Magnetic Field Gradient Waveforms Research Articles

Explicit phenomenological solutions for magnetization exposed to an arbitrary NMR diffusion steady state pulse sequence.

Explicit phenomenological solutions to recurrence relations for the bulk transverse and longitudinal magnetization found using the Torrey-Bloch equations with relaxation effects are used to investigate nuclear magnetic resonance (NMR) diffusion measurements. Of particular interest are steady state NMR (self-)diffusion measurements that reduce experimental time that can extend the techniques to quickly reacting systems. The solutions for bulk transverse and longitudinal magnetization presented here are used to investigate the average behavior of the transverse and longitudinal magnetization in forming a steady state and are used to derive new expressions for the steady state longitudinal magnetization. These solutions can be applied to a noninteracting spin 1/2 ensemble undergoing free diffusion exposed to an arbitrary NMR pulse sequence containing arbitrary magnetic field gradient waveforms. The closed algebraic form method presented here has an advantage over iterative procedures for calculating transverse and longitudinal magnetization for the analysis and development of steady state pulse sequences. Previous theoretical results for steady state diffusion measurements are also reproduced. The Mathematica code for these solutions is provided in the supplementary material.

A Statistical Robust Approach to Design Parallel Transmit Radiofrequency Excitations in MRI

In MRI, at ultrahigh field, the use of parallel transmit radiofrequency (RF) arrays is very beneficial to better control spin excitation spatially. In that framework, the so-called “universal pulse” technique, proposed recently for head imaging at 7 tesla, gives access to “plug-and-play” nonadiabatic solutions exhibiting good robustness against intersubject variations in the resonant transmit fields. This new type of solution has been defined so far as the result of numerical pulse optimizations performed across a collection of RF field maps acquired on a small population sample (pulse design database). In this work, we investigate an alternative universal pulse design approach in the linear small tip angle regime whereby the database of RF field maps is first transformed into a second-order statistical model and which then exploits a statistical robust design formalism for the optimization of the RF and magnetic field gradient waveforms. Experimental validation with an eightfold transmit RF coil for 7 tesla brain imaging shows that this new approach brings some benefit in terms of computational efficiency. Hence, for a design database composed of 35 maps, the computation time initially of 50 min could be reduced down to 3 min. The proposed statistical approach thus enables integration of large databases, presumably necessary to ensure robust solutions. Finally, it provides means to compute flip angle statistics and, along with it, simple performance metrics for quality assurance (RF pulse performance) or guidance in the optimization of TX array architectures.

Universal nonselective excitation and refocusing pulses with improved robustness to off-resonance for Magnetic Resonance Imaging at 7 Tesla with parallel transmission.

In MRI at ultra-high field, the -point and spiral nonselective (SPINS) pulse design techniques can be advantageously combined with the parallel transmission (pTX) and universal pulse techniques to create uniform excitation in a calibration-free manner. However, in these approaches, pulse duration is typically increased as compared to standard hard pulses, and excitation quality in regions exhibiting large resonance frequency offsets often suffer. This limitation is inherent to structure of -point or SPINS pulse, and likely can be mitigated using parameterization-free pulse design approaches. The Gradient Ascent Pulse Engineering (GRAPE) algorithm was used to design parameterization-free RF and magnetic field gradient (MFG) waveforms for creating excitation, up to scalable refocusing and inversion, nonselectively across the brain. Simulations were performed to provide flip angle normalized root-mean-squares error (FA-NRMSE) estimations for the and the -point, SPINS, and GRAPE pulses. GRAPE pulses were tested experimentally with anatomical head scans at 7T. As compared to -points and SPINS, GRAPE provided substantial improvement of excitation, refocusing, and inversion quality at off-resonance while at least preserving the same global FA-NRMSE performance. As compared to -points, GRAPE allowed for a substantial reduction of the pulse duration for the excitation and the refocusing. Parameterization-free universal nonselective pTX-pulses were successfully computed using GRAPE. Performance gains as compared to -points were validated numerically and experimentally for three imaging protocols. In its current implementation, the computational burden of GRAPE limits its use to applications where pulse computations are not subject to time constraints.

