A Method to measure arbitrary k-space trajectories for rapid MR imaging

A method to measure arbitrary k-space trajectories was developed to compensate for nonideal gradient performance during rapid magnetic resonance (MR) imaging with actively or nonactively shielded gradients at a magnetic field strength of 4.1 T. Accurate MR image reconstruction requires knowledge of the k-trajectory produced by the gradient waveforms during k-space sampling. Even with shielded gradients, residual eddy currents and imperfections in gradient amplifier performance can cause the true k-space trajectory to deviate from the ideal trajectory. The k-space determination was used for spiral gradient-echo imaging of the human brain. While individual calibrations are needed for new pulse sequences, the method of k-space determination can be used for any sequence of preparation pulses and readout gradient waveforms and should prove useful for other trajectories, including the rastered lines of echo-planar imaging.     

Isotropic diffusion-weighted and spiral-navigated interleaved EPI for routine imaging of acute stroke

An interleaved echo-planar imaging (EPI) technique is presented for the rapid acquisition of isotropic diffusion-weighted images of stroke patients. Sixteen isotropic diffusion-weighted images at three b values are acquired in less than 3 min. A spiral navigator echo is used to measure the constant and linear phase shifts across the head in both the x and y directions which result from motion during the isotropic diffusion- sensitizing gradients. The measured k-space errors are corrected during a gridding reconstruction. The gridding kernel has a constant width in k_x and a variable width in k_y which eliminates variable data-density ghosts. The resulting isotropic diffusion-weighted images have excellent lesion-to-normal brain contrast, very good spatial resolution, and little sensitivity to susceptibility effects in the base of the brain. Examples of diffusion-weighted images and ADC maps from several stroke patients are shown.     

Real time blood flow imaging by spiral scan phase velocity mapping

The work describes the development of a novel sequence that uses rapid spiral k-space sampling, combined with phase velocity mapping, for real time flow velocity imaging. The performance of the technique is assessed on phantoms for both through-plane and in-plane flows. The flow measurements compared well with those measured using a bucket and stopwatch. One advantage of the technique is that flow related signal loss is minimal due to the early acquisition of the center of k-space data. Flow artifacts were observed for in-plane flow and these were understood with the aid of computer simulations. In vivo studies involved cine velocity mapping in normal volunteers; aortic blood flow waveforms acquired by spiral scanning in two cardiac cycles compared well with data from a conventional gradient-echo sequence. Potential applications of the method are demonstrated by studying the response of aortic flow to physical exercise and the real time monitoring of aortic flow during a valsalver maneuver.     

Variable‐density spiral‐in/out functional magnetic resonance imaging

A variable‐density spiral k‐space trajectory is introduced for brain functional magnetic resonance imaging. The proposed spiral trajectory consists of an Archimedean spiral from the k‐space origin to an arbitrary fraction r of the maximum k‐space radius, extending beyond this point with a variable‐density spiral in which the sampling density decreases as the k‐space radius increases. It, therefore, permits a reduction in readout time at the expense of undersampling only the high spatial frequencies, in which the energy in T₂*‐weighted brain images is low. The trajectory was implemented in a two‐dimensional spiral‐in/out sequence, and single‐shot high‐resolution (1.72 × 1.72 mm² in‐plane) functional magnetic resonance imaging data were acquired from human volunteers. Compared with a two‐shot fully Archimedean spiral sequence with the same spatial coverage and total scan time, the variable‐density sequence yielded greater activation magnitudes with improved temporal efficiency and minor artifacts. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.     

Frequency resolved single-shot MR imaging using stochastic k-space trajectories

A new single-shot stochastic imaging technique with a random k-space path that provides very selective filtering with respect to chemical shift or off-resonance signals of the investigated tissue is proposed. It is demonstrated that in stochastic imaging only on-resonance compartments are visible whereas frequency shifted compartments cancel to noise that is distributed over the whole image. This method can be used as a single-shot chemical shift selective imaging technique and allows to calculate frequency resolved spectra for each spatial position of the image based on a single signal aquisition. The single-shot stochastic imaging sequence makes high demands on the gradient system and the theoretical k-space trajectory is distorted by imperfect gradient performance. Therefore an additional k-space guided imaging technique that uses the true, measured k-space trajectory to correct artifacts generated by eddy currents and delay times of the rapid switched gradients is presented. In vitro and in vivo measurements demonstrate the successful implementation of single-shot stochastic imaging on a conventional MR scanner with unshielded gradient systems.     

