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Open Access Publications from the University of California

Scholarly Works (6 results)

  • Article
  • Peer Reviewed
UC San Diego Previously Published Works (2017)
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.
    Cover page: The global signal in fMRI: Nuisance or Information?
    • Article
    • Peer Reviewed
    UC San Diego Previously Published Works (2017)
    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.
      Cover page: Global signal regression acts as a temporal downweighting process in resting-state fMRI.
      • Article
      • Peer Reviewed
      UC San Diego Previously Published Works (2019)
      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.
        Cover page: Nuisance effects and the limitations of nuisance regression in dynamic functional connectivity fMRI.
        • Thesis
        • Peer Reviewed
        UC San Diego Electronic Theses and Dissertations (2019)

        This dissertation considers the problems of sparse signal recovery (SSR) and nuisance regression in functional MRI (fMRI). The first part of the dissertation introduces a Bayesian framework to recover sparse non-negative solutions in under-determined systems of linear equations. A novel class of probability density functions named Rectified Gaussian Scale Mixtures (R-GSM) is proposed to model the sparse non-negative solution of interest. A Bayesian inference algorithm called Rectified Sparse Bayesian Learning (R-SBL) is developed, which robustly recovers the solution in numerous experimental settings and outperforms the state-of-the-art SSR approaches by a large margin.

        The rest of the dissertation investigates the effects of nuisance regression in fMRI. Chapter 3 proposes a mathematical framework to investigate the effects of global signal regression (GSR). GSR is a widely used nuisance removal approach in resting-state fMRI, however its use has been controversial since it introduces artifactual anti-correlations between pairs of fMRI signals. The proposed framework shows that the main effects of GSR can be well-approximated as a temporal down-weighting or temporal censoring process, in which the data from time points with relatively large GS magnitudes are greatly attenuated (or censored) while data from time points with relatively small GS magnitudes are largely retained. The censoring approximation reveals that the anti-correlated networks are intrinsic to the brain's functional organization and are not simply an artifact of GSR.

        In Chapters 4 and 5, the effects of nuisance terms on the relationship between pairs of fMRI signals both before and after nuisance regression are investigated. It is shown that geometric norms of various nuisance regressors can significantly influence the correlation-based functional connectivity (FC) estimates in both static FC and dynamic FC studies. It is demonstrated that nuisance regression is largely ineffective in removing the significant correlations observed between FC estimates and nuisance norms. Consequently, a mathematical bound is derived on the difference between correlation coefficients before and after nuisance regression. This bound restricts the removal of nuisance norm effects from FC estimates.

          Cover page: Rectified Sparse Bayesian Learning and Effects and Limitations of Nuisance Regression in Functional MRI
          • Article
          • Peer Reviewed
          UC San Diego Previously Published Works (2018)
          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.
            Cover page: Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem
            • Article
            • Peer Reviewed
            UC San Diego Previously Published Works (2018)
            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.
              Cover page: A unified framework for sparse non-negative least squares using multiplicative updates and the non-negative matrix factorization problem
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