Density compensation functions for spiral MRI

Rapid mapping of flow velocity using a new PARSE method

A new method for flow velocity mapping is presented here. Instead of the conventional approach of employing two images (velocity sensitive and control) to generate velocity information, in the new method one determines the velocity directly from a single-shot acquisition by solving an inverse problem. This technique is a variant of single-shot parameter assessment by retrieval from signal encoding (SS-PARSE). The results of simulation and phantom studies show strong agreement with the actual velocities. The prototype method can measure velocities in the range of -50 to 50 cm/s, which is roughly appropriate for future applications in dynamic blood flow measurement in carotid arteries.

Strategies for inner volume 3D fast spin echo magnetic resonance imaging using nonselective refocusing radio frequency pulses

Fast spin echo (FSE) trains elicited by nonselective "hard" refocusing radio frequency (RF) pulses have been proposed as a means to enable application of FSE methods for high-resolution 3D magnetic resonance imaging (MRI). Hard-pulse FSE (HPFSE) trains offer short (3-4 ms) echo spacings, but are unfortunately limited to imaging the entire sample within the coil sensitivity thus requiring lengthy imaging times, consequently limiting clinical application. In this work we formulate and analyze two general-purpose combinations of 3D HPFSE with inner volume (IV) MR imaging to circumvent this limitation. The first method employs a 2D selective RF excitation followed by the HPFSE train and focuses on required properties of the spatial excitation profile with respect to limiting RF pulse duration in the 5-6 ms range. The second method employs two orthogonally selective 1D RF excitations (a 90x degrees - 180y degrees pair) to generate an echo from magnetization within the volume defined by their intersection. Subsequent echoes are formed via the HPFSE train, placing the focus of the method on (a) avoiding spurious echoes that may arise from transverse magnetization located outside the slab intersection when it is unavoidably affected by the nonselective refocusing pulses and (b) avoiding signal losses due to the necessarily different spacing (in time) of the RF pulse applications. The performance of each method is experimentally measured using Carr-Purcell-Meiboom-Gill (CPMG) multi-echo imaging, enabling examination of the magnetization evolution throughout the echo train. The methods as implemented achieve 95% to 97% outer volume signal suppression, and higher suppression appears to be well within reach, by further refinement of the selective RF excitations. Example images of the human brain and spine are presented with each technique. We conclude that the SNR efficiency of volume imaging in conjunction with the short echo spacing afforded by hard pulse trains enables high-resolution 3D HPFSE MRI of a small field-of-view (FOV) with minimal aliasing artifact.

Decomposed direct matrix inversion for fast non-cartesian SENSE reconstructions

A new k-space direct matrix inversion (DMI) method is proposed here to accelerate non-Cartesian SENSE reconstructions. In this method a global k-space matrix equation is established on basic MRI principles, and the inverse of the global encoding matrix is found from a set of local matrix equations by taking advantage of the small extension of k-space coil maps. The DMI algorithm's efficiency is achieved by reloading the precalculated global inverse when the coil maps and trajectories remain unchanged, such as in dynamic studies. Phantom and human subject experiments were performed on a 1.5T scanner with a standard four-channel phased-array cardiac coil. Interleaved spiral trajectories were used to collect fully sampled and undersampled 3D raw data. The equivalence of the global k-space matrix equation to its image-space version, was verified via conjugate gradient (CG) iterative algorithms on a 2x undersampled phantom and numerical-model data sets. When applied to the 2x undersampled phantom and human-subject raw data, the decomposed DMI method produced images with small errors (< or = 3.9%) relative to the reference images obtained from the fully-sampled data, at a rate of 2 s per slice (excluding 4 min for precalculating the global inverse at an image size of 256 x 256). The DMI method may be useful for noise evaluations in parallel coil designs, dynamic MRI, and 3D sodium MRI with fixed coils and trajectories.

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.

