Bayesian source separation of fMRI signals

In analyzing the results of functional magnetic resonance imaging, the identification of significant activation in voxels is a crucial task. In computing the activation level, a standard method is to select an assumed to be known reference function and perform a multiple regression of the time courses on it and a linear trend. Once the linear trend is found, the correlation between the assumed to be known reference function and the detrended observed time-course in each voxel is computed and voxels colored according to their correlation. But the most important question is: How do we choose the reference function? This paper develops a Bayesian statistical approach to determining the underlying source reference function based on Bayesian source separation, and uses it on both simulated and real fMRI data. This underlying reference function is the unobserved response due the presentation of the experimental stimulus

Signal Processing Spreads a Voxel’s Temporal Frequency Task-Activated Peak and Induces Spatial Correlations in Dual-Task Complex-Valued fMRI

Roll 213. Barth's Counsel Schedule / Bannon's History Copies. Image 7 of 21. (13 October, 1955) [PHO 1.213.7]The Boleslaus Lukaszewski (Father Luke) Photographs contain more than 28,000 images of Saint Louis University people, activities, and events between 1951 and 1970. The photographs were taken by Boleslaus Lukaszewski (Father Luke), a Jesuit priest and member of the University's Philosophy Department faculty

Complex-valued Time Series Modeling for Improved Activation Detection in fMRI Studies

A complex-valued data-based model with th order autoregressive errors and general real/imaginary error covariance structure is proposed as an alternative to the commonly used magnitude-only data-based autoregressive model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and compared for experimental and simulated data. For a dataset from a right-hand finger-tapping experiment, the activation map obtained using complex-valued modeling more clearly identifies the primary activation region (left functional central sulcus) than the magnitude-only model. Such improved accuracy in mapping the left functional central sulcus has important implications in neurosurgical planning for tumor and epilepsy patients. Additionally, we develop magnitude and phase detrending procedures for complex-valued time series and examine the effect of spatial smoothing. These methods improve the power of complex-valued data-based activation statistics. Our results advocate for the use of the complex-valued data and the modeling of its dependence structures as a more efficient and reliable tool in fMRI experiments over the current practice of using only magnitude-valued datasets

Quantifying the Statistical Impact of GRAPPA in fcMRI Data with a Real-Valued Isomorphism

The interpolation of missing spatial frequencies through the generalized auto-calibrating partially parallel acquisitions (GRAPPA) parallel magnetic resonance imaging (MRI) model implies a correlation is induced between the acquired and reconstructed frequency measurements. As the parallel image reconstruction algorithms in many medical MRI scanners are based on the GRAPPA model, this study aims to quantify the statistical implications that the GRAPPA model has in functional connectivity studies. The linear mathematical framework derived in the work of Rowe , 2007, is adapted to represent the complex-valued GRAPPA image reconstruction operation in terms of a real-valued isomorphism, and a statistical analysis is performed on the effects that the GRAPPA operation has on reconstructed voxel means and correlations. The interpolation of missing spatial frequencies with the GRAPPA model is shown to result in an artificial correlation induced between voxels in the reconstructed images, and these artificial correlations are shown to reside in the low temporal frequency spectrum commonly associated with functional connectivity. Through a real-valued isomorphism, such as the one outlined in this manuscript, the exact artificial correlations induced by the GRAPPA model are not simply estimated, as they would be with simulations, but are precisely quantified. If these correlations are unaccounted for, they can incur an increase in false positives in functional connectivity studies

Complex-Valued Time-Series Correlation Increases Sensitivity in FMRI Analysis

Purpose To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis. Materials and Methods The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform of MO and CV correlations for varying degrees of task related magnitude and phase amplitude change in the time-series. The increased sensitivity of the complex-valued Fourier representation of correlation is also demonstrated with experimental human data. Since the correlation description in the temporal frequency domain is represented as a summation of second order temporal frequencies, the correlation is easily divided into experimentally relevant frequency bands for each voxel\u27s temporal frequency spectrum. The MO and CV correlations for the experimental human data are analyzed for four voxels of interest (VOIs) to show the framework with high and low contrast-to-noise ratios in the motor cortex and the supplementary motor cortex. Results The simulation demonstrates the increased strength of CV correlations over MO correlations for low magnitude contrast-to-noise time-series. In the experimental human data, the MO correlation maps are noisier than the CV maps, and it is more difficult to distinguish the motor cortex in the MO correlation maps after spatial processing. Conclusions Including both magnitude and phase in the spatial correlation computations more accurately defines the correlated left and right motor cortices. Sensitivity in correlation analysis is important to preserve the signal of interest in fMRI data sets with high noise variance, and avoid excessive processing induced correlation

