Shrinkage prediction of seed-voxel brain connectivity using resting state fMRI

Similar functional networks predict performance in both perceptual and value-based decision tasks

There are numerous commonalities between perceptual and preferential decision processes. For instance, previous studies have shown that both of these decision types are influenced by context. Also, the same computational models can explain both. However, the neural processes and functional connections that underlie these similarities between perceptual and value-based decisions are still unclear. Hence, in the current study, we examine whether perceptual and preferential processes can be explained by similar functional networks utilizing data from the Human Connectome Project. We used resting-state functional magnetic resonance imaging data to predict performance of 2 different decision-making tasks: a value-related task (the delay discounting task) and a perceptual task (the flanker task). We then examined the existence of shared predictive-network features across these 2 decision tasks. Interestingly, we found a significant positive correlation between the functional networks, which predicted the value-based and perceptual tasks. In addition, a larger functional connectivity between visual and frontal decision brain areas was a critical feature in the prediction of both tasks. These results demonstrate that functional connections between perceptual and value-related areas in the brain are inherently related to decision-making processes across domains.

Moderated t-tests for group-level fMRI analysis

In recent years, there has been significant criticism of functional magnetic resonance imaging (fMRI) studies with small sample sizes. The argument is that such studies have low statistical power, as well as reduced likelihood for statistically significant results to be true effects. The prevalence of these studies has led to a situation where a large number of published results are not replicable and likely false. Despite this growing body of evidence, small sample fMRI studies continue to be regularly performed; likely due to the high cost of scanning. In this report we investigate the use of a moderated t-statistic for performing group-level fMRI analysis to help alleviate problems related to small sample sizes. The proposed approach, implemented in the popular R-package LIMMA (linear models for microarray data), has found wide usage in the genomics literature for dealing with similar issues. Utilizing task-based fMRI data from the Human Connectome Project (HCP), we compare the performance of the moderated t-statistic with the standard t-statistic, as well as the pseudo t-statistic commonly used in non-parametric fMRI analysis. We find that the moderated t-test significantly outperforms both alternative approaches for studies with sample sizes less than 40 subjects. Further, we find that the results were consistent both when using voxel-based and cluster-based thresholding. We also introduce an R-package, LIMMI (linear models for medical images), that provides a quick and convenient way to apply the method to fMRI data.

Amygdala hyperconnectivity in the paranoid state: A transdiagnostic study

BACKGROUND

Paranoia significantly contributes to social impairments across clinical diagnoses, and amygdala dysfunction has been identified as a neurobiological marker of paranoia among individuals with schizophrenia. Therefore, we aimed to investigate amygdala functional connectivity (FC) in paranoia across diagnoses.

METHODS

Forty-five patients with recent history of clinically significant paranoid ideation and a current DSM-5 diagnosis of any disorder underwent resting-state functional magnetic resonance imaging either in a paranoid (N = 23) or non-paranoid (N = 22) state. Amygdala FC were compared between paranoid and non-paranoid patients. Supplemental correlation analyses between amygdala FC and paranoia score were performed separately in patients and a non-equivalent healthy control (HC; N = 60) group.

RESULTS

Increased FC was found between right amygdala and the prefrontal cortex (PFC) [bilateral medial superior frontal gyrus, anterior cingulate, medial frontal gyrus, the triangular part and the opercular part of the inferior frontal gyrus (IFG); right orbital part of IFG], the frontal cortex (bilateral median cingulate, left precentral gyrus), and subcortical areas (right insula) in the paranoid group compared with the non-paranoid group. No significant between-group differences were observed in left amygdala FC. FC between right amygdala and PFC and frontal cortex was positively correlated with paranoia in patient and HC groups.

CONCLUSION

Paranoia is associated with right amygdala hyperconnectivity with PFC, frontal cortex, and insula. This hyperconnectivity was evident regardless of diagnosis and therefore identify a likely transdiagnostic neural mechanism, which may help to identify treatment targets that could potentially improve the social functioning of individuals with clinical diagnoses.

