Tangent functional connectomes uncover more unique phenotypic traits

Functional connectomes (FCs) contain pairwise estimations of functional couplings based on pairs of brain regions activity. FCs are commonly represented as correlation matrices that are symmetric positive definite (SPD) lying on or inside the SPD manifold. Since the geometry on the SPD manifold is non-Euclidean, the inter-related entries of FCs undermine the use of Euclidean-based distances. By projecting FCs into a tangent space, we can obtain tangent functional connectomes (tangent-FCs). Tangent-FCs have shown a higher predictive power of behavior and cognition, but no studies have evaluated the effect of such projections with respect to fingerprinting. We hypothesize that tangent-FCs have a higher fingerprint than regular FCs. Fingerprinting was measured by identification rates (ID rates) on test-retest FCs as well as on monozygotic and dizygotic twins. Our results showed that identification rates are systematically higher when using tangent-FCs. Specifically, we found: (i) Riemann and log-Euclidean matrix references systematically led to higher ID rates. (ii) In tangent-FCs, Main-diagonal regularization prior to tangent space projection was critical for ID rate when using Euclidean distance, whereas barely affected ID rates when using correlation distance. (iii) ID rates were dependent on condition and fMRI scan length. (iv) Parcellation granularity was key for ID rates in FCs, as well as in tangent-FCs with fixed regularization, whereas optimal regularization of tangent-FCs mostly removed this effect. (v) Correlation distance in tangent-FCs outperformed any other configuration of distance on FCs or on tangent-FCs across the fingerprint gradient (here sampled by assessing test-retest, Monozygotic and Dizygotic twins). (vi)ID rates tended to be higher in task scans compared to resting-state scans when accounting for fMRI scan length.Comment: 29 pages, 10 figures, 2 table

Estimating the spatial correlation structure of measurement error in functional magnetic resonance imaging (fMRI) to improve multivariate inference

Multi-voxel pattern analysis (MVPA) provides a powerful framework for making statistical inferences on the information present in brain activity patterns as measured by functional magnetic resonance imaging (fMRI). Many recent studies suggest that MVPA performance benefits from taking into account the spatial voxel-to-voxel correlations in the measurement noise. However, estimating these noise correlations is challenging due to the limited data points and large voxel counts. To address this issue, it is common practice to shrink the empirical correlation estimate towards its identity matrix, which biases the estimate towards the incorrect assumption that voxels are independent. We therefore propose an anatomically-informed model of measurement noise in fMRI, which takes into account the distances of voxels in the measurement volume, their distance on the cortical sheet, and the depth at which they sample the cortex. Our model can predict the noise-correlation structure in new participants and datasets. It improves the noise correlation estimate when used as a shrinkage target, thereby also potentially improving statistical inferences in MVPA

Predicting future cognitive decline from non-brain and multimodal brain imaging data in healthy and pathological aging

Previous literature has focused on predicting a diagnostic label from structural brain imaging. Since subtle changes in the brain precede a cognitive decline in healthy and pathological aging, our study predicts future decline as a continuous trajectory instead. Here, we tested whether baseline multimodal neuroimaging data improve the prediction of future cognitive decline in healthy and pathological aging. Nonbrain data (demographics, clinical, and neuropsychological scores), structural MRI, and functional connectivity data from OASIS-3 (N = 662; age = 46–96 years) were entered into cross-validated multitarget random forest models to predict future cognitive decline (measured by CDR and MMSE), on average 5.8 years into the future. The analysis was preregistered, and all analysis code is publicly available. Combining non-brain with structural data improved the continuous prediction of future cognitive decline (best test-set performance: R2 = 0.42). Cognitive performance, daily functioning, and subcortical volume drove the performance of our model. Including functional connectivity did not improve predictive accuracy. In the future, the prognosis of age-related cognitive decline may enable earlier and more effective individualized cognitive, pharmacological, and behavioral interventions

Re-visiting Riemannian geometry of symmetric positive definite matrices for the analysis of functional connectivity