Iterative RF pulse design for multidimensional, small-tip-angle selective excitation

The excitation k-space perspective on small-tip-angle selective excitation has facilitated RF pulse designs in a range of MR applications. In this paper, k-space-based design of multidimensional RF pulses is formulated as a quadratic optimization problem, and solved efficiently by the iterative conjugate-gradient (CG) algorithm. Compared to conventional design approaches, such as the conjugate-phase (CP) method, the new design approach is beneficial in several regards. It generally produces more accurate excitation patterns. The improvement is particularly significant when k-space is undersampled, and it can potentially shorten pulse lengths. A prominent improvement in accuracy is also observed when large off-resonance gradients are present. A further boost in excitation accuracy can be accomplished in regions of interest (ROIs) if they are specified together with "don't-care" regions. The density compensation function (DCF) is no longer required. In addition, regularization techniques allow control over integrated and peak pulse power.

Free-breathing, three-dimensional coronary artery magnetic resonance angiography: comparison of sequences

PURPOSE

To compare six free-breathing, three-dimensional, magnetization-prepared coronary magnetic resonance angiography (MRA) sequences.

MATERIALS AND METHODS

Six bright-blood sequences were evaluated: Cartesian segmented gradient echo (C-SGE), radial SGE (R-SGE), spiral SGE (S-SGE), spiral gradient echo (S-GE), Cartesian steady-state free precession (C-SSFP), and radial SSFP (R-SSFP). The right coronary artery (RCA) was imaged in 10 healthy volunteers using all six sequences in randomized order. Images were evaluated by two observers with respect to signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), visible vessel length, vessel edge sharpness, and vessel diameter.

RESULTS

C-SSFP depicted RCA over the longest distance with high vessel sharpness, good SNR, and excellent background suppression. S-GE provided best SNR and CNR in proximal segments, but more vessel blurring and poorer background suppression, resulting in poor visualization of distal segments. R-SSFP images showed good background suppression and best vessel sharpness, but only moderate SNR. C-SGE provided good SNR and reasonable CNR, but lowest vessel sharpness. S-SGE and R-SGE visualized the RCA over the smallest distance, mostly due to vessel blurring and low SNR, respectively.

CONCLUSION

Overall, Cartesian SSFP provided the best image quality with excellent vessel sharpness, visualization of long vessel segments, and good SNR and CNR.

Iterative Next-Neighbor Regridding (INNG): improved reconstruction from nonuniformly sampled k-space data using rescaled matrices

The reconstruction of MR images from nonrectilinearly sampled data is complicated by the fact that the inverse 2D Fourier transform (FT) cannot be performed directly on the acquired k-space data set. k-Space gridding is commonly used because it is an efficient reconstruction method. However, conventional gridding requires optimized density compensation functions (DCFs) to avoid profile distortions. Oftentimes, the calculation of optimized DCFs presents an additional challenge in obtaining an accurately gridded reconstruction. Another type of gridding algorithm, the block uniform resampling (BURS) algorithm, often requires singular value decomposition (SVD) regularization to avoid amplification of data imperfections, and under some conditions it is difficult to adjust the regularization parameters. In this work, new reconstruction algorithms for nonuniformly sampled k-space data are presented. In the newly proposed algorithms, high-quality reconstructed images are obtained from an iterative reconstruction that is performed using matrices scaled to sizes greater than that of the target image matrix. A second version partitions the sampled k-space region into several blocks to avoid limitations that could result from performing multiple 2D-FFTs on large data matrices. The newly proposed algorithms are a simple alternative approach to previously proposed optimized gridding algorithms.

Theoretical and numerical aspects of transmit SENSE

The ideas of parallel imaging techniques, designed to shorten the acquisition time by the simultaneous use of multiple receive coils, can be adapted for parallel transmission of a spatially selective multidimensional RF pulse. In analogy to data acquisition, a multidimensional RF pulse follows a certain trajectory in k-space. Shortening this trajectory shortens the pulse duration. The use of multiple transmit coils, each with its own time-dependent waveform and spatial sensitivity, compensates for the missing parts of k-space. This results in a maintained spatial definition of the pulse profile while its duration is reduced. This paper describes the basic equations of parallel transmission with arbitrarily shaped transmit coils ("Transmit SENSE") focusing on two-dimensional RF pulses. Results of numerical studies are presented demonstrating the theoretical feasibility of the approach.

