Sparse Estimation of Resting-State Effective Connectivity From fMRI Cross-Spectra

15 Years MR-encephalography

Objective

This review article gives an account of the development of the MR-encephalography (MREG) method, which started as a mere ‘Gedankenexperiment’ in 2005 and gradually developed into a method for ultrafast measurement of physiological activities in the brain. After going through different approaches covering k-space with radial, rosette, and concentric shell trajectories we have settled on a stack-of-spiral trajectory, which allows full brain coverage with (nominal) 3 mm isotropic resolution in 100 ms. The very high acceleration factor is facilitated by the near-isotropic k-space coverage, which allows high acceleration in all three spatial dimensions.

Methods

The methodological section covers the basic sequence design as well as recent advances in image reconstruction including the targeted reconstruction, which allows real-time feedback applications, and—most recently—the time-domain principal component reconstruction (tPCR), which applies a principal component analysis of the acquired time domain data as a sparsifying transformation to improve reconstruction speed as well as quality.

Applications

Although the BOLD-response is rather slow, the high speed acquisition of MREG allows separation of BOLD-effects from cardiac and breathing related pulsatility. The increased sensitivity enables direct detection of the dynamic variability of resting state networks as well as localization of single interictal events in epilepsy patients. A separate and highly intriguing application is aimed at the investigation of the glymphatic system by assessment of the spatiotemporal patterns of cardiac and breathing related pulsatility.

Discussion

MREG has been developed to push the speed limits of fMRI. Compared to multiband-EPI this allows considerably faster acquisition at the cost of reduced image quality and spatial resolution.

Fusion of ULS Group Constrained High- and Low-Order Sparse Functional Connectivity Networks for MCI Classification

Functional connectivity networks, derived from resting-state fMRI data, have been found as effective biomarkers for identifying mild cognitive impairment (MCI) from healthy elderly. However, the traditional functional connectivity network is essentially a low-order network with the assumption that the brain activity is static over the entire scanning period, ignoring temporal variations among the correlations derived from brain region pairs. To overcome this limitation, we proposed a new type of sparse functional connectivity network to precisely describe the relationship of temporal correlations among brain regions. Specifically, instead of using the simple pairwise Pearson's correlation coefficient as connectivity, we first estimate the temporal low-order functional connectivity for each region pair based on an ULS Group constrained-UOLS regression algorithm, where a combination of ultra-least squares (ULS) criterion with a Group constrained topology structure detection algorithm is applied to detect the topology of functional connectivity networks, aided by an Ultra-Orthogonal Least Squares (UOLS) algorithm to estimate connectivity strength. Compared to the classical least squares criterion which only measures the discrepancy between the observed signals and the model prediction function, the ULS criterion takes into consideration the discrepancy between the weak derivatives of the observed signals and the model prediction function and thus avoids the overfitting problem. By using a similar approach, we then estimate the high-order functional connectivity from the low-order connectivity to characterize signal flows among the brain regions. We finally fuse the low-order and the high-order networks using two decision trees for MCI classification. Experimental results demonstrate the effectiveness of the proposed method on MCI classification.

Sparse coupled logistic regression to estimate co-activation and modulatory influences of brain regions

Accurate mapping of the functional interactions between remote brain areas with resting-state functional magnetic resonance imaging requires the quantification of their underlying dynamics. In conventional methodological pipelines, a spatial scale of interest is first selected, and dynamic analysis then proceeds at this hypothesised level of complexity. If large-scale functional networks or states are studied, more local regional rearrangements are then not described, potentially missing important neurobiological information. Here, we propose a novel mathematical framework that jointly estimates resting-state functional networks, and spatially more localised cross-regional modulations. To do so, the changes in activity of each brain region are modelled by a logistic regression including co-activation coefficients (reflective of network assignment, as they highlight simultaneous activations across areas) and causal interplays (denoting finer regional cross-talks, when one region active at timetmodulates thettot+1 transition likelihood of another area). A two-parameter L1 regularisation scheme is used to make these two sets of coefficients sparse: one controls overall sparsity, while the other governs the trade-off between co-activations and causal interplays, enabling to properly fit the data despite the yet unknown balance between both types of couplings. Across a range of simulation settings, we show that the framework successfully retrieves the two types of cross-regional interactions at once. Performance across noise and sample size settings was globally on par with that of other existing methods, with the potential to reveal more precise information missed by alternative approaches. Preliminary application to experimental data revealed that in the resting brain, co-activations and causal modulations co-exist with a varying balance across regions. Our methodological pipeline offers a conceptually elegant alternative for the assessment of functional brain dynamics, and can be downloaded at https://c4science.ch/source/Sparse_logistic_regression.git.

ACOEC-FD: Ant Colony Optimization for Learning Brain Effective Connectivity Networks From Functional MRI and Diffusion Tensor Imaging

Identifying brain effective connectivity (EC) networks from neuroimaging data has become an effective tool that can evaluate normal brain functions and the injuries associated with neurodegenerative diseases. So far, there are many methods used to identify EC networks. However, most of the research currently focus on learning EC networks from single modal imaging data such as functional magnetic resonance imaging (fMRI) data. This paper proposes a new method, called ACOEC-FD, to learn EC networks from fMRI and diffusion tensor imaging (DTI) using ant colony optimization (ACO). First, ACOEC-FD uses DTI data to acquire some positively correlated relations among regions of interest (ROI), and takes them as anatomical constraint information to effectively restrict the search space of candidate arcs in an EC network. ACOEC-FD then achieves multi-modal imaging data integration by incorporating anatomical constraint information into the heuristic function of probabilistic transition rules to effectively encourage ants more likely to search for connections between structurally connected regions. Through simulation studies on generated datasets and real fMRI-DTI datasets, we demonstrate that the proposed approach results in improved inference results on EC compared to some methods that only used fMRI data.