Conjugate phase MRI reconstruction with spatially variant sample density correction

A new image reconstruction method to correct for the effects of magnetic field inhomogeneity in non-Cartesian sampled magnetic resonance imaging (MRI) is proposed. The conjugate phase reconstruction method, which corrects for phase accumulation due to applied gradients and magnetic field inhomogeneity, has been commonly used for this case. This can lead to incomplete correction, in part, due to the presence of gradients in the field inhomogeneity function. Based on local distortions to the k-space trajectory from these gradients, a spatially variant sample density compensation function is introduced as part of the conjugate phase reconstruction. This method was applied to both simulated and experimental spiral imaging data and shown to produce more accurate image reconstructions. Two approaches for fast implementation that allow the use of fast Fourier transforms are also described. The proposed method is shown to produce fast and accurate image reconstructions for spiral sampled MRI.     

A New Distortion Model for Strong Inhomogeneity Problems in Echo-Planar MRI

This paper proposes a new distortion model for strong inhomogeneity problems in echo planar imaging (EPI). Fast imaging sequences in magnetic resonance imaging (MRI), such as EPI, are very important in applications where temporal resolution or short total acquisition time is essential. Unfortunately, fast imaging sequences are very sensitive to variations in the homogeneity of the main magnetic field. The inhomogeneity leads to geometrical distortions and intensity changes in the image reconstructed via fast Fourier transform. Also, under strong inhomogeneity, the accelerated intravoxel dephase may overly attenuate signals coming from regions with higher inhomogeneity variations. Moreover, coarse discretization schemes for the inhomogeneity are not able to cope with this problem, producing discretization artifacts when large inhomogeneity variations occur. Most of the existing models do not attempt to solve this problem. In this paper, we propose a modification of the discrete distortion model to incorporate the effects of the intravoxel inhomogeneity and to minimize the discretization artifacts. As a result, these problems are significantly reduced. Extensive experiments are shown to demonstrate the achieved improvements. Also, the performance of the new model is evaluated for conjugate phase, least squares method (minimized iteratively using conjugated gradients), and regularized methods (using a total variation penalty).      

Multishot rosette trajectories for spectrally selective MR imaging

In nuclear magnetic resonance, different spectral components often correspond to different chemical species and as such, spectral selectivity can be a valuable tool for diagnostic imaging. In the work presented here, a multishot image acquisition method based upon rosette k-space trajectories has been developed and implemented for spectrally selective magnetic resonance imaging (MRI). Parametric forms for the gradient waveforms and design constraints are derived, and an example multishot gradient design is presented. The spectral behaviour for this imaging method is analyzed in a simulation model. For frequencies that are near to the resonant frequency, this method results in a lower intensity, but undistorted image, while for frequencies that are off-resonance by a large amount, the object is incoherently dephased into noise. A method by which acquisitions are delayed by small amounts is introduced to further reduce the residual intensity for off-resonant signals. An image reconstruction method based on convolution gridding, including a correction method for small amounts of magnetic field inhomogeneity, is implemented. Finally, the spectral selectivity is demonstrated in vivo in a study in which both water and lipid images are generated from a single imaging data set     

Off-resonance correction of MR images

In magnetic resonance imaging (MRI), the spatial inhomogeneity of the static magnetic field can cause degraded images if the reconstruction is based on inverse Fourier transformation. This paper presents and discusses a range of fast reconstruction algorithms that attempt to avoid such degradation by taking the field inhomogeneity into account. Some of these algorithms are new, others are modified versions of known algorithms. Speed and accuracy of all these algorithms are demonstrated using spiral MRI.     

Polynomial modeling and reduction of RF body coil spatial inhomogeneity in MRI

The usefulness of statistical clustering algorithms developed for automatic segmentation of lesions and organs in magnetic resonance imaging (MRI) intensity data sets suffers from spatial nonstationarities introduced into the data sets by the acquisition instrumentation. The major intensity inhomogeneity in MRI is caused by variations in the B1-field of the radio frequency (RF) coil. A three-step method was developed to model and then reduce the effect. Using a least squares formulation, the inhomogeneity is modeled as a maximum variation order two polynomial. In the log domain the polynomial model is subtracted from the actual patient data set resulting in a compensated data set. The compensated data set is exponentiated and rescaled. Statistical comparisons indicate volumes of significant corruption undergo a large reduction in the inhomogeneity, whereas volumes of minimal corruption are not significantly changed. Acting as a preprocessor, the proposed technique can enhance the role of statistical segmentation algorithms in body MRI data sets.     

