neural populations in the network persists between the extremes of either quickly dying out or activating the whole network. Hierarchical modular networks were previously found to show a wider parameter range for LSA than random or small-world networks not possessing hierarchical organization or multiple modules. Here we explored how variation in the number of hierarchical levels and modules per level influenced network dynamics and occurrence of LSA. We tested hierarchical configurations of different network sizes, approximating the large-scale networks linking cortical columns in one hemisphere of the rat, cat, or macaque monkey brain. Scaling of the network size affected the number of hierarchical levels and modules in the optimal networks, also depending on whether global edge density or the numbers of connections per node were kept constant. For constant edge density, only few network configurations, possessing an intermediate number of levels and a large number of modules, led to a large range of LSA independent of brain size. For a constant number of node connections, there was a trend for optimal configurations in larger-size networks to possess a larger number of hierarchical levels or more modules. These results may help to explain the trend to greater network complexity apparent in larger brains and may indicate that this complexity is required for maintaining stable levels of neural activation.
doi:10.3389/fninf.2010.00008
PMCID: PMC2876872  PMID: 20514144
modularity; functional criticality; brain connectivity; neural dynamics; neural networks; cerebral cortex
16.  Hierarchy and Dynamics of Neural Networks 
doi:10.3389/fninf.2010.00112
PMCID: PMC2938979  PMID: 20844605
17.  Reducing influenza spreading over the airline network 
PLoS Currents  2009;1:RRN1005.
Disease spreading through human travel networks has been a topic of great interest in recent years, such as with swine influenza or SARS pandemics.
Most studies have proposed removing highly connected nodes (hubs) to control spreading. Here, we test alternative strategies using edge removal (flight cancellation) for spreading over the airline network. Flight cancellation was more efficient than shutting down whole airports: spreading took 81% longer if solely selected flights were removed, compared to a 52% reduction when entire airports were shutdown, affecting the same number of flights.
doi:10.1371/currents.RRN1005
PMCID: PMC2762335  PMID: 20020673
18.  Temporal Interactions between Cortical Rhythms 
Frontiers in Neuroscience  2008;2(2):145-154.
Multiple local neuronal circuits support different, discrete frequencies of network rhythm in neocortex. Relationships between different frequencies correspond to mechanisms designed to minimise interference, couple activity via stable phase interactions, and control the amplitude of one frequency relative to the phase of another. These mechanisms are proposed to form a framework for spectral information processing. Individual local circuits can also transform their frequency through changes in intrinsic neuronal properties and interactions with other oscillating microcircuits. Here we discuss a frequency transformation in which activity in two co-active local circuits may combine sequentially to generate a third frequency whose period is the concatenation sum of the original two. With such an interaction, the intrinsic periodicity in each component local circuit is preserved – alternate, single periods of each original rhythm form one period of a new frequency – suggesting a robust mechanism for combining information processed on multiple concurrent spatiotemporal scales.
doi:10.3389/neuro.01.034.2008
PMCID: PMC2622758  PMID: 19225587
EEG; neocortex; gamma rhythm; beta rhythm; inhibition
19.  Period Concatenation Underlies Interactions between Gamma and Beta Rhythms in Neocortex 
The neocortex generates rhythmic electrical activity over a frequency range covering many decades. Specific cognitive and motor states are associated with oscillations in discrete frequency bands within this range, but it is not known whether interactions and transitions between distinct frequencies are of functional importance. When coexpressed rhythms have frequencies that differ by a factor of two or more interactions can be seen in terms of phase synchronization. Larger frequency differences can result in interactions in the form of nesting of faster frequencies within slower ones by a process of amplitude modulation. It is not known how coexpressed rhythms, whose frequencies differ by less than a factor of two may interact. Here we show that two frequencies (gamma – 40 Hz and beta2 – 25 Hz), coexpressed in superficial and deep cortical laminae with low temporal interaction, can combine to generate a third frequency (beta1 – 15 Hz) showing strong temporal interaction. The process occurs via period concatenation, with basic rhythm-generating microcircuits underlying gamma and beta2 rhythms forming the building blocks of the beta1 rhythm by a process of addition. The mean ratio of adjacent frequency components was a constant – approximately the golden mean – which served to both minimize temporal interactions, and permit multiple transitions, between frequencies. The resulting temporal landscape may provide a framework for multiplexing – parallel information processing on multiple temporal scales.
doi:10.3389/neuro.03.001.2008
PMCID: PMC2525927  PMID: 18946516
EEG; neocortex; gamma rhythm; beta rhythm; inhibition
20.  Predicting the connectivity of primate cortical networks from topological and spatial node properties 
BMC Systems Biology  2007;1:16.
