Analysis of temporal encoding efficiency of MR fingerprinting sequences.

PURPOSE: MR Fingerprinting (MRF) relies on highly-undersampled images to simultaneously estimate multiple tissue parameters of interest. While a good understanding of the encoding principle behind MRF exists, we want to shed light on the question of when parameters are encoded during an MRF acquisition. THEORY AND METHODS: We analyze the importance of each time point by leaving it out during matching (leave-one-out, LOO) assuming linear reconstruction is applied and study its influence on the reconstructed parameter map. To accelerate the analysis, we treat LOO as a small perturbation (LOOP) to the full matching problem and derive an analytical formula by leveraging Stolk and Sbrizzi's analysis on the interplay of k-space sampling and transient state dynamics. To study the influence of geometry and parameter distribution, we deploy LOOP on randomly sliced 3D brain geometries with randomized T1/T2 values to identify primary encoding regions independent of geometry. RESULTS: LOOP can be evaluated orders of magnitude faster than conventional matching and visualizes temporal encoding efficiency. We use the findings to accelerate an MRF sequence by truncation as well as to remove undersampling artifacts through an iterative omission scheme in an ill-working MRF sequence in both in-silico and in-vivo experiments. CONCLUSION: LOOP is an analytical approach to quantify and visualize parameter encoding in MRF.

Ramping down a clinical 3 T scanner: a journey into MRI and MRS at 0.75 T.

OBJECT: Lower-field MR is reemerging as a viable, potentially cost-effective alternative to high-field MR, thanks to advances in hardware, sequence design, and reconstruction over the past decades. Evaluation of lower field strengths, however, is limited by the availability of lower-field systems on the market and their considerable procurement costs. In this work, we demonstrate a low-cost, temporary alternative to purchasing a dedicated lower-field MR system. MATERIALS AND METHODS: By ramping down an existing clinical 3 T MRI system to 0.75 T, proton signals can be acquired using repurposed 13C transmit/receive hardware and the multi-nuclei spectrometer interface. We describe the ramp-down procedure and necessary software and hardware changes to the system. RESULTS: Apart from presenting system characterization results, we show in vivo examples of cardiac cine imaging, abdominal two- and three-point Dixon-type water/fat separation, water/fat-separated MR Fingerprinting, and point-resolved spectroscopy. In addition, the ramp-down approach allows unique comparisons of, e.g., gradient fidelity of the same MR system operated at different field strengths using the same receive chain, gradient coils, and amplifiers. DISCUSSION: Ramping down an existing MR system may be seen as a viable alternative for lower-field MR research in groups that already own multi-nuclei hardware and can also serve as a testing platform for custom-made multi-nuclei transmit/receive coils.

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 T1 and T2 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 T1 and increasing T2 * for decreasing field strengths. Using measured T1 , T2 and T2 * as input and using field-dependent echo time and bandwidth scaling, simulated Cramér-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.

Characterization and correction of diffusion gradient-induced eddy currents in second-order motion-compensated echo-planar and spiral cardiac DTI.

PURPOSE: Very high gradient amplitudes played out over extended time intervals as required for second-order motion-compensated cardiac DTI may violate the assumption of a linear time-invariant gradient system model. The aim of this work was to characterize diffusion gradient-related system nonlinearity and propose a correction approach for echo-planar and spiral spin-echo motion-compensated cardiac DTI. METHODS: Diffusion gradient-induced eddy currents of 9 diffusion directions were characterized at b values of 150 s/mm2 and 450 s/mm2 for a 1.5 Tesla system and used to correct phantom, ex vivo, and in vivo motion-compensated cardiac DTI data acquired with echo-planar and spiral trajectories. Predicted trajectories were calculated using gradient impulse response function and diffusion gradient strength- and direction-dependent zeroth- and first-order eddy current responses. A reconstruction method was implemented using the predicted k $$ k $$ -space trajectories to additionally include off-resonances and concomitant fields. Resulting images were compared to a reference reconstruction omitting diffusion gradient-induced eddy current correction. RESULTS: Diffusion gradient-induced eddy currents exhibited nonlinear effects when scaling up the gradient amplitude and could not be described by a 3D basis alone. This indicates that a gradient impulse response function does not suffice to describe diffusion gradient-induced eddy currents. Zeroth- and first-order diffusion gradient-induced eddy current effects of up to -1.7 rad and -16 to +12 rad/m, respectively, were identified. Zeroth- and first-order diffusion gradient-induced eddy current correction yielded improved image quality upon image reconstruction. CONCLUSION: The proposed approach offers correction of diffusion gradient-induced zeroth- and first-order eddy currents, reducing image distortions to promote improvements of second-order motion-compensated spin-echo cardiac DTI.

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.

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.

Comparison of interpolation methods of predominant cardiomyocyte orientation from in vivo and ex vivo cardiac diffusion tensor imaging data.