Reducing chemical shift artifacts in MRI in time-varying gradients

An image processing algorithm to reduce chemical shift artifacts in MRI (magnetic resonance imaging) with time-varying gradients and to obtain the chemical shift images without increasing the imaging time is presented. It is known that when both gradients in two directions of the imaging plane are time-varying, such as in the spiral-type scanning MRI, the chemical shift artifacts appear as a blurred image. The artifacts cannot be neglected, since the total power of the out-of-focus point spread function (PSF) for the blurred image equals that of the in-focus PSF. The proposed algorithm separates the chemical shift images by iteratively estimating the artifacts under an a priori constraint that the original images should have a real and nonnegative value. Computer simulation results show that the average amplitude of the artifacts can be reduced significantly after several iterations, and that the algorithm works well even when the observation noise exists.     

On the induced electric field gradients in the human body for magnetic stimulation by gradient coils in MRI

Prior theoretical studies indicate that the negative spatial derivative of the electric field induced by magnetic stimulation may be one of the main factors contributing to depolarization of the nerve fiber. This paper studies this parameter for peripheral nerve stimulation (PNS) induced by time-varying gradient fields during MRI scans. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic human, full-body model. Whole-body cylindrical and planar gradient sets in MRI systems and various input signals have been explored. The spatial distributions of the induced electric field and their gradients are calculated and attempts are made to correlate these areas with reported experimental stimulation data. The induced electrical field pattern is similar for both the planar coils and cylindrical coils. This study provides some insight into the spatial characteristics of the induced field gradients for PNS in MRI, which may be used to further evaluate the sites where magnetic stimulation is likely to occur and to optimize gradient coil design.     

Minimizing interference from magnetic resonance imagers duringelectrocardiography

Magnetic resonance imaging (MRI) allows a physician to obtain images of internal organs noninvasively. Imaging a moving organ such as the heart requires a trigger so that successive scans can be synchronized. In the case of cardiac imaging this trigger is the electrocardiogram (ECG). When a patient is in an MRI scanner he/she is subjected to both static and dynamic magnetic fields which can cause interference In the ECG. The dynamic fields consist of 8- to 64-MHz radio frequency (RF) pulses and low-frequency magnetic gradient pulses with frequency components below 100 Hz. Conventional bandpass filters are only moderately effective because the passband allows magnetic gradient-induced interference to be superimposed on the ECG, causing distortion of the signal. This paper describes a technique which can be used to remove induced MRI gradient interference from an ECG recorded on a patient inside the bore of a MRI scanner. Induced signal from an external loop is subtracted from the ECG to minimize the low-frequency interference. The gradient induced low-frequency interference was reduced to approximately 20% of its magnitude when using conventional ECG amplifiers     

Reconstruction by weighted correlation for MRI with time-varying gradients

A general reconstruction algorithm for magnetic resonance imaging (MRI) with gradients having arbitrary time dependence is presented. This method estimates spin density by calculating the weighted correlation of the observed free induction decay signal and the phase modulation function at each point. A theorem which states that this method can be derived from the conditions of linearity and shift invariance is presented. Since these conditions are general, most of the MRI reconstruction algorithms proposed so far are equivalent to the weighted correlation method. An explicit representation of the point spread function (PSF) in the weighted correlation method is given. By using this representation, a method to control the PSF and the static field inhomogeneity effects is studied. A correction method for the inhomogeneity is proposed, and a limitation is clarified. Some simulation results are presented.     

Electromagnetics in magnetic resonance imaging

Magnetic resonance imaging (MRI) is a powerful new imaging method, which produces cross-sectional tomographic and three-dimensional images similar to those of x-ray computed tomography (CT). However, rather than relying on harmful ionizing radiation, MRT is based on the interaction between RF fields and certain atomic nuclei in the body, when they are in the presence of a strong magnetic field. An MRI system is one of the few complete systems in which the design relies heavily upon a knowledge of electromagnetics. We give a tutorial on the electromagnetic analysis and design of three key components of an MRI system, namely, the magnet, the gradient coil, and the radiofrequency (RF) coil. We also discuss the analysis and characterization of the interactions of RF electromagnetic fields with biological subjects     

