Inhomogeneous Static Magnetic Field Research Articles

A flexible two-dimensional phase correction for interleaved echo-planar imaging reconstruction

Interleaved echo-planar imaging (EPI) is a fast clinical magnetic resonance imaging (MRI) scheme that obtains multiple echoes with a proper phase encoding (PE) strategy to generate multiple k-space PE lines. Since these PE data lines are from different echoes that may carry different phase and amplitude errors originating from the static magnetic field inhomogeneity and nuclear spin relaxation, to form an image free of artifacts, both phase and amplitude errors need to be compensated properly. To address this issue, we have developed a general image reconstruction technique which is capable of accomplishing two-dimensional (2D) phase correction for image reconstruction of interleaved EPI data. In this technique we formulated the reconstruction as a problem of finding an optimal solution to a set of linear algebraic equations corresponding to an imaging measurement. The phase errors, as well as other constraints, can be incorporated into these equations. The final solution can be obtained by inverting the coefficient matrix of the equation via a complex singular value decomposition (SVD) procedure, free of k-space data gridding. 2D phase corrected images have been successfully reconstructed using a set of imaging data acquired on a clinical MRI scanner. The significance of the work is that it has demonstrated that the 2D spatial phase correction can be accomplished for a set of interleaved EPI acquisition. Also, this is a flexible image reconstruction method for further improving the resulting image quality.

Inductive measurement of magnetic field gradients for magnetic resonance imaging

A simple device for highly accurate and real-time measurement of magnetic field gradient pulses is presented. It uses analog integration of the differential voltage induced in a pair of sensor coils placed along the investigated gradient direction. By this principle, the method is insensitive to static magnetic field inhomogeneities. It does not need either a main field or imaging apparatus and hence can be used in the process of gradient system design and optimization. Two different solutions for analog integration are suggested. The measurement accuracy is analyzed, taking into account errors due to the sensor coils and to both analog integration schemes. Sensor coils and integrators have been built to perform measurements on various gradient systems. Measurements of an actual whole-body gradient system are presented. The measurement accuracy is in the 5–10−4 range, and the reproducibility is better than 10−4, relative to the maximum gradient amplitude. These performances are better than any other presented in literature. They have allowed precise adjustment of a preemphasis unit so as to suppress eddy currents influence below 0.01%, and placed into evidence the thermal drift of standard power amplifier.

STEAM-Burst: a single-shot, multi-slice imaging sequence without rapid gradient switching.

The stimulated-echo acquisition mode-Burst sequence is a single-shot, multi-slice imaging technique that does not involve rapid gradient switching. A Burst excitation pulse train is followed by a 90 degrees hard pulse and, after a mixing time, by a 90 degrees slice-selective pulse. A read gradient refocuses a set of stimulated echoes, which can be phase-encoded to form an image. By repeating the selective pulse N times, each time with the carrier frequency offset differently, it is possible to sample N slices in a single-shot. A comparison is made of the sequence with other three-dimensional single-shot methods. Experiments implementing the technique on a 3 T whole-body imaging system and a 2 T, 31-cm bore animal imager are described. Both phantom and brain images are presented. The principal advantages of the new sequence are its speed, the absence of rapid gradient switching and corresponding freedom from artifacts, its insensitivity to static magnetic field inhomogeneities, and its low acoustic noise. The main disadvantages are the low signal-to-noise ratio of the images produced and the concomitant limitation in resolution.

Width dependent collisionless electron dynamics in the static fields of the shock ramp, 2, Phase space portrait

Abstract. We study numerically in detail the behaviour of electrons in the strongly inhomogeneous static magnetic and electric fields, which are typical for thin quasiperpendicular collisionless shocks. We pay particular attention to the dependence of the final electron velocities on their initial velocities, for different shock widths. Electrons are completely magnetized when the shock is wide, but become demagnetized, and the energies that they acquire rapidly increase with the steepening of the field structure. One of the clear manifestations of the electron demagnetization is the loss of even approximate one-to-one correspondence of the downstream perpendicular velocity to the upstream perpendicular velocity. Electron reflection occurs despite the large cross-shock potential which accelerates electrons along the magnetic field (the regime of complete magnetization) or across the shock (strong demagnetization). The reflected ion fraction is sensitive to the potential, magnetic field jump, and ramp width.

