Machine learning in a graph framework for subcortical segmentation

Automated and reliable segmentation of subcortical structures from human brain magnetic resonance images is of great importance for volumetric and shape analyses in quantitative neuroimaging studies. However, poor boundary contrast and variable shape of these structures make the automated segmentation a tough task. We propose a 3D graph-based machine learning method, called LOGISMOS-RF, to segment the caudate and the putamen from brain MRI scans in a robust and accurate way. An atlas-based tissue classification and bias-field correction method is applied to the images to generate an initial segmentation for each structure. Then a 3D graph framework is utilized to construct a geometric graph for each initial segmentation. A locally trained random forest classifier is used to assign a cost to each graph node. The max-flow algorithm is applied to solve the segmentation problem. Evaluation was performed on a dataset of T1-weighted MRI's of 62 subjects, with 42 images used for training and 20 images for testing. For comparison, FreeSurfer and FSL approaches were also evaluated using the same dataset. Dice overlap coefficients and surface-to-surfaces distances between the automated segmentation and expert manual segmentations indicate the results of our method are statistically significantly more accurate than the other two methods, for both the caudate (Dice: 0.89 ± 0.03) and the putamen (0.89 ± 0.03).

Simulation of diffusion using a modular cell dynamic simulation system

A variety of mathematical models is used to describe and simulate the multitude of natural processes examined in life sciences. In this paper we present a scalable and adjustable foundation for the simulation of natural systems. Based on neighborhood relations in graphs and the complex interactions in cellular automata, the model uses recurrence relations to simulate changes on a mesoscopic scale. This implicit definition allows for the manipulation of every aspect of the model even during simulation. The definition of value rules ω facilitates the accumulation of change during time steps. Those changes may result from different physical, chemical or biological phenomena. Value rules can be combined into modules, which in turn can be used to create baseline models. Exemplarily, a value rule for the diffusion of chemical substances was designed and its applicability is demonstrated. Finally, the stability and accuracy of the solutions is analyzed.

CHALLENGES IN MATCHING SECONDARY STRUCTURES IN CRYO-EM: AN EXPLORATION

Cryo-electron microscopy is a fast emerging biophysical technique for structural determination of large protein complexes. While more atomic structures are being determined using this technique, it is still challenging to derive atomic structures from density maps produced at medium resolution when no suitable templates are available. A critical step in structure determination is how a protein chain threads through the 3-dimensional density map. A dynamic programming method was previously developed to generate K best matches of secondary structures between the density map and its protein sequence using shortest paths in a related weighted graph. We discuss challenges associated with the creation of the weighted graph and explore heuristic methods to solve the problem of matching secondary structures.

Network rewiring dynamics with convergence towards a star network

Network rewiring as a method for producing a range of structures was first introduced in 1998 by Watts & Strogatz (Nature393, 440-442. (doi:10.1038/30918)). This approach allowed a transition from regular through small-world to a random network. The subsequent interest in scale-free networks motivated a number of methods for developing rewiring approaches that converged to scale-free networks. This paper presents a rewiring algorithm (RtoS) for undirected, non-degenerate, fixed size networks that transitions from regular, through small-world and scale-free to star-like networks. Applications of the approach to models for the spread of infectious disease and fixation time for a simple genetics model are used to demonstrate the efficacy and application of the approach.

Cross-hairs: a scatterplot for meta-analysis in R

We describe a meta-analytic scatterplot that indicates precision of points for two variables paired within studies; this is equivalent in form to a 'cross-hairs' plot used to portray specificity and sensitivity in diagnostic testing. At the user's discretion, the plot also displays boxplots for each of the X and Y variable distributions, means for each of the variables, and the correlation between the two. The cross-hairs may be suppressed for dense point clouds. The program is written in R, so it can be modified by the user and can serve as a companion to existing meta-analysis programs. Some of the program's novel uses are described and illustrated with (1) independent effect sizes, (2) dependent effect sizes, and (3) shrunken estimates. Copyright © 2016 John Wiley & Sons, Ltd.