Reliability modelling of resting-state functional connectivity

Resting-state functional magnetic resonance imaging (rs-fMRI) has an inherently low signal-to-noise ratio largely due to thermal and physiological noise that attenuates the functional connectivity (FC) estimates. Such attenuation limits the reliability of FC and may bias its association with other traits. Low reliability also limits heritability estimates. Classical test theory can be used to obtain a true correlation estimate free of random measurement error from parallel tests, such as split-half sessions of a rs-fMRI scan. We applied a measurement model to split-half FC estimates from the resting-state fMRI data of 1003 participants from the Human Connectome Project (HCP) to examine the benefit of reliability modelling of FC in association with traits from various domains. We evaluated the efficiency of the measurement model on extracting a stable and reliable component of FC and its association with several traits for various sample sizes and scan durations. In addition, we aimed to replicate our previous findings of increased heritability estimates when using a measurement model in a longitudinal adolescent twin cohort. The split-half measurement model improved test-retest reliability of FC on average with +0.33 points (from +0.49 to +0.82), improved strength of associations between FC and various traits on average 1.2-fold (range 1.09-1.35), and increased heritability estimates on average with +20% points (from 39% to 59%) for the full HCP dataset. On average, about half of the variance in split-session FC estimates was attributed to the stable and reliable component of FC. Shorter scan durations showed greater benefit of reliability modelling (up to 1.6-fold improvement), with an additional gain for smaller sample sizes (up to 1.8-fold improvement). Reliability modelling of FC based on a split-half using a measurement model can benefit genetic and behavioral studies by extracting a stable and reliable component of FC that is free from random measurement error and improves genetic and behavioral associations.

Bayesian modeling of dependence in brain connectivity data

Brain connectivity studies often refer to brain areas as graph nodes and connections between nodes as edges, and aim to identify neuropsychiatric phenotype-related connectivity patterns. When performing group-level brain connectivity alternation analyses, it is critical to model the dependence structure between multivariate connectivity edges to achieve accurate and efficient estimates of model parameters. However, specifying and estimating dependencies between connectivity edges presents formidable challenges because (i) the dimensionality of parameters in the covariance matrix is high (of the order of the fourth power of the number of nodes); (ii) the covariance between a pair of edges involves four nodes with spatial location information; and (iii) the dependence structure between edges can be related to unknown network topological structures. Existing methods for large covariance/precision matrix regularization and spatial closeness-based dependence structure specification/estimation models may not fully address the complexity and challenges. We develop a new Bayesian nonparametric model that unifies information from brain network areas (nodes), connectivity (edges), and covariance between edges by constructing the function of covariance matrix based on the underlying network topological structure. We perform parameter estimation using an efficient Markov chain Monte Carlo algorithm. We apply our method to resting-state functional magnetic resonance imaging data from 60 subjects of a schizophrenia study and simulated data to demonstrate the performance of our method.

Untangling the relatedness among correlations, part III: Inter-subject correlation analysis through Bayesian multilevel modeling for naturalistic scanning

While inter-subject correlation (ISC) analysis is a powerful tool for naturalistic scanning data, drawing appropriate statistical inferences is difficult due to the daunting task of accounting for the intricate relatedness in data structure as well as handling the multiple testing issue. Although the linear mixed-effects (LME) modeling approach (Chen et al., 2017a) is capable of capturing the relatedness in the data and incorporating explanatory variables, there are a few challenging issues: 1) it is difficult to assign accurate degrees of freedom for each testing statistic, 2) multiple testing correction is potentially over-penalizing due to model inefficiency, and 3) thresholding necessitates arbitrary dichotomous decisions. Here we propose a Bayesian multilevel (BML) framework for ISC data analysis that integrates all regions of interest into one model. By loosely constraining the regions through a weakly informative prior, BML dissolves multiplicity through conservatively pooling the effect of each region toward the center and improves collective fitting and overall model performance. In addition to potentially achieving a higher inference efficiency, BML improves spatial specificity and easily allows the investigator to adopt a philosophy of full results reporting. A dataset of naturalistic scanning is utilized to illustrate the modeling approach with 268 parcels and to showcase the modeling capability, flexibility and advantages in results reporting. The associated program will be available as part of the AFNI suite for general use.