1H-spectroscopic imaging with read gradient during acquisition in inhomogeneous fields: analysis, measurement strategy, and data processing.

The proton magnetic resonance spectroscopic imaging techniques that use read gradient during acquisition produce proton spectra with high spatial and moderately high spectroscopic resolution in a reasonable time for in vivo applications. These techniques suffer mainly from the spatial and spectral distortions caused by the convolution of spectral/spatial information (chemical-shift artifacts) and from the spectral shifts caused by static magnetic field inhomogeneities. The investigators analyze the chemical-shift artifacts in the presence of nonnegligible static magnetic field inhomogeneities and propose a postdetection processing scheme to correct for such effects. Spectral artifacts caused by chemical shifts, spectral line overlapping, streak broadening, and magnetic field inhomogeneities are discussed. The postdetection data processing scheme is demonstrated on measurements of a phantom as well as a human leg.

An MRI method for measuring T2 in the presence of static and RF magnetic field inhomogeneities.

A magnetic resonance imaging method for measuring the T2 relaxation time constant is proposed. It is based on the assumption that, under very general conditions, the MR signal near a spin echo has a special symmetry arising from the refocusing nature of the 180 degrees RF pulse. A gradient echo sampling of the spin echo (GESSE) sequence is implemented to evaluate T2 by collecting multiple gradient echoes before and after the spin echo. This approach is a modification of the GESFIDE sequence proposed by Ma and Wehrli. However, our approach compares images that are not separated by any RF pulses and, as a result, is insensitive to slice profile imperfections. In addition, the calculated T2 value does not rely on any special assumptions about the MRI signal behavior in the presence of an inhomogeneous static magnetic field and, hence, is insensitive to the presence of static magnetic field inhomogeneities.

Theory and application of static field inhomogeneity effects in gradient-echo imaging.

The influence of local static magnetic field inhomogeneities on gradient-echo imaging is discussed and the underlying theoretical aspects are reviewed. A high-resolution approach is suggested to suppress image distortion and restore signal loss due to spin dephasing. Acquisition of three-dimensional data sets not only overcomes part of the limitations associated with gradient echoes but also makes it possible to extract local information about the strength or direction of background gradients and relative susceptibility changes between different tissues. Applications of the suggested approach in the human brain for anatomical imaging as well as for extraction of physical and physiological parameters are presented and discussed.

Measurement of AC magnetic field distribution using magnetic resonance imaging.

Electric currents are applied to body in numerous applications in medicine such as electrical impedance tomography, cardiac defibrillation, electrocautery, and physiotherapy. If the magnetic field within a region is measured, the currents generating these fields can be calculated using the curl operator. In this study, magnetic fields generated within a phantom by currents passing through an external wire is measured using a magnetic resonance imaging (MRI) system. A pulse sequence that is originally designed for mapping static magnetic field inhomogeneity is adapted. AC current in the form of a burst sine wave is applied synchronously with the pulse sequence. The frequency of the applied current is in the audio range with an amplitude of 175-mA rms. It is shown that each voxel value of sequential images obtained by the proposed pulse sequence is modulated similar to a single tone broadband frequency modulated (FM) waveform with the ac magnetic field strength determining the modulation index. An algorithm is developed to calculate the ac magnetic field intensity at each voxel using the frequency spectrum of the voxel signal. Experimental results show that the proposed algorithm can be used to calculate ac magnetic field distribution within a conducting sample that is placed in an MRI system.

