Nuisance effects in inter-scan functional connectivity estimates before and after nuisance regression.

In resting-state functional MRI, the correlation between blood-oxygenation-level-dependent (BOLD) signals across brain regions is used to estimate the functional connectivity (FC) of the brain. FC estimates are prone to the influence of nuisance factors including scanner-related artifacts and physiological modulations of the BOLD signal. Nuisance regression is widely performed to reduce the effect of nuisance factors on FC estimates on a per-scan basis. However, a dedicated analysis of nuisance effects on the variability of FC metrics across a collection of scans has been lacking. This work investigates the effects of nuisance factors on the variability of FC estimates across a collection of scans both before and after nuisance regression. Inter-scan variations in FC estimates are shown to be significantly correlated with the geometric norms of various nuisance terms, including head motion measurements, signals derived from white-matter and cerebrospinal regions, and the whole-brain global signal (GS) both before and after nuisance regression. In addition, it is shown that GS regression (GSR) can introduce GS norm-related fluctuations that are negatively correlated with inter-scan FC estimates. The empirical results are shown to be largely consistent with the predictions of a theoretical framework previously developed for the characterization of dynamic FC measures. This work shows that caution must be exercised when interpreting inter-scan FC measures across scans both before and after nuisance regression.

Nuisance effects and the limitations of nuisance regression in dynamic functional connectivity fMRI.

In resting-state fMRI, dynamic functional connectivity (DFC) measures are used to characterize temporal changes in the brain's intrinsic functional connectivity. A widely used approach for DFC estimation is the computation of the sliding window correlation between blood oxygenation level dependent (BOLD) signals from different brain regions. Although the source of temporal fluctuations in DFC estimates remains largely unknown, there is growing evidence that they may reflect dynamic shifts between functional brain networks. At the same time, recent findings suggest that DFC estimates might be prone to the influence of nuisance factors such as the physiological modulation of the BOLD signal. Therefore, nuisance regression is used in many DFC studies to regress out the effects of nuisance terms prior to the computation of DFC estimates. In this work we examined the relationship between seed-specific sliding window correlation-based DFC estimates and nuisance factors. We found that DFC estimates were significantly correlated with temporal fluctuations in the magnitude (norm) of various nuisance regressors. Strong correlations between the DFC estimates and nuisance regressor norms were found even when the underlying correlations between the nuisance and fMRI time courses were relatively small. We then show that nuisance regression does not necessarily eliminate the relationship between DFC estimates and nuisance norms, with significant correlations observed between the DFC estimates and nuisance norms even after nuisance regression. We present theoretical bounds on the difference between DFC estimates obtained before and after nuisance regression and relate these bounds to limitations in the efficacy of nuisance regression with regards to DFC estimates.

Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem.

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares problem (S-NNLS). We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R-GSM), to model the sparsity enforcing prior distribution for the signal of interest. The R-GSM prior encompasses a variety of heavy-tailed distributions such as the rectified Laplacian and rectified Student-t distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM-based method, we estimate the hyper-parameters and obtain a point estimate for the solution of interest. We refer to this proposed method as rectified Sparse Bayesian Learning (R-SBL). We provide four EM-based R-SBL variants that offer a range of options to trade-off computational complexity to the quality of the E-step computation. These methods include the Markov Chain Monte Carlo EM, linear minimum mean square estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery, and is very robust against the structure of the design matrix.

A unified framework for sparse non-negative least squares using multiplicative updates and the non-negative matrix factorization problem.

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.

The global signal in fMRI: Nuisance or Information?

The global signal is widely used as a regressor or normalization factor for removing the effects of global variations in the analysis of functional magnetic resonance imaging (fMRI) studies. However, there is considerable controversy over its use because of the potential bias that can be introduced when it is applied to the analysis of both task-related and resting-state fMRI studies. In this paper we take a closer look at the global signal, examining in detail the various sources that can contribute to the signal. For the most part, the global signal has been treated as a nuisance term, but there is growing evidence that it may also contain valuable information. We also examine the various ways that the global signal has been used in the analysis of fMRI data, including global signal regression, global signal subtraction, and global signal normalization. Furthermore, we describe new ways for understanding the effects of global signal regression and its relation to the other approaches.

