Original contributionA deconvolution-based approach to identifying large-scale effective connectivity
Introduction
An open question in neuroimaging is whether whole-brain resting state functional magnetic resonance imaging (fMRI) blood-oxygen-level dependent (BOLD) signal contains sufficient information to consistently and accurately identify causal relationships between brain regions. Currently, large scale functional brain organization analyses, such as independent component analyses and graph theory analyses [1], [2] rely primarily on non-causal measures, i.e. functional connectivity. Given the common understanding that the human brain operates as a distributed network of information processing [3], it is essential that we develop methods that accurately characterize causal connectivity networks, i.e., effective connectivity [4], in order to foster an understanding of both normative and pathological brain processes. Moreover, addressing this open question is a crucial step toward unifying functional brain organization with theoretical [5] and physiological [6] understanding of neural systems, which is deeply rooted in networks of causal information processing elements.
FMRI captures neuronal activity dependent changes in local magnetic fields [7], [8], [9]. Neuronal activity induces an influx of oxygenated hemoglobin molecules into the region of activity which alters the ratio between oxygenated and deoxygenated hemoglobin molecules in the local blood supply [10]; due to oxygen's role in masking the magnetic field of hemoglobin, this changing ratio alters the local magnetic field surrounding the neural activity and is captured as BOLD. The causal relationship between neural activation and BOLD contrast is well-approximated by the hemodynamic response function (HRF) [11], [12]. In the HRF model, a BOLD response is formed in proportion to the neural activation according to a nonlinear kernel function, well-approximated by a double gamma distribution, shown in Fig. 1a. The HRF model also assumes that kernels are linearly additive; neural events occurring in close temporal proximity produce a BOLD response that combines the individual HRF kernels, depicted in Fig. 1b. Noise processes (both physiological and thermal) confound real-world fMRI BOLD signal acquisition [13], [14], as depicted in Fig. 1c.
It is well-known that there exists significant temporal variability (+/− 2 s) in the HRF kernel’s time-to-peak across different regions of the brain [15], [16], [17], [18]. Thus, there exists conflicting conclusions in the most recent literature on the viability of causal modeling based on fMRI BOLD. Smith et al. [19] used simulations of small scale brain activation networks to conduct a comparative survey of algorithms that estimate functional connectivity and effective connectivity directly from BOLD. However, this work cited, but failed to address, earlier work by David et al. [20] which called into question the value of causal inference computed directly from BOLD [20], [21]. By pairing high-temporal fidelity intracerebral EEG recordings with fMRI recordings of the same brain regions, David et al. convincingly demonstrated that region-wise variations in HRF confounded the discovery of the system’s key causal relationship directly from BOLD. Rather, identification of the BOLD signal’s underlying HRF (in this case, through temporal comparison of EEG and fMRI BOLD) followed by explicit deconvolution was found to be a necessary condition for identifying the true, directed brain organization.
Causal inference from whole-brain resting state fMRI BOLD also raises concerns about algorithmic scale-up. Progress has been made toward solving causal inference on small-scale neural systems via dynamic causal modeling (DCM), a form of Bayesian model comparison which estimates the causal structure of coupled dynamical systems [22], as well as structural equation modeling (SEM) [23], [24], [25], Granger causal modeling (GCM) [26], [27], and autoregressive methods [26], [28]. There are, however, computational limits to scaling DCM to whole-brain as it is not feasible to search model spaces of this magnitude [19], a weakness also of structural equation modeling (SEM). Also, external system inputs are unknown or undefined for causal models of resting state data. Similar computational scale-up limitations have been reported for autoregressive approaches [28].
The purpose of this work is to explore an effective connectivity estimation approach that scales to whole-brain fMRI BOLD signals via massively parallelized maximum likelihood estimation of structured neural activation models. A key innovation of this work is to avoid the computational complexity of existing approaches by separating the neural activity identification step (i.e. deconvolution) from the effective connectivity identification step. This two-step process greatly reduces the size of the search space, making whole-brain causal structure identification tractable within the constraints of existing hardware. Separation of these search steps also facilitates independent verification of the effective connectivity estimation via controlled simulation experiments in which neural activity is known. This validation technique avoids questions surrounding the validity of causal inferences under hemodynamic variability [21].
The remainder of this manuscript details the connectivity estimation algorithm as well as supporting algorithms and implementation techniques required for its scale to whole brain; a simulation of whole-brain neural activation; the collection and subsequent deconvolution of real-world whole-brain fMRI BOLD signal; the effective connectivity estimation algorithm; and, the analysis methods by which effective connectivity was validated both in simulation and on real-world, human data.
Section snippets
Effective connectivity estimation
Our approach to effective connectivity estimation incorporates anatomical constraints to the problem [29], [30] via a spatio-temporally structured model of neural activations underlying fMRI BOLD, as depicted in Fig. 2. The proposed estimation method requires two inputs: 1) a dataset of estimated whole-brain neural activations (i.e., deconvolved fMRI BOLD), and 2) estimates of intra-voxel communication lag. The quantity L(vi, vj) describes the time required for a neural activation in voxel, vi,
Simulation experiments
Our simulation experiments explore the performance and robustness of the effective connectivity estimation approach to various confounding factors, specifically, network size, deconvolution performance, and uncertainty of inter-voxel communication lag. Then, using the simulation results as parametric guidance, we applied the approach to estimate effective connectivity in human resting-state fMRI BOLD signal.
Simulation results
A summary of the performance and computational complexity of the effective connectivity approach (applied in simulation) is presented in Fig. 4. As would be expected, estimation performance is negatively impacted by network size and deconvolution precision. The upper bound of statistically significant estimation is V = 500, which is achieved only in the case of near perfect deconvolution performance. Significant estimation performance is achievable for realistic deconvolution precisions for
Whole-brain resting state BOLD experiments
Guided by the simulation results, each of the 17 subjects’ whole-brain fMRI BOLD images was parcellated into ROI networks of V ∈ [10, 60] sampled at intervals of 10 ROIs. In accordance with the procedures described in 2.6 Data parcellation method, 2.7 BOLD deconvolution, BOLD signals were extracted from the parcellations and deconvolved. Thirty (S = 30) unique lag models were sampled by uniformly, randomly sampling neural communication velocities from the range calculated in Section 2. We fit
Discussion
We have described an effective connectivity approach, based on deconvolution and anatomical lag constraints, that is designed for scale to whole-brain fMRI BOLD. A key insight of this approach is that it decouples the identification of neural events occurring within an ROI from the estimation of the conditional probabilities by which ROIs communicate. This decoupling serves two roles. First, it dramatically reduces the search space of possible solutions. Second, it provides insight into a
Acknowledgments
This work was supported in part by National Institutes of Health grants R21MH097784-01 and R01DA036360-01 as well as by as the National Science Foundation grants CRI CNS-0855248 and MRI ACI-1429160.
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