Magnetostatic state-selective deflection of a beam of laser-cooled atoms

We have demonstrated the transverse state-selective deflection of a beam of free-falling laser-cooled caesium 6 2 S 1 2 , F = 4 atoms by the inhomogeneous static magnetic field of a current-carrying wire. With currents of up to 45 A the positions of atoms in individual magnetic substates are clearly resolved and deflection angles as large as 25° are observed. By optically pumping the atoms toward the m F = 4 substate in the ground state, most of the atoms are deflected through the same angle. The current-carrying wire can be considered as a simple magnetostatic atomic-optical element.

Manipulating Beams of Ultra-cold Atoms with a Static Magnetic Field

We report preliminary results on the deflection of a beam of ultra-cold atoms by a static magnetic field. Caesium atoms trapped in a magneto-optical trap (MOT) are cooled using optical molasses, and then fall freely under gravity to form a beam of ultra-cold atoms. The atoms pass through a static inhomogeneous magnetic field produced by a single current-carrying wire, and are deflected by a force ▽(µB) dependent on the magnetic substate of the atom. The population of atoms in various magnetic substates can be altered by using resonant laser radiation to optically pump the atoms.

Analysis and correction of geometric distortions in 1.5 T magnetic resonance images for use in radiotherapy treatment planning

The aim of this study is to investigate and correct for machine- and object-related distortions in magnetic resonance images for use in radiotherapy treatment planning. Patients with brain tumours underwent magnetic resonance imaging (MRI) in the radiotherapy position with the head fixed by a plastic cast in a Perspex localization frame. The imaging experiments were performed on a 1.5 T whole body MRI scanner with 3 mT m-1 maximum gradient capability. Image distortions, caused by static magnetic field inhomogeneity, were studied by varying the direction of the read-out gradient. For purposes of accuracy assessment, external and internal landmarks were indicated. Tubes attached to the cast and in the localization frame served as external landmarks. In the midsagittal plane the brain-sinus sphenoidalis interface, the pituitary gland-sinus sphenoidalis interface, the sphenoid bone and the corpora of the cervical vertebra served as internal landmarks. Landmark displacements as observed in the reversed read-out gradient experiments were analysed with respect to the contributions of machine-related static magnetic field inhomogeneity and susceptibility and chemical shift artifacts. The machine-related static magnetic field inhomogeneity in the midsagittal plane was determined from measurements on a grid phantom. Distortions due to chemical shift effects were estimated for bone marrow containing structures such as the sphenoid bone and the corpora of the cervical vertebra using the values obtained from the literature. Susceptibility-induced magnetic field perturbations are caused by the patient and the localization frame. Magnetic field perturbations were calculated for a typical patient dataset. The midsagittal head image was converted into a susceptibility distribution by segmenting the image into water-equivalent tissues and air; also the Perspex localization frame was included in the susceptibility distribution. Given the susceptibility distribution, the magnetic field was calculated by numerically solving the Maxwell equations for a magnetostatic field. Results were shown as magnetic field perturbations and corresponding spatial distortions of internal and external landmarks. The midsagittal head images were corrected for the machine imperfections (gradient non-linearity and static magnetic field inhomogeneity). The locations of the external landmarks in the frame were also corrected for susceptibility artifacts. The efficacy of the corrections was evaluated for these external landmarks in the localization frame with known geometry. In this study at 1.5 T with read-out gradient strength of 3 mT m-1, machine-related, chemical shift and susceptibility-induced static magnetic held inhomogeneity were of the same order, resulting in spatial distortions between -2 and 2 mm with only negative values for the chemical shift effect. Both the patient and the localization frame proved to perturb the magnetic field. The field perturbations were shown to be additive. In total, static magnetic field inhomogeneity led to spatial distortions ranging from -2 to 4 mm in the direction of the read-out gradient. Non-linearity of the gradients resulted in spatial distortions ranging from -3.5 to 0.5 mm. After correction for the machine imperfections and susceptibility artifacts, the geometric accuracy of the landmarks in the localization frame was better than 1.3 mm.

