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 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

Acceleration Methods for MRI

Acceleration methods are a critical area of research for MRI. Two of the most important acceleration techniques involve parallel imaging and compressed sensing. These advanced signal processing techniques have the potential to drastically reduce scan times and provide radiologists with new information for diagnosing disease. However, many of these new techniques require solving difficult optimization problems, which motivates the development of more advanced algorithms to solve them. In addition, acceleration methods have not reached maturity in some applications, which motivates the development of new models tailored to these applications. This dissertation makes advances in three different areas of accelerations. The first is the development of a new algorithm (called B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithm or BARISTA), that solves a parallel MRI optimization problem with compressed sensing assumptions. BARISTA is shown to be 2-3 times faster and more robust to parameter selection than current state-of-the-art variable splitting methods. The second contribution is the extension of BARISTA ideas to non-Cartesian trajectories that also leads to a 2-3 times acceleration over previous methods. The third contribution is the development of a new model for functional MRI that enables a 3-4 factor of acceleration of effective temporal resolution in functional MRI scans. Several variations of the new model are proposed, with an ROC curve analysis showing that a combination low-rank/sparsity model giving the best performance in identifying the resting-state motor network.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120841/1/mmuckley_1.pd

Improving fMRI Analysis and MR Reconstruction with the Incorporation of MR Relaxivities and Correlation Effect Examination

Functional magnetic resonance imaging (fMRI) and functional connectivity MRI (fcMRI) use the physical principles of nuclear MR to provide high resolution representations of brain activity and connectivity. As the fMRI and fcMRI signals are detected from the excited hydrogen atoms in a magnetic field, the acquired data is determined by the underlying physical processes, such as the MR relaxivities. In fMRI and fcMRI, the Fourier encoded frequency space measurements are reconstructed into brain images, then spatiotemporal processing operations are applied before computing the brain activation and connectivity statistics. This dissertation seeks to utilize the magnetic resonance (MR) relaxivities at different stages of the fMRI pipeline, and aims to observe the statistical implications of the spatiotemporal processing operators on the fMRI and fcMRI data. We first develop a new statistical complex-valued nonlinear fMRI activation model that incorporates the MR relaxivities of gray matter into the brain activation statistics by utilizing the physical MR magnetization equation and the first scans of the fMRI data. We provide both theoretical and experimental comparison between the proposed model with the conventional linear magnitude-only and complex-valued fMRI activation models. Our statistical analysis results show that the new model provides better accuracy in computing brain activation statistics while theoretically eliminating false positives in non-gray matter areas. We then develop a linear Fourier reconstruction operator that incorporates the MR relaxivities into the image reconstruction process to account for their effects. The utilization of a linear system makes it achievable to theoretically compute the statistical implications of the use of the proposed operator. By focusing on longitudinal relaxation time, T1, to include into the image reconstruction, we show that the application of the proposed Fourier reconstruction operator provides better image contrast in the reconstructed images by recovering the information of the tissue characteristics that exist prior to T1 equilibrium. We finally examine the effects of time series preprocessing on computed functional correlations through the use of linear operators and provide ways of accounting for such effects in computing functional activity and connectivity statistics. Using both theoretical and experimentally acquired functional connectivity data, we examine the correlations induced by commonly used spatial and temporal processing operations. Furthermore, we provide the expansion of the statistical fcMRI and fMRI models to incorporate the quantified processing induced correlations in computing brain activity and connectivity statistics

Determination Of Correlations Induced By The Sense And Grappa Pmri Models With An Application To Mri Rf Coil Design

Functional connectivity MRI is fast becoming a widely used non-invasive means of observing the connectivity between regions of the brain. In order to more accurately observe fluctuations in the blood oxygenation level of hemoglobin, parallel MRI reconstruction models such as SENSE and GRAPPA can be used to reduce data acquisition time, effectively increasing spatial and temporal resolution. However, the statistical implications of these models are not generally known or considered in the final analysis of the reconstructed data. In this dissertation, the non-biological correlations artificially induced by the SENSE and GRAPPA models are precisely quantified through the development of a real-valued isomorphism that represents each model in terms of a series of linear matrix operators. Using both theoretical and experimentally acquired functional connectivity data, these artificial correlations are shown to corrupt functional connectivity conclusions by incurring false positives, where regions of the brain appear to be correlated when they are not, and false negatives, where regions of the brain appear to be uncorrelated when they actually are. With a precise quantification of the artificial correlations induced by SENSE, a new cost function for optimizing the design of RF coil arrays has also been developed and implemented to generate more favorable magnetic fields for functional connectivity studies in specific brain regions. Images reconstructed with such arrays have an improved signal-to-noise ratio and a minimal SENSE induced correlation within the regions of interest, effectively improving the accuracy and reliability of functional connectivity studies