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

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

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

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

Greenhouse gas emissions from soils under organic management

This report was presented at the UK Organic Research 2002 Conference. Land emissions of N2O, CO2 and NH3 have been subject to little study under organic systems, yet form important aspects of sustainability of such systems. We describe innovative methods developed at SAC to assess trace gas emission using both automatic closed chamber systems (intensive, short term monitoring) and manually-operated closed chamber systems (occasional, long term monitoring). Long-term data were collected from organic ley-arable rotation trials in North-east of Scotland. Short term data were collected to show the effect of timing and depth of ploughing-out of the ley phase on gas emissions. Ploughing gave a shortterm stimulation of CO2 and, more markedly, of N2O emission. Emissions of N2O from organic grass-clover leys were considerably lower than from conventional grass. However, some N2O emissions from organic arable are higher than from conventional systems, particularly in the first year after ploughing out ley. Ammonia emissions after spreading manure on grass were significant in the summer, though only short-lived

Noise Assumptions in Complex-Valued SENSE MR Image Reconstruction

In fMRI, brain images are not measured instantaneously and a volume of images can take two seconds to acquire at a low 64x64 resolution. Significant effort has been put forth on many fronts to decrease image acquisition time including parallel imaging. In parallel imaging, sub-sampled spatial frequency points are measured in parallel and combined to form a single image. Measurement time is decreased at the expense of increased image reconstruction difficulty and time. One significant parallel imaging technique known as SENSE utilizes a complex-valued regression coefficient estimation process with transposes replaced by conjugate transposes. However, in SENSE the noise structure is not properly modeled. This work properly models the noise structure for complex-valued least squares regression. Differences in estimated images between SENSE and our new estimation procedure are evaluated

Signal and Noise in Complex-Valued SENSE MR Image Reconstruction

In fMRI, brain images are not measured instantaneously and a volume of images can take two seconds to acquire at a low 64x64 resolution. Significant effort has been put forth on many fronts to decrease image acquisition time including parallel imaging. In parallel imaging, sub-sampled spatial frequency points are measured in parallel and combined to form a single image. Measurement time is decreased at the expense of increased image reconstruction difficulty and time. One significant parallel imaging technique known as SENSE utilizes a complex-valued regression coefficient estimation process with transposes replaced by conjugate transposes. However, in SENSE the noise structure is not properly modeled. This work properly models the noise structure for complex-valued least squares regression. Differences in estimated images between SENSE and our new estimation procedure are evaluated

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

The uncertainty contagion: Revealing the interrelated, cascading uncertainties of managed retreat

Managed retreat presents a dilemma for at-risk communities, and the planning practitioners and decisionmakers working to address natural hazard and climate change risks. The dilemma boils down to the countervailing imperatives of moving out of harm’s way versus retaining ties to community and place. While there are growing calls for its use, managed retreat remains challenging in practice—across diverse settings. The approach has been tested with varied success in a number of countries, but significant uncertainties remain, such as regarding who ‘manages’ it, when and how it should occur, at whose cost, and to where? Drawing upon a case study of managed retreat in New Zealand, this research uncovers intersecting and compounding arenas of uncertainty regarding the approach, responsibilities, legality, funding, politics and logistics of managed retreat. Where uncertainty is present in one domain, it spreads into others creating a cascading series of political, personal and professional risks that impact trust in science and authority and affect people’s lives and risk exposure. In revealing these mutually dependent dimensions of uncertainty, we argue there is merit in refocusing attention away from policy deficits, barrier approaches or technical assessments as a means to provide ‘certainty’, to instead focus on the relations between forms of knowledge and coordinating interactions between the diverse arenas: scientific, governance, financial, political and socio-cultural; otherwise uncertainty can spread like a contagion, making inaction more likely