Robust Refocusing Pulses of Limited Power

A series of optimized 180° refocusing pulses are derived using simulated annealing. These pulses are insensitive to simultaneous RF and static magnetic field inhomogeneity. They are superior to previously published pulses with similar characteristics, including a series derived by a different numerical optimization approach. The effect of limited integrated rotation angles (which are manifested as power and pulse length) on the phase dispersion and magnitude performance of the refocusing was investigated. Both phase uniformity and magnitude performance improve with increasing integrated rotation angle. Performance gain from optimization is substantial only at an integrated rotation angle of 2.5π or higher. At a particular integrated rotation angle, there is tradeoff between the phase uniformity and magnitude performance of refocusing. The tradeoff becomes more significant at smaller integrated rotation angle. Because of the need to limit pulse power forin vivoMR applications, the findings highlight the importance of optimizing pulse design for individual applications.

Correction for geometric distortion in echo planar images from B0 field variations

A method is described for the correction of geometric distortions occurring in echo planar images. The geometric distortions are caused in large part by static magnetic field inhomogeneities, leading to pixel shifts, particularly in the phase encode direction. By characterizing the field inhomogeneities from a field map, the image can be unwarped so that accurate alignment to conventionally collected images can be made. The algorithm to perform the unwarping is described, and results from echo planar images collected at 1.5 and 4 Tesla are shown.

Phase Constrained Encoding (PACE): A Technique for MRI in Large Static Field Inhomogeneities

In spin echo imaging, magnetization is assigned to a location defined by its frequency of rotation. In the presence of a static magnetic field inhomogeneity, however, this location does not correspond to the true location of the magnetization. This paper describes a magnetic resonance imaging technique called phase constrained encoding (PACE) that assigns magnetization to its true location through the use of a spin echo train and alternating readout gradients. Small artifactual side-bands occur in the point spread function but can be minimized or eliminated using higher gradient strengths, more echoes, and/or additional acquisitions. Implementation of a simple version of this technique confirms simulations.

Measurements of Magnetic Field Variations in the Human Brain Using a 3D‐FT Multiple Gradient Echo Technique

A magnetic resonance 3DFT multiple gradient-echo technique was used for measurements of the proton spectrum for each voxel in the measured slice. Water, fat, magnetic field and T2 distributions in the head of a normal volunteer and a patient with intracerebral hematoma were computed. Magnetic field variations caused by the head were calculated after correction for the static magnetic field inhomogeneity. Large local magnetic field variations up to 3 ppm were found in the human brain near interfaces between air or bone and brain tissues and 0.5 ppm between hematoma and brain tissue. Information about magnetic field variations could be useful for shimming procedures in vivo and for correcting artifacts in imaging and spectroscopy.

Theory of NMR signal behavior in magnetically inhomogeneous tissues: The static dephasing regime

This paper is devoted to a theory of the NMR signal behavior in biological tissues in the presence of static magnetic field inhomogeneities. We have developed an approach that analytically describes the NMR signal in the static dephasing regime where diffusion phenomena may be ignored. This approach has been applied to evaluate the NMR signal in the presence of a blood vessel network (with an application to functional imaging), bone marrow (for two specific trabecular structures, asymmetrical and columnar) and a ferrite contrast agent. All investigated systems have some common behavior. If the echo time TE is less than a known characteristic time tc for a given system, then the signal decays exponentially with an argument which depends quadratically on TE. This is equivalent to an R2* relaxation rate which is a linear function of TE. In the opposite case, when TE is greater than tc, the NMR signal follows a simple exponential decay and the relaxation rate does not depend on the echo time. For this time interval, R2* is a linear function of a) volume fraction sigma occupied by the field-creating objects, b) magnetic field Bo or just the objects' magnetic moment for ferrite particles, and c) susceptibility difference delta chi between the objects and the medium.