Parsing local signal evolution directly from a single-shot MRI signal: a new approach for fMRI

In this work a new single-shot MRI method, single-shot parameter assessment by retrieval from signal encoding (SS-PARSE), is introduced. This method abandons a fundamental simplifying assumption that is used in conventional MRI methods. Established MRI methods implicitly assume that the local intrinsic signal does not change its amplitude or phase during signal acquisition, even though these changes may be substantial, especially during the relatively long signals used in single-shot image acquisitions. SS-PARSE, on the other hand, acknowledges local decay and phase evolution, and models each signal datum as a sample from (k,t)-space rather than k-space. Because of this more accurate signal model, SS-PARSE promises improved performance in terms of accuracy and robustness, but requires more intensive reconstruction computations. The theoretical properties of the method are discussed, and simulation results are presented that demonstrate more robust and accurate measurements of relaxation rate changes associated with brain activation in functional MRI (fMRI), freedom from geometric errors due to off-resonance frequencies, and better tolerance of the large susceptibility gradients that occur naturally in parts of the brain. In addition, this technique has the potential to assess nonexponential relaxation behavior during a single-shot signal.

2D-RF-pulse-encoded curved-slice imaging

A new approach to curved-slice imaging is described in which spatial resolution is achieved using 2D-RF-pulse- and conventional-frequency encoding. This approach offers the opportunity to image curved anatomical structures directly using curved single-slice MRI. A set of 2D-RF pulses is employed to excite transverse magnetization in an arbitrarily shaped curved-slice profile in three-dimensional space. Spatial resolution along the curved-slice direction is achieved by encoding the different volume elements of the slice using a set of specially designed RF pulses and an appropriate encoding scheme. The remaining spatial direction is measured using conventional-frequency encoding. Phantom and in vivo experiments were carried out to illustrate the basic feasibility and the limitations of this approach.

An improved gridding method for spiral MRI using nonuniform fast Fourier transform

The algorithm of Liu and Nguyen [IEEE Microw. Guided Wave Lett. 8 (1) (1998) 18; SIAM J. Sci. Comput. 21 (1) (1999) 283] for nonuniform fast Fourier transform (NUFFT) has been extended to two dimensions to reconstruct images using spiral MRI. The new gridding method, called LS_NUFFT, minimizes the reconstruction approximation error in the Least Square sense by generated convolution kernels that fit for the spiral k-space trajectories. For analytical comparison, the LS_NUFFT has been fitted into a consistent framework with the conventional gridding methods using Kaiser-Bessel gridding and a recently proposed generalized FFT (GFFT) approach. Experimental comparison was made by assessing the performance of the LS_NUFFT with that of the standard direct summation method and the Kaiser-Bessel gridding method, using both digital phantom data and in vivo experimental data. Because of the explicitly optimized convolution kernel in LS_NUFFT, reconstruction results showed that the LS_NUFFT yields smaller reconstruction approximation error than the Kaiser-Bessel gridding method, but with the same computation complexity.

Improved depiction of small anatomic structures in MR images using Gaussian-weighted spirals and zero-filled interpolation

Partial-volume artifacts reduce the contrast and continuity of small structures in magnetic resonance images. Zero-filled interpolation (ZFI) has been known for some time as a useful technique to reduce partial-volume artifacts and improve the appearance of small structures and edges. However, its use is limited by the fact that ZFI can exacerbate image artifacts. For example, it can exacerbate Gibbs ringing, also known as the truncation artifact, which manifests itself as spurious ringing around sharp edges. Currently, the most common technique to address this problem is post-acquisition filtering, which causes blurring in the image. Using ZFI in conjunction with a variable-density sampling method designed to reduce ringing is proposed as a possible solution to this problem. This approach is demonstrated with a Gaussian-weighted spiral and is compared to conventional spiral sampling both with and without the application of a filter used to reduce ringing. The two spiral sampling techniques are compared using simulations, phantom images, and in vivo brain images. The Gaussian-weighted spiral demonstrates reduced ringing without the loss of spatial resolution commonly associated with post-acquisition filtering. Additionally, this sampling technique is shown to work well in conjunction with ZFI to reduce partial-volume artifacts without the apparent increase in Gibbs ringing usually associated with zero-filled reconstruction. This approach will be most useful for imaging techniques such as MR angiography which are known to be sensitive to partial-volume effects, as well as when imaging anatomic regions associated with more severe Gibbs ringing.

