Iain P. Bruce

A statistical examination of SENSE image reconstruction via an isomorphism representation.

In magnetic resonance imaging, the parallel acquisition of subsampled spatial frequencies from an array of multiple receiver coils has become a common means of reducing data acquisition time. SENSitivity Encoding (SENSE) is a popular parallel image reconstruction model that uses a complex-valued least squares estimation process to unfold aliased images. In this article, the linear mathematical framework derived in Rowe et al. [J Neurosci Meth 159 (2007) 361-369] is built upon to perform image reconstruction with subsampled data acquired from multiple receiver coils, where the SENSE model is represented as a real-valued isomorphism. A statistical analysis is performed of the various image reconstruction operators utilized in the SENSE model, with an emphasis placed on the effects of each operator on voxel means, variances and correlations. It is shown that, despite the attractiveness of models that unfold the aliased images from subsampled data, there is an artificial correlation induced between reconstructed voxels from the different folds of aliased images. As such, the mathematical framework outlined in this manuscript could be further developed to provide a means of accounting for this unavoidable correlation induced by image reconstruction operators.

3D-MB-MUSE: A robust 3D multi-slab, multi-band and multi-shot reconstruction approach for ultrahigh resolution diffusion MRI

Abstract Recent advances in achieving ultrahigh spatial resolution (e.g. sub‐millimeter) diffusion MRI (dMRI) data have proven highly beneficial in characterizing tissue microstructures in organs such as the brain. However, the routine acquisition of in‐vivo dMRI data at such high spatial resolutions has been largely prohibited by factors that include prolonged acquisition times, motion induced artifacts, and low SNR. To overcome these limitations, we present here a framework for acquiring and reconstructing 3D multi‐slab, multi‐band and interleaved multi‐shot EPI data, termed 3D‐MB‐MUSE. Through multi‐band excitations, the simultaneous acquisition of multiple 3D slabs enables whole brain dMRI volumes to be acquired in‐vivo on a 3 T clinical MRI scanner at high spatial resolution within a reasonably short amount of time. Representing a true 3D model, 3D‐MB‐MUSE reconstructs an entire 3D multi‐band, multi‐shot dMRI slab at once while simultaneously accounting for coil sensitivity variations across the slab as well as motion induced artifacts commonly associated with both 3D and multi‐shot diffusion imaging. Such a reconstruction fully preserves the SNR advantages of both 3D and multi‐shot acquisitions in high resolution dMRI images by removing both motion and aliasing artifacts across multiple dimensions. By enabling ultrahigh resolution dMRI for routine use, the 3D‐MB‐MUSE framework presented here may prove highly valuable in both clinical and research applications. HighlightsAcquisition of whole brain diffusion volumes with ultrahigh resolution and high SNR.3D‐MB‐MUSE framework reconstructs 3D multi‐slab, multi‐band and multi‐shot EPI data.3D‐MB‐MUSE accounts for motion artifacts throughout 3D multi‐shot acquisition.Reconstruction incorporates variable coil sensitivities across a thick 3D slab.Facilitates routine clinical acquisition of DTI at submillimeter resolutions.

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.

The SENSE-Isomorphism Theoretical Image Voxel Estimation (SENSE-ITIVE) model for reconstruction and observing statistical properties of reconstruction operators

The acquisition of sub-sampled data from an array of receiver coils has become a common means of reducing data acquisition time in MRI. Of the various techniques used in parallel MRI, SENSitivity Encoding (SENSE) is one of the most common, making use of a complex-valued weighted least squares estimation to unfold the aliased images. It was recently shown in Bruce et al. [Magn. Reson. Imag. 29(2011):1267-1287] that when the SENSE model is represented in terms of a real-valued isomorphism,it assumes a skew-symmetric covariance between receiver coils, as well as an identity covariance structure between voxels. In this manuscript, we show that not only is the skew-symmetric coil covariance unlike that of real data, but the estimated covariance structure between voxels over a time series of experimental data is not an identity matrix. As such, a new model, entitled SENSE-ITIVE, is described with both revised coil and voxel covariance structures. Both the SENSE and SENSE-ITIVE models are represented in terms of real-valued isomorphisms, allowing for a statistical analysis of reconstructed voxel means, variances, and correlations resulting from the use of different coil and voxel covariance structures used in the reconstruction processes to be conducted. It is shown through both theoretical and experimental illustrations that the miss-specification of the coil and voxel covariance structures in the SENSE model results in a lower standard deviation in each voxel of the reconstructed images, and thus an artificial increase in SNR, compared to the standard deviation and SNR of the SENSE-ITIVE model where both the coil and voxel covariances are appropriately accounted for. It is also shown that there are differences in the correlations induced by the reconstruction operations of both models, and consequently there are differences in the correlations estimated throughout the course of reconstructed time series. These differences in correlations could result in meaningful differences in interpretation of results.

A statistical fMRI model for differential T2* contrast incorporating T1 and T2* 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.

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.

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.

Simultaneous and inherent correction of B0 and eddy-current induced distortions in high-resolution diffusion MRI using reversed polarity gradients and multiplexed sensitivity encoding (RPG-MUSE)

&NA; In diffusion MRI (dMRI), static magnetic field (B0) inhomogeneity and time varying gradient eddy currents induce spatial distortions in reconstructed images. These distortions are exacerbated when high spatial resolutions are used, and many field‐mapping based correction techniques often only acquire maps of static B0 distortion, which are not adequate for correcting eddy current induced image distortions. This report presents a novel technique, termed RPG‐MUSE, for achieving distortion‐free high‐resolution diffusion MRI by integrating reversed polarity gradients (RPG) into the multi‐shot echo planar imaging acquisition scheme used in multiplexed sensitivity encoding (MUSE). By alternating the phase encoding direction between shots in both baseline and diffusion‐weighted acquisitions, maps of both static B0 and eddy current induced field inhomogeneities can be inherently derived, without the need for additional data acquisition. Through both 2D and 3D encoded dMRI acquisitions, it is shown that an RPG‐MUSE reconstruction can simultaneously achieve high spatial resolution, high spatial fidelity, and subsequently, high accuracy in diffusion metrics.