Fundamentals of turbulent flow spectrum imaging

Purpose To introduce a mathematical framework and in-silico validation of turbulent flow spectrum imaging (TFSI) of stenotic flow using phase-contrast MRI, evaluate systematic errors in quantitative turbulence parameter estimation, and propose a novel method for probing the Lagrangian velocity spectra of turbulent flows. Theory and Methods The spectral response of velocity-encoding gradients is derived theoretically and linked to turbulence parameter estimation including the velocity autocorrelation function spectrum. Using a phase-contrast MRI simulation framework, the encoding properties of bipolar gradient waveforms with identical first gradient moments but different duration are investigated on turbulent flow data of defined characteristics as derived from computational fluid dynamics. Based on theoretical insights, an approach using velocity-compensated gradient waveforms is proposed to specifically probe desired ranges of the velocity autocorrelation function spectrum with increased accuracy. Results Practical velocity-encoding gradients exhibit limited encoding power of typical turbulent flow spectra, resulting in up to 50% systematic underestimation of intravoxel SD values. Depending on the turbulence level in fluids, the error due to a single encoding gradient spectral response can vary by 20%. When using tailored velocity-compensated gradients, improved quantification of the Lagrangian velocity spectrum on a voxel-by-voxel basis is achieved and used for quantitative correction of intravoxel SD values estimated with velocity-encoding gradients. Conclusion To address systematic underestimation of turbulence parameters using bipolar velocity-encoding gradients in phase-contrast MRI of stenotic flows with short correlation times, tailored velocity-compensated gradients are proposed to improve quantitative mapping of turbulent blood flow characteristics

Encoding and readout strategies in magnetic resonance elastography

Magnetic resonance elastography (MRE) has evolved significantly since its inception. Advances in motion‐encoding gradient design and readout strategies have led to improved encoding and signal‐to‐noise ratio (SNR) efficiencies, which in turn allow for higher spatial resolution, increased coverage, and/or shorter scan times. The purpose of this review is to summarize MRE wave‐encoding and readout approaches in a unified mathematical framework to allow for a comparative assessment of encoding and SNR efficiency of the various methods available. Besides standard full‐ and fractional‐wave‐encoding approaches, advanced techniques including flow compensation, sample interval modulation and multi‐shot encoding are considered. Signal readout using fast k‐space trajectories, reduced field of view, multi‐slice, and undersampling techniques are summarized and put into perspective. The review is concluded with a foray into displacement and diffusion encoding as alternative and/or complementary techniques

Direct comparison of gradient Fidelity and acoustic noise of the same MRI system at 3 T and 0.75 T

Purpose To analyze the difference between gradient fidelity and acoustic noise of the same MRI scanner operated at product field strength (3 T) and lower field strength (0.75 T). Methods Gradient modulation transfer functions (GMTFs) were measured using a four-slice 2D phase-encoded chirp-based sequence on the same scanner operated at 3 T and, following ramp-down, at 0.75 T with identical gradient specifications (40 mT/m, 200 T/m/s). Calibrated audio measurements were performed at both field strengths to correlate audio spectra with GMTFs. Results While eddy currents were independent of field strength, mechanical resonances were substantially decreased at lower field, resulting in a reduction of GMTF distortions by up to 95% (88% on average) at the mechanical resonances of the gradient system. Audio spectra amplitudes were reduced by up to 87% when comparing 0.75 T versus 3 T. Conclusion Lower static fields lead to reduced Lorentz forces on the gradient coil and, in turn, to reduced mechanical resonances, thereby improving gradient fidelity. Simultaneously, the reduction of acoustic noise may help to improve patient comfort.ISSN:0740-3194ISSN:1522-259

