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Table Of Integrals Series And Products

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Regularization Of Inverse Problems

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Magnetic Resonance Imaging Physical Principles And Sequence Design

Chemical exchange saturation transfer (CEST) of metabolite protons that undergo exchange processes with the abundant water pool enables a specific contrast for magnetic resonance imaging (MRI). The CEST image contrast depends on physical and physiological parameters that characterize the microenvironment such as temperature, pH, and metabolite concentration. However, CEST imaging in vivo is a complex technique because of interferences with direct water saturation (spillover effect), the involvement of other exchanging pools, in particular macromolecular systems (magnetization transfer, MT), and nuclear Overhauser effects (NOEs). Moreover, there is a strong dependence of the diverse effects on the employed parameters of radiofrequency irradiation for selective saturation which makes interpretation of acquired signals difficult. This review considers analytical solutions of the Bloch–McConnell (BM) equation system which enable deep insight and theoretical description of CEST and the equivalent off-resonant spinlock (SL) experiments. We derive and discuss proposed theoretical treatments in detail to understand the influence of saturation parameters on the acquired Z-spectrum and how the different effects interfere and can be isolated in MR Z-spectroscopy. Finally, we provide an overview of reported CEST effects in vivo and discuss proposed methods and technical approaches applicable to in vivo CEST studies on clinical MRI systems.

https://iopscience.iop.org/article/10.1088/0031-9155/58/22/R221/pdf

Chemical exchange saturation transfer (CEST) and MR Z-spectroscopy in vivo: a review of theoretical approaches and methods.

Endogenous chemical exchange saturation transfer (CEST) effects are always diluted by competing effects, such as direct water proton saturation (spillover) and semi-solid macromolecular magnetization transfer (MT). This leads to unwanted T2 and MT signal contributions that lessen the CEST signal specificity to the underlying biochemical exchange processes. A spillover correction is of special interest for clinical static field strengths and protons resonating near the water peak. This is the case for all endogenous CEST agents, such as amide proton transfer, -OH-CEST of glycosaminoglycans, glucose or myo-inositol, and amine exchange of creatine or glutamate. All CEST effects also appear to be scaled by the T1 relaxation time of water, as they are mediated by the water pool. This forms the motivation for simple metrics that correct the CEST signal. Based on eigenspace theory, we propose a novel magnetization transfer ratio (MTRRex ), employing the inverse Z-spectrum, which eliminates spillover and semi-solid MT effects. This metric can be simply related to Rex , the exchange-dependent relaxation rate in the rotating frame, and ka , the inherent exchange rate. Furthermore, it can be scaled by the duty cycle, allowing for simple translation to clinical protocols. For verification, the amine proton exchange of creatine in solutions with different agar concentrations was studied experimentally at a clinical field strength of 3 T, where spillover effects are large. We demonstrate that spillover can be properly corrected and that quantitative evaluation of pH and creatine concentration is possible. This proves that MTRRex is a quantitative and biophysically specific CEST-MRI metric. Applied to acute stroke induced in rat brain, the corrected CEST signal shows significantly higher contrast between the stroke area and normal tissue, as well as less B1 dependence, than conventional approaches.

Inverse Z-spectrum analysis for spillover-, MT-, and T1 -corrected steady-state pulsed CEST-MRI--application to pH-weighted MRI of acute stroke.

Purpose Together with the development of MRI contrasts that are inherently small in their magnitude, increased magnetic field accuracy is also required. Hence, mapping of the static magnetic field (B0 ) and the excitation field (B1 ) is not only important to feedback shim algorithms, but also for postprocess contrast-correction procedures. Methods A novel field-inhomogeneity mapping method is presented that allows simultaneous mapping of the water shift and B1 (WASABI) using an off-resonant rectangular preparation pulse. The induced Rabi oscillations lead to a sinc-like spectrum in the frequency-offset dimension and allow for determination of B0 by its symmetry axis and of B1 by its oscillation frequency. Results Stability of the WASABI method with regard to the influences of T1 , T2 , magnetization transfer, and repetition time was investigated and its convergence interval was verified. B0 and B1 maps obtained simultaneously by means of WASABI in the human brain at 3 T and 7 T can compete well with maps obtained by standard methods. Finally, the method was applied successfully for B0 and B1 correction of chemical exchange saturation transfer MRI (CEST-MRI) data of the human brain. Conclusion The proposed WASABI method yields a novel simultaneous B0 and B1 mapping within 1 min that is robust and easy to implement. Magn Reson Med 77:571-580, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

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Simultaneous mapping of water shift and B1(WASABI)—Application to field‐Inhomogeneity correction of CEST MRI data

Purpose
To develop a model-based reconstruction technique for single-shot T1 mapping with high spatial resolution, accuracy, and precision using an inversion-recovery (IR) fast low-angle shot (FLASH) acquisition with radial encoding.

Methods
The proposed model-based reconstruction jointly estimates all model parameters, that is, the equilibrium magnetization, steady-state magnetization, 1/ T1*, and all coil sensitivities from the data of a single-shot IR FLASH acquisition with a small golden-angle radial trajectory. Joint sparsity constraints on the parameter maps are exploited to improve the performance of the iteratively regularized Gauss-Newton method chosen for solving the nonlinear inverse problem. Validations include both a numerical and experimental T1 phantom, as well as in vivo studies of the human brain and liver at 3 T.