Impacts of Simultaneous Multislice Acquisition on Sensitivity and Specificity in fMRI

Simultaneous multislice (SMS) imaging can be used to decrease the time between acquisition of fMRI volumes, which can increase sensitivity by facilitating the removal of higher-frequency artifacts and boosting effective sample size. The technique requires an additional processing step in which the slices are separated, or unaliased, to recover the whole brain volume. However, this may result in signal “leakage” between aliased locations, i.e., slice “leakage,” and lead to spurious activation (decreased specificity). SMS can also lead to noise amplification, which can reduce the benefits of decreased repetition time. In this study, we evaluate the original slice-GRAPPA (no leak block) reconstruction algorithmand acceleration factor (AF = 8) used in the fMRI data in the young adult Human Connectome Project (HCP). We also evaluate split slice-GRAPPA (leak block), which can reduce slice leakage. We use simulations to disentangle higher test statistics into true positives (sensitivity) and false positives (decreased specificity). Slice leakage was greatly decreased by split slice-GRAPPA. Noise amplification was decreased by using moderate acceleration factors (AF = 4). We examined slice leakage in unprocessed fMRI motor task data from the HCP. When data were smoothed, we found evidence of slice leakage in some, but not all, subjects. We also found evidence of SMS noise amplification in unprocessed task and processed resting-state HCP data

A Bayesian Factor Analysis Model with Generalized Prior Information

In the Bayesian approach to factor analysis, available prior knowledge regarding the model parameters is quantified in the form of prior distributions and incorporated into the inferences. The incorporation of prior knowledge has the added consequence of eliminating the ambiguity of rotation found in the traditional factor analysis model. Previous Bayesian factor analysis work (Press & Shigemasu 1989, & Press 1998, Rowe 2000a, and Rowe 2000b), has considered mainly natural conjugate prior distributions for the model parameters. As is mentioned in Press (1982), Rothenburg (1963) pointed out that with a natural conjugate prior distribution, the elements in the covariance matrices are constrained and thus may not be rich enough to permit freedom of assessment. In this paper, generalized natural conjugate distributions are used to quantify and incorporate available prior information which permit complete freedom of assessment

Bayesian Source Separation with Jointly Distributed Mean and Mixing Coefficients vie MCMC and ICM

Recent source separation work has described a model which assumes a nonzero overall mean and incorporates prior knowledge regarding it. This is significant because source separation models that have previously been presented have assumed that the overall mean is zero. However, this work specified that the prior distribution which quantifies available prior knowledge regarding the overall mean be independent of the mixing coefficient matrix. The current paper generalizes this work by quantifying available prior information regarding the overall mean and mixing matrix with the use of joint prior distributions. This prior knowledge in the prior distributions is incorporated into the inferences along with the current data. Conjugate normal and generalized conjugate normal distributions are used. Algorithms for estimating the parameters of the model from the joint posterior distribution using both Gibbs sampling a Markov chain Monte Carlo method and the iterated conditional modes algorithm a deterministic optimization technique for marginal mean and maximum a posterior estimates respectively

A Model for Bayesian Source Separation with the Overall Mean

Typically in source separation models the overall mean as well as the mean of the sources are assumed to be zero. This paper assumes a nonzero overall mean and a nonzero source mean, quantifies available prior knowledge regarding them and other parameters. This prior knowledge is incorporated into the inferences along with the current data in the Bayesian approach to source separation. Vague, conjugate normal, and generalized conjugate normal distributions are used to quantify knowledge for the overall mean vector. Algorithms for estimating the parameters of the model from the joint posterior distribution are derived and determined statistically from the posterior distribution using both Gibbs sampling a Markov chain Monte Carlo method and the iterated conditional modes algorithm a deterministic optimization technique for marginal mean and maximum a posterior estimates respectively. This is a methodological paper which outlines the model without the use of a numerical example