Ristretto MRE: A generalized multi‐shot GRE‐MRE sequence

In order to acquire consistent k-space data in MR elastography, a fixed temporal relationship between the MRI sequence and the underlying period of the wave needs to be ensured. To this end, conventional GRE-MRE enforces synchronization through repeated triggering of the transducer and forcing the sequence repetition time to be equal to an integer multiple of the wave period. For wave frequencies below 100 Hz, however, this leads to prolonged acquisition times, as the repetition time scales inversely with frequency. A previously developed multi-shot approach (eXpresso MRE) to multi-slice GRE-MRE tackles this issue by acquiring an integer number of slices per wave period, which allows acquisition to be accelerated in typical scenarios by a factor of two or three. In this work, it is demonstrated that the constraints imposed by the eXpresso scheme are overly restrictive. We propose a generalization of the sequence in three steps by incorporating sequence delays into imaging shots and allowing for interleaved wave-phase acquisition. The Ristretto scheme is compared in terms of imaging shot and total scan duration relative to eXpresso and conventional GRE-MRE and is validated in three different phantom studies. First, the agreement of measured displacement fields in different stages of the sequence generalization is shown. Second, performance is compared for 25, 36, 40, and 60 Hz actuation frequencies. Third, the performance is assessed for the acquisition of different numbers of slices (13 to 17). In vivo feasibility is demonstrated in the liver and the breast. Here, Ristretto is compared with an optimized eXpresso sequence, leading to scan accelerations of 15% and 5%, respectively, without compromising displacement field and stiffness estimates in general. The Ristretto concept allows us to choose imaging shot durations on a fine grid independent of the number of slices and the wave frequency, permitting 2- to 4.5-fold acceleration of conventional GRE-MRE acquisitions

A unifying view on extended phase graphs and Bloch simulations for quantitative MRI

Quantitative MRI methods and learning-based algorithms require exact forward simulations. One critical factor to correctly describe magnetization dynamics is the effect of slice-selective RF pulses. While contemporary simulation techniques correctly capture their influence, they only provide final magnetization distributions, require to be run for each parameter set separately, and make it hard to derive general theoretical conclusions and to generate a fundamental understanding of echo formation in the presence of slice-profile effects. This work aims to provide a mathematically exact framework, which is equally intuitive as extended phase graphs (EPGs), but also considers slice-profiles through their natural spatial representation. We show, through an analytical, hybrid Bloch-EPG formalism, that the spatially-resolved EPG approach allows to exactly predict the signal dependency on off-resonance, spoiling moment, microscopic dephasing, and echo time. We also demonstrate that our formalism allows to use the same phase graph to simulate both gradient-spoiled and balanced SSFP-based MR sequences. We present a derivation of the formalism and identify the connection to existing methods, i.e. slice-selective Bloch, slice-selective EPG, and the partitioned EPG. As a use case, the proposed hybrid Bloch-EPG framework is applied to MR Fingerprinting.ISSN:2045-232

Fundamentals of turbulent flow spectrum imaging

Purpose To introduce a mathematical framework and in-silico validation of turbulent flow spectrum imaging (TFSI) of stenotic flow using phase-contrast MRI, evaluate systematic errors in quantitative turbulence parameter estimation, and propose a novel method for probing the Lagrangian velocity spectra of turbulent flows. Theory and Methods The spectral response of velocity-encoding gradients is derived theoretically and linked to turbulence parameter estimation including the velocity autocorrelation function spectrum. Using a phase-contrast MRI simulation framework, the encoding properties of bipolar gradient waveforms with identical first gradient moments but different duration are investigated on turbulent flow data of defined characteristics as derived from computational fluid dynamics. Based on theoretical insights, an approach using velocity-compensated gradient waveforms is proposed to specifically probe desired ranges of the velocity autocorrelation function spectrum with increased accuracy. Results Practical velocity-encoding gradients exhibit limited encoding power of typical turbulent flow spectra, resulting in up to 50% systematic underestimation of intravoxel SD values. Depending on the turbulence level in fluids, the error due to a single encoding gradient spectral response can vary by 20%. When using tailored velocity-compensated gradients, improved quantification of the Lagrangian velocity spectrum on a voxel-by-voxel basis is achieved and used for quantitative correction of intravoxel SD values estimated with velocity-encoding gradients. Conclusion To address systematic underestimation of turbulence parameters using bipolar velocity-encoding gradients in phase-contrast MRI of stenotic flows with short correlation times, tailored velocity-compensated gradients are proposed to improve quantitative mapping of turbulent blood flow characteristics.ISSN:0740-3194ISSN:1522-259