Gradient Response Harvesting for Continuous System Characterization During MR Sequences.

MRI gradient systems are required to generate magnetic field gradient waveforms with very high fidelity. This is commonly implemented by gradient system calibration and pre-emphasis. However, a number of mechanisms, particularly thermal changes, cause variation in the gradient response over time, which cannot be addressed by calibration approaches. To overcome this limitation, we present a novel method termed gradient response harvesting, where the gradient response is continuously characterized during the course of a normal MR sequence. Snippets of field measurements are repeatedly acquired during an MR sequence, and from these multiple field measurements and the known nominal MR sequence gradients, the gradient response and gradient/field offsets are calculated. The calculation is implemented in a model-based and a model-free variant. The method is demonstrated for EPI with high gradient duty-cycle, where the continuous gradient characterization is used to obtain k-space trajectory estimates that are employed in the subsequent image reconstruction. During the course of the MR sequence, changes in both the envelope and the phase of the gradient response functions were observed, including shifts of mechanical resonances. The gradient response changes were also reflected in the calculated uninterrupted gradient waveforms and thus in the k-space trajectories. Using the updated encoding information in the image reconstruction removed ghosting artifacts, that otherwise impaired the image quality. We introduced the concept of gradient response harvesting and demonstrated its feasibility. The obtained gradient response functions may be used for quality assurance/preventive maintenance, real-time adaptation of gradient pre-emphasis or to calculate uninterrupted gradient field evolutions.

Evaluation of magnetic resonance imaging acoustic noise reduction technology by magnetic gradient waveform control

BackgroundComforTone is a noise reduction technology used in magnetic resonance imaging (MRI) systems; it suppresses acoustic noise by modifying pulse sequences, which appropriately changes the magnetic field gradient waveforms. Although ComforTone can be used to solve the acoustic noise problems that affect patients who are exposed to acoustic noise from MRI, to the best of our knowledge, the associated technical details have not been published and its effects on acoustic noise reduction remain unclear. PurposeTo evaluate the efficacy of acoustic noise reduction and the impact of acoustic noise reduction technology involving magnetic field gradient waveform control on image quality. PopulationThe study included 18 healthy volunteers (11 males and 7 females; median age, 34 years; age range, 24–51 years). Field strength1.5 T Philips Ingenia using a SENSE head–spine coil. AssessmentThe sound pressure level (SPL) and 1/3 octave spectra of MRI acoustic noise with the human head positioned in the iso-center of the MRI system were measured for five different pulse sequences used in clinical MRI. This subjective evaluation of noise included 18 healthy volunteers. The degree of discomfort experienced by the subjects was measured using a visual analog scale. The image quality was assessed objectively and subjectively. For objective assessment, signal-to-noise ratio (SNR) and contrast-to -noise ratio (CNR) of diffusion-weighted images were measured; for subjective assessment, visual evaluation was performed by two radiologists. Statistical testsData were analyzed using Welch's t-test, and a p value <0.05 defined significance. ResultsComforTone could recognize a decrease in sound pressure, and the sound pressure of the acute high-frequency portion of the auditory characteristics was reduced. As reported by the subjects, discomfort caused by the sound pressure was significantly alleviated with ComforTone (p < 0.01). The sound pressure reduction in the high-frequency region with high audibility characteristics was recognized by ComforTone. The visual evaluation of the image quality of the diffusion-weighted images revealed that although there was no difference between SNR and CNR, the image quality was reduced by distortion artifacts. Data conclusionComforTone reduced the SPL in the frequency range where auditory characteristics were sensitive, suggesting that ComforTone was useful for auditory protection and alleviation of discomfort in patients undergoing MRI. However, because magnetic field gradient waveform control is involved, such noise-reducing techniques should be used by considering their possible influence on the image quality.