Automated construction of arterial and venous trees in retinal images

While many approaches exist to segment retinal vessels in fundus photographs, only a limited number focus on the construction and disambiguation of arterial and venous trees. Previous approaches are local and/or greedy in nature, making them susceptible to errors or limiting their applicability to large vessels. We propose a more global framework to generate arteriovenous trees in retinal images, given a vessel segmentation. In particular, our approach consists of three stages. The first stage is to generate an overconnected vessel network, named the vessel potential connectivity map (VPCM), consisting of vessel segments and the potential connectivity between them. The second stage is to disambiguate the VPCM into multiple anatomical trees, using a graph-based metaheuristic algorithm. The third stage is to classify these trees into arterial or venous (A/V) trees. We evaluated our approach with a ground truth built based on a public database, showing a pixel-wise classification accuracy of 88.15% using a manual vessel segmentation as input, and 86.11% using an automatic vessel segmentation as input.

Automatic graph-based localization of cochlear implant electrodes in CT

Cochlear Implants (CIs) restore hearing using an electrode array that is surgically implanted into the cochlea. Research has indicated there is a link between electrode location within the cochlea and hearing outcomes, however, comprehensive analysis of this phenomenon has not been possible because techniques proposed for locating electrodes only work for specific implant models or are too labor intensive to be applied on large datasets. We present a general and automatic graph-based method for localizing electrode arrays in CTs that is effective for various implant models. It relies on a novel algorithm for finding an optimal path of fixed length in a graph and achieves maximum localization errors that are sub-voxel. These results indicate that our methods could be used on a large scale to study the link between electrode placement and outcome across electrode array types, which could lead to advances that improve hearing outcomes for CI users.

A Dynamic Programming Algorithm for Finding the Optimal Placement of a Secondary Structure Topology in Cryo-EM Data

The determination of secondary structure topology is a critical step in deriving the atomic structures from the protein density maps obtained from electron cryomicroscopy technique. This step often relies on matching the secondary structure traces detected from the protein density map to the secondary structure sequence segments predicted from the amino acid sequence. Due to inaccuracies in both sources of information, a pool of possible secondary structure positions needs to be sampled. One way to approach the problem is to first derive a small number of possible topologies using existing matching algorithms, and then find the optimal placement for each possible topology. We present a dynamic programming method of Θ(Nq(2)h) to find the optimal placement for a secondary structure topology. We show that our algorithm requires significantly less computational time than the brute force method that is in the order of Θ(q(N) h).

Improving clustering by imposing network information

Cluster analysis is one of the most popular data analysis tools in a wide range of applied disciplines. We propose and justify a computationally efficient and straightforward-to-implement way of imposing the available information from networks/graphs (a priori available in many application areas) on a broad family of clustering methods. The introduced approach is illustrated on the problem of a noninvasive unsupervised brain signal classification. This task is faced with several challenging difficulties such as nonstationary noisy signals and a small sample size, combined with a high-dimensional feature space and huge noise-to-signal ratios. Applying this approach results in an exact unsupervised classification of very short signals, opening new possibilities for clustering methods in the area of a noninvasive brain-computer interface.

Spatial analyses of wildlife contact networks

Datasets from which wildlife contact networks of epidemiological importance can be inferred are becoming increasingly common. A largely unexplored facet of these data is finding evidence of spatial constraints on who has contact with whom, despite theoretical epidemiologists having long realized spatial constraints can play a critical role in infectious disease dynamics. A graph dissimilarity measure is proposed to quantify how close an observed contact network is to being purely spatial whereby its edges are completely determined by the spatial arrangement of its nodes. Statistical techniques are also used to fit a series of mechanistic models for contact rates between individuals to the binary edge data representing presence or absence of observed contact. These are the basis for a second measure that quantifies the extent to which contacts are being mediated by distance. We apply these methods to a set of 128 contact networks of field voles (Microtus agrestis) inferred from mark–recapture data collected over 7 years and from four sites. Large fluctuations in vole abundance allow us to demonstrate that the networks become increasingly similar to spatial proximity graphs as vole density increases. The average number of contacts, , was (i) positively correlated with vole density across the range of observed densities and (ii) for two of the four sites a saturating function of density. The implications for pathogen persistence in wildlife may be that persistence is relatively unaffected by fluctuations in host density because at low density is low but hosts move more freely, and at high density is high but transmission is hampered by local build-up of infected or recovered animals.