Echo-planar spin-echo and inversion pulses

The echo-planar k-space trajectory can be used as the basis for any two-dimensional selective pulse. The main application is spectral-spatial pulses, which must be based on the echoplanar trajectory. In this paper we show how echo-planar spinecho (EPSE) pulses may be designed.     

Density compensation functions for spiral MRI

In interleaved spiral MRI, an object's Fourier transform is sampled along a set of curved trajectories in the spatial frequency domain (k-space). An image of the object is then reconstructed, usually by interpolating the sampled Fourier data onto a Cartesian grid and applying the fast Fourier transform (FFT) algorithm. To obtain accurate results, it is necessary to account for the nonuniform density with which k-space is sampled. An analytic density compensation function (DCF) for spiral MRI, based on the Jacobian determinant for the transformation between Cartesian coordinates and the spiral sampling parameters of time and interleaf rotation angle, is derived in this paper, and the reconstruction accuracy achieved using this function is compared with that obtained using several previously published expressions. Various non-ideal conditions, including intersecting trajectories, are considered. The new DCF eliminated intensity cupping that was encountered in images reconstructed with other functions, and significantly reduced the level of artifact observed when unevenly spaced sampling trajectories, such as those achieved with trapezoidal gradient waveforms, were employed. Modified forms of this function were found to provide similar improvements when intersecting trajectories made the spiral-Cartesian transformation noninvertible, and when the shape of the spiral trajectory varied between interleaves.     

Calculation of signal intensities in hybrid sequences for fast NMR imaging

A number of techniques that recently have been used for fast NMR-imaging are based on a hybrid sequence of echo planar imaging (EPI) and FLASH imaging: after each NMR excitation several k-space lines are measured. The complete k-space is covered by performance of several excitations. It has been observed that there is usually an optimal hybrid sequence that maximizes the signal-to-noise ratio. In this work, a method is presented that allows a determination of the optimal sequence as a function of the relaxation times T₁ and T₂^*.     

Time of flight quantification of coronary flow with echo-planar MRI

Detection and quantification of flow of the left anterior descending (LAD) coronary artery in healthy volunteers are demonstrated using echo-planar imaging (EPI). A time-of-flight TOF) model was used to derive coronary flow velocities from wash-in curves, free of cardiac wall motion contamination. Short-axis cardiac studies were performed using a gated, gradient echo EPI technique to limit the effect of cardiac wall motion on coronary vessel imaging. A series of 10 to 20 single or multislice images were acquired within a single breath-hold. Real-time cine series showed the LAD coronary artery with a detectability of 91% (n = 23) and revealed beat-to-beat variability in vessel position of a magnitude equal to or greater than its diameter. Flow velocity was measured in the proximal portion of the artery at rest and during exercise. The data demonstrated the known phasic pattern of LAD flow:-V_systole ≤ 5 cm/s and peak V_diastole = 14 ± 3 cm/s (n = 11, V = mean laminar flow velocity). During isometric exercise, a LAD flow velocity increase (52 ± 24%) was detected in eight of nine subjects. The capacity of the EPI TOF method to detect flow velocity changes should prove clinically useful for future assessment of coronary flow reserve.     

Alternate k-space sampling in EPI: Compensation for T2* and adjustable T2 weighting

In this work, preliminary results are described for a modification of the MBEST sampling scheme such that image resolution can be increased while preserving image contrast. In this new approach, a single spin-echo is used in sampling k-space. The basic idea relies on acquiring a conventional EPI image from the center of k-space and applying a ψ pulse to permit the acquisition of the two outer edges of k-space. Using this new approach, it is possible to obtain an enhancement in EPI image resolution, while reducing the extent of T₂* weighting. As a result, the resulting images possess reduced T₂* contrast and suffer less signal loss from T₂* effects such as spatial variations in susceptibility and field inhomogeneity.     