Simulation of nuclear magnetic resonance spin echoes using the Bloch equation: Influence of magnetic field inhomogeneities

There are a number of low cost nuclear magnetic resonance (NMR) applications that are based on measurements of spin-spin (T2) and spin-lattice (T1) relaxation times. Pulsed rf magnetic fields are typically used to flip the nuclear spins in these measurements. The ability to perform these measurements in relatively nonuniform magnetic fields is a factor in minimizing costs. In this work, we explore the limitations of field inhomogeneity on spin echo techniques for measuring relaxation times. Using a computer model that was developed for this study, we numerically integrate the Bloch equation to simulate spin echo peaks for CPMG and other pulse sequences. We quantify how higher intensity rf pulses result in increased amplitudes of spin echo peaks in an inhomogeneous static magnetic field. An rf amplitude which is five times the maximum inhomogeneity in the static field results in less than 0.5% attenuation between even numbered peaks in a CPMG sequence.

Phase-space study of the Stern-Gerlach experiment

We study the motion of neutral spinning particles in static inhomogeneous magnetic fields, where the orbital motion and spin dynamics do not factorize. Using the phase-space representation of quantum mechanics, the Moyal propagator is obtained for the case of a linearized field. As an example, the evolution of particles in coherent rotational states is calculated. In order to interpret the Wigner state function in a classical mechanical way, we calculated the Husimi functions.

Simultaneous Determination of the Macroscopic and Microscopic Static Magnetic Field Inhomogeneity (MAGSUS)

A simple nuclear magnetic resonance imaging method for simultaneous mapping of the macroscopic static field B and the microscopic Larmor frequency distribution Ψ within the picture elements (pixels) is presented using multiecho acquisition. The sequence (45°)-τ 1, 1 -(−45°)-τ D-(180°)-τ D + τ 1, 1 /2-echo 1-τ-echo 2-τ-echo 3 . is based on the 1- 1 hard-pulse excitation which provides a transverse magnetization with narrow minima as a function of offset from the transmitter frequency. This excitation results in images with dark lines of constant Larmor frequency for B field mapping. The slice-selective spin-echo rephasing mode with additional gradient echoes allows one to take advantage of the phases of the transverse magnetization components with different Larmor frequencies. The interference of the magnetization of the spin ensembles within the pixels depends strongly on the time interval between the slice-selective 180° pulse and the data acquisition. For "echo 1," high contrast C max/min = S max/ S min > 5 between the signals of pixels at excitation maximum ( S max) and excitation minimum ( S min) is obtained even in cases with broad Larmor frequency distribution in each pixel. Images from "echo 2" and subsequent echoes show clearly reduced contrast C max/min < 2 of the line pattern in regions of pronounced microscopic inhomogeneity. For example, trabecular bone marrow shows a broadened width of the field distribution with a range of more than 20 Hz within each picture element. The contrast C max/min in the second or later echo images is not clearly reduced in muscle tissue or subcutaneous fat with better microscopic field homogeneity. The sequence is used to find volumes of interest with good macroscopic and microscopic homogeneity for localized spectroscopy in vivo and to determine the Larmor frequency distribution within bone marrow for correlations with the trabecular bone density. The MAGSUS method does not require further data processing.

MR flow measurement using RF phase gradients in receiver coil arrays.

Radio frequency (RF) phase gradients in the receiver coil field pattern can encode flow velocity information in magnetic resonance (MR) images in the form of phase variations. These phase variations are not readily observed in MR images because they are relatively small compared to phase variations caused by static magnetic field (B0) inhomogeneities, susceptibility variations, and other sources. However, the phase contributions from these other sources are independent of the receiver coil. Therefore, the RF phase gradient encoded flow information can be recovered by subtracting images obtained simultaneously using arrays of independent receiver coils and a multiple channel receiver. This flow velocity information can be extracted retrospectively from standard imaging sequences, including flow-compensated sequences. No additional time is required for the flow study as the flow measurements are made using sequences chosen for optimal imaging, and the images from each coil are obtained simultaneously. Initial results indicate that sufficient sensitivity is obtained to make flow measurements in the range of velocities commonly found in the carotid arteries and other major vessels. In principle, the method works with only two receiver coils. However, additional elements provide additional phase measurements that can be used to increase accuracy, remove ambiguities in flow direction or velocity calculations, and increase the region over which velocity measurements can be accurately made.