Predicting Functional Connectivity From Observed and Latent Structural Connectivity via Eigenvalue Mapping

Can structure predict function at individual level in the human connectome?

Several studies predicting Functional Connectivity (FC) from Structural Connectivity (SC) at individual level have been published in recent years, each promising increased performance and utility. We investigated three of these studies, analyzing whether the results truly represent a meaningful individual-level mapping from SC to FC. Using data from the Human Connectome Project shared accross the three studies, we constructed a predictor by averaging FC of training data and analyzed its performance in the same way. In each case, we found that group average FC is an equivalent or better predictor of individual FC than the predictive models in terms of raw prediction performance. Furthermore, we showed that additional analyses performed by the authors of the three studies, in which they attempt to show that their predicted FC has value beyond raw prediction performance, could also be reproduced using the group average FC predictor. This makes it unclear whether any of the three methods represent a meaningful individual-level predictive model. We conclude that either the methods are not appropriate for the data, that the sample size is too small, or that the data does not contain sufficient information to learn a mapping from SC to FC. We advise future individual-level studies to explicitly report results in comparison to the performance of the group average, and carefully demonstrate that their predictions contain meaningful individual-level information. Finally, we believe that investigating alternatives for the construction of SC and FC may improve the chances of developing a meaningful individual-level mapping from SC to FC.

Spectral graph model for fMRI: a biophysical, connectivity-based generative model for the analysis of frequency-resolved resting state fMRI

Resting state functional MRI (rs-fMRI) is a popular and widely used technique to explore the brain's functional organization and to examine if it is altered in neurological or mental disorders. The most common approach for its analysis targets the measurement of the synchronized fluctuations between brain regions, characterized as functional connectivity (FC), typically relying on pairwise correlations in activity across different brain regions. While hugely successful in exploring state- and disease-dependent network alterations, these statistical graph theory tools suffer from two key limitations. First, they discard useful information about the rich frequency content of the fMRI signal. The rich spectral information now achievable from advances in fast multiband acquisitions is consequently being under-utilized. Second, the analyzed FCs are phenomenological without a direct neurobiological underpinning in the underlying structures and processes in the brain. There does not currently exist a complete generative model framework for whole brain resting fMRI that is informed by its underlying biological basis in the structural connectome. Here we propose that a different approach can solve both challenges at once: the use of an appropriately realistic yet parsimonious biophysical signal generation model followed by graph spectral (i.e. eigen) decomposition. We call this model a Spectral Graph Model (SGM) for fMRI, using which we can not only quantify the structure-function relationship in individual subjects, but also condense the variable and individual-specific repertoire of fMRI signal's spectral and spatial features into a small number of biophysically-interpretable parameters. We expect this model-based inference of rs-fMRI that seamlessly integrates with structure can be used to examine state and trait characteristics of structure-function relations in a variety of brain disorders.

Mode-based morphometry: A multiscale approach to mapping human neuroanatomy

Voxel-based morphometry (VBM) and surface-based morphometry (SBM) are two widely used neuroimaging techniques for investigating brain anatomy. These techniques rely on statistical inferences at individual points (voxels or vertices), clusters of points, or a priori regions-of-interest. They are powerful tools for describing brain anatomy, but offer little insights into the generative processes that shape a particular set of findings. Moreover, they are restricted to a single spatial resolution scale, precluding the opportunity to distinguish anatomical variations that are expressed across multiple scales. Drawing on concepts from classical physics, here we develop an approach, called mode-based morphometry (MBM), that can describe any empirical map of anatomical variations in terms of the fundamental, resonant modes-eigenmodes-of brain anatomy, each tied to a specific spatial scale. Hence, MBM naturally yields a multiscale characterization of the empirical map, affording new opportunities for investigating the spatial frequency content of neuroanatomical variability. Using simulated and empirical data, we show that the validity and reliability of MBM are either comparable or superior to classical vertex-based SBM for capturing differences in cortical thickness maps between two experimental groups. Our approach thus offers a robust, accurate, and informative method for characterizing empirical maps of neuroanatomical variability that can be directly linked to a generative physical process.