Cardiac electrophysiology and cardiac mechanics both depend on the average cardiomyocyte long-axis orientation. In the realm of personalized medicine, knowledge of the patient-specific changes in cardiac microstructure plays a crucial role. Patient-specific computational modelling has emerged as a tool to better understand disease progression. In vivo cardiac diffusion tensor imaging (cDTI) is a vital tool to non-destructively measure the average cardiomyocyte long-axis orientation in the heart. However, cDTI suffers from long scan times, rendering volumetric, high-resolution acquisitions challenging. Consequently, interpolation techniques are needed to populate bio-mechanical models with patient-specific average cardiomyocyte long-axis orientations. In this work, we compare five interpolation techniques applied to in vivo and ex vivo porcine input data. We compare two tensor interpolation approaches, one rule-based approximation, and two data-driven, low-rank models. We demonstrate the advantage of tensor interpolation techniques, resulting in lower interpolation errors than do low-rank models and rule-based methods adapted to cDTI data. In an ex vivo comparison, we study the influence of three imaging parameters that can be traded off against acquisition time: in-plane resolution, signal to noise ratio, and number of acquired short-axis imaging slices.

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.

Shear wave cardiovascular MR elastography using intrinsic cardiac motion for transducer-free non-invasive evaluation of myocardial shear wave velocity.

Changes in myocardial stiffness may represent a valuable biomarker for early tissue injury or adverse remodeling. In this study, we developed and validated a novel transducer-free magnetic resonance elastography (MRE) approach for quantifying myocardial biomechanics using aortic valve closure-induced shear waves. Using motion-sensitized two-dimensional pencil beams, septal shear waves were imaged at high temporal resolution. Shear wave speed was measured using time-of-flight of waves travelling between two pencil beams and corrected for geometrical biases. After validation in phantoms, results from twelve healthy volunteers and five cardiac patients (two left ventricular hypertrophy, two myocardial infarcts, and one without confirmed pathology) were obtained. Torsional shear wave speed in the phantom was 3.0 ± 0.1 m/s, corresponding with reference speeds of 2.8 ± 0.1 m/s. Geometrically-biased flexural shear wave speed was 1.9 ± 0.1 m/s, corresponding with simulation values of 2.0 m/s. Corrected septal shear wave speeds were significantly higher in patients than healthy volunteers [14.1 (11.0-15.8) m/s versus 3.6 (2.7-4.3) m/s, p = 0.001]. The interobserver 95%-limits-of-agreement in healthy volunteers were ± 1.3 m/s and interstudy 95%-limits-of-agreement - 0.7 to 1.2 m/s. In conclusion, myocardial shear wave speed can be measured using aortic valve closure-induced shear waves, with cardiac patients showing significantly higher shear wave speeds than healthy volunteers. This non-invasive measure may provide valuable insights into the pathophysiology of heart failure.

Analysis and correction of off-resonance artifacts in echo-planar cardiac diffusion tensor imaging.

PURPOSE: Cardiac diffusion tensor imaging using EPI readout is prone to image distortions in the presence of field inhomogeneities. In this work, a framework to analyze and correct image distortions in cardiac diffusion tensor imaging is presented. METHODS: A multi-coil reconstruction framework was implemented to enable field map-based off-resonance correction. Numerical simulations were used to examine reconstruction performance for EPI phase-encode directions blip up-down and down-up for different degrees of off-resonance gradients and varying field map resolution. The impact of coil encoding was analyzed using the g-factor and normalized RMSE. Finally, the proposed method was tested on free-breathing in vivo cardiac diffusion tensor imaging data acquired in healthy subjects at 3 Tesla. RESULTS: Depending on the local field map gradient strength and polarity and the selected phase-encode direction, field inhomogeneities lead to either local spatial compression or stretching with standard image reconstruction. Although spatial compression results in loss of image resolution upon field map-based reconstruction, spatial stretching can be recovered once multiple receive coils are utilized. Multi-coil reconstruction was found to reduce the normalized RMSE from 34.3% to 8.1% for image compression, and 33.6% to 1.8% for image stretching, with resulting average g-factors 14.7 ± 2.9 and 1.2 ± 0.1, respectively. In vivo, multi-coil field map-based reconstruction yielded improved alignment of angle maps with anatomical cine data. CONCLUSION: Multi-coil, field map-based image reconstruction for echo-planar cardiac diffusion tensor imaging allows accurate image reconstruction provided that the phase-encode direction and polarity is chosen to principally align with the direction and polarity of the prominent gradients of field inhomogeneities.

Unipolar MR elastography: Theory, numerical analysis and implementation.

