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 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

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

Quantification of the Statistical Effects of Spatiotemporal Processing of Nontask fMRI Data

Nontask functional magnetic resonance imaging (fMRI) has become one of the most popular noninvasive areas of brain mapping research for neuroscientists. In nontask fMRI, various sources of “noise” corrupt the measured blood oxygenation level-dependent signal. Many studies have aimed to attenuate the noise in reconstructed voxel measurements through spatial and temporal processing operations. While these solutions make the data more “appealing,” many commonly used processing operations induce artificial correlations in the acquired data. As such, it becomes increasingly more difficult to derive the true underlying covariance structure once the data have been processed. As the goal of nontask fMRI studies is to determine, utilize, and analyze the true covariance structure of acquired data, such processing can lead to inaccurate and misleading conclusions drawn from the data if they are unaccounted for in the final connectivity analysis. In this article, we develop a framework that represents the spatiotemporal processing and reconstruction operations as linear operators, providing a means of precisely quantifying the correlations induced or modified by such processing rather than by performing lengthy Monte Carlo simulations. A framework of this kind allows one to appropriately model the statistical properties of the processed data, optimize the data processing pipeline, characterize excessive processing, and draw more accurate functional connectivity conclusions

Diffusion in Sephadex Gel Structures: Time Dependency Revealed by Multi-Sequence Acquisition over a Broad Diffusion Time Range

It has been increasingly reported that in biological tissues diffusion-weighted MRI signal attenuation deviates from mono-exponential decay, especially at high b-values. A number of diffusion models have been proposed to characterize this non-Gaussian diffusion behavior. One of these models is the continuous-time random-walk (CTRW) model, which introduces two new parameters: a fractional order time derivative α and a fractional order spatial derivative β. These new parameters have been linked to intravoxel diffusion heterogeneities in time and space, respectively, and are believed to depend on diffusion times. Studies on this time dependency are limited, largely because the diffusion time cannot vary over a board range in a conventional spin-echo echo-planar imaging sequence due to the accompanying T2 decays. In this study, we investigated the time-dependency of the CTRW model in Sephadex gel phantoms across a broad diffusion time range by employing oscillating-gradient spin-echo, pulsed-gradient spin-echo, and pulsed-gradient stimulated echo sequences. We also performed Monte Carlo simulations to help understand our experimental results. It was observed that the diffusion process fell into the Gaussian regime at extremely short diffusion times whereas it exhibited a strong time dependency in the CTRW parameters at longer diffusion times

A fractional motion diffusion model for grading pediatric brain tumors

Objectives: To demonstrate the feasibility of a novel fractional motion (FM) diffusion model for distinguishing low- versus high-grade pediatric brain tumors; and to investigate its possible advantage over apparent diffusion coefficient (ADC) and/or a previously reported continuous-time random-walk (CTRW) diffusion model. Materials and methods: With approval from the institutional review board and written informed consents from the legal guardians of all participating patients, this study involved 70 children with histopathologically-proven brain tumors (30 low-grade and 40 high-grade). Multi-b-value diffusion images were acquired and analyzed using the FM, CTRW, and mono-exponential diffusion models. The FM parameters, Dfm, φ, ψ (non-Gaussian diffusion statistical measures), and the CTRW parameters, Dm, α, β (non-Gaussian temporal and spatial diffusion heterogeneity measures) were compared between the low- and high-grade tumor groups by using a Mann-Whitney-Wilcoxon U test. The performance of the FM model for differentiating between low- and high-grade tumors was evaluated and compared with that of the CTRW and the mono-exponential models using a receiver operating characteristic (ROC) analysis. Results: The FM parameters were significantly lower (p < 0.0001) in the high-grade (Dfm: 0.81 ± 0.26, φ: 1.40 ± 0.10, ψ: 0.42 ± 0.11) than in the low-grade (Dfm: 1.52 ± 0.52, φ: 1.64 ± 0.13, ψ: 0.67 ± 0.13) tumor groups. The ROC analysis showed that the FM parameters offered better specificity (88% versus 73%), sensitivity (90% versus 82%), accuracy (88% versus 78%), and area under the curve (AUC, 93% versus 80%) in discriminating tumor malignancy compared to the conventional ADC. The performance of the FM model was similar to that of the CTRW model. Conclusions: Similar to the CTRW model, the FM model can improve differentiation between low- and high-grade pediatric brain tumors over ADC