A decade of test-retest reliability of functional connectivity: A systematic review and meta-analysis

BACKGROUND

Once considered mere noise, fMRI-based functional connectivity has become a major neuroscience tool in part due to early studies demonstrating its reliability. These fundamental studies revealed only the tip of the iceberg; over the past decade, many test-retest reliability studies have continued to add nuance to our understanding of this complex topic. A summary of these diverse and at times contradictory perspectives is needed.

OBJECTIVES

We aimed to summarize the existing knowledge regarding test-retest reliability of functional connectivity at the most basic unit of analysis: the individual edge level. This entailed (1) a meta-analytic estimate of reliability and (2) a review of factors influencing reliability.

METHODS

A search of Scopus was conducted to identify studies that estimated edge-level test-retest reliability. To facilitate comparisons across studies, eligibility was restricted to studies measuring reliability via the intraclass correlation coefficient (ICC). The meta-analysis included a random effects pooled estimate of mean edge-level ICC, with studies nested within datasets. The review included a narrative summary of factors influencing edge-level ICC.

RESULTS

From an initial pool of 212 studies, 44 studies were identified for the qualitative review and 25 studies for quantitative meta-analysis. On average, individual edges exhibited a "poor" ICC of 0.29 (95% CI = 0.23 to 0.36). The most reliable measurements tended to involve: (1) stronger, within-network, cortical edges, (2) eyes open, awake, and active recordings, (3) more within-subject data, (4) shorter test-retest intervals, (5) no artifact correction (likely due in part to reliable artifact), and (6) full correlation-based connectivity with shrinkage.

CONCLUSION

This study represents the first meta-analysis and systematic review investigating test-retest reliability of edge-level functional connectivity. Key findings suggest there is room for improvement, but care should be taken to avoid promoting reliability at the expense of validity. By pooling existing knowledge regarding this key facet of accuracy, this study supports broader efforts to improve inferences in the field.

Prediction of Brain Connectivity Map in Resting-State fMRI Data Using Shrinkage Estimator

Introduction:

In recent years, brain functional connectivity studies are extended using the advanced statistical methods. Functional connectivity is identified by synchronous activation in a spatially distinct region of the brain in resting-state functional Magnetic Resonance Imaging (MRI) data. For this purpose there are several methods such as seed-based correlation analysis based on temporal correlation between different Regions of Interests (ROIs) or between brain’s voxels of prior seed.

Methods:

In the current study, test-retest Resting State functional MRI (rs-fMRI) data of 21 healthy subjects were analyzed to predict second replication connectivity map using first replication data. A potential estimator is “raw estimator” that uses the first replication data from each subject to predict the second replication connectivity map of the same subject. The second estimator, “mean estimator” uses the average of all sample subjects' connectivity to estimate the correlation map. Shrinkage estimator is made by shrinking raw estimator towards the average connectivity map of all subjects' first replicate. Prediction performance of the second replication correlation map is evaluated by Mean Squared Error (MSE) criteria.

Results:

By the employment of seed-based correlation analysis and choosing precentral gyrus as the ROI over 21 subjects in the study, on average MSE for raw, mean and shrinkage estimator were 0.2169, 0.1118, and 0.1103, respectively. Also, percent reduction of MSE for shrinkage and mean estimator in comparison with raw estimator is 49.14 and 48.45, respectively.

Conclusion:

Shrinkage approach has the positive effect on the prediction of functional connectivity. When data has a large between session variability, prediction of connectivity map can be improved by shrinking towards population mean.

Inferring Brain Signals Synchronicity from a Sample of EEG Readings

Inferring patterns of synchronous brain activity from a heterogeneous sample of electroencephalograms (EEG) is scientifically and methodologically challenging. While it is intuitively and statistically appealing to rely on readings from more than one individual in order to highlight recurrent patterns of brain activation, pooling information across subjects presents non-trivial methodological problems. We discuss some of the scientific issues associated with the understanding of synchronized neuronal activity and propose a methodological framework for statistical inference from a sample of EEG readings. Our work builds on classical contributions in time-series, clustering and functional data analysis, in an effort to reframe a challenging inferential problem in the context of familiar analytical techniques. Some attention is paid to computational issues, with a proposal based on the combination of machine learning and Bayesian techniques.