Transmit SENSE

The idea of using parallel imaging to shorten the acquisition time by the simultaneous use of multiple receive coils can be adapted for the parallel transmission of a spatially-selective multidimensional RF pulse. As in data acquisition, a multidimensional RF pulse follows a certain k-space trajectory. Shortening this trajectory shortens the pulse duration. The use of multiple transmit coils, each with its own time-dependent waveform and spatial sensitivity, can compensate for the missing parts of the excitation k-space. This results in a maintained spatial definition of the pulse profile, while its duration is reduced. This work introduces the concept of parallel transmission with arbitrarily shaped transmit coils (termed "Transmit SENSE"). Results of numerical studies demonstrate the theoretical feasibility of the approach. The experimental proof of principle is provided on a commercial MR scanner. The lack of multiple independent transmit channels was addressed by combining the excitation patterns from two separate subexperiments with different transmit setups. Shortening multidimensional RF pulses could be an interesting means of making 3D RF pulses feasible even for fast T(2)(*) relaxing species or strong main field inhomogeneities. Other applications might benefit from the ability of Transmit SENSE to improve the spatial resolution of the pulse profile while maintaining the transmit duration.

Effects of constant frequency noise in magnetic resonance imaging with nonuniform k-space sampling

Magnetic resonance images can be compromised by constant frequency (CF) noise, such as radio frequency (RF) noise. We investigate the effects of CF noise in four imaging methods with non-uniform k-space sampling: single-shot echo-planar imaging (EPI) with sinusoidal readout gradients, phase-encoded echo-planar spectroscopic imaging (EPSI) with sinusoidal readout gradients, projection-reconstruction imaging, and single-shot spiral imaging. The characteristics of the CF artifacts in each imaging method are studied with numerical simulations. CF noise is found to cause artifacts of nonclassic forms in the reconstructed images. Specifically, dashed-line, streak, and spiral patterns of CF noise appear in EPI/EPSI with sinusoidal readout gradients, projection-reconstruction imaging, and spiral imaging, respectively. The analytical expression for dashed-line artifacts is found to be a weighted sum of Bessel functions and is verified with in vivo experiments. The CF artifacts can be removed during post-processing by eliminating the noise spikes in the Fourier domain of the raw data.

Reconstruction of MR images from data acquired on an arbitrary k-space trajectory using the same-image weight

A sampling density compensation function denoted "same-image (SI) weight" is proposed to reconstruct MR images from the data acquired on an arbitrary k-space trajectory. An equation for the SI weight is established on the SI criterion and an iterative scheme is developed to find the weight. The SI weight is then used to reconstruct images from the data calculated on a random trajectory in a numerical phantom case and from the data acquired on interleaved spirals in an in vivo experiment, respectively. In addition, Pipe and Menon's weight (MRM 1999;41:179-186) is also used in the reconstructions to make a comparison. The images obtained with the SI weight were found to be slightly more accurate than those obtained with Pipe's weight.

Three-dimensional spiral MR imaging: Application to renal multiphase contrast-enhanced angiography

A fast MR pulse sequence with spiral in-plane readout and conventional 3D partition encoding was developed for multiphase contrast-enhanced magnetic resonance angiography (CE-MRA) of the renal vasculature. Compared to a standard multiphase 3D CE-MRA with FLASH readout, an isotropic in-plane spatial resolution of 1.4 x 1.4 mm(2) over 2.0 x 1.4 mm(2) could be achieved with a temporal resolution of 6 sec. The theoretical gain of spatial resolution by using the spiral pulse sequence and the performance in the presence of turbulent flow was evaluated in phantom measurements. Multiphase 3D CE-MRA of the renal arteries was performed in five healthy volunteers using both techniques. A deblurring technique was used to correct the spiral raw data. Thereby, the off-resonance frequencies were determined by minimizing the imaginary part of the data in image space. The chosen correction algorithm was able to reduce image blurring substantially in all MRA phases. The image quality of the spiral CE-MRA pulse sequence was comparable to that of the FLASH CE-MRA with increased spatial resolution and a 25% reduced contrast-to-noise ratio. Additionally, artifacts specific to spiral MRI could be observed which had no impact on the assessment of the renal arteries.