Presenting parasitological data: the good, the bad and the error bar

Visual displays of data in the parasitology literature are often presented in a way which is not very informative regarding the distribution of the data. An example being simple barcharts with half an error bar on top to display the distribution of parasitaemia and biomarkers of host immunity. Such displays obfuscate the shape of the data distribution through displaying too few statistical measures to explain the spread of all the data and selecting statistical measures which are influenced by skewness and outliers. We describe more informative, yet simple, visual representations of the data distribution commonly used in statistics and provide guidance with regards to the display of estimates of population parameters (e.g. population mean) and measures of precision (e.g. 95% confidence interval) for statistical inference. In this article we focus on visual displays for numerical data and demonstrate such displays using an example dataset consisting of total IgG titres in response to three Plasmodium blood antigens measured in pregnant women and parasitaemia measurements from the same study. This tutorial aims to highlight the importance of displaying the data distribution appropriately and the role such displays have in selecting statistics to summarize its distribution and perform statistical inference.

Quantitative Analysis of Myelin and Axonal Remodeling in the Uninjured Motor Network After Stroke

Contralesional brain connectivity plasticity was previously reported after stroke. This study aims at disentangling the biological mechanisms underlying connectivity plasticity in the uninjured motor network after an ischemic lesion. In particular, we measured generalized fractional anisotropy (GFA) and magnetization transfer ratio (MTR) to assess whether poststroke connectivity remodeling depends on axonal and/or myelin changes. Diffusion-spectrum imaging and magnetization transfer MRI at 3T were performed in 10 patients in acute phase, at 1 and 6 months after stroke, which was affecting motor cortical and/or subcortical areas. Ten age- and gender-matched healthy volunteers were scanned 1 month apart for longitudinal comparison. Clinical assessment was also performed in patients prior to magnetic resonance imaging (MRI). In the contralesional hemisphere, average measures and tract-based quantitative analysis of GFA and MTR were performed to assess axonal integrity and myelination along motor connections as well as their variations in time. Mean and tract-based measures of MTR and GFA showed significant changes in a number of contralesional motor connections, confirming both axonal and myelin plasticity in our cohort of patients. Moreover, density-derived features (peak height, standard deviation, and skewness) of GFA and MTR along the tracts showed additional correlation with clinical scores than mean values. These findings reveal the interplay between contralateral myelin and axonal remodeling after stroke.

Using a high-dimensional graph of semantic space to model relationships among words

The GOLD model (Graph Of Language Distribution) is a network model constructed based on co-occurrence in a large corpus of natural language that may be used to explore what information may be present in a graph-structured model of language, and what information may be extracted through theoretically-driven algorithms as well as standard graph analysis methods. The present study will employ GOLD to examine two types of relationship between words: semantic similarity and associative relatedness. Semantic similarity refers to the degree of overlap in meaning between words, while associative relatedness refers to the degree to which two words occur in the same schematic context. It is expected that a graph structured model of language constructed based on co-occurrence should easily capture associative relatedness, because this type of relationship is thought to be present directly in lexical co-occurrence. However, it is hypothesized that semantic similarity may be extracted from the intersection of the set of first-order connections, because two words that are semantically similar may occupy similar thematic or syntactic roles across contexts and thus would co-occur lexically with the same set of nodes. Two versions the GOLD model that differed in terms of the co-occurence window, bigGOLD at the paragraph level and smallGOLD at the adjacent word level, were directly compared to the performance of a well-established distributional model, Latent Semantic Analysis (LSA). The superior performance of the GOLD models (big and small) suggest that a single acquisition and storage mechanism, namely co-occurrence, can account for associative and conceptual relationships between words and is more psychologically plausible than models using singular value decomposition (SVD).