Inside the Developing Brain to Understand Teen Behavior From Rat Models: Metabolic, Structural, and Functional-Connectivity Alterations Among Limbic Structures Across Three Pre-adolescent Stages

Adolescence is an age of transition when most brain structures undergo drastic modifications, becoming progressively more interconnected and undergoing several changes from a metabolic and structural viewpoint. In the present study, three MR techniques are used in rats to investigate how metabolites, structures and patterns of connectivity do change. We focused in particular on areas belonging to the limbic system, across three post-weaning developmental stages: from "early" (PND 21-25) to "mid" (i.e., a juvenile transition, PND 28-32) and then to "late" (i.e., the adolescent transition, PND 35-39). The rs-fMRI data, with comparison between early and mid (juvenile transition) age-stage rats, highlights patterns of enhanced connectivity from both Striata to both Hippocampi and from there to (left-sided) Nucleus accumbens (NAcc) and Orbitofrontal Cortex (OFC). Also, during this week there is a maturation of pathways from right Striatum to ipsilateral NAcc, from right OFC to ipsilateral NAcc and vice versa, from left Prefrontal Cortex to ipsilateral OFC and eventually from left Striatum, NAcc and Prefrontal Cortex to contralateral OFC. After only 1 week, in late age-stage rats entering into adolescence, the first pathway mentioned above keeps on growing while other patterns appear: both NAcc are reached from contralateral Striatum, right Hippocampus from both Amygdalae, and left NAcc -further- from right Hippocampus. It's interesting to notice the fact that, independently from the age when these connections develop, Striata of both hemispheres send axons to both Hippocampi and both NAcc sides, both Hippocampi reach left NAcc and OFC and finally both NAcc sides reach right OFC. Intriguingly, the Striatum only indirectly reaches the OFC by passing through Hippocampus and NAcc. Data obtained with DTI highlight how adolescents' neurite density may be affected within sub-cortical gray matter, especially for NAcc and OFC at "late" age-stage (adolescence). Finally, levels of metabolites were investigated by 1H-MRS in the anterior part of the hippocampus: we put into evidence an increase in myo-inositol during juvenile transition and a taurine reduction plus a total choline increase during adolescent transition. In this paper, the aforementioned pattern guides the formulation of hypotheses concerning the correlation between the establishment of novel brain connections and the emergence of behavioral traits that are typical of adolescence.

Influences on the Test-Retest Reliability of Functional Connectivity MRI and its Relationship with Behavioral Utility

Best practices are currently being developed for the acquisition and processing of resting-state magnetic resonance imaging data used to estimate brain functional organization—or “functional connectivity.” Standards have been proposed based on test–retest reliability, but open questions remain. These include how amount of data per subject influences whole-brain reliability, the influence of increasing runs versus sessions, the spatial distribution of reliability, the reliability of multivariate methods, and, crucially, how reliability maps onto prediction of behavior. We collected a dataset of 12 extensively sampled individuals (144 min data each across 2 identically configured scanners) to assess test–retest reliability of whole-brain connectivity within the generalizability theory framework. We used Human Connectome Project data to replicate these analyses and relate reliability to behavioral prediction. Overall, the historical 5-min scan produced poor reliability averaged across connections. Increasing the number of sessions was more beneficial than increasing runs. Reliability was lowest for subcortical connections and highest for within-network cortical connections. Multivariate reliability was greater than univariate. Finally, reliability could not be used to improve prediction; these findings are among the first to underscore this distinction for functional connectivity. A comprehensive understanding of test–retest reliability, including its limitations, supports the development of best practices in the field.