Common representations of functional networks of resting state fMRI time series, including covariance, precision, and cross-correlation matrices, belong to the family of symmetric positive definite (SPD) matrices forming a special mathematical structure called Riemannian manifold. Due to its geometric properties, the analysis and operation of functional connectivity matrices may well be performed on the Riemannian manifold of the SPD space. Analysis of functional networks on the SPD space takes account of all the pairwise interactions (edges) as a whole, which differs from the conventional rationale of considering edges as independent from each other. Despite its geometric characteristics, only a few studies have been conducted for functional network analysis on the SPD manifold and inference methods specialized for connectivity analysis on the SPD manifold are rarely found. The current study aims to show the significance of connectivity analysis on the SPD space and introduce inference algorithms on the SPD manifold, such as regression analysis of functional networks in association with behaviors, principal geodesic analysis, clustering, state transition analysis of dynamic functional networks and statistical tests for network equality on the SPD manifold. We applied the proposed methods to both simulated data and experimental resting state fMRI data from the human connectome project and argue the importance of analyzing functional networks under the SPD geometry. All the algorithms for numerical operations and inferences on the SPD manifold are implemented as a MATLAB library, called SPDtoolbox, for public use to expediate functional network analysis on the right geometry.ope

Investigating Brain Functional Networks in a Riemannian Framework

The brain is a complex system of several interconnected components which can be categorized at different Spatio-temporal levels, evaluate the physical connections and the corresponding functionalities. To study brain connectivity at the macroscale, Magnetic Resonance Imaging (MRI) technique in all the different modalities has been exemplified to be an important tool. In particular, functional MRI (fMRI) enables to record the brain activity either at rest or in different conditions of cognitive task and assist in mapping the functional connectivity of the brain. The information of brain functional connectivity extracted from fMRI images can be defined using a graph representation, i.e. a mathematical object consisting of nodes, the brain regions, and edges, the link between regions. With this representation, novel insights have emerged about understanding brain connectivity and providing evidence that the brain networks are not randomly linked. Indeed, the brain network represents a small-world structure, with several different properties of segregation and integration that are accountable for specific functions and mental conditions. Moreover, network analysis enables to recognize and analyze patterns of brain functional connectivity characterizing a group of subjects. In recent decades, many developments have been made to understand the functioning of the human brain and many issues, related to the biological and the methodological perspective, are still need to be addressed. For example, sub-modular brain organization is still under debate, since it is necessary to understand how the brain is functionally organized. At the same time a comprehensive organization of functional connectivity is mostly unknown and also the dynamical reorganization of functional connectivity is appearing as a new frontier for analyzing brain dynamics. Moreover, the recognition of functional connectivity patterns in patients affected by mental disorders is still a challenging task, making plausible the development of new tools to solve them. Indeed, in this dissertation, we proposed novel methodological approaches to answer some of these biological and neuroscientific questions. We have investigated methods for analyzing and detecting heritability in twin's task-induced functional connectivity profiles. in this approach we are proposing a geodesic metric-based method for the estimation of similarity between functional connectivity, taking into account the manifold related properties of symmetric and positive definite matrices. Moreover, we also proposed a computational framework for classification and discrimination of brain connectivity graphs between healthy and pathological subjects affected by mental disorder, using geodesic metric-based clustering of brain graphs on manifold space. Within the same framework, we also propose an approach based on the dictionary learning method to encode the high dimensional connectivity data into a vectorial representation which is useful for classification and determining regions of brain graphs responsible for this segregation. We also propose an effective way to analyze the dynamical functional connectivity, building a similarity representation of fMRI dynamic functional connectivity states, exploiting modular properties of graph laplacians, geodesic clustering, and manifold learning

Population shrinkage of covariance (PoSCE) for better individual brain functional-connectivity estimation

International audienceEstimating covariances from functional Magnetic Resonance Imaging at rest (r-fMRI) can quantify interactions between brain regions. Also known as brain functional connectivity, it reflects inter-subject variations in behavior and cognition, and characterizes neuropathologies. Yet, with noisy and short time-series, as in r-fMRI, covariance estimation is challenging and calls for penalization, as with shrinkage approaches. We introduce population shrinkage of covariance estimator (PoSCE) : a covariance estimator that integrates prior knowledge of covariance distribution over a large population, leading to a non-isotropic shrinkage. The shrinkage is tailored to the Riemannian geometry of symmetric positive definite matrices. It is coupled with a probabilistic modeling of the individual and population covariance distributions. Experiments on two large r-fMRI datasets (HCP n=815, Cam-CAN n=626) show that PoSCE has a better bias-variance trade-off than existing covariance estimates: this estimator relates better functional-connectivity measures to cognition while capturing well intra-subject functional connectivity