Reproducibility of graph metrics of human brain structural networks

Recent interest in human brain connectivity has led to the application of graph theoretical analysis to human brain structural networks, in particular white matter connectivity inferred from diffusion imaging and fiber tractography. While these methods have been used to study a variety of patient populations, there has been less examination of the reproducibility of these methods. A number of tractography algorithms exist and many of these are known to be sensitive to user-selected parameters. The methods used to derive a connectivity matrix from fiber tractography output may also influence the resulting graph metrics. Here we examine how these algorithm and parameter choices influence the reproducibility of proposed graph metrics on a publicly available test-retest dataset consisting of 21 healthy adults. The dice coefficient is used to examine topological similarity of constant density subgraphs both within and between subjects. Seven graph metrics are examined here: mean clustering coefficient, characteristic path length, largest connected component size, assortativity, global efficiency, local efficiency, and rich club coefficient. The reproducibility of these network summary measures is examined using the intraclass correlation coefficient (ICC). Graph curves are created by treating the graph metrics as functions of a parameter such as graph density. Functional data analysis techniques are used to examine differences in graph measures that result from the choice of fiber tracking algorithm. The graph metrics consistently showed good levels of reproducibility as measured with ICC, with the exception of some instability at low graph density levels. The global and local efficiency measures were the most robust to the choice of fiber tracking algorithm.

An investigation of Hebbian phase sequences as assembly graphs

Hebb proposed that synapses between neurons that fire synchronously are strengthened, forming cell assemblies and phase sequences. The former, on a shorter scale, are ensembles of synchronized cells that function transiently as a closed processing system; the latter, on a larger scale, correspond to the sequential activation of cell assemblies able to represent percepts and behaviors. Nowadays, the recording of large neuronal populations allows for the detection of multiple cell assemblies. Within Hebb's theory, the next logical step is the analysis of phase sequences. Here we detected phase sequences as consecutive assembly activation patterns, and then analyzed their graph attributes in relation to behavior. We investigated action potentials recorded from the adult rat hippocampus and neocortex before, during and after novel object exploration (experimental periods). Within assembly graphs, each assembly corresponded to a node, and each edge corresponded to the temporal sequence of consecutive node activations. The sum of all assembly activations was proportional to firing rates, but the activity of individual assemblies was not. Assembly repertoire was stable across experimental periods, suggesting that novel experience does not create new assemblies in the adult rat. Assembly graph attributes, on the other hand, varied significantly across behavioral states and experimental periods, and were separable enough to correctly classify experimental periods (Naïve Bayes classifier; maximum AUROCs ranging from 0.55 to 0.99) and behavioral states (waking, slow wave sleep, and rapid eye movement sleep; maximum AUROCs ranging from 0.64 to 0.98). Our findings agree with Hebb's view that assemblies correspond to primitive building blocks of representation, nearly unchanged in the adult, while phase sequences are labile across behavioral states and change after novel experience. The results are compatible with a role for phase sequences in behavior and cognition.

The consensus problem in networks with transmission delays

We study discrete- and continuous-time consensus problems on networks in the presence of distributed time delays. We focus on information transmission delays, as opposed to information processing delays, so that each node of the network compares its current state with the past states of its neighbours. We consider directed and weighted networks where the connection structure is described by a normalized Laplacian matrix and show that consensus is achieved if and only if the underlying graph contains a directed spanning tree. This statement holds independently of the transmission delays, which is in contrast to the case of processing delays. Furthermore, we calculate the consensus value explicitly, and show that it is determined by the history of the system over an interval of time, unlike the case of processing delays where the consensus value depends only on the initial state of the system at time zero. This provides the consensus algorithm with improved robustness against noise.

Toward breaking the histone code: bayesian graphical models for histone modifications

BACKGROUND

Histones are proteins that wrap DNA around in small spherical structures called nucleosomes. Histone modifications (HMs) refer to the post-translational modifications to the histone tails. At a particular genomic locus, each of these HMs can either be present or absent, and the combinatory patterns of the presence or absence of multiple HMs, or the histone codes, are believed to coregulate important biological processes. We aim to use raw data on HM markers at different genomic loci to (1) decode the complex biological network of HMs in a single region, and (2) demonstrate how the HM networks differ in different regulatory regions. We suggest that these differences in network attributes form a significant link between histones and genomic functions.

METHODS AND RESULTS

We develop a powerful graphical model under the Bayesian paradigm. Posterior inference is fully probabilistic, allowing us to compute the probabilities of distinct dependence patterns of the HMs using graphs. Furthermore, our model-based framework allows for easy but important extensions for inference on differential networks under various conditions, such as the different annotations of the genomic locations (eg, promoters versus insulators). We applied these models to ChIP-Seq data based on CD4+ T lymphocytes. The results confirmed many existing findings and provided a unified tool to generate various promising hypotheses. Differential network analyses revealed new insights on coregulation of HMs of transcriptional activities in different genomic regions.