Enhanced brain structure-function tethering in transmodal cortex revealed by high-frequency eigenmodes

While the link between brain structure and function remains an ongoing challenge, the prevailing hypothesis is that the structure-function relationship may itself be gradually decoupling from unimodal to transmodal cortex. However, this hypothesis is constrained by the underlying models which may neglect requisite information. Here we relate structural and functional connectivity derived from diffusion and functional MRI through orthogonal eigenmodes governing frequency-specific diffusion patterns. We find that low-frequency eigenmodes contribute little to functional interactions in transmodal cortex, resulting in divergent structure-function relationships. Conversely, high-frequency eigenmodes predominantly support neuronal coactivation patterns in these areas, inducing structure-function convergence along a unimodal-transmodal hierarchy. High-frequency information, although weak and scattered, could enhance the structure-function tethering, especially in transmodal association cortices. Our findings suggest that the structure-function decoupling may not be an intrinsic property of brain organization, but can be narrowed through multiplexed and regionally specialized spatiotemporal propagation regimes.

A joint subspace mapping between structural and functional brain connectomes

Understanding the connection between the brain's structural connectivity and its functional connectivity is of immense interest in computational neuroscience. Although some studies have suggested that whole brain functional connectivity is shaped by the underlying structure, the rule by which anatomy constraints brain dynamics remains an open question. In this work, we introduce a computational framework that identifies a joint subspace of eigenmodes for both functional and structural connectomes. We found that a small number of those eigenmodes are sufficient to reconstruct functional connectivity from the structural connectome, thus serving as low-dimensional basis function set. We then develop an algorithm that can estimate the functional eigen spectrum in this joint space from the structural eigen spectrum. By concurrently estimating the joint eigenmodes and the functional eigen spectrum, we can reconstruct a given subject's functional connectivity from their structural connectome. We perform elaborate experiments and demonstrate that the proposed algorithm for estimating functional connectivity from the structural connectome using joint space eigenmodes gives competitive performance as compared to the existing benchmark methods with better interpretability.

Mode-based morphometry: A multiscale approach to mapping human neuroanatomy

Voxel-based morphometry (VBM) and surface-based morphometry (SBM) are two widely used neuroimaging techniques for investigating brain anatomy. These techniques rely on statistical inferences at individual points (voxels or vertices), clusters of points, or a priori regions-of-interest. They are powerful tools for describing brain anatomy, but offer little insights into the generative processes that shape a particular set of findings. Moreover, they are restricted to a single spatial resolution scale, precluding the opportunity to distinguish anatomical variations that are expressed across multiple scales. Drawing on concepts from classical physics, here we develop an approach, called mode-based morphometry (MBM), that can describe any empirical map of anatomical variations in terms of the fundamental, resonant modes--eigenmodes--of brain anatomy, each tied to a specific spatial scale. Hence, MBM naturally yields a multiscale characterization of the empirical map, affording new opportunities for investigating the spatial frequency content of neuroanatomical variability. Using simulated and empirical data, we show that the validity and reliability of MBM are either comparable or superior to classical vertex-based SBM for capturing differences in cortical thickness maps between two experimental groups. Our approach thus offers a robust, accurate, and informative method for characterizing empirical maps of neuroanatomical variability that can be directly linked to a generative physical process.

Structure-function models of temporal, spatial, and spectral characteristics of non-invasive whole brain functional imaging

We review recent advances in using mathematical models of the relationship between the brain structure and function that capture features of brain dynamics. We argue the need for models that can jointly capture temporal, spatial, and spectral features of brain functional activity. We present recent work on spectral graph theory based models that can accurately capture spectral as well as spatial patterns across multiple frequencies in MEG reconstructions.