New approach to gridding using regularization and estimation theory

When sampling under time-varying gradients, data is acquired over a non-equally spaced grid in k-space. The most computationally efficient method of reconstruction is first to interpolate the data onto a Cartesian grid, enabling the subsequent use of the inverse fast Fourier transform (IFFT). The most commonly used interpolation technique is called gridding, and is comprised of four steps: precompensation, convolution with a Kaiser-Bessel window, IFFT, and postcompensation. Recently, the author introduced a new gridding method called Block Uniform ReSampling (BURS), which is both optimal and efficient. The interpolation coefficients are computed by solving a set of linear equations using singular value decomposition (SVD). BURS requires neither the pre- nor the postcompensation steps, and resamples onto an n x n grid rather than the 2n x 2n matrix required by conventional gridding. This significantly decreases the computational complexity. Several authors have reported that although the BURS algorithm is very accurate, it is also sensitive to noise. As a consequence, even in the presence of a low level of measurement noise, the resulting image is often highly contaminated with noise. In this work, the origin of the noise sensitivity is traced back to the potentially ill-posed matrix inversion performed by BURS. Two approaches to the solution are presented. The first uses regularization theory to stabilize the inversion process. The second formulates the interpolation as an estimation problem, and employs estimation theory for the solution. The new algorithm, called rBURS, contains a regularization parameter, which is used to trade off the accuracy of the result against the signal-to-noise ratio (SNR). The results of the new method are compared with those obtained using conventional gridding via simulations. For the SNR performance of conventional gridding, it is shown that the rBURS algorithm exhibits equal or better accuracy. This is achieved at a decreased computational cost compared to conventional gridding.

Direct reconstruction of MR images from data acquired on a non-Cartesian grid using an equal-phase-line algorithm

The equal-phase line (EPL) algorithm is proposed as a means of allowing rapid Fourier transform (FT) reconstruction of MR image data acquired on a non-Cartesian grid. The pixels on the image are grouped according to their positions. The pixels in a group have the same phase in the complex exponential function -exp[j2pi(xu + yv)] and receive the same contribution from a data point. Each group is related to an EPL in the image space. The contribution of a data point can then be distributed to the pixels along the EPLs. The described EPL algorithm enables a decrease of the reconstruction time to about 40% of the direct FT (DrFT) for the non-Cartesian data. A numerical phantom and two sets of in vivo spiral data were used to investigate an optimal number of the EPLs and to measure the reconstruction time. The EPL algorithm runs nearly as fast as the look-up table (LUT) method (Dale et al. IEEE Trans Med Imaging 2001;20:207-217), but it does not require a large memory to store the coefficients in advance, as is required in the LUT method. Thus, the EPL algorithm can be used to reconstruct images up to 512 x 512 pixels in size in a PC of limited memory, and may be more conveniently applied to a multiprocessor system.

Quiet imaging with interleaved spiral read-out

The acoustic noise generated during an MRI sequence can be effectively reduced with the help of soft gradient pulses using sinusoidal ramps. The long slope duration, however, leads to long acquisition times. The use of interleaved spiral trajectories, calculated with long gradient slopes, is proposed to reduce the acquisition time while maintaining low acoustic noise levels. The practicality of this approach is demonstrated on phantom and volunteer images.

Modified block uniform resampling (BURS) algorithm using truncated singular value decomposition: fast accurate gridding with noise and artifact reduction

The block uniform resampling (BURS) algorithm is a newly proposed regridding technique for nonuniformly-sampled k-space MRI. Even though it is a relatively computationally intensive algorithm, since it uses singular value decomposition (SVD), its procedure is simple because it requires neither a pre- nor a postcompensation step. Furthermore, the reconstructed image is generally of high quality since it provides accurate gridded values when the local k-space data SNR is high. However, the BURS algorithm is sensitive to noise. Specifically, inaccurate interpolated data values are often generated in the BURS algorithm if the original k-space data are corrupted by noise, which is virtually guaranteed to occur to some extent in MRI. As a result, the reconstructed image quality is degraded despite excellent performance under ideal conditions. In this article, a method is presented which avoids inaccurate interpolated k-space data values from noisy sampled data with the BURS algorithm. The newly proposed technique simply truncates a series of singular values after the SVD is performed. This reduces the computational demand when compared with the BURS algorithm, avoids amplification of noise resulting from small singular values, and leads to image SNR improvements over the original BURS algorithm.