Analysis and improvement of motion encoding in magnetic resonance elastography

Magnetic resonance elastography (MRE) utilizes phase contrast magnetic resonance imaging (MRI), which is phase locked to externally generated mechanical vibrations, to measure the three-dimensional wave displacement field. At least four measurements with linear-independent encoding directions are necessary to correct for spurious phase contributions if effects from imaging gradients are non-negligible. In MRE, three encoding schemes have been used: unbalanced four- and six-point and balanced four-point ('tetrahedral') encoding. The first two sensitize to motion with orthogonal gradients, with the four-point method acquiring a single reference scan without motion sensitization, whereas three additional scans with inverted gradients are used with six-point encoding, leading to two-fold higher displacement-to-noise ratio (DNR) and 50% longer scan duration. Balanced four-point (tetrahedral) encoding encodes along the four diagonals of a cube, with one direction serving as a reference for the other three encoding directions, similar to four-point encoding. The objective of this work is to introduce a theoretical framework to compare different motion sensitization strategies with respect to their motion encoding efficiency in two fundamental encoding limits, the gradient strength limit and the dynamic range limit, which are both placed in relation to conventional gradient recalled echo (GRE)- and spin echo (SE)-based MRE sequences. We apply the framework to the three aforementioned schemes and show that the motion encoding efficiency of unbalanced four- and six-point encoding schemes in the gradient-limited regime can be increased by a factor of 1.5 when using all physical gradient channels concurrently. Furthermore, it is demonstrated that reversing the direction of the reference in balanced four-point (tetrahedral) encoding results in the Hadamard encoding scheme, which leads to increased DNR by 2 compared with balanced four-point encoding and 2.8 compared with unbalanced four-point encoding. As an example, we show that optimal encoding can be utilized to reduce the acquisition time of standard liver MRE in vivo from four to two breath holds

Preliminary experience of cardiac proton spectroscopy at 0.75 T

Recent work on high-performance lower-field MR systems has renewed the interest in assessing relative advantages and disadvantages of magnetic fields less than 1 T. The objective of the present work was to investigate signal-to-noise ratio (SNR) scaling of point-resolved spectroscopy as a function of field strength and to test the feasibility of proton MRS of triglycerides (TGs) in human in vivo myocardium at 0.75 T relative to 1.5 T and 3 T. Measurements at 0.75 T were obtained by temporarily ramping down a clinical 3 T MR scanner. System configurations at 0.75, 1.5 and 3 T featured identical hard- and software, except for differences in transmit/receive coil geometries and receive channel count, which were accounted for in SNR comparisons. Proton MRS was performed at 0.75 T, 1.5 T and 3 T in ex vivo tissue and in vivo calf muscle to measure T-1 and T-2 values as a function of field strength, which in turn served as input to simulations of SNR scaling and field-dependent TG fit errors. Preliminary in vivo spectra of myocardium were acquired at 0.75 T, 1.5 T and 3 T in healthy subjects. Measurements of both ex vivo tissue and in vivo muscle tissue at 0.75 T versus 1.5 T and 3 T confirmed decreasing T-1 and increasing T-2* for decreasing field strengths. Using measured T-1, T-2 and T-2* as input and using field-dependent echo time and bandwidth scaling, simulated Cramer-Rao lower bounds of TG amplitudes at 0.75 T were 2.3 and 4.5 times larger with respect to 1.5 T and 3 T, respectively. In vivo measurements demonstrate that human proton spectroscopy of TGs in cardiac muscle is feasible at 0.75 T, supporting the potential practical value of lower-field high-performance MR systems.ISSN:0952-3480ISSN:1099-149

Analysis and improvement of motion encoding in magnetic resonance elastography

Magnetic resonance elastography (MRE) utilizes phase contrast magnetic resonance imaging (MRI), which is phase locked to externally generated mechanical vibrations, to measure the three-dimensional wave displacement field. At least four measurements with linear-independent encoding directions are necessary to correct for spurious phase contributions if effects from imaging gradients are non-negligible. In MRE, three encoding schemes have been used: unbalanced four- and six-point and balanced four-point (‘tetrahedral’) encoding. The first two sensitize to motion with orthogonal gradients, with the four-point method acquiring a single reference scan without motion sensitization, whereas three additional scans with inverted gradients are used with six-point encoding, leading to two-fold higher displacement-to-noise ratio (DNR) and 50% longer scan duration. Balanced four-point (tetrahedral) encoding encodes along the four diagonals of a cube, with one direction serving as a reference for the other three encoding directions, similar to four-point encoding. The objective of this work is to introduce a theoretical framework to compare different motion sensitization strategies with respect to their motion encoding efficiency in two fundamental encoding limits, the gradient strength limit and the dynamic range limit, which are both placed in relation to conventional gradient recalled echo (GRE)- and spin echo (SE)-based MRE sequences. We apply the framework to the three aforementioned schemes and show that the motion encoding efficiency of unbalanced four- and six-point encoding schemes in the gradient-limited regime can be increased by a factor of 1.5 when using all physical gradient channels concurrently. Furthermore, it is demonstrated that reversing the direction of the reference in balanced four-point (tetrahedral) encoding results in the Hadamard encoding scheme, which leads to increased DNR by compared with balanced four-point encoding and 2.8 compared with unbalanced four-point encoding. As an example, we show that optimal encoding can be utilized to reduce the acquisition time of standard liver MRE in vivo from four to two breath holds