Regression DCM for fMRI

Abstract

The development of large-scale network models that infer the effective (directed) connectivity among neuronal populations from neuroimaging data represents a key challenge for computational neuroscience. Dynamic causal models (DCMs) of neuroimaging and electrophysiological data are frequently used for inferring effective connectivity but are presently restricted to small graphs (typically up to 10 regions) in order to keep model inversion computationally feasible. Here, we present a novel variant of DCM for functional magnetic resonance imaging (fMRI) data that is suited to assess effective connectivity in large (whole-brain) networks. The approach rests on translating a linear DCM into the frequency domain and reformulating it as a special case of Bayesian linear regression. This paper derives regression DCM (rDCM) in detail and presents a variational Bayesian inversion method that enables extremely fast inference and accelerates model inversion by several orders of magnitude compared to classical DCM. Using both simulated and empirical data, we demonstrate the face validity of rDCM under different settings of signal-to-noise ratio (SNR) and repetition time (TR) of fMRI data. In particular, we assess the potential utility of rDCM as a tool for whole-brain connectomics by challenging it to infer effective connection strengths in a simulated whole-brain network comprising 66 regions and 300 free parameters. Our results indicate that rDCM represents a computationally highly efficient approach with promising potential for inferring whole-brain connectivity from individual fMRI data.

A generative model of whole-brain effective connectivity

“…Hence, for scenarios where the fMRI data is subject to inherently low SNR (e.g., subcortical regions), the current implementation of sparse rDCM likely shows poor sensitivity. This is not too surprising, considering that the initial version of sparse rDCM reported in this paper is based on the original rDCM implementation, which itself suffers from these limitations (Fr€ assle et al, 2017). Furthermore, enforcing sparsity has an intrinsic tendency to favoring specificity at the expense of sensitivity.…”

“…Consequently, in its classical formulation, DCM cannot accommodate whole-brain networks. Recently, cross-spectral DCM (Friston et al, 2014a) has been combined with an approach to constrain the effective number of parameters (Seghier and Friston, 2013) to invert networks comprising 36 brain regions .Regression DCM (rDCM) has recently been introduced as a novel variant of DCM for fMRI that has promising potential for the application to large (whole-brain) neural networks (Fr€ assle et al, 2017). In brief, rDCM converts the numerically costly problem of estimating coupling parameters in differential equations (of a linear DCM in the time domain) into an efficiently solvable Bayesian linear regression in the frequency domain.…”

“…The current implementation of rDCM is designed to work with experimentally controlled perturbations (the driving inputs in a linear DCM) and hence task fMRI (although it can, in principle, also be applied to "resting state" data, see Discussion). rDCM scales gracefully (polynomially, as opposed to exponentially) with the number of nodes (with the inversion of a covariance matrix being the computationally most expensive operation), and previous simulations demonstrated that it can be applied to networks that are (at least) one order of magnitude larger than the ones afforded in classical DCM implementations (Fr€ assle et al, 2017). In particular, we showed that rDCM can accurately estimate effective connectivity in a network comprising 66 brain regions and 300 free (neuronal) connectivity parameters, based on a realistic human structural connectome (Hagmann et al, 2008).…”

“…In brief, these include (i) translating state and observation equations from time to frequency domain, (ii) linearizing the hemodynamic forward model, (iii) a mean field assumption across regions (i.e., independence of connectivity parameters targeting different regions), and (iv) specifying conjugate priors to enable analytic update equations. We only briefly outline these steps here; for details, see Fr€ assle et al (2017).The neuronal state equation of rDCM corresponds to a linear DCM:Using the differential property of the Fourier transform and a fixed hemodynamic convolution kernel h with additive Gaussian noise as forward model, one obtains an algebraic equation in the frequency domain:Here, y denotes the measured BOLD signal, N is the number of data points, T is the time interval between subsequent points, m is a vector of frequency indices, υ is the observation noise, and the hat symbol (^)represents the discrete Fourier transform (DFT). In Eq.…”

“…In simulations shown below, we systematically varied p i 0 to evaluate the impact of this choice on the accuracy of sparse rDCM. We propose a principled approach to optimizing p i 0 for empirical datasets (where the "true" degree of network sparsity is unknown) that performs model inversion for different p i 0 values and selects the one that yields the highest negative free energy.In this paper, the prior densities over connectivity parameters and noise precision were defined as in Fr€ assle et al (2017). Specifically, we used the standard neuronal priors from DCM10 as implemented in the Statistical Parametric Mapping software package SPM8 (version R4290; www.fil.ion.ucl.ac.uk/spm).…”