A rapid look-up table method for reconstructing MR images from arbitrary K-space trajectories

Look-up tables (LUTs) are a common method for increasing the speed of many algorithms. Their use can be extended to the reconstruction of nonuniformly sampled k-space data using either a discrete Fourier transform (DFT) algorithm or a convolution-based gridding algorithm. A table for the DFT would be precalculated arrays of weights describing how each data point affects all of image space. A table for a convolution-based gridding operation would be a precalculated table of weights describing how each data point affects a small k-space neighborhood. These LUT methods were implemented in C++ on a modest personal computer system; they allowed a radial k-space acquisition sequence, consisting of 180 views of 256 points each, to be gridded in 36.2 ms, or, in approximately 800 ns/point. By comparison, a similar implementation of the gridding operation, without LUTs, required 45 times longer (1639.2 ms) to grid the same data. This was possible even while using a 4 x 4 Kaiser-Bessel convolution kernel, which is larger than typically used. These table-based computations will allow real time reconstruction in the future and can currently be run concurrently with the acquisition allowing for completely real-time gridding.

Applying the uniform resampling (URS) algorithm to a lissajous trajectory: fast image reconstruction with optimal gridding

Various kinds of nonrectilinear Cartesian k-space trajectories have been studied, such as spiral, circular, and rosette trajectories. Although the nonrectilinear Cartesian sampling techniques generally have the advantage of fast data acquisition, the gridding process prior to 2D-FFT image reconstruction usually requires a number of additional calculations, thus necessitating an increase in the computation time. Further, the reconstructed image often exhibits artifacts resulting from both the k-space sampling pattern and the gridding procedure. To date, it has been demonstrated in only a few studies that the special geometric sampling patterns of certain specific trajectories facilitate fast image reconstruction. In other words, the inherent link among the trajectory, the sampling scheme, and the associated complexity of the regridding/reconstruction process has been investigated to only a limited extent. In this study, it is demonstrated that a Lissajous trajectory has the special geometric characteristics necessary for rapid reconstruction of nonrectilinear Cartesian k-space trajectories with constant sampling time intervals. Because of the applicability of a uniform resampling (URS) algorithm, a high-quality reconstructed image is obtained in a short reconstruction time when compared to other gridding algorithms.

On the optimality of the gridding reconstruction algorithm

Gridding reconstruction is a method to reconstruct data onto a Cartesian grid from a set of nonuniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction error. Least squares reconstruction (LSR), on the other hand, is another method which is optimal in the sense that it minimizes the reconstruction error. This method is computationally intensive and, in many cases, sensitive to measurement noise. Hence, it is rarely used in practice. Despite their seemingly different approaches, the gridding and LSR methods are shown to be closely related. The similarity between these two methods is accentuated when they are properly expressed in a common matrix form. It is shown that the gridding algorithm can be considered an approximation to the least squares method. The optimal gridding parameters are defined as the ones which yield the minimum approximation error. These parameters are calculated by minimizing the norm of an approximation error matrix. This problem is studied and solved in the general form of approximation using linearly structured matrices. This method not only supports more general forms of the gridding algorithm, it can also be used to accelerate the reconstruction techniques from incomplete data. The application of this method to a case of two-dimensional (2-D) spiral magnetic resonance imaging shows a reduction of more than 4 dB in the average reconstruction error.

Reduced aliasing artifacts using variable-density k-space sampling trajectories

A variable-density k-space sampling method is proposed to reduce aliasing artifacts in MR images. Because most of the energy of an image is concentrated around the k-space center, aliasing artifacts will contain mostly low-frequency components if the k-space is uniformly undersampled. On the other hand, because the outer k-space region contains little energy, undersampling that region will not contribute severe aliasing artifacts. Therefore, a variable-density trajectory may sufficiently sample the central k-space region to reduce low-frequency aliasing artifacts and may undersample the outer k-space region to reduce scan time and to increase resolution. In this paper, the variable-density sampling method was implemented for both spiral imaging and two-dimensional Fourier transform (2DFT) imaging. Simulations, phantom images and in vivo cardiac images show that this method can significantly reduce the total energy of aliasing artifacts. In general, this method can be applied to all types of k-space sampling trajectories.