Global signal regression acts as a temporal downweighting process in resting-state fMRI.

In resting-state functional MRI (rsfMRI), the correlation between blood oxygenation level dependent (BOLD) signals across different brain regions is used to estimate the functional connectivity of the brain. This approach has led to the identification of a number of resting-state networks, including the default mode network (DMN) and the task positive network (TPN). Global signal regression (GSR) is a widely used pre-processing step in rsfMRI that has been shown to improve the spatial specificity of the estimated resting-state networks. In GSR, a whole brain average time series, known as the global signal (GS), is regressed out of each voxel time series prior to the computation of the correlations. However, the use of GSR is controversial because it can introduce artifactual negative correlations. For example, it has been argued that anticorrelations observed between the DMN and TPN are primarily an artifact of GSR. Despite the concerns about GSR, there is currently no consensus regarding its use. In this paper, we introduce a new framework for understanding the effects of GSR. In particular, we show that the main effects of GSR can be well approximated as a temporal downweighting process in which the data from time points with relatively large GS magnitudes are greatly attenuated while data from time points with relatively small GS magnitudes are largely unaffected. Furthermore, we show that a limiting case of this downweighting process in which data from time points with large GS magnitudes are censored can also approximate the effects of GSR. In other words, the correlation maps obtained after GSR show a high degree of spatial similarity (including the presence of anticorrelations between the DMN and TPN) with maps obtained using only the uncensored (i.e. retained) time points. Since the data from these retained time points are unaffected by the censoring process, this finding suggests that the observed anticorrelations inherently exist in the data from time points with small GS magnitudes and are not simply an artifact of GSR.

The Effects of Global Signal Regression on Estimates of Resting-State Blood Oxygen-Level-Dependent Functional Magnetic Resonance Imaging and Electroencephalogram Vigilance Correlations.

Global signal regression (GSR) is a commonly used although controversial preprocessing approach in the analysis of resting-state blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) data. Although the effects of GSR on resting-state functional connectivity measures have received much attention, there has been relatively little attention devoted to its effects on studies looking at the relationship between resting-state BOLD measures and independent measures of brain activity. In this study, we used simultaneously acquired electroencephalogram (EEG)-fMRI data in humans to examine the effects of GSR on the correlation between resting-state BOLD fluctuations and EEG vigilance measures. We show that GSR leads to a positive shift in the correlation between the BOLD and vigilance measures. This shift leads to a reduction in the spatial extent of negative correlations in widespread brain areas, including the visual cortex, but leads to the appearance of positive correlations in other areas, such as the cingulate gyrus. The results obtained using GSR are consistent with those of a temporal censoring process in which the correlation is computed using a temporal subset of the data. Since the data from these retained time points are unaffected by the censoring process, this finding suggests that the positive correlations in cingulate gyrus are not simply an artifact of GSR.

A computer vision based candidate for functional balance test.

Balance in humans is a motor skill based on complex multimodal sensing, processing and control. Ability to maintain balance in activities of daily living (ADL) is compromised due to aging, diseases, injuries and environmental factors. Center for Disease Control and Prevention (CDC) estimate of the costs of falls among older adults was $34 billion in 2013 and is expected to reach $54.9 billion in 2020. In this paper, we present a brief review of balance impairments followed by subjective and objective tools currently used in clinical settings for human balance assessment. We propose a novel computer vision (CV) based approach as a candidate for functional balance test. The test will take less than a minute to administer and expected to be objective, repeatable and highly discriminative in quantifying ability to maintain posture and balance. We present an informal study with preliminary data from 10 healthy volunteers, and compare performance with a balance assessment system called BTrackS Balance Assessment Board. Our results show high degree of correlation with BTrackS. The proposed system promises to be a good candidate for objective functional balance tests and warrants further investigations to assess validity in clinical settings, including acute care, long term care and assisted living care facilities. Our long term goals include non-intrusive approaches to assess balance competence during ADL in independent living environments.