Capturing heterogeneous group differences using mixture-of-experts: Application to a study of aging.

In MRI studies, linear multi-variate methods are often employed to identify regions or connections that are affected due to disease or normal aging. Such linear models inherently assume that there is a single, homogeneous abnormality pattern that is present in all affected individuals. While kernel-based methods can implicitly model a non-linear effect, and therefore the heterogeneity in the affected group, extracting and interpreting information about affected regions is difficult. In this paper, we present a method that explicitly models and captures heterogeneous patterns of change in the affected group relative to a reference group of controls. For this purpose, we use the Mixture-of-Experts (MOE) framework, which combines unsupervised modeling of mixtures of distributions with supervised learning of classifiers. MOE approximates the non-linear boundary between the two groups with a piece-wise linear boundary, thus allowing discovery of multiple patterns of group differences. In the case of patient/control comparisons, each such pattern aims to capture a different dimension of a disease, and hence to identify patient subgroups. We validated our model using multiple simulation scenarios and performance measures. We applied this method to resting state functional MRI data from the Baltimore Longitudinal Study of Aging, to investigate heterogeneous effects of aging on brain function in cognitively normal older adults (>85years) relative to a reference group of normal young to middle-aged adults (<60years). We found strong evidence for the presence of two subgroups of older adults, with similar age distributions in each subgroup, but different connectivity patterns associated with aging. While both older subgroups showed reduced functional connectivity in the Default Mode Network (DMN), increases in functional connectivity within the pre-frontal cortex as well as the bilateral insula were observed only for one of the two subgroups. Interestingly, the subgroup showing this increased connectivity (unlike the other subgroup) was, cognitively similar at baseline to the young and middle-aged subjects in two of seven cognitive domains, and had a faster rate of cognitive decline in one of seven domains. These results suggest that older individuals whose baseline cognitive performance is comparable to that of younger individuals recruit their "cognitive reserve" later in life, to compensate for reduced connectivity in other brain regions.

Identifying Sparse Connectivity Patterns in the brain using resting-state fMRI.

The human brain processes information via multiple distributed networks. An accurate model of the brain's functional connectome is critical for understanding both normal brain function as well as the dysfunction present in neuropsychiatric illnesses. Current methodologies that attempt to discover the organization of the functional connectome typically assume spatial or temporal separation of the underlying networks. This assumption deviates from an intuitive understanding of brain function, which is that of multiple, inter-dependent spatially overlapping brain networks that efficiently integrate information pertinent to diverse brain functions. It is now increasingly evident that neural systems use parsimonious formations and functional representations to efficiently process information while minimizing redundancy. Hence we exploit recent advances in the mathematics of sparse modeling to develop a methodological framework aiming to understand complex resting-state fMRI connectivity data. By favoring networks that explain the data via a relatively small number of participating brain regions, we obtain a parsimonious representation of brain function in terms of multiple "Sparse Connectivity Patterns" (SCPs), such that differential presence of these SCPs explains inter-subject variability. In this manner the sparsity-based framework can effectively capture the heterogeneity of functional activity patterns across individuals while potentially highlighting multiple sub-populations within the data that display similar patterns. Our results from simulated as well as real resting state fMRI data show that SCPs are accurate and reproducible between sub-samples as well as across datasets. These findings substantiate existing knowledge of intrinsic functional connectivity and provide novel insights into the functional organization of the human brain.

White matter atlas generation using HARDI based automated parcellation.

Most diffusion imaging studies have used subject registration to an atlas space for enhanced quantification of anatomy. However, standard diffusion tensor atlases lack information in regions of fiber crossing and are based on adult anatomy. The degree of error associated with applying these atlases to studies of children for example has not yet been estimated but may lead to suboptimal results. This paper describes a novel technique for generating population-specific high angular resolution diffusion imaging (HARDI)-based atlases consisting of labeled regions of homogenous white matter. Our approach uses a fiber orientation distribution (FOD) diffusion model and a data driven clustering algorithm. White matter regional labeling is achieved by our automated data driven clustering algorithm that has the potential to delineate white matter regions based on fiber complexity and orientation. The advantage of such an atlas is that it is study specific and more comprehensive in describing regions of white matter homogeneity as compared to standard anatomical atlases. We have applied this state of the art technique to a dataset consisting of adolescent and preadolescent children, creating one of the first examples of a HARDI-based atlas, thereby establishing the feasibility of the atlas creation framework. The white matter regions generated by our automated clustering algorithm have lower FOD variance than when compared to the regions created from a standard anatomical atlas.

Heterogeneity of structural and functional imaging patterns of advanced brain aging revealed via machine learning methods.

Disentangling the heterogeneity of brain aging in cognitively normal older adults is challenging, as multiple co-occurring pathologic processes result in diverse functional and structural changes. Capitalizing on machine learning methods applied to magnetic resonance imaging data from 400 participants aged 50 to 96 years in the Baltimore Longitudinal Study of Aging, we constructed normative cross-sectional brain aging trajectories of structural and functional changes. Deviations from typical trajectories identified individuals with resilient brain aging and multiple subtypes of advanced brain aging. We identified 5 distinct phenotypes of advanced brain aging. One group included individuals with relatively extensive structural and functional loss and high white matter hyperintensity burden. Another subgroup showed focal hippocampal atrophy and lower posterior-cingulate functional coherence, low white matter hyperintensity burden, and higher medial-temporal connectivity, potentially reflecting high brain tissue reserve counterbalancing brain loss that is consistent with early stages of Alzheimer's disease. Other subgroups displayed distinct patterns. These results indicate that brain changes should not be measured seeking a single signature of brain aging but rather via methods capturing heterogeneity and subtypes of brain aging. Our findings inform future studies aiming to better understand the neurobiological underpinnings of brain aging imaging patterns.