On the performance and accuracy of 2D navigator pulses

The purpose of this study was to investigate and to optimize the performance of two-dimensional spatially selective excitation pulses used for navigator applications on a clinical scanner. The influence of gradient imperfections, off-resonance effects, and incomplete k-space covering on the pencil beam-shaped spatial excitation profile of the 2D RF pulse was studied. The studies involved experiments performed on phantoms and in vivo. In addition, simulations were carried out by numerical integration of the Bloch equations. The accuracy of positioning of the pencil beam was increased by a factor of three by employing a simple correction scheme for the compensation of gradient distortions. The spatial selectivity of the 2D RF pulse was improved by taking sampling density corrections into account. The 2D RF pulse performance was found to be sufficient to monitor the diaphragm motion even at moderate gradient strength. For applications, where a high spatial resolution is required or a less characteristic contrast is present a strong gradient system is recommended.

Improvements in spiral MR imaging

The basic principles of spiral MR image acquisition and reconstruction are summarised with the aim to explain how high quality spiral images can be obtained. The sensitivity of spiral imaging to off-resonance effects, gradient system imperfections and concomitant fields are outlined and appropriate measures for corrections are discussed in detail. Phantom experiments demonstrate the validity of the correction approaches. Furthermore, in-vivo results are shown to demonstrate the applicability of the corrections under in-vivo conditions. The spiral image quality thus obtained was found to be comparable to that obtainable with robust spin warp sequences.

Spiral reconstruction by regridding to a large rectilinear matrix: a practical solution for routine systems

Spiral trajectories offer a number of attractive features for fast imaging. A practical problem for the implementation on routine magnetic resonance scanners is the lack of appropriate and efficient reconstruction algorithms in the available scanner software. In this paper, a simple way to implement a spiral reconstruction algorithm is described that avoids the data interpolation required by gridding approaches commonly used. Using the optimized fast Fourier transform built into each scanner, it offers image reconstruction times of less than 1 second and thus allows the introduction of spiral imaging to routine scanners.

Resampling of data between arbitrary grids using convolution interpolation

For certain medical applications resampling of data is required. In magnetic resonance tomography (MRT) or computer tomography (CT), e.g., data may be sampled on nonrectilinear grids in the Fourier domain. For the image reconstruction a convolution-interpolation algorithm, often called gridding, can be applied for resampling of the data onto a rectilinear grid. Resampling of data from a rectilinear onto a nonrectilinear grid are needed, e.g., if projections of a given rectilinear data set are to be obtained. In this paper we introduce the application of the convolution interpolation for resampling of data from one arbitrary grid onto another. The basic algorithm can be split into two steps. First, the data are resampled from the arbitrary input grid onto a rectilinear grid and second, the rectilinear data is resampled onto the arbitrary output grid. Furthermore, we like to introduce a new technique to derive the sampling density function needed for the first step of our algorithm. For fast, sampling-pattern-independent determination of the sampling density function the Voronoi diagram of the sample distribution is calculated. The volume of the Voronoi cell around each sample is used as a measure for the sampling density. It is shown that the introduced resampling technique allows fast resampling of data between arbitrary grids. Furthermore, it is shown that the suggested approach to derive the sampling density function is suitable even for arbitrary sampling patterns. Examples are given in which the proposed technique has been applied for the reconstruction of data acquired along spiral, radial, and arbitrary trajectories and for the fast calculation of projections of a given rectilinearly sampled image.

Functional MRI of human brain during breath holding by BOLD and FAIR techniques

BOLD (blood oxygenation level-dependent) and FAIR (flow-sensitive alternating inversion recovery) imaging techniques were used to investigate the oxygenation and hemodynamic responses of human brain during repeated challenges of breath holding and prolonged single breath holding. The effects of different breathing techniques on BOLD and FAIR image contrasts were carefully examined. With a periodic breath-holding paradigm of 30 s, global changes in gray matter were observable both in T*2-weighted and FAIR images. T*2-weighted images showed 1-4% relative signal intensity increases, while FAIR images demonstrated relative cerebral blood flow (CBF) increase up to 30-70%. The activated pixels depicted in FAIR images were about three times less than those seen in T*2-weighted images. With prolonged breath holding, it was observed that signal intensities in T*2-weighted and FAIR images were dependent on the breathing techniques used. Breath holding after expiration gave rise to immediate signal intensity increases in T*2-weighted and FAIR images, whereas breath holding performed after deep inspiration signals showed a biphasic change both in flow and T*2-weighted. T*2-weighted and FAIR signals showed a transient decrease before rising above the baseline level.

