A generative model of whole-brain effective connectivity

Abstract

A B S T R A C TThe development of whole-brain models that can infer effective (directed) connection strengths from fMRI data represents a central challenge for computational neuroimaging. A recently introduced generative model of fMRI data, regression dynamic causal modeling (rDCM), moves towards this goal as it scales gracefully to very large networks. However, large-scale networks with thousands of connections are difficult to interpret; additionally, one typically lacks information (data points per free parameter) for precise estimation of all model parameters.This paper introduces sparsity constraints to the variational Bayesian framework of rDCM as a solution to these problems in the domain of task-based fMRI. This sparse rDCM approach enables highly efficient effective connectivity analyses in whole-brain networks and does not require a priori assumptions about the network's connectivity structure but prunes fully (all-to-all) connected networks as part of model inversion. Following the derivation of the variational Bayesian update equations for sparse rDCM, we use both simulated and empirical data to assess the face validity of the model. In particular, we show that it is feasible to infer effective connection strengths from fMRI data using a network with more than 100 regions and 10,000 connections. This demonstrates the feasibility of whole-brain inference on effective connectivity from fMRI data -in single subjects and with a run-time below 1 min when using parallelized code. We anticipate that sparse rDCM may find useful application in connectomics and clinical neuromodeling -for example, for phenotyping individual patients in terms of wholebrain network structure. IntroductionThe human brain comprises multiple levels of organization, with cognitive functions arising from the interplay of functional specialization and integration (Sporns, 2013;Tononi et al., 1994). With the advent of non-invasive neuroimaging techniques, such as functional magnetic resonance imaging (fMRI), researchers have begun to systematically study these fundamental properties of human brain organization. While early neuroimaging studies focused on localizing cognitive processes to specific brain regions, contemporary studies are commonly concerned with functional integration of these regions; this requires analyzing brain connectivity (Smith, 2012). In addition to analyses of structural (anatomical) connections, assessments of functional connectivity (statistical dependencies between network nodes) play a major role. Particularly, functional connectivity has been used frequently for studying the functional organization of large (whole-brain) networks both in tasks and in the "resting state" (i.e., unconstrained cognition in the absence of external perturbations). Various methods have been proposed (for a comprehensive review, see Karahanoglu and Van De Ville, 2017), ranging from conventional correlation or coherence analyses which assume stationarity (Fox et al., 2005) to sliding-window correlation analyses that can capture dyna...

MOU-EC: model-based whole-brain effective connectivity to extract biomarkers for brain dynamics from fMRI data and study distributed cognition

“…2B embody the spatio-temporal BOLD structure in the range of "high" frequencies close to the Nyquist frequency equal to 0.5 Hz. The recent extension of the DCM to analyze resting-state fMRI data reproduces the BOLD statistics via the cross-spectrum [62,120,56], which is in line with our approach. Recall that this contrasts with earlier versions of the 295 DCM that reproduced the BOLD time series themselves for stimulation protocols [61,98].…”

“…The MOU-EC estimation was developed to solve the trade-off between robust estimation and application to large brain network (70+ ROIs) by 290 using linear dynamics [69]. Since then, the DCM has been applied to whole-brain fMRI data [120,56].…”

“…The typical description of the whole-brain activity in these methods is a ROI-ROI matrix, which we refer to as connectivity measure.Recently, fMRI studies for both rest and tasks have also evolved to incorporate the temporal structure of BOLD signals in their analysis [83,90,30,108,69, 74, 25,151], in addition to the spatial structure. Models have also been developed to formalize the link between the observed 60 BOLD and the neuronal activity [61,98,41,103,69,56,151]. This has led to many definitions for connectivity measures and variations thereof.…”

Spectral graph theory of brain oscillations

“…Hence, they address the second order covariance structures of brain activity. In particular, recent spectral DCM and regression DCM models [77][78][79] with local neural masses are formulated in the steady-state frequency-domain, and the resulting whole-brain cross-spectra are evaluated. The goals of these models are to derive model cross-spectra that define the effective connectivity in the frequency domain and are compared with empirical cross-spectra.…”

“…Second, our model is more parsimonious compared to most of these above-mentioned models which have many more degrees of freedom because they often allow for regions and their interactions to have different parameters. Our model parameterization, with only a few global parameters, lends itself to efficient computations over fine-scale wholebrain parcellations, whereas most DCMs (with the exception of recent spectral and regression DCMS [77][78][79] ) are suited for examining smaller networks but involve large effective connectivity matrices and region-specific parameters. Furthermore, parameters of our model remain grounded and interpretable in terms of the underlying biophysics, i.e.…”