Learning-based structurally-guided construction of resting-state functional correlation tensors

Abstract

Functional magnetic resonance imaging (fMRI) measures changes in blood-oxygenation-level-dependent (BOLD) signals to detect brain activities. It has been recently reported that the spatial correlation patterns of resting-state BOLD signals in the white matter (WM) also give WM information often measured by diffusion tensor imaging (DTI). These correlation patterns can be captured using functional correlation tensor (FCT), which is analogous to the diffusion tensor (DT) obtained from DTI. In this paper, we propose a noise-robust FCT method aiming at further improving its quality, and making it eligible for further neuroscience study. The novel FCT estimation method consists of three major steps: First, we estimate the initial FCT using a patch-based approach for BOLD signal correlation to improve the noise robustness. Second, by utilizing the relationship between functional and diffusion data, we employ a regression forest model to learn the mapping between the initial FCTs and the corresponding DTs using the training data. The learned forest can then be applied to predict the DTI-like tensors given the initial FCTs from the testing fMRI data. Third, we re-estimate the enhanced FCT by utilizing the DTI-like tensors as a feedback guidance to further improve FCT computation. We have demonstrated the utility of our enhanced FCTs in Alzheimer's disease (AD) diagnosis by identifying mild cognitive impairment (MCI) patients from normal subjects.

Introduction

Functional magnetic resonance imaging (fMRI) has emerged as the primary non-invasive technique for measuring neural activity in the brain. Since the introduction of fMRI in the early 1990s, it has been widely used for its sensitivity to developmental, aging and pathological processes of various organs [1]. fMRI is designed to detect hemodynamic changes in the gray matter (GM) regions, which are known to be associated with the neural activity [2]. An increase of the neural activation usually causes increased local cerebral blood flow to supply the metabolic demands [3]. The measurement of such variation is called blood-oxygenation-level-dependent (BOLD) time series.

Extensions of fMRI have been proposed for the needs in different clinical and research fields. For example, task-based fMRI [4] was developed to localize functionally specialized brain regions under specific task stimulus. On the other hand, the resting-state fMRI (rs-fMRI) [5] is collected in a task-free state and has usually been applied to discover correlated activity patterns or functional connectivity (FC) among different brain regions, in an either local or distant manner [49]. However, in contrast to the GM regions, it is much harder to detect the BOLD signals in the brain white matter (WM), as WM is irrigated by much less dense vasculature [6] and the blood flow in WM is approximately one-fourth of that in GM [7].

Diffusion tensor imaging (DTI), or more generally, the diffusion-weighted magnetic resonance imaging (DWI), has been recognized as an effective tool in the study of the WM [8]. DTI quantifies the diffusion patterns of water molecules using a diffusion tensor (DT) represented by a 3 × 3 symmetric matrix. The movement of water molecules is less constrained in the axonal direction than the perpendicular directions. Thus, using a diffusion tensor model, the distribution of movement of water molecules can be simply represented by an ellipsoid, with the axonal direction given by the major axis. Various diffusion parameters, such as fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD) and radial diffusivity (RD), can be calculated based on the DTs. These parameters have been used extensively for WM abnormality detection for various neurological and psychiatric diseases [9]. Furthermore, the directions of the DTs can be further employed using diffusion tractography to map WM fiber pathways [10], complementary to the GM connectivity information given by FC networks [11].

fMRI has also been used to investigate connectivity in WM. For instance, it was found in [12] that fMRI activation can also be observed in the genu of the corpus callosum. This finding was confirmed by D'Arcy et al. [13] using a Sperry task. Activation in the splenium of the corpus callosum was also observed, providing the first fMRI evidence of posterior callosal activation associated with an interhemispheric transfer task. The work in Mazerolle et al. [14] expanded and refined the approach taken by D'Arcy et al. [13]. Outside of the corpus callosum, BOLD fMRI activation has also been reported, such as in the internal capsule. For example, Mosier and colleagues reported activation associated with swallowing in the internal capsule, as well as the corpus callosum [15]. Also, Gawryluk et al. [16] found that activation can be detected in the internal capsule during a motor task (i.e., finger tapping), which was later confirmed by Mazerolle et al. in [17]. These findings indicate that the BOLD fMRI signals potentially exist in the WM regions due to the existence and detectability of the vasculature, cerebral blood flow (CBF), and cerebral blood volume (CBV) in the WM [18]. Marussich et al. [19] also investigated spatiotemporal correlation of BOLD fMRI signals in WM, comparing between eye-closed resting state and visual-perception tasks. They showed WM functional connectivity in the resting-state session, as well as significant correlations between optical radiations and multiple cortical visual networks.

Recently, Ding et al. [20] found the weak but putative local temporal correlation of BOLD signals that persists over a long distance along the same WM neuronal fiber tracts using rs-fMRI. This study found functional anisotropy of local FCs between a central WM voxel and its neighboring voxels. They captured this anisotropy using a local spatiotemporal correlation tensor and demonstrated that the realistic fiber bundle can be obtained by tracing the directions of FCs. They subsequently introduced “functional correlation tensor (FCT)” in [21] and demonstrated the ability of FCT in revealing several major WM fiber bundles, indicating that FCT is coherent with DTI. However, our experiments indicate that FCTs are sensitive to noise. Since there is only 1–3% signal variability associated with the BOLD signal in GM [22], while it is much less in WM [23], computing FC in WM is challenging.

To address the aforementioned issues, here we propose a novel framework for further improving FCT estimation with the guidance of DT information. The aim is to reduce the influence of noise in WM to the FCT estimation, which is referred from the finding of the consistency between the WM fiber direction and the spatiotemporal correlation pattern of the WM BOLD signals [20], [21]. The main contribution in this paper is four-fold: First, we develop a novel strategy, aiming at increasing the noise robustness of FCT using a patch-based approach. Second, to cater to the possibility that only rs-fMRI but not DTI data are available, we intend to predict DTI-like tensors from the computed FCTs. Specifically, we incorporate the regression forest method to train the learning-based model, which has been successfully applied in many medical image analysis domains, such as image segmentation [24], [25], [26] and reconstruction [27]. We further adopt the cascaded learning strategy using the auto-context model introduced in [28] to boost the performance. Third, we further refine the estimation of FCTs by weighting the dominant directions on the basis of DTI-like tensors. Finally, we have demonstrated the utility of the enhanced FCT in early-stage mild cognitive impairment (eMCI) diagnosis.