ADC mapping by means of a single-shot spiral MRI technique with application in acute cerebral ischemia

Diffusion-weighted MRI based on single-shot echo planar imaging (EPI) has been established as a useful tool to study acute cerebral ischemia. However, EPI is prone to spatial distortion and ghosting artifacts. In this study, a pulse sequence for diffusion-weighted imaging (DWI) based on a single-shot spiral readout is presented. Using this technique, multislice apparent diffusion coefficient (ADC) mapping can be performed in an interleaved fashion with the same temporal resolution as EPI. Other advantages associated with ADC mapping by the single-shot spiral method include minimal ghosting artifacts, reduced spatial distortion, and capability to scan in arbitrary planes. This technique has been successfully tested in five normal volunteers and three stroke patients. It has been demonstrated that the single-shot spiral technique is capable of producing high quality DWI and ADC trace maps (128 x 128) in the axial, sagittal, and coronal planes, which facilitate clinical diagnosis.

Sampling density compensation in MRI: rationale and an iterative numerical solution

Data collection of MRI which is sampled nonuniformly in k-space is often interpolated onto a Cartesian grid for fast reconstruction. The collected data must be properly weighted before interpolation, for accurate reconstruction. We propose a criterion for choosing the weighting function necessary to compensate for nonuniform sampling density. A numerical iterative method to find a weighting function that meets that criterion is also given. This method uses only the coordinates of the sampled data; unlike previous methods, it does not require knowledge of the trajectories and can easily handle trajectories that "cross" in k-space. Moreover, the method can handle sampling patterns that are undersampled in some regions of k-space and does not require a post-gridding density correction. Weighting functions for various data collection strategies are shown. Synthesized and collected in vivo data also illustrate aspects of this method.

On spatially selective RF excitation and its analogy with spiral MR image acquisition

The basic principles of the design of spatially selective RF pulses are described, and their analogy with MR image acquisition and reconstruction is shown. The paper focuses on RF-pulse design and imaging schemes in which spiral k-space trajectories are used. The sensitivity of RF excitation to gradient-system imperfections and to spatially varying off-resonance are analyzed, and suitable measures of correction are discussed. The spatial resolution obtainable with selective RF pulses and the consequences of the linearity of the pulse-design problem are examined. Phantom experiments showing the performance of multidimensional spatially selective RF pulses further illustrate the analogy with MR image acquisition.

An optimal and efficient new gridding algorithm using singular value decomposition

The problem of handling data that falls on a nonequally spaced grid occurs in numerous fields of science, ranging from radio-astronomy to medical imaging. In MRI, this condition arises when sampling under time-varying gradients in sequences such as echo-planar imaging (EPI), spiral scans, or radial scans. The technique currently being used to interpolate the nonuniform samples onto a Cartesian grid is called the gridding algorithm. In this paper, a new method for uniform resampling is presented that is both optimal and efficient. It is first shown that the resampling problem can be formulated as a problem of solving a set of linear equations Ax = b, where x and b are vectors of the uniform and nonuniform samples, respectively, and A is a matrix of the sinc interpolation coefficients. In a procedure called Uniform Re-Sampling (URS), this set of equations is given an optimal solution using the pseudoinverse matrix which is computed using singular value decomposition (SVD). In large problems, this solution is neither practical nor computationally efficient. Another method is presented, called the Block Uniform Re-Sampling (BURS) algorithm, which decomposes the problem into solving a small set of linear equations for each uniform grid point. These equations are a subset of the original equations Ax = b and are once again solved using SVD. The final result is both optimal and computationally efficient. The results of the new method are compared with those obtained using the conventional gridding algorithm via simulations.