Magnetic field gradient waveform correction of motion-sensitized SPRITE by pre-equalization.

Eddy currents caused by pulsed field gradients in magnetic resonance measurements of high-speed flow cause the magnetic field gradient amplitude waveform experienced by the sample to be different from the waveform demanded of the magnetic field gradient amplifiers. By measuring and using the system impulse response, pre-equalization magnetic field gradient waveform correction can be used to counteract the resulting errors in measured signal phase at the cost of minimal additional experimental time. The effectiveness of the pre-equalization method of magnetic field gradient waveform correction is tested with a motion-sensitized (pulsed field gradient) version of the SPRITE imaging pulse sequence which requires extreme gradient slew rates in excess of 1000 T/m/s in a 6.7-cm-bore set of gradient windings. Pre-equalized, motion-sensitized SPRITE is used to create velocity maps of high-speed (c. 4 m/s) water flow through a pipe constriction.

A high-pressure metallic core holder for magnetic resonance based on Hastelloy-C.

A metallic core holder, fabricated from non-magnetic Hastelloy-C276, has been designed for Magnetic Resonance (MR) and Magnetic Resonance Imaging (MRI) of core plug samples at high pressures and temperatures. Core plug samples, 1.5″ in diameter and 2″ in length, can be tested in the core holder at elevated pressures and temperatures, up to 5000 psi and 80 °C. These are conditions commonly found in petroleum reservoirs. A radio frequency probe, which excites and detects magnetic resonance signals, was placed inside the metal vessel. Proximity to the sample improves the signal to noise ratio of the resulting measurements. The metallic core holder is positioned between the poles of a 0.2 T permanent magnet and subjected to rapidly switched magnetic field gradients as part of the imaging process. This switching induces eddy currents on the conductive core holder, which degrades the magnetic field gradient waveform in the sample space. The low electrical-conductivity of Hastelloy-C276 minimizes the duration and the magnitude of such eddy currents. A recently developed pre-equalization technique was employed to ensure that magnetic field gradient pulses, required for MRI, are near ideal in the sample space. A representative core flooding experiment was undertaken in conjunction with MR/MRI measurements.

Accuracy of the Magnetic Field Gradient Waveform Monitor Technique and Consequent Accuracy of Pre‐Equalized Gradient Waveform

AbstractThe magnetic field gradient waveform monitor (MFGM) technique permits characterization of the temporal evolution of magnetic field gradients in magnetic resonance (MR) instruments (MRIs). Knowledge of the gradient waveform performance permits the development of further techniques, such as gradient waveform pre‐equalization, that correct and optimize gradient waveform distortions due to eddy currents induced during the application of switched magnetic fields and other system limitations. The accuracy of the MFGM technique is important since the overall uncertainty of the gradient waveform measurement will propagate into an uncertainty in corrected gradient waveforms impacting the precision of the resulting MR/MRI measurements. The accuracy of MFGM is investigated through a treatment of the noise present in a MRI. A noisy receiver model provides the basis for characterization of the noise and permits examination of the overall impact of noise on the phase accumulated in a pure‐phase encoded MR signal. Ultimately, a relationship between the signal‐to‐noise ratio of a measurement and the corresponding MFGM uncertainty is developed. The theoretical development is supported through simulation in conjunction with experimental results. The propagation of uncertainties to gradient waveform pre‐equalization is also discussed.

Fractional motion model for characterization of anomalous diffusion from NMR signals.

Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

A comparison of magnetic resonance methods for spatially resolved T2 distribution measurements in porous media

Naturally occurring porous media are usually characterized by a distribution of pore sizes. If the material is fluid saturated, the 1H magnetic resonance (MR) signal depends on the pore size, the surface relaxivity and the fluid itself. Measurement of the transverse relaxation time T2 is a well-established technique to characterize material samples by means of MR. T2 distribution measurements, including T2 distribution mapping, are widely employed in clinical applications and in petroleum engineering. T2 distribution measurements are the most basic measurement employed to determine the fluid-matrix properties in MR core analysis. Three methods for T2 distribution mapping, namely spin-echo single point imaging (SE-SPI), DANTE-Z Carr–Purcell–Meiboom–Gill (CPMG) and adiabatic inversion CPMG are compared in terms of spatial resolution, minimum observable T2 and sensitivity. Bulk CPMG measurement is considered to be the gold standard for T2 determination. Bulk measurement of uniform samples is compared to the three spatially resolved measurements. SE-SPI is an imaging method, which measures spatially resolved T2s in samples of interest. A variant is introduced in this work that employs pre-equalized magnetic field gradient waveforms and is therefore able to measure shorter T2s than previously reported. DANTE-Z CPMG and adiabatic inversion CPMG are faster, non-imaging, local T2 distribution measurements. The DANTE-Z pulse train and adiabatic inversion pulse are compared in terms of T1 or T2 relaxation time effects during the RF pulse application, minimum pulse duration, requisite RF pulse power, and inversion profile quality. In addition to experimental comparisons, simulation results are presented.

Arbitrary magnetic field gradient waveform correction using an impulse response based pre-equalization technique

The time-varying magnetic fields used in magnetic resonance applications result in the induction of eddy currents on conductive structures in the vicinity of both the sample under investigation and the gradient coils. These eddy currents typically result in undesired degradations of image quality for MRI applications. Their ubiquitous nature has resulted in the development of various approaches to characterize and minimize their impact on image quality.This paper outlines a method that utilizes the magnetic field gradient waveform monitor method to directly measure the temporal evolution of the magnetic field gradient from a step-like input function and extracts the system impulse response. With the basic assumption that the gradient system is sufficiently linear and time invariant to permit system theory analysis, the impulse response is used to determine a pre-equalized (optimized) input waveform that provides a desired gradient response at the output of the system. An algorithm has been developed that calculates a pre-equalized waveform that may be accurately reproduced by the amplifier (is physically realizable) and accounts for system limitations including system bandwidth, amplifier slew rate capabilities, and noise inherent in the initial measurement. Significant improvements in magnetic field gradient waveform fidelity after pre-equalization have been realized and are summarized.

Investigation of Magnetic Field Gradient Waveforms in the Presence of a Metallic Vessel in Magnetic Resonance Imaging Through Simulation

We have previously established the ability to characterize eddy currents and their impact on the magnetic fields in metal vessel magnetic resonance imaging applications through comparison with measured data. We now use simulation to investigate the spatiotemporal characteristics of eddy currents and their magnetic fields encountered in metal vessel magnetic resonance imaging that may not easily be experimentally verified. Simulations using CST EM Studio have revealed the impact of an offset in the positioning of the metal vessel in a superconducting magnet bore as well as the consequences of the different amplitude magnetic gradients employed during imaging experiments. Furthermore, we investigate the response of the metal vessel to magnetic field gradients generated from nonplanar and planar gradient coil geometries (encountered in superconducting and permanent magnet-based systems). Establishing the basic electromagnetic properties of the metal vessel in a magnetic resonance sense through simulation permits us to replace our simple metal vessel with a more sophisticated rock core holder design and investigate its properties.

Simulation and Verification of Magnetic Field Gradient Waveforms in the Presence of a Metallic Vessel in Magnetic Resonance Imaging

We present simulation and experimental results regarding the generation of eddy currents due to switched magnetic field gradients during the use of metallic vessels in high-pressure magnetic resonance imaging (MRI) applications. The induced eddy currents result in a corruption of the applied magnetic field gradient as experienced by the object being imaged. Simulations using CST EM Studio™ have revealed the spatial distribution and temporal evolution of eddy currents, the resulting magnetic fields, and their dependence on vessel material and orientation of the applied switched magnetic field gradient. The simulation results have been compared to measured data with excellent agreement. Agreement between simulated and measured data permits increasingly sophisticated models to be developed such that simulation results reliably guide the design of improved metal vessels.