Discriminative sparse connectivity patterns for classification of fMRI Data.

Functional connectivity using resting-state fMRI has emerged as an important research tool for understanding normal brain function as well as changes occurring during brain development and in various brain disorders. Most prior work has examined changes in pairwise functional connectivity values using a multi-variate classification approach, such as Support Vector Machines (SVM). While it is powerful, SVMs produce a dense set of high-dimensional weight vectors as output, which are difficult to interpret, and require additional post-processing to relate to known functional networks. In this paper, we propose a joint framework that combines network identification and classification, resulting in a set of networks, or Sparse Connectivity Patterns (SCPs) which are functionally interpretable as well as highly discriminative of the two groups. Applied to a study of normal development classifying children vs. adults, the proposed method provided accuracy of 76%(AUC= 0.85), comparable to SVM (79%,AUC=0.87), but with dramatically fewer number of features (50 features vs. 34716 for the SVM). More importantly, this leads to a tremendous improvement in neuro-scientific interpretability, which is specially advantageous in such a study where the group differences are wide-spread throughout the brain. Highest-ranked discriminative SCPs reflect increases in long-range connectivity in adults between the frontal areas and posterior cingulate regions. In contrast, connectivity between the bilateral parahippocampal gyri was decreased in adults compared to children.

IDENTIFYING PATTERNS IN TEMPORAL VARIATION OF FUNCTIONAL CONNECTIVITY USING RESTING STATE FMRI.

Estimating functional brain networks from fMRI data has been the focus of much research in recent years. Low sample sizes (time-points) and high dimensionality of fMRI has restricted estimation to a temporally averaged connectivity matrix per subject, due to which the dynamics of functional connectivity is largely unknown. In this paper, we propose a novel method based on constrained matrix factorization that addresses two major issues. Firstly, it finds a set of basis networks that are the semantic parts of the time-varying whole-brain functional networks. The whole-brain network at any point in time, for any subject, is a non-negative combination of these basis networks. Secondly, significant dimensionality reduction is achieved by projecting the data onto this basis, facilitating subsequent analysis of temporal dynamics. Results on simulated fMRI data show that our method can effectively recover underlying basis networks. We apply this method on a normative dataset of resting state fMRI scans. Results indicate that the functional connectivity of a subject at any point during the scan is composed of combinations of overlapping task-positive/negative pairs of sub-networks.

Unsupervised learning of functional network dynamics in resting state fMRI.

Research in recent years has provided some evidence of temporal non-stationarity of functional connectivity in resting state fMRI. In this paper, we present a novel methodology that can decode connectivity dynamics into a temporal sequence of hidden network "states" for each subject, using a Hidden Markov Modeling (HMM) framework. Each state is characterized by a unique covariance matrix or whole-brain network. Our model generates these covariance matrices from a common but unknown set of sparse basis networks, which capture the range of functional activity co-variations of regions of interest (ROIs). Distinct hidden states arise due to a variation in the strengths of these basis networks. Thus, our generative model combines a HMM framework with sparse basis learning of positive definite matrices. Results on simulated fMRI data show that our method can effectively recover underlying basis networks as well as hidden states. We apply this method on a normative dataset of resting state fMRI scans. Results indicate that the functional activity of a subject at any point during the scan is composed of combinations of overlapping task-positive/negative pairs of networks as revealed by our basis. Distinct hidden temporal states are produced due to a different set of basis networks dominating the covariance pattern in each state.

Sparse dictionary learning of resting state fMRI networks.

Research in resting state fMRI (rsfMRI) has revealed the presence of stable, anti-correlated functional subnetworks in the brain. Task-positive networks are active during a cognitive process and are anti-correlated with task-negative networks, which are active during rest. In this paper, based on the assumption that the structure of the resting state functional brain connectivity is sparse, we utilize sparse dictionary modeling to identify distinct functional sub-networks. We propose two ways of formulating the sparse functional network learning problem that characterize the underlying functional connectivity from different perspectives. Our results show that the whole-brain functional connectivity can be concisely represented with highly modular, overlapping task-positive/negative pairs of sub-networks.

HARDI based pattern classifiers for the identification of white matter pathologies.

The paper presents a method for creating abnormality classifiers from high angular resolution diffusion imaging (HARDI) data. We utilized the fiber orientation distribution (FOD) diffusion model to represent the local WM architecture of each subject. The FOD images are then spatially normalized to a common template using a non-linear registration technique. Regions of homogeneous white matter architecture (ROIs) are determined by applying a parcellation algorithm to the population average FOD image. Orientation invariant features of each ROI's mean FOD are determined and concatenated into a feature vector to represent each subject. Principal component analysis (PCA) was used for dimensionality reduction and a linear support vector machine (SVM) classifier is trained on the PCA coefficients. The classifier assigns each test subject a probabilistic score indicating the likelihood of belonging to the patient group. The method was validated using a 5 fold validation scheme on a population containing autism spectrum disorder (ASD) patients and typically developing (TD) controls. A clear distinction between ASD patients and controls was obtained with a 77% accuracy.