Category representations in the brain are both discretely localized and widely distributed

Whether category information is discretely localized or represented widely in the brain remains a contentious issue. Initial functional MRI studies supported the localizationist perspective that category information is represented in discrete brain regions. More recent fMRI studies using machine learning pattern classification techniques provide evidence for widespread distributed representations. However, these latter studies have not typically accounted for shared information. Here, we find strong support for distributed representations when brain regions are considered separately. However, localized representations are revealed by using analytical methods that separate unique from shared information among brain regions. The distributed nature of shared information and the localized nature of unique information suggest that brain connectivity may encourage spreading of information but category-specific computations are carried out in distinct domain-specific regions. NEW & NOTEWORTHY Whether visual category information is localized in unique domain-specific brain regions or distributed in many domain-general brain regions is hotly contested. We resolve this debate by using multivariate analyses to parse functional MRI signals from different brain regions into unique and shared variance. Our findings support elements of both models and show information is initially localized and then shared among other regions leading to distributed representations being observed.

Improved estimation of subject-level functional connectivity using full and partial correlation with empirical Bayes shrinkage

Reliability of subject-level resting-state functional connectivity (FC) is determined in part by the statistical techniques employed in its estimation. Methods that pool information across subjects to inform estimation of subject-level effects (e.g., Bayesian approaches) have been shown to enhance reliability of subject-level FC. However, fully Bayesian approaches are computationally demanding, while empirical Bayesian approaches typically rely on using repeated measures to estimate the variance components in the model. Here, we avoid the need for repeated measures by proposing a novel measurement error model for FC describing the different sources of variance and error, which we use to perform empirical Bayes shrinkage of subject-level FC towards the group average. In addition, since the traditional intra-class correlation coefficient (ICC) is inappropriate for biased estimates, we propose a new reliability measure denoted the mean squared error intra-class correlation coefficient (ICCMSE) to properly assess the reliability of the resulting (biased) estimates. We apply the proposed techniques to test-retest resting-state fMRI data on 461 subjects from the Human Connectome Project to estimate connectivity between 100 regions identified through independent components analysis (ICA). We consider both correlation and partial correlation as the measure of FC and assess the benefit of shrinkage for each measure, as well as the effects of scan duration. We find that shrinkage estimates of subject-level FC exhibit substantially greater reliability than traditional estimates across various scan durations, even for the most reliable connections and regardless of connectivity measure. Additionally, we find partial correlation reliability to be highly sensitive to the choice of penalty term, and to be generally worse than that of full correlations except for certain connections and a narrow range of penalty values. This suggests that the penalty needs to be chosen carefully when using partial correlations.

Individual parcellation of resting fMRI with a group functional connectivity prior

Cortical parcellation based on resting fMRI is an important tool for investigating the functional organization and connectivity of the cerebral cortex. Group parcellation based on co-registration of anatomical images to a common atlas will inevitably result in errors in the locations of the boundaries of functional parcels when they are mapped back from the atlas to the individual. This is because areas of functional specialization vary across individuals in a manner that cannot be fully determined from the sulcal and gyral anatomy that is used for mapping between atlas and individual. We describe a method that avoids this problem by refining an initial group parcellation so that for each subject the parcel boundaries are optimized with respect to that subject's resting fMRI. Initialization with a common parcellation results in automatic correspondence between parcels across subjects. Further, by using a group sparsity constraint to model connectivity, we exploit group similarities in connectivity between parcels while optimizing their boundaries for each individual. We applied this approach with initialization on both high and low density group cortical parcellations and used resting fMRI data to refine across a group of individuals. Cross validation studies show improved homogeneity of resting activity within the refined parcels. Comparisons with task-based localizers show consistent reduction of variance of statistical parametric maps within the refined parcels relative to the group-based initialization indicating improved delineation of regions of functional specialization. This method enables a more accurate estimation of individual subject functional areas, facilitating group analysis of functional connectivity, while maintaining consistency across individuals with a standardized topological atlas.