Results
In comparison to previous reconstruction methods for single-shot T1 mapping, which are based on real-time MRI with pixel-wise fitting and a model-based approach with a predetermination of coil sensitivities, the proposed method presents with improved robustness against phase errors and numerical precision in both phantom and in vivo studies.

Conclusion
The comprehensive model-based reconstruction with L1 regularization offers rapid and robust T1 mapping with high accuracy and precision. The method warrants accelerated computing and online implementation for extended clinical trials. Magn Reson Med 79:730–740, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Model-based T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH.

Purpose

To provide multidimensional velocity compensation for real-time phase-contrast flow MRI.



Methods

The proposed method introduces asymmetric gradient echoes for highly undersampled radial FLASH MRI with phase-sensitive image reconstruction by regularized nonlinear inversion (NLINV). Using an adapted gradient delay correction the resulting image quality was analyzed by simulations and experimentally validated at 3 Tesla. For real-time flow MRI the reduced gradient-echo timing allowed for the incorporation of velocity-compensating waveforms for all imaging gradients at even shorter repetition times.



Results

The results reveal a usable degree of 20% asymmetry. Real-time flow MRI with full velocity compensation eliminated signal void in a flow phantom, confirmed flow parameters in healthy subjects and demonstrated signal recovery and phase conservation in a patient with aortic valve insufficiency and stenosis. Exemplary protocols at 1.4–1.5 mm resolution and 6 mm slice thickness achieved total acquisition times of 33.3–35.7 ms for two images (7 spokes each) with and without flow-encoding gradient.



Conclusion

Asymmetric gradient echoes were successfully implemented for highly undersampled radial trajectories. The resulting temporal gain offers full velocity compensation for real-time phase-contrast flow MRI which minimizes false-positive contributions from complex flow and further enhances the temporal resolution compared with acquisitions with symmetric echoes. Magn Reson Med, 2015. © 2015 Wiley Periodicals, Inc.

Advances in real-time phase-contrast flow MRI using asymmetric radial gradient echoes

Purpose To develop a model-based reconstruction technique for real-time phase-contrast flow MRI with improved spatiotemporal accuracy in comparison to methods using phase differences of two separately reconstructed images with differential flow encodings. Methods The proposed method jointly computes a common image, a phase-contrast map, and a set of coil sensitivities from every pair of flow-compensated and flow-encoded datasets obtained by highly undersampled radial FLASH. Real-time acquisitions with five and seven radial spokes per image resulted in 25.6 and 35.7 ms measuring time per phase-contrast map, respectively. The signal model for phase-contrast flow MRI requires the solution of a nonlinear inverse problem, which is accomplished by an iteratively regularized Gauss-Newton method. Aspects of regularization and scaling are discussed. The model-based reconstruction was validated for a numerical and experimental flow phantom and applied to real-time phase-contrast MRI of the human aorta for 10 healthy subjects and 2 patients. Results Under all conditions, and compared with a previously developed real-time flow MRI method, the proposed method yields quantitatively accurate phase-contrast maps (i.e., flow velocities) with improved spatial acuity, reduced phase noise and reduced streaking artifacts. Conclusion This novel model-based reconstruction technique may become a new tool for clinical flow MRI in real time. Magn Reson Med 77:1082-1093, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Model‐based reconstruction for real‐time phase‐contrast flow MRI: Improved spatiotemporal accuracy

Purpose

To develop a method for spoiling transverse magnetizations without additional gradients to minimize repetition times for radial fast low angle shot (FLASH) MRI.



Methods

Residual steady state transverse magnetizations and corresponding image artifacts were analyzed for radial gradient echo sequences with constant and randomized RF phases in comparison with a sequence with refocused frequency-encoding gradients, constant spoiler gradient, and conventional RF spoiling (gold standard). The spoiling performance was assessed for different radial trajectories using numerical simulations, phantom experiments, and in vivo MRI studies of the human brain.



Results

Simulations as well as phantom and in vivo measurements reveal a highly efficient spoiling capacity for randomized RF phases and radial FLASH sequences without the need for gradient rewinding and spoiler gradients. The data also demonstrate a strong dependence of the spoiling performance on the chosen radial trajectory (ie, the azimuthal angular increment between successive projections) with excellent results for an interleaved multiturn scheme.



Conclusion

Effective spoiling of transverse magnetizations in radial FLASH MRI may be achieved by randomized RF phases without additional spoiler gradients. The technique allows for short repetition times as required for high-speed real-time MRI. Magn Reson Med, 2015. © 2015 Wiley Periodicals, Inc.

Volkert Roeloffs

Papers

Simultaneous mapping of water shift and B1(WASABI)—Application to field‐Inhomogeneity correction of CEST MRI data

Model-based T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH.

Advances in real-time phase-contrast flow MRI using asymmetric radial gradient echoes

Model‐based reconstruction for real‐time phase‐contrast flow MRI: Improved spatiotemporal accuracy

Spoiling without additional gradients: Radial FLASH MRI with randomized radiofrequency phases