CONCLUSIONS

The use of Bayesian graphical models and borrowing strength across different conditions provide high power to infer histone networks and their differences.

Online interactive tutorials for creating graphs with excel 2007 or 2010

Graphic display of clinical data is a useful tool for the behavior-analytic clinician. However, graphs can sometimes be difficult to create. We describe how to access and use an online interactive tutorial that teaches the user to create a variety of graphs often used by behavior analysts. Three tutorials are provided that cover the basics of Microsoft Excel 2007 or 2010, creating graphs for clinical purposes, and creating graphs for research purposes. The uses for this interactive tutorial and other similar programs are discussed.

FLOW-BASED NETWORK MEASURES OF BRAIN CONNECTIVITY IN ALZHEIMER'S DISEASE

We present a new flow-based method for modeling brain structural connectivity. The method uses a modified maximum-flow algorithm that is robust to noise in the diffusion data and guided by biologically viable pathways and structure of the brain. A flow network is first created using a lattice graph by connecting all lattice points (voxel centers) to all their neighbors by edges. Edge weights are based on the orientation distribution function (ODF) value in the direction of the edge. The maximum-flow is computed based on this flow graph using the flow or the capacity between each region of interest (ROI) pair by following the connected tractography fibers projected onto the flow graph edges. Network measures such as global efficiency, transitivity, path length, mean degree, density, modularity, small world, and assortativity are computed from the flow connectivity matrix. We applied our method to diffusion-weighted images (DWIs) from 110 subjects (28 normal elderly, 56 with early and 11 with late mild cognitive impairment, and 15 with AD) and segmented co-registered anatomical MRIs into cortical regions. Experimental results showed better performance compared to the standard fiber-counting methods when distinguishing Alzheimer's disease from normal aging.

A weighted and directed interareal connectivity matrix for macaque cerebral cortex

Retrograde tracer injections in 29 of the 91 areas of the macaque cerebral cortex revealed 1,615 interareal pathways, a third of which have not previously been reported. A weight index (extrinsic fraction of labeled neurons [FLNe]) was determined for each area-to-area pathway. Newly found projections were weaker on average compared with the known projections; nevertheless, the 2 sets of pathways had extensively overlapping weight distributions. Repeat injections across individuals revealed modest FLNe variability given the range of FLNe values (standard deviation <1 log unit, range 5 log units). The connectivity profile for each area conformed to a lognormal distribution, where a majority of projections are moderate or weak in strength. In the G_{29 × 29} interareal subgraph, two-thirds of the connections that can exist do exist. Analysis of the smallest set of areas that collects links from all 91 nodes of the G_{29 × 91} subgraph (dominating set analysis) confirms the dense (66%) structure of the cortical matrix. The G_{29 × 29} subgraph suggests an unexpectedly high incidence of unidirectional links. The directed and weighted G_{29 × 91} connectivity matrix for the macaque will be valuable for comparison with connectivity analyses in other species, including humans. It will also inform future modeling studies that explore the regularities of cortical networks.

Pro-cognitive drug effects modulate functional brain network organization

Previous studies document that cholinergic and noradrenergic drugs improve attention, memory and cognitive control in healthy subjects and patients with neuropsychiatric disorders. In humans neural mechanisms of cholinergic and noradrenergic modulation have mainly been analyzed by investigating drug-induced changes of task-related neural activity measured with functional magnetic resonance imaging (fMRI). Endogenous neural activity has often been neglected. Further, although drugs affect the coupling between neurons, only a few human studies have explicitly addressed how drugs modulate the functional connectome, i.e., the functional neural interactions within the brain. These studies have mainly focused on synchronization or correlation of brain activations. Recently, there are some drug studies using graph theory and other new mathematical approaches to model the brain as a complex network of interconnected processing nodes. Using such measures it is possible to detect not only focal, but also subtle, widely distributed drug effects on functional network topology. Most important, graph theoretical measures also quantify whether drug-induced changes in topology or network organization facilitate or hinder information processing. Several studies could show that functional brain integration is highly correlated with behavioral performance suggesting that cholinergic and noradrenergic drugs which improve measures of cognitive performance should increase functional network integration. The purpose of this paper is to show that graph theory provides a mathematical tool to develop theory-driven biomarkers of pro-cognitive drug effects, and also to discuss how these approaches can contribute to the understanding of the role of cholinergic and noradrenergic modulation in the human brain. Finally we discuss the "global workspace" theory as a theoretical framework of pro-cognitive drug effects and argue that pro-cognitive effects of cholinergic and noradrenergic drugs might be related to higher network integration.