Predicting individual brain functional connectivity using a Bayesian hierarchical model

Network-oriented analysis of functional magnetic resonance imaging (fMRI), especially resting-state fMRI, has revealed important association between abnormal connectivity and brain disorders such as schizophrenia, major depression and Alzheimer's disease. Imaging-based brain connectivity measures have become a useful tool for investigating the pathophysiology, progression and treatment response of psychiatric disorders and neurodegenerative diseases. Recent studies have started to explore the possibility of using functional neuroimaging to help predict disease progression and guide treatment selection for individual patients. These studies provide the impetus to develop statistical methodology that would help provide predictive information on disease progression-related or treatment-related changes in neural connectivity. To this end, we propose a prediction method based on Bayesian hierarchical model that uses individual's baseline fMRI scans, coupled with relevant subject characteristics, to predict the individual's future functional connectivity. A key advantage of the proposed method is that it can improve the accuracy of individualized prediction of connectivity by combining information from both group-level connectivity patterns that are common to subjects with similar characteristics as well as individual-level connectivity features that are particular to the specific subject. Furthermore, our method also offers statistical inference tools such as predictive intervals that help quantify the uncertainty or variability of the predicted outcomes. The proposed prediction method could be a useful approach to predict the changes in individual patient's brain connectivity with the progression of a disease. It can also be used to predict a patient's post-treatment brain connectivity after a specified treatment regimen. Another utility of the proposed method is that it can be applied to test-retest imaging data to develop a more reliable estimator for individual functional connectivity. We show there exists a nice connection between our proposed estimator and a recently developed shrinkage estimator of connectivity measures in the neuroimaging community. We develop an expectation-maximization (EM) algorithm for estimation of the proposed Bayesian hierarchical model. Simulations studies are performed to evaluate the accuracy of our proposed prediction methods. We illustrate the application of the methods with two data examples: the longitudinal resting-state fMRI from ADNI2 study and the test-retest fMRI data from Kirby21 study. In both the simulation studies and the fMRI data applications, we demonstrate that the proposed methods provide more accurate prediction and more reliable estimation of individual functional connectivity as compared with alternative methods.

sGraSP: A graph-based method for the derivation of subject-specific functional parcellations of the brain

BACKGROUND

Resting-state fMRI (rs-fMRI) has emerged as a prominent tool for the study of functional connectivity. The identification of the regions associated with the different brain functions has received significant interest. However, most of the studies conducted so far have focused on the definition of a common set of regions, valid for an entire population. The variation of the functional regions within a population has rarely been accounted for.

NEW METHOD

In this paper, we propose sGraSP, a graph-based approach for the derivation of subject-specific functional parcellations. Our method generates first a common parcellation for an entire population, which is then adapted to each subject individually.

RESULTS

Several cortical parcellations were generated for 859 children being part of the Philadelphia Neurodevelopmental Cohort. The stability of the parcellations generated by sGraSP was tested by mixing population and subject rs-fMRI signals, to generate subject-specific parcels increasingly closer to the population parcellation. We also checked if the parcels generated by our method were better capturing a development trend underlying our data than the original parcels, defined for the entire population.

COMPARISON WITH EXISTING METHODS

We compared sGraSP with a simpler and faster approach based on a Voronoi tessellation, by measuring their ability to produce functionally coherent parcels adapted to the subject data.

CONCLUSIONS

Our parcellations outperformed the Voronoi tessellations. The parcels generated by sGraSP vary consistently with respect to signal mixing, the results are highly reproducible and the neurodevelopmental trend is better captured with the subject-specific parcellation, under all the signal mixing conditions.

Statistical estimation of T1 relaxation times using conventional magnetic resonance imaging

Quantitative T1 maps estimate T1 relaxation times and can be used to assess diffuse tissue abnormalities within normal-appearing tissue. T1 maps are popular for studying the progression and treatment of multiple sclerosis (MS). However, their inclusion in standard imaging protocols remains limited due to the additional scanning time and expert calibration required and susceptibility to bias and noise. Here, we propose a new method of estimating T1 maps using four conventional MR images, which are intensity-normalized using cerebellar gray matter as a reference tissue and related to T1 using a smooth regression model. Using cross-validation, we generate statistical T1 maps for 61 subjects with MS. The statistical maps are less noisy than the acquired maps and show similar reproducibility. Tests of group differences in normal-appearing white matter across MS subtypes give similar results using both methods.