Echo-volume imaging

Two single-shot volume imaging techniques are described. The first, single-echo echo-volume imaging, is essentially the echo-volume imaging (EVI) sequence suggested by Mansfield (J. Phys. C. 10, L55 (1977)). The second is a multi-spin-echo approach in which one plane of k-space is collected during each spin echo. In both techniques, phase encoding gradients are applied in the z direction, and three-dimensional k-space is filled by a raster pattern in Cartesian coordinates. Spatial saturation is used to avoid aliasing in the y direction, and a selective pulse is applied to excite the desired slab of tissue and eliminate aliasing in z. The average echo-times, measured from the center of the 90° pulse to the center of the acquisition k-space(k_x= k_y k_z = 0), were 45 and 104 ms for single echo and multi-echo methods, respectively. Images of the human brain using both sequences are shown.     

RARE spiral T2-weighted imaging

Spiral imaging has a number of advantages for fast imaging, including an efficient use of gradient hardware. However, inhomogeneity-induced blurring is proportional to the data acquisition duration. In this paper, we combine spiral data acquisition with a RARE echo train. This allows a long data acquisition interval per excitation, while limiting the effects of inhomogeneity. Long spiral k-space trajectories are partitioned into smaller, annular ring trajectories. Each of these annular rings is acquired during echoes of a RARE echo train. The RARE refocusing RF pulses periodically refocus off-resonant spins while building a long data acquisition. We describe both T₂-weighted single excitation and interleaved RARE spiral sequences. A typical sequence acquires a complete data set in three excitations (32 cm FOV, 192 × 192 matrix). At a TR = 2000 ms, we can average two acquisitions in an easy breath-hold interval. A multifrequency reconstruction algorithm minimizes the effects of any off-resonant spins. Though this algorithm needs a field map, we demonstrate how signal averaging can provide the necessary phase data while increasing SNR. The field map creation causes no scan time penalty and essentially no loss in SNR efficiency. Multiple slice, 14-s breath-hold scans acquired on a conventional gradient system demonstrate the performance.     

Estimation of k‐space trajectories in spiral MRI

For non‐Cartesian data acquisition in MRI, k‐space trajectory infidelity due to eddy current effects and other hardware imperfections will blur and distort the reconstructed images. Even with the shielded gradients and eddy current compensation techniques of current scanners, the deviation between the actual k‐space trajectory and the requested trajectory remains a major reason for image artifacts in non‐Cartesian MRI. It is often not practical to measure the k‐space trajectory for each imaging slice. It has been reported that better image quality is achieved in radial scanning by correcting anisotropic delays on different physical gradient axes. In this article the delay model is applied in spiral k‐space trajectory estimation to reduce image artifacts. Then a novel estimation method combining the anisotropic delay model and a simple convolution eddy current model further reduces the artifact level in spiral image reconstruction. The root mean square error and peak error in both phantom and in vivo images reconstructed using the estimated trajectories are reduced substantially compared to the results achieved by only tuning delays. After a one‐time calibration, it is thus possible to get an accurate estimate of the spiral trajectory and a high‐quality image reconstruction for an arbitrary scan plane. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Excitation of arbitrary shapes by gradient optimized random walk in discrete k-space

A new technique for the excitation of arbitrary shapes is proposed. It is based on a parallel sequence of small tip angle RF pulses and gradient pulses. The small tip angle rotations co-add yielding a 90° excitation pulse within the selected excitation profile while outside the profile, the rotations cancel each other. A full theory of the completely arbitrary regional volume excitation (CARVE) method is presented and experimentally verified. In CARVE, k-space is discrete because the RF is applied in pulses. The discrete character of k-space permits an arbitrary trajectory for the k-space walk. The optimal random trajectory is found by minimizing the gradient load using simulated annealing. It is shown, both theoretically and experimentally, that such a trajectory is much better than any other systematic or random trajectory in k-space.     