Direct measurement of magnetic field gradient waveforms

As eddy currents increase with gradient amplitude and faster slew rate, they have become a greater problem with the advent of higher-performance gradients in modern MRI scanners. Success in eddy current reduction techniques such as active gradient shielding and waveform pre-emphasis, however, require that the residual eddy currents must be measured with high accuracy for image improvement. Traditional MR based gradient calibration techniques, whether based on an entire FID or a gradient echo, measure the integral of gradient waveforms. We have however previously proposed a different category of methods, which employ pure phase encode FIDs and have proven advantageous in directly measuring the gradient waveforms. In this article, we review the basis of these pure phase encode methods. In keeping with the instructional nature of CMRA, we undertake this review by describing specific experiments and the line of the thought behind the experiments. The pure phase encode approach is sensitive to low amplitude gradients (0.001–1 G/cm), and also permits measurement of high amplitude gradients (10–300 G/cm). The inverse Fourier transform permits ready understanding of these pure phase encode methods. The accuracy of pure phase encode gradient measurement is significantly improved by a multiple FID point acquisition, which permits high temporal resolution of the gradient waveform. The accuracy of gradient measurements is also analyzed and improved through elimination of potential artifacts. As one example of the capability of these methods, waveform measurements were undertaken to reduce the repetition time TR for centric scan SPRITE experiments. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part A 36A: 349–360, 2010.

Non-Cartesian sampled centric scan SPRITE imaging with magnetic field gradient and B0( t) field measurements for MRI in the vicinity of metal structures

This paper proposes the possibility of spatially resolved MRI measurements undertaken inside metallic cells. MRI has been rarely usable inside conducting vessels due to the eddy currents in the walls caused by switching magnetic field gradients, which render most advanced MRI pulse sequences impossible. We propose magnetic field gradient waveform monitoring (MFGM) for MRI of samples inside metallic cells. In this work the MFGM method was extended to measure the B 0 field temporal evolution associated with gradient waveforms. MFGM was used to observe and correct eddy current effects associated with a metallic cell. High quality centric scan SPRITE images result from such corrections. MRI of samples held under pressure, most notably rock core samples, traditionally employs cells that are non-magnetic and fabricated from polymeric materials. The natural material for high-pressure MRI is however non-ferromagnetic metal given their high tensile strengths and high thermal conductivity. MRI measurement of macroscopic samples at high pressure would be generally possible if metallic pressure vessels could be employed. This study will form the basis of new MRI compatible metallic pressure vessels, which will permit MRI of macroscopic systems at high pressure.

A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments.

Based on a description introduced by Robertson, Grebenkov recently introduced a powerful formalism to represent the diffusion-attenuated NMR signal for simple pore geometries such as slabs, cylinders, and spheres analytically. In this work, we extend this multiple correlation function formalism by allowing for possible variations in the direction of the magnetic field gradient waveform. This extension is necessary, for example, to incorporate the effects of imaging gradients in diffusion-weighted NMR imaging scans and in characterizing anisotropy at different length scales via double pulsed field gradient (PFG) experiments. In cylindrical and spherical pores, respectively, two- and three-dimensional vector operators are employed whose form is deduced from Grebenkov's results via elementary operator algebra for the case of cylinders and the Wigner-Eckart theorem for the case of spheres. The theory was validated by comparison with known findings and with experimental double-PFG data obtained from water-filled microcapillaries.