True energy-minimal and finite-size biplanar gradient coil designfor MRI

Finite-sized high-performance planar magnetic field gradient coils in today's open configuration magnetic resonance imaging (MRI) systems have always been desirable for ever demanding imaging applications. The authors present a Lagrange multiplier technique for designing a minimum-energy gradient coil under a finite-size planar geometry constraint in addition to a set of magnetic field constraints. In this new design methodology, the surface current density on a finite size plane is represented by a two-dimensional (2-D) Fourier series expansion. Following the standard approach, the authors construct a functional F in terms of the stored magnetic energy and a set of field constraint points which are chosen over the desired imaging volume. Minimizing F, the authors obtain the continuous current density distribution for the finite-size planar gradient coil. Applying the stream function technique to the resulting continuous current distribution, the discrete current pattern can be generated. Employing the Biot-Savart law to the discrete current loops, the gradient magnetic field has been re-evaluated in order to validate the theory. Using this approach, the authors have been able to design a finite-size biplanar z-gradient coil which is capable of generating a gradient field of 40 mT /m @ 266 A. The excellent agreement between the analytical and numerical results has been achieved     

Magnetically induced currents in the canine heart: a finite elementstudy

A moderately detailed three-dimensional (3-D) finite element model of the conductive anatomy of a canine thorax was used to determine the fields and currents induced by a time-varying magnetic field that has been shown to cause irregular heart beats in canines. The 3-D finite element model of the canine thorax was constructed from CT scans and includes seven isotropic tissue conductivities and the anisotropic conductivity of skeletal muscle. The authors use this model to estimate the stimulation threshold associated with stimulation of the heart by the time-varying magnetic field of a figure-eight coil. Variants of the thoracic model were also constructed to examine the sensitivity of model results to variations in model size, shape, and conductive inhomogeneity and anisotropy. The authors' results show that myocardial fields were only mildly sensitive to thoracic size. However, model shape and conductive inhomogeneity and anisotropy substantially influenced the magnitude and distribution of myocardial fields and currents. The authors' results suggest that an induced peak field magnitude of ≈1 V/cm is required to stimulate the heart with the magnetic excitation simulated in this study     

A simple design methodology for elliptical cross-section,transverse, asymmetric, head gradient coils for MRI

A simple design process for the design of elliptical cross-section, transverse gradient coils for use in magnetic resonance imaging (MRI) is presented. This process is based on a flexible stochastic optimization method and results in designs of high linearity and efficiency with low switching times. A design study of a shielded, transverse asymmetric elliptical coil set for use in neural imaging is presented and includes the minimization of the torques experienced by the gradient set     

Method of propulsion of a ferromagnetic core in the cardiovascular system through magnetic gradients generated by an MRI system

This paper reports the use of a magnetic resonance imaging (MRI) system to propel a ferromagnetic core. The concept was studied for future development of microdevices designed to perform minimally invasive interventions in remote sites accessible through the human cardiovascular system. A mathematical model is described taking into account various parameters such as the size of blood vessels, the velocities and viscous properties of blood, the magnetic properties of the materials, the characteristics of MRI gradient coils, as well as the ratio between the diameter of a spherical core and the diameter of the blood vessels. The concept of magnetic propulsion by MRI is validated experimentally by measuring the flow velocities that magnetized spheres (carbon steel 1010/1020) can withstand inside cylindrical tubes under the different magnetic forces created with a Siemens Magnetom Vision 1.5 T MRI system. The differences between the velocities predicted by the theoretical model and the experiments are approximately 10%. The results indicate that with the technology available today for gradient coils used in clinical MRI systems, it is possible to generate sufficient gradients to propel a ferromagnetic sphere in the larger sections of the arterial system. In other words, the results show that in the larger blood vessels where the diameter of the microdevices could be as large as a couple a millimeters, the few tens of mT/m of gradients required for displacement against the relatively high blood flow rate is well within the limits of clinical MRI systems. On the other hand, although propulsion of a ferromagnetic core with diameter of approximately 600 microm may be possible with existing clinical MRI systems, gradient amplitudes of several T/m would be required to propel a much smaller ferromagnetic core in small vessels such as capillaries and additional gradient coils would be required to upgrade existing MRI systems for operations at such a scale.     