Fast Inference for the Latent Space Network Model Using a Case-Control Approximate Likelihood

Network models are widely used in social sciences and genome sciences. The latent space model proposed by (Hoff et al. 2002), and extended by (Handcock et al. 2007) to incorporate clustering, provides a visually interpretable model-based spatial representation of relational data and takes account of several intrinsic network properties. Due to the structure of the likelihood function of the latent space model, the computational cost is of order O(N²), where N is the number of nodes. This makes it infeasible for large networks. In this paper, we propose an approximation of the log likelihood function. We adopt the case-control idea from epidemiology and construct a case-control likelihood which is an unbiased estimator of the full likelihood. Replacing the full likelihood by the case-control likelihood in the MCMC estimation of the latent space model reduces the computational time from O(N²) to O(N), making it feasible for large networks. We evaluate its performance using simulated and real data. We fit the model to a large protein-protein interaction data using the case-control likelihood and use the model fitted link probabilities to identify false positive links.

General and specific functional connectivity disturbances in first-episode schizophrenia during cognitive control performance

BACKGROUND

Cognitive control impairments in schizophrenia are thought to arise from dysfunction of interconnected networks of brain regions, but interrogating the functional dynamics of large-scale brain networks during cognitive task performance has proved difficult. We used functional magnetic resonance imaging to generate event-related whole-brain functional connectivity networks in participants with first-episode schizophrenia and healthy control subjects performing a cognitive control task.

METHODS

Functional connectivity during cognitive control performance was assessed between each pair of 78 brain regions in 23 patients and 25 control subjects. Network properties examined were region-wise connectivity, edge-wise connectivity, global path length, clustering, small-worldness, global efficiency, and local efficiency.

RESULTS

Patients showed widespread functional connectivity deficits in a large-scale network of brain regions, which primarily affected connectivity between frontal cortex and posterior regions and occurred irrespective of task context. A more circumscribed and task-specific connectivity impairment in frontoparietal systems related to cognitive control was also apparent. Global properties of network topology in patients were relatively intact.

CONCLUSIONS

The first episode of schizophrenia is associated with a generalized connectivity impairment affecting most brain regions but that is particularly pronounced for frontal cortex. Superimposed on this generalized deficit, patients show more specific cognitive-control-related functional connectivity reductions in frontoparietal regions. These connectivity deficits occur in the context of relatively preserved global network organization.

Reconstructing disease outbreaks from genetic data: a graph approach

Epidemiology and public health planning will increasingly rely on the analysis of genetic sequence data. In particular, genetic data coupled with dates and locations of sampled isolates can be used to reconstruct the spatiotemporal dynamics of pathogens during outbreaks. Thus far, phylogenetic methods have been used to tackle this issue. Although these approaches have proved useful for informing on the spread of pathogens, they do not aim at directly reconstructing the underlying transmission tree. Instead, phylogenetic models infer most recent common ancestors between pairs of isolates, which can be inadequate for densely sampled recent outbreaks, where the sample includes ancestral and descendent isolates. In this paper, we introduce a novel method based on a graph approach to reconstruct transmission trees directly from genetic data. Using simulated data, we show that our approach can efficiently reconstruct genealogies of isolates in situations where classical phylogenetic approaches fail to do so. We then illustrate our method by analyzing data from the early stages of the swine-origin A/H1N1 influenza pandemic. Using 433 isolates sequenced at both the hemagglutinin and neuraminidase genes, we reconstruct the likely history of the worldwide spread of this new influenza strain. The presented methodology opens new perspectives for the analysis of genetic data in the context of disease outbreaks.