A Bayesian Variable Selection Approach Yields Improved Detection of Brain Activation From Complex-Valued fMRI

Voxel functional magnetic resonance imaging (fMRI) time courses are complex-valued signals giving rise to magnitude and phase data. Nevertheless, most studies use only the magnitude signals and thus discard half of the data that could potentially contain important information. Methods that make use of complex-valued fMRI (CV-fMRI) data have been shown to lead to superior power in detecting active voxels when compared to magnitude-only methods, particularly for small signal-to-noise ratios (SNRs). We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data. We develop models with complex-valued spike-and-slab priors on the activation parameters that are able to combine the magnitude and phase information. We present a complex-valued EM variable selection algorithm that leads to fast detection at the voxel level in CV-fMRI slices and also consider full posterior inference via Markov chain Monte Carlo (MCMC). Model performance is illustrated through extensive simulation studies, including the analysis of physically based simulated CV-fMRI slices. Finally, we use the complex-valued Bayesian approach to detect active voxels in human CV-fMRI from a healthy individual who performed unilateral finger tapping in a designed experiment. The proposed approach leads to improved detection of activation in the expected motor-related brain regions and produces fewer false positive results than other methods for CV-fMRI. Supplementary materials for this article are available online

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

Incorporating Relaxivities to More Accurately Reconstruct MR Images

Purpose To develop a mathematical model that incorporates the magnetic resonance relaxivities into the image reconstruction process in a single step. Materials and methods In magnetic resonance imaging, the complex-valued measurements of the acquired signal at each point in frequency space are expressed as a Fourier transformation of the proton spin density weighted by Fourier encoding anomalies: T2⁎, T1, and a phase determined by magnetic field inhomogeneity (∆B) according to the MR signal equation. Such anomalies alter the expected symmetry and the signal strength of the k-space observations, resulting in images distorted by image warping, blurring, and loss in image intensity. Although T1 on tissue relaxation time provides valuable quantitative information on tissue characteristics, the T1 recovery term is typically neglected by assuming a long repetition time. In this study, the linear framework presented in the work of Rowe et al., 2007, and of Nencka et al., 2009 is extended to develop a Fourier reconstruction operation in terms of a real-valued isomorphism that incorporates the effects of T2⁎, ∆B, and T1. This framework provides a way to precisely quantify the statistical properties of the corrected image-space data by offering a linear relationship between the observed frequency space measurements and reconstructed corrected image-space measurements. The model is illustrated both on theoretical data generated by considering T2⁎, T1, and/or ∆B effects, and on experimentally acquired fMRI data by focusing on the incorporation of T1. A comparison is also made between the activation statistics computed from the reconstructed data with and without the incorporation of T1 effects. Result Accounting for T1 effects in image reconstruction is shown to recover image contrast that exists prior to T1 equilibrium. The incorporation of T1 is also shown to induce negligible correlation in reconstructed images and preserve functional activations. Conclusion With the use of the proposed method, the effects of T2⁎ and ∆B can be corrected, and T1 can be incorporated into the time series image-space data during image reconstruction in a single step. Incorporation of T1 provides improved tissue segmentation over the course of time series and therefore can improve the precision of motion correction and image registration

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

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

A Statistical fMRI Model for Differential T\u3csub\u3e2\u3c/sub\u3e* Contrast Incorporating T\u3csub\u3e1\u3c/sub\u3e and T\u3csub\u3e2\u3c/sub\u3e* of Gray Matter

Relaxation parameter estimation and brain activation detection are two main areas of study in magnetic resonance imaging (MRI) and functional magnetic resonance imaging (fMRI). Relaxation parameters can be used to distinguish voxels containing different types of tissue whereas activation determines voxels that are associated with neuronal activity. In fMRI, the standard practice has been to discard the first scans to avoid magnetic saturation effects. However, these first images have important information on the MR relaxivities for the type of tissue contained in voxels, which could provide pathological tissue discrimination. It is also well-known that the voxels located in gray matter (GM) contain neurons that are to be active while the subject is performing a task. As such, GM MR relaxivities can be incorporated into a statistical model in order to better detect brain activation. Moreover, although the MR magnetization physically depends on tissue and imaging parameters in a nonlinear fashion, a linear model is what is conventionally used in fMRI activation studies. In this study, we develop a statistical fMRI model for Differential T2⁎ ConTrast Incorporating T1 and T2⁎ of GM, so-called DeTeCT-ING Model, that considers the physical magnetization equation to model MR magnetization; uses complex-valued time courses to estimate T1 and T2⁎ for each voxel; then incorporates gray matter MR relaxivities into the statistical model in order to better detect brain activation, all from a single pulse sequence by utilizing the first scans

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