Connectome and Maturation Profiles of the Developing Mouse Brain Using Diffusion Tensor Imaging.

This paper presents a comprehensive effort to establish a structural mouse connectome using diffusion tensor magnetic resonance imaging coupled with connectivity analysis tools. This work lays the foundation for imaging-based structural connectomics of the mouse brain, potentially facilitating a whole-brain network analysis to quantify brain changes in connectivity during development, as well as deviations from it related to genetic effects. A connectomic trajectory of maturation during postnatal ages 2-80 days is presented in the C57BL/6J mouse strain, using a whole-brain connectivity analysis, followed by investigations based on local and global network features. The global network measures of density, global efficiency, and modularity demonstrated a nonlinear relationship with age. The regional network metrics, namely degree and local efficiency, displayed a differential change in the major subcortical structures such as the thalamus and hippocampus, and cortical regions such as visual and motor cortex. Finally, the connectomes were used to derive an index of "brain connectivity index," which demonstrated a high correlation (r = 0.95) with the chronological age, indicating that brain connectivity is a good marker of normal age progression, hence valuable in detecting subtle deviations from normality caused by genetic, environmental, or pharmacological manipulations.

PUNCH: Population Characterization of Heterogeneity.

Neuropsychiatric disorders are notoriously heterogeneous in their presentation, which precludes straightforward and objective description of the differences between affected and typical populations that therefore makes finding reliable biomarkers a challenge. This difficulty underlines the need for reliable methods to capture sample characteristics of heterogeneity using a single continuous measure, incorporating the multitude of scores used to describe different aspects of functioning. This study addresses this challenge by proposing a general method of identifying and quantifying the heterogeneity of any clinical population using a severity measure called the PUNCH (Population Characterization of Heterogeneity). PUNCH is a decision level fusion technique to incorporate decisions of various phenotypic scores, while providing interpretable weights for scores. We provide applications of our framework to simulated datasets and to a large sample of youth with Autism Spectrum Disorder (ASD). Next we stratify PUNCH scores in our ASD sample and show how severity moderates findings of group differences in diffusion weighted brain imaging data; more severely affected subgroups of ASD show expanded differences compared to age and gender matched healthy controls. Results demonstrate the ability of our measure in quantifying the underlying heterogeneity of the clinical samples, and suggest its utility in providing researchers with reliable severity assessments incorporating population heterogeneity.

On characterizing population commonalities and subject variations in brain networks.

Brain networks based on resting state connectivity as well as inter-regional anatomical pathways obtained using diffusion imaging have provided insight into pathology and development. Such work has underscored the need for methods that can extract sub-networks that can accurately capture the connectivity patterns of the underlying population while simultaneously describing the variation of sub-networks at the subject level. We have designed a multi-layer graph clustering method that extracts clusters of nodes, called 'network hubs', which display higher levels of connectivity within the cluster than to the rest of the brain. The method determines an atlas of network hubs that describes the population, as well as weights that characterize subject-wise variation in terms of within- and between-hub connectivity. This lowers the dimensionality of brain networks, thereby providing a representation amenable to statistical analyses. The applicability of the proposed technique is demonstrated by extracting an atlas of network hubs for a population of typically developing controls (TDCs) as well as children with autism spectrum disorder (ASD), and using the structural and functional networks of a population to determine the subject-level variation of these hubs and their inter-connectivity. These hubs are then used to compare ASD and TDCs. Our method is generalizable to any population whose connectivity (structural or functional) can be captured via non-negative network graphs.

Joint analysis of band-specific functional connectivity and signal complexity in autism.

Examination of resting state brain activity using electrophysiological measures like complexity as well as functional connectivity is of growing interest in the study of autism spectrum disorders (ASD). The present paper jointly examined complexity and connectivity to obtain a more detailed characterization of resting state brain activity in ASD. Multi-scale entropy was computed to quantify the signal complexity, and synchronization likelihood was used to evaluate functional connectivity (FC), with node strength values providing a sensor-level measure of connectivity to facilitate comparisons with complexity. Sensor level analysis of complexity and connectivity was performed at different frequency bands computed from resting state MEG from 26 children with ASD and 22 typically developing controls (TD). Analyses revealed band-specific group differences in each measure that agreed with other functional studies in fMRI and EEG: higher complexity in TD than ASD, in frontal regions in the delta band and occipital-parietal regions in the alpha band, and lower complexity in TD than in ASD in delta (parietal regions), theta (central and temporal regions) and gamma (frontal-central boundary regions); increased short-range connectivity in ASD in the frontal lobe in the delta band and long-range connectivity in the temporal, parietal and occipital lobes in the alpha band. Finally, and perhaps most strikingly, group differences between ASD and TD in complexity and FC appear spatially complementary, such that where FC was elevated in ASD, complexity was reduced (and vice versa). The correlation of regional average complexity and connectivity node strength with symptom severity scores of ASD subjects supported the overall complementarity (with opposing sign) of connectivity and complexity measures, pointing to either diminished connectivity leading to elevated entropy due to poor inhibitory regulation or chaotic signals prohibiting effective measure of connectivity.

Identifying group discriminative and age regressive sub-networks from DTI-based connectivity via a unified framework of non-negative matrix factorization and graph embedding.

Diffusion tensor imaging (DTI) offers rich insights into the physical characteristics of white matter (WM) fiber tracts and their development in the brain, facilitating a network representation of brain's traffic pathways. Such a network representation of brain connectivity has provided a novel means of investigating brain changes arising from pathology, development or aging. The high dimensionality of these connectivity networks necessitates the development of methods that identify the connectivity building blocks or sub-network components that characterize the underlying variation in the population. In addition, the projection of the subject networks into the basis set provides a low dimensional representation of it, that teases apart different sources of variation in the sample, facilitating variation-specific statistical analysis. We propose a unified framework of non-negative matrix factorization and graph embedding for learning sub-network patterns of connectivity by their projective non-negative decomposition into a reconstructive basis set, as well as, additional basis sets representing variational sources in the population like age and pathology. The proposed framework is applied to a study of diffusion-based connectivity in subjects with autism that shows localized sparse sub-networks which mostly capture the changes related to pathology and developmental variations.