Spatial encoding strategies for ultrafast multidimensional nuclear magnetic resonance

Multidimensional spectroscopy plays a central role in contemporary magnetic resonance. A general feature of multidimensional NMR is its inherent multiscan nature, stemming from the methodology's reliance on a series of independent acquisitions to sample the spins' evolutions throughout the indirect time domains. Contrasting this traditional feature, an acquisition scheme has recently been reported that enables the collection of complete of multidimensional NMR data sets within one single scan. Provided that the signals to be observed are sufficiently strong, this new "ultrafast" protocol can thus shorten the acquisition times of multidimensional NMR experiments by several orders of magnitude. This new methodology operates by departing from temporal encoding principles used since the advent of Fourier-transform NMR, replacing them with a spatial encoding of the spin interactions. Spatial encoding operates in turn on the basis of novel radiofrequency irradiation and magnetic field gradient waveform manipulations, designed so as to impart on the sample a coherent spin magnetization pattern that reflects the internal interactions to be measured. Given the central role played by this new kind of spectroscopic-oriented manipulations in ultrafast NMR, we devote this review to surveying different variants that have hitherto been proposed for their implementation. These include both discrete and continuous versions, real- and constant-time implementations, as well as amplitude- and phase-modulated alternatives. The principles underlying these various spatial encoding approaches are treated, their operation is graphically illustrated as well as formally derived within suitable theoretical frameworks, and an in-depth comparison of their line shape characteristics is discussed.

Simple phase method for measurement of magnetic field gradient waveforms

Magnetic field gradients play a fundamental role in MR imaging and localized spectroscopy. The MRI experiment, in particular fast MRI, relies on precise gradient switching, which has become more demanding with the constantly growing number of fast imaging techniques. Here we present a simple MR method to measure the behavior of a magnetic field gradient waveform in an MR scanner. The method employs excitation of a thin slice, followed by application of the studied gradient and simultaneous FID acquisition. Measurements of different gradient waveforms were performed with a spherical phantom filled with doped water and positioned at the isocenter of the gradient set. The presented experiments demonstrate the capability of the technique to measure different gradient waveforms with an estimated error of less than 200 microT/m.

Single point measurements of magnetic field gradient waveform

Pulsed magnetic field gradients are fundamental to spatial encoding and diffusion weighting in magnetic resonance. The ideal pulsed magnetic field gradient should have negligible rise and fall times, however, there are physical limits to how fast the magnetic field gradient may change with time. Finite gradient switching times, and transient, secondary, induced magnetic field gradients (eddy currents) alter the ideal gradient waveform and may introduce a variety of undesirable image artifacts. We have developed a new method to measure the complete magnetic field gradient waveform. The measurement employs a heavily doped test sample with short MR relaxation times ( T 1, T 2, and T 2 *<100 μs ) and a series of closely spaced broadband radiofrequency excitations, combined with single point data acquisition. This technique, a measure of evolving signal phase, directly determines the magnetic field gradient waveform experienced by the test sample. The measurement is sensitive to low level transient magnetic fields produced by eddy currents and other short and long time constant non-ideal gradient waveform behaviors. Data analysis is particularly facile permitting a very ready experimental check of gradient performance.

An NMR technique for measurement of magnetic field gradient waveforms

Almost all NMR imaging and localized spectroscopic methods fundamentally rely on the use of magnetic field gradients. It follows that precise information on gradient waveform shape and rise-times is often most useful in experimental MRI. We present a very simple and robust method for measuring the time evolution of a magnetic field gradient. The method is based on the analysis of the NMR signal in the time domain, and requires no specialized field measurement probes for its implementation. The technique makes use of the principal that for small flip angles the excitation profile is a good approximation to the Fourier transform of the radio frequency pulse shape. Creation of the NMR signal can be considered as an inverse Fourier transform and thus variation of the gradient strength during the excitation pulse influences the shape of the NMR signal. Although originally designed for measurement of the rise time only, we have now extended the technique to measure the exact time course of the gradient. The theory is confirmed by experimental results for gradient waveform field measurements in a high-field vertical bore system.