In MR elastography (MRE), zeroth moment balanced motion-encoding gradients (MEGs) are incorporated into MRI sequences to induce a phase shift proportional to the local displacement caused by external actuation. To maximize the signal-to-noise ratio (SNR), fractional encoding is employed, i.e., the MEG duration is reduced below the wave period. Here, gradients encode primarily the velocity of the motion-reducing encoding efficiency. Thus, in GRE-MRE, T2 * decay and motion sensitivity have to be balanced, imposing a lower limit on repetition times (TRs). We propose to use a single trapezoidal gradient, a "unipolar gradient", to directly encode spin displacement. Such gradients cannot be used in conventional sequences as they exhibit a large zeroth moment and dephase magnetization. By time-reversing a spoiled SSFP sequence, the spoiling gradient becomes an efficient unipolar MEG. The proposed "unipolar MRE" technique benefits from this approach in three ways: first, displacement encoding is split over multiple TRs increasing motion sensitivity; second, spoiler and MEG coincide, allowing a reduction in TR; third, motion sensitivity of a typical unipolar lobe is of an order of magnitude higher than a bipolar MEG of equal duration. In this work, motion encoding using unipolar MRE is analyzed using the extended phase graph (EPG) formalism with a periodic motion propagator. As an approximation, the two-transverse TR approximation for diffusion-weighted SSFP is extended to incorporate cyclic motion. A complex encoding efficiency metric is introduced to compare the displacement fields of unipolar and conventional GRE-MRE sequences in both magnitude and phase. The derived theoretical encoding equations are used to characterize the proposed sequence using an extensive parameter study. Unipolar MRE is validated against conventional GRE-MRE in a phantom study showing excellent agreement between measured displacement fields. In addition, unipolar MRE yields significantly increased octahedral shear strain-SNR relative to conventional GRE-MRE and allows for the recovery of high stiffness inclusions, where conventional GRE-MRE fails.

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 novel magnetic resonance elastography transducer concept based on a rotational eccentric mass: preliminary experiences with the gravitational transducer.

BACKGROUND: Magnetic resonance elastography (MRE) is used to non-invasively estimate biomechanical tissue properties via the imaging of propagating mechanical shear waves. Several factors including mechanical transducer design, MRI sequence design and viscoelastic reconstruction influence data quality and hence the reliability of the derived biomechanical properties. PURPOSE: To design and characterize a novel mechanical MRE transducer concept based on a rotational eccentric mass, coined the gravitational transducer. MATERIALS AND METHODS: Table top measurements were performed using accelerometers to characterize the frequency response of the new transducer concept at different driving frequencies (f VIB) and different rotating masses. These were compared to a commercially available pneumatically driven MRE transducer. MR data were acquired on a 3T scanner using a fractionally encoded gradient echo MRE sequence in three healthy volunteers. Acceleration and displacement spectra were plotted in units of g and mm, respectively, and visually compared, emphasizing the ratio between the peaks at f VIB and its 2nd harmonic, a known cause of error in the reconstruction of biomechanical properties as is explored in more detail in numerical simulations here. No formal statistical testing was performed in this proof-of-principle paper. RESULTS: The new transducer concept shows-as expected from theory-a quadratic or linear increase of acceleration amplitude with increase in f VIB or mass, respectively. Furthermore, different versions of the transducer show markedly lower 2nd harmonic-to-f VIB ratios compared to the commercially available pneumatically driven transducer. Displacement was constant over a range of f VIB, in accordance with theory. Phantom and in vivo data show low nonlinearity and excellent data quality. CONCLUSION: The table top measurements are in concordance with the theory behind a transducer based on a rotational eccentric mass. The resulting constant displacement amplitude irrespective of f VIB and low 2nd harmonic-to-f VIB ratio result in low nonlinearity and high data fidelity in both phantom and in vivo examples.

Rheological determinants for simultaneous staging of hepatic fibrosis and inflammation in patients with chronic liver disease.

The purpose of this study is to investigate the use of fundamental rheological parameters as quantified by MR elastography (MRE) to measure liver fibrosis and inflammation simultaneously in humans. MRE was performed on 45 patients at 3 T using a vibration frequency of 56 Hz. Fibrosis and inflammation scores were obtained from liver biopsies. Biomechanical properties were quantified in terms of complex shear modulus G* as well as shear wave phase velocity c and shear wave attenuation α. A rheological fractional derivative order model was used to investigate the linear dependence of the free model parameters (dispersion slope y, intrinsic speed c0 , and intrinsic relaxation time τ) on histopathology. Leave-one-out cross-validation was then utilized to demonstrate the effectiveness of the model. The intrinsic speed c0 increases with hepatic fibrosis, while an increased relaxation time τ is reflective of more inflammation of the liver parenchyma. The dispersion slope y does not depend either on fibrosis or on inflammation. The proposed rheological model, given this specific parameterization, establishes the functional dependences of biomechanical parameters on histological fibrosis and inflammation. The leave-one-out cross-validation demonstrates that the model allows identification, from the MRE measurements, of the histology scores when grouped into low-/high-grade fibrosis and low-/high-grade inflammation with significance levels of P = 0.0004 (fibrosis) and P = 0.035 (inflammation). The functional dependences of intrinsic speed and relaxation time on fibrosis and inflammation, respectively, shed new light onto the impact hepatic pathological changes on liver tissue biomechanics in humans. The dispersion slope y appears to represent a structural parameter of liver parenchyma not impacted by the severity of fibrosis/inflammation present in this patient cohort. This specific parametrization of the well-established rheological fractional order model is valuable for the clinical assessment of both fibrosis and inflammation scores, going beyond the capability of the plain shear modulus measurement commonly used for MRE.

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.

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.