Background
The organization of the connectivity between mammalian cortical areas has become a major subject of study, because of its important role in scaffolding the macroscopic aspects of animal behavior and intelligence. In this study we present a computational reconstruction approach to the problem of network organization, by considering the topological and spatial features of each area in the primate cerebral cortex as subsidy for the reconstruction of the global cortical network connectivity. Starting with all areas being disconnected, pairs of areas with similar sets of features are linked together, in an attempt to recover the original network structure.
Results
Inferring primate cortical connectivity from the properties of the nodes, remarkably good reconstructions of the global network organization could be obtained, with the topological features allowing slightly superior accuracy to the spatial ones. Analogous reconstruction attempts for the C. elegans neuronal network resulted in substantially poorer recovery, indicating that cortical area interconnections are relatively stronger related to the considered topological and spatial properties than neuronal projections in the nematode.
Conclusion
The close relationship between area-based features and global connectivity may hint on developmental rules and constraints for cortical networks. Particularly, differences between the predictions from topological and spatial properties, together with the poorer recovery resulting from spatial properties, indicate that the organization of cortical networks is not entirely determined by spatial constraints.
doi:10.1186/1752-0509-1-16
PMCID: PMC1831788  PMID: 17408506
21.  Nonoptimal Component Placement, but Short Processing Paths, due to Long-Distance Projections in Neural Systems  
PLoS Computational Biology  2006;2(7):e95.
It has been suggested that neural systems across several scales of organization show optimal component placement, in which any spatial rearrangement of the components would lead to an increase of total wiring. Using extensive connectivity datasets for diverse neural networks combined with spatial coordinates for network nodes, we applied an optimization algorithm to the network layouts, in order to search for wire-saving component rearrangements. We found that optimized component rearrangements could substantially reduce total wiring length in all tested neural networks. Specifically, total wiring among 95 primate (Macaque) cortical areas could be decreased by 32%, and wiring of neuronal networks in the nematode Caenorhabditis elegans could be reduced by 48% on the global level, and by 49% for neurons within frontal ganglia. Wiring length reductions were possible due to the existence of long-distance projections in neural networks. We explored the role of these projections by comparing the original networks with minimally rewired networks of the same size, which possessed only the shortest possible connections. In the minimally rewired networks, the number of processing steps along the shortest paths between components was significantly increased compared to the original networks. Additional benchmark comparisons also indicated that neural networks are more similar to network layouts that minimize the length of processing paths, rather than wiring length. These findings suggest that neural systems are not exclusively optimized for minimal global wiring, but for a variety of factors including the minimization of processing steps.
Synopsis
What constraints shape the organization and spatial layout of neural networks? One influential idea in theoretical neuroscience has been that the overall wiring of neural networks should be as short as possible. Wire-saving could be achieved, for instance, through an optimal spatial arrangement of the connected network components. The authors evaluated this concept of component placement optimization in two representative systems, the neuronal network of the Caenorhabditis elegans worm and the long-range cortical connections of the primate brain. Contrary to previous results, they found many network layouts with substantially shorter total wiring than that of the original biological networks. This nonoptimal component placement arose from the existence of long-distance connections in the networks. Such connections may come at a developmental and metabolic cost; however, as the analyses reported in this article show, they also help to reduce the number of signal processing steps across the networks. Therefore, the organization of neural networks is shaped by trade-offs from multiple constraints, among them total wiring length and the average number of processing steps.
doi:10.1371/journal.pcbi.0020095
PMCID: PMC1513269  PMID: 16848638

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