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

A Fourier Description of Covariance, and Separation of Simultaneously Encoded Slices with In-Plane Acceleration in fMRI

Functional magnetic resonance imaging (fMRI) studies aim to identify localized neural regions associated with a cognitive task performed by the subject. An indirect measure of the brain activity is the blood oxygenation level dependent (BOLD) signal fluctuations observed within the complex-valued spatial frequencies measured over time. The standard practice in fMRI is to discard the phase information after image reconstruction, even with evidence of biological task-related change in the phase time-series. In the first aim of this dissertation, a complex-valued time-series covariance is derived as a linear combination of second order temporal Fourier frequency coefficients. As opposed to magnitude-only analysis, the complex-valued covariance increases the sensitivity and specificity in fMRI correlation analysis, which is particularly advantageous for low contrast-to-noise ratio (CNR) fMRI time-series. In the remaining aims, increased statistical significance is achieved through a higher sampling rate of the fMRI time-course, by simultaneously magnetizing multiple slice images. With multi-frequency band excitations, a single k-space readout reconstructs to an image of composite aliased slice images. To disentangle the signal, or aliased voxels, phase and coil encoding techniques are incorporated into the data acquisition and image reconstruction. Inter-slice signal leakage, which also manifests as improper placement of the BOLD signal, presents in the separated slice images from induced correlations as a result of suboptimal simultaneous multi-slice (SMS) reconstruction methods. In the second aim of this dissertation, the Multi-coil Separation of Parallel Encoded Complex-valued Slices (mSPECS) reconstruction method is proposed as a solution to preserve the activation statistics in the separated slice images through a Bayesian approach of sampling calibration images. In the third aim of this dissertation, the mSPECS reconstruction is extended to include In-Plane Acceleration (mSPECS-IPA), to reconstruct aliased slice images with additional in-plane subsampling using a two-dimensional orthogonal phase encoding derivation of Hadamard encoding. Mitigating induced correlations with mSPECS(-IPA), results in accurately placed functional activation in the previously aliased complex-valued slice images. The development of novel complex-valued analysis and reconstruction methods in fMRI strengthens the significance of the activation statistics and precludes inter-slice signal leakage, so the true underlying neural dynamics are modeled in complex-valued fMRI data analysis

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

Separation of Parallel Encoded Complex-Valued Slices (SPECS) From A Single Complex-Valued Aliased Coil Image

Purpose Achieving a reduction in scan time with minimal inter-slice signal leakage is one of the significant obstacles in parallel MR imaging. In fMRI, multiband-imaging techniques accelerate data acquisition by simultaneously magnetizing the spatial frequency spectrum of multiple slices. The SPECS model eliminates the consequential inter-slice signal leakage from the slice unaliasing, while maintaining an optimal reduction in scan time and activation statistics in fMRI studies. Materials and Methods When the combined k-space array is inverse Fourier reconstructed, the resulting aliased image is separated into the un-aliased slices through a least squares estimator. Without the additional spatial information from a phased array of receiver coils, slice separation in SPECS is accomplished with acquired aliased images in shifted FOV aliasing pattern, and a bootstrapping approach of incorporating reference calibration images in an orthogonal Hadamard pattern. Result The aliased slices are effectively separated with minimal expense to the spatial and temporal resolution. Functional activation is observed in the motor cortex, as the number of aliased slices is increased, in a bilateral finger tapping fMRI experiment. Conclusion The SPECS model incorporates calibration reference images together with coefficients of orthogonal polynomials into an un-aliasing estimator to achieve separated images, with virtually no residual artifacts and functional activation detection in separated images

CSF Signal as a Complex-Valued RETROICOR Regressor Removes Unwanted Physiological Signal and Increases the Accuracy of Spatial Correlation in Complex-Valued fMRI

Discarding the phase component of the time-series removes relevant biological information from a complex-valued signal. Although, commonly implemented retrospective image correction techniques fail to account for physiological artifacts in both the magnitude and phase components of the time-series. Using the CSF signal, observed during the data acquisition, as a complex-valued regressor increases the statistical power of fMRI analysis, through reducing unwanted physiological variability in the complex-valued signal of interest. The improved performance of implementing the complex-valued image correction methods is demonstrated with a comparison of magnitude-only and complex-valued spatial correlations