Group-regularized individual prediction: theory and application to pain

Multivariate pattern analysis (MVPA) has become an important tool for identifying brain representations of psychological processes and clinical outcomes using fMRI and related methods. Such methods can be used to predict or 'decode' psychological states in individual subjects. Single-subject MVPA approaches, however, are limited by the amount and quality of individual-subject data. In spite of higher spatial resolution, predictive accuracy from single-subject data often does not exceed what can be accomplished using coarser, group-level maps, because single-subject patterns are trained on limited amounts of often-noisy data. Here, we present a method that combines population-level priors, in the form of biomarker patterns developed on prior samples, with single-subject MVPA maps to improve single-subject prediction. Theoretical results and simulations motivate a weighting based on the relative variances of biomarker-based prediction-based on population-level predictive maps from prior groups-and individual-subject, cross-validated prediction. Empirical results predicting pain using brain activity on a trial-by-trial basis (single-trial prediction) across 6 studies (N=180 participants) confirm the theoretical predictions. Regularization based on a population-level biomarker-in this case, the Neurologic Pain Signature (NPS)-improved single-subject prediction accuracy compared with idiographic maps based on the individuals' data alone. The regularization scheme that we propose, which we term group-regularized individual prediction (GRIP), can be applied broadly to within-person MVPA-based prediction. We also show how GRIP can be used to evaluate data quality and provide benchmarks for the appropriateness of population-level maps like the NPS for a given individual or study.

Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization

Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a complicated covariance structure. Partial covariance assesses the unique variance shared between two brain regions excluding any widely shared variance, hence is appropriate for the analysis of multivariate fMRI datasets. However, calculation of partial covariance requires inversion of the covariance matrix, which, in most functional connectivity studies, is not invertible owing to rank deficiency. Here we apply Ledoit-Wolf shrinkage (L2 regularization) to invert the high dimensional BOLD covariance matrix. We investigate the network organization and brain-state dependence of partial covariance-based functional connectivity. Although RSNs are conventionally defined in terms of shared variance, removal of widely shared variance, surprisingly, improved the separation of RSNs in a spring embedded graphical model. This result suggests that pair-wise unique shared variance plays a heretofore unrecognized role in RSN covariance organization. In addition, application of partial correlation to fMRI data acquired in the eyes open vs. eyes closed states revealed focal changes in uniquely shared variance between the thalamus and visual cortices. This result suggests that partial correlation of resting state BOLD time series reflect functional processes in addition to structural connectivity.

Improving reliability of subject-level resting-state fMRI parcellation with shrinkage estimators

A recent interest in resting state functional magnetic resonance imaging (rsfMRI) lies in subdividing the human brain into anatomically and functionally distinct regions of interest. For example, brain parcellation is often a necessary step for defining the network nodes used in connectivity studies. While inference has traditionally been performed on group-level data, there is a growing interest in parcellating single subject data. However, this is difficult due to the inherent low signal-to-noise ratio of rsfMRI data, combined with typically short scan lengths. A large number of brain parcellation approaches employ clustering, which begins with a measure of similarity or distance between voxels. The goal of this work is to improve the reproducibility of single-subject parcellation using shrinkage-based estimators of such measures, allowing the noisy subject-specific estimator to "borrow strength" in a principled manner from a larger population of subjects. We present several empirical Bayes shrinkage estimators and outline methods for shrinkage when multiple scans are not available for each subject. We perform shrinkage on raw inter-voxel correlation estimates and use both raw and shrinkage estimates to produce parcellations by performing clustering on the voxels. While we employ a standard spectral clustering approach, our proposed method is agnostic to the choice of clustering method and can be used as a pre-processing step for any clustering algorithm. Using two datasets - a simulated dataset where the true parcellation is known and is subject-specific and a test-retest dataset consisting of two 7-minute resting-state fMRI scans from 20 subjects - we show that parcellations produced from shrinkage correlation estimates have higher reliability and validity than those produced from raw correlation estimates. Application to test-retest data shows that using shrinkage estimators increases the reproducibility of subject-specific parcellations of the motor cortex by up to 30%.