Functionally driven brain networks using multi-layer graph clustering.

Connectivity analysis of resting state brain has provided a novel means of investigating brain networks in the study of neurodevelpmental disorders. The study of functional networks, often represented by high dimensional graphs, predicates on the ability of methods in succinctly extracting meaningful representative connectivity information at the subject and population level. This need motivates the development of techniques that can extract underlying network modules that characterize the connectivity in a population, while capturing variations of these modules at the individual level. In this paper, we propose a multi-layer raph clustering technique that fuses the information from a collection of connectivity networks of a population to extract the underlying common network modules that serve as network hubs for the population. These hubs form a functional network atlas. In addition, our technique provides subject-specific factors designed to characterize and quantify the degree of intra- and inter- connectivity between hubs, thereby providing a representation that is amenable to group level statistical analyses. We demonstrate the utility of the technique by creating a population network atlas of connectivity by examining MEG based functional connectivity in typically developing children, and using this to describe the individualized variation in those diagnosed with autism spectrum disorder.

Connectivity subnetwork learning for pathology and developmental variations.

Network representation of brain connectivity has provided a novel means of investigating brain changes arising from pathology, development or aging. The high dimensionality of these networks demands methods that are not only able to extract the patterns that highlight these sources of variation, but describe them individually. In this paper, we present a unified framework for learning subnetwork patterns of connectivity by their projective non-negative decomposition into a reconstructive basis set, as well as, additional basis sets representing development and group discrimination. In order to obtain these components, we exploit the geometrical distribution of the population in the connectivity space by using a graph-theoretical scheme that imposes locality-preserving properties. In addition, the projection of the subject networks into the basis set provides a low dimensional representation of it, that teases apart the different sources of variation in the sample, facilitating variation-specific statistical analysis. The proposed framework is applied to a study of diffusion-based connectivity in subjects with autism.

Locality preserving non-negative basis learning with graph embedding.

The high dimensionality of connectivity networks necessitates the development of methods identifying the connectivity building blocks that not only characterize the patterns of brain pathology but also reveal representative population patterns. In this paper, we present a non-negative component analysis framework for learning localized and sparse sub-network patterns of connectivity matrices by decomposing them into two sets of discriminative and reconstructive bases. In order to obtain components that are designed towards extracting population differences, we exploit the geometry of the population by using a graphtheoretical scheme that imposes locality-preserving properties as well as maintaining the underlying distance between distant nodes in the original and the projected space. The effectiveness of the proposed framework is demonstrated by applying it to two clinical studies using connectivity matrices derived from DTI to study a population of subjects with ASD, as well as a developmental study of structural brain connectivity that extracts gender differences.

Dominant component analysis of electrophysiological connectivity networks.

Connectivity matrices obtained from various modalities (DTI, MEG and fMRI) provide a unique insight into brain processes. Their high dimensionality necessitates the development of methods for population-based statistics, in the face of small sample sizes. In this paper, we present such a method applicable to functional connectivity networks, based on identifying the basis of dominant connectivity components that characterize the patterns of brain pathology and population variation. Projection of individual connectivity matrices into this basis allows for dimensionality reduction, facilitating subsequent statistical analysis. We find dominant components for a collection of connectivity matrices by using the projective non-negative component analysis technique which ensures that the components have non-negative elements and are non-negatively combined to obtain individual subject networks, facilitating interpretation. We demonstrate the feasibility of our novel framework by applying it to simulated connectivity matrices as well as to a clinical study using connectivity matrices derived from resting state magnetoencephalography (MEG) data in a population of subjects diagnosed with autism spectrum disorder (ASD).

Graph-Laplacian features for neural waveform classification.

Analysis of extracellular recordings of neural action potentials (known as spikes) is highly dependent upon the accuracy of neural waveform classification, commonly referred to as spike sorting. Feature extraction is an important stage of this process because it can limit the quality of clustering that is performed in the feature space. Principal components analysis (PCA) is the most commonly used feature extraction method employed for neural spike recordings. To improve upon PCA's feature extraction performance for neural spike sorting, we revisit the PCA procedure to analyze its weaknesses and describe an improved feature extraction method. This paper proposes a linear feature extraction technique that we call graph-Laplacian features, which simultaneously minimizes the graph Laplacian and maximizes variance. The algorithm's performance is compared with PCA and a wavelet-coefficient-based feature extraction algorithm on simulated single-electrode neural data. A cluster-quality metric is proposed to quantitatively measure the algorithm performance. The results show that the proposed algorithm produces more compact and well-separated clusters compared to the other approaches.

A graph-Laplacian-based feature extraction algorithm for neural spike sorting.

Analysis of extracellular neural spike recordings is highly dependent upon the accuracy of neural waveform classification, commonly referred to as spike sorting. Feature extraction is an important stage of this process because it can limit the quality of clustering which is performed in the feature space. This paper proposes a new feature extraction method (which we call Graph Laplacian Features, GLF) based on minimizing the graph Laplacian and maximizing the weighted variance. The algorithm is compared with Principal Components Analysis (PCA, the most commonly-used feature extraction method) using simulated neural data. The results show that the proposed algorithm produces more compact and well-separated clusters compared to PCA. As an added benefit, tentative cluster centers are output which can be used to initialize a subsequent clustering stage.