The use of adaptive algorithms for obtaining optimal electricalshimming in magnetic resonance imaging (MRI)

A method of determining the dc coil current values to electrically shim the static magnetic fields used in magnetic resonance imaging (MRI) using modified steepest descent adaptive algorithm is described. Using a 32 cm diameter by a 40 cm long water phantom as the test volume, the algorithm achieved field homogeneities of 0.2 parts per million (ppm) peak-to-peak within a 20 cm diameter spherical imaging volume, and 1.3 ppm peak-to-peak within the entire phantom. The algorithm achieved an inhomogeneity variance of 0.18 ppm2. The shim system was successfully modeled as a sum of adaptive linear combiners. The model contains 13 parameters that can be varied, 12 shim coil currents, and the receiver mixer frequency. The model was then used to predict key adaptive algorithm parameters. Experimental verification of these parameters lends support to the accuracy of the model.     

Measurement of AC magnetic field distribution using magneticresonance 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     

A homogeneity correction method for magnetic resonance imaging with time-varying gradients

When time-varying gradients are used for imaging, the off-resonance behavior does not just cause geometric distortion as is the case with spin-warp imaging, but changes the shape of the impulse response and causes blurring. This effect is well known for projection reconstruction and spiral k-space scanning sequences. The authors introduce a reconstruction and homogeneity correction method to correct for the zeroth order effects of inhomogeneity using prior knowledge of the inhomogeneity. In this method, the data are segmented according to collection time, reconstructed using some fast, linear algorithm, correlated for inhomogeneity, and then superimposed to yield a homogeneity corrected image. This segmented method is compared to a conjugate phase reconstruction in terms of degree of correction and execution time. The authors apply this method to in vivo images using projection-reconstruction and spiral-scan sequences.     

Performance analysis for magnetic resonance imaging with nonlinear encoding fields

Nonlinear spatial encoding fields for magnetic resonance imaging (MRI) hold great promise to improve on the linear gradient approaches by, for example, enabling reduced imaging times. Imaging schemes that employ general nonlinear encoding fields are difficult to analyze using traditional measures. In particular, the resolution is spatially varying, characterized by a position-dependent point spread function (PSF). Likewise, the use of nonlinear encoding fields creates an additional spatial dependence on the signal-to-noise ratio (SNR). Although the two properties of resolution and SNR are linked, in this work we focus on the latter. To this end, we examine the pixel variance, which requires a computation that is often not feasible for nonlinear encoding schemes. This paper presents a general formulation for the performance analysis of imaging schemes using arbitrary encoding fields. The analysis leads to the derivation of a practical and computationally efficient performance metric, which is demonstrated through simulation examples.     

Cartesian echo planar hybrid scanning with two to eight echoes

A method of fast nuclear magnetic resonance (NMR) imaging which uses only square wave gradient shapes and also collects data on Cartesian coordinates in a way similar to the blipped echo planar imaging method (BEPI) is described. The method is a heuristic attempt at finding an optimal data collection strategy for NMR imaging. Its advantages and disadvantages compared to other methods are carefully analyzed. Clinical size anatomical (head and body) images are shown. It is found that the interecho phase-angle discrepancies that are caused bv the B(0) inhomogeneity and by the gradient wave form distortion can largely be eliminated by using the half Fourier method with full Fourier phase map correction, but one phase map is required for each echo. GRASS/FLASH spoiling techniques are incorporated into the method in order to allow multiecho speed increases for scans which would run under 10 s using a single-echo method. The technique can be applied directly to GRASS/FLASH itself, as is demonstrated by a two-echo GRASS scan. The fastest image was 1.9 s.     

Accurate alignment of functional EPI data to anatomical MRI using a physics-based distortion model

Mapping of functional magnetic resonance imaging (fMRI) to conventional anatomical MRI is a valuable step in the interpretation of fMRI activations. One of the main limits on the accuracy of this alignment arises from differences in the geometric distortion induced by magnetic field inhomogeneity. This paper describes an approach to the registration of echo planar image (EPI) data to conventional anatomical images which takes into account this difference in geometric distortion. We make use of an additional spin echo EPI image and use the known signal conservation in spin echo distortion to derive a specialized multimodality nonrigid registration algorithm. We also examine a plausible modification using log-intensity evaluation of the criterion to provide increased sensitivity in areas of low EPI signal. A phantom-based imaging experiment is used to evaluate the behavior of the different criteria, comparing nonrigid displacement estimates to those provided by a imagnetic field mapping acquisition. The algorithm is then applied to a range of nine brain imaging studies illustrating global and local improvement in the anatomical alignment and localization of fMRI activations.