Reducing flow artifacts in echo-planar imaging

Echo-planar imaging (EPI) is very susceptible to flow artifacts. Two ways to improve its flow properties are presented. First, “partial flyback” is proposed to reduce artifacts arising from flow in the readout direction. Near the center of k-space, only the even echoes of the EPI echo-train are used. Partial flyback is shown to improve the readout-flow properties at the expense of a slight worsening of the phase-encode flow and off-resonance properties. We recommend that the flyback region acquire 95% of the energy in k-space. Second, “inside-out” EPI is used to reduce artifacts arising from flow in the phase-encode direction. Data collection begins at the center of k-space, with separate interleaves to acquire the top and bottom halves of k-space. Partial flyback is combined with partial-Fourier EPI and inside-out EPI. Partial-flyback inside-out EPI has worse off-resonance properties than partial-flyback partial-Fourier EPI but demonstrates better flow properties and does not require partial k-space reconstruction.     

Cine Spiral Imaging

Interleaved spiral scanning of k-space is an efficient and fast method for imaging dynamic processes. In this article, a cine version of interleaved spiral imaging is presented. The method is shown to overcome the “lightning-flash” artifacts of the conventional triggered (gated) method. Compared with the segmented k-space 2DFT method, it achieves better temporal resolution in a comparable or shorter scan time. Preliminary human studies show that the method is a promising tool for imaging dynamic processes.     

Analytical resolution and noise characteristics of linearly reconstructed magnetic resonance data with arbitraryk-space sampling

The effects of time-varying readout gradients and data sampling with variable dwell times in magnetic resonance imaging are examined. General reconstruction formulas are given for linear reconstruction with even k-space weighting. Closed analytic expressions for estimator variance are given for data sampling during arbitrary gradient waveforms with both uniform k_x step size and nonuniform k_x step size. It is shown that estimator variance increases (the signal-to-noise ratio decreases) for nonconstant gradient waveforms. It is also shown that estimator variance is greater for constant k-space sampling strategies than for constant time sampling at the Nyquist rate. Data collected during a triangular readout gradient waveform, with either constant time or constant k-space sampling, versus conventional (constant gradient) collection confirms theoretical predictions for estimator variance. The benefits of collecting data while the readout gradient is ramping up from and down to zero are discussed.     

Gradient moment smoothing: A new flow compensation technique for multi-shot echo-planar imaging

This work identifies an additional source of phase error across k_y in multi-shot echo-planar imaging resulting from flow or motion along the phase-encoding direction. A velocity-independent flow compensation technique, gradient moment smoothing, is presented that corrects this error by forcing the phase to have smooth quadratic behavior. The correction is implemented, without compromising scan time, by changing the first moment of a bipolar prephaser pulse on a shot-by-shot basis. In phantom and in vivo experiments, gradient moment smoothing effectively eliminates ghosting and signal loss due to phase-encoding flow. When used in conjunction with a “flyback” echo-planar readout, which compensates for flow in the frequency-encoding direction, gradient moment smoothing renders multi-shot echo-planar imaging relatively insensitive to in-plane flow. This can make multi-shot echo-planar imaging a viable technique for accurately imaging in-plane flow and may desensitize it to the otherwise serious problem of in-plane motion.     

Multisection T1-weighted hybrid-rare: A pulse sequence for MR imaging of the entire liver during suspended respiration

It is shown that the maximum average-data-collection-speed (ADCS) of multisection 2D hybrid-RARE sequences is independent of TR and TE_eff, and a monotonically increasing function of echo-train-length (ETL). This result was used in the design of an optimized T₁-weighted hybrid-RARE sequence that produces 20 images of the abdomen in 31 s divided into four breath-hold periods. The resulting ADCS is 58 lines in k-space per second. Twenty-four subjects (2 healthy volunteers and 22 patients) were imaged with a protocol that also included: (a) breath-hold T₁-weighted FLASH which acquires data at 34 lines in k-space per second (49 s scan time), and (b) T₁-weighted conventional spin-echo (9:44 minutes scan time) with respiratory compensation. The experiments show that this T₁-weighted-hybrid-RARE sequence has: (1) a level of T₁ weighting that is comparable with the conventional sequences, (2) very low vulnerability to susceptibility artifacts, (3) high data acquisition efficiency, and (4) higher SNR than T₁-weighted-FLASH. In conclusion, the T₁-weighted-hybrid-RARE sequence described herein is an efficacious and reproducible technique for rapid imaging of the upper abdomen during suspended respiration.