GRAPPA Reconstruction Research Articles

Nonlinear GRAPPA: A kernel approach to parallel MRI reconstruction

GRAPPA linearly combines the undersampled k-space signals to estimate the missing k-space signals where the coefficients are obtained by fitting to some auto-calibration signals (ACS) sampled with Nyquist rate based on the shift-invariant property. At high acceleration factors, GRAPPA reconstruction can suffer from a high level of noise even with a large number of auto-calibration signals. In this work, we propose a nonlinear method to improve GRAPPA. The method is based on the so-called kernel method which is widely used in machine learning. Specifically, the undersampled k-space signals are mapped through a nonlinear transform to a high-dimensional feature space, and then linearly combined to reconstruct the missing k-space data. The linear combination coefficients are also obtained through fitting to the ACS data but in the new feature space. The procedure is equivalent to adding many virtual channels in reconstruction. A polynomial kernel with explicit mapping functions is investigated in this work. Experimental results using phantom and in vivo data demonstrate that the proposed nonlinear GRAPPA method can significantly improve the reconstruction quality over GRAPPA and its state-of-the-art derivatives.

Adaptive self-calibrating iterative GRAPPA reconstruction

Parallel magnetic resonance imaging in k-space such as generalized auto-calibrating partially parallel acquisition exploits spatial correlation among neighboring signals over multiple coils in calibration to estimate missing signals in reconstruction. It is often challenging to achieve accurate calibration information due to data corruption with noises and spatially varying correlation. The purpose of this work is to address these problems simultaneously by developing a new, adaptive iterative generalized auto-calibrating partially parallel acquisition with dynamic self-calibration. With increasing iterations, under a framework of the Kalman filter spatial correlation is estimated dynamically updating calibration signals in a measurement model and using fixed-point state transition in a process model while missing signals outside the step-varying calibration region are reconstructed, leading to adaptive self-calibration and reconstruction. Noise statistic is incorporated in the Kalman filter models, yielding coil-weighted de-noising in reconstruction. Numerical and in vivo studies are performed, demonstrating that the proposed method yields highly accurate calibration and thus reduces artifacts and noises even at high acceleration.

Design, evaluation and application of an eight channel transmit/receive coil array for cardiac MRI at 7.0 T

The objective of this work is to design, examine and apply an eight channel transmit/receive coil array tailored for cardiac magnetic resonance imaging at 7.0T that provides image quality suitable for clinical use, patient comfort, and ease of use. The cardiac coil array was designed to consist of a planar posterior section and a modestly curved anterior section. For radio frequency (RF) safety validation, numerical computations of the electromagnetic field (EMF) and the specific absorption rate (SAR) distribution were conducted. In vivo cardiac imaging was performed using a 2D CINE FLASH technique. For signal-to-noise ratio (SNR) assessment reconstructed images were scaled in SNR units. The parallel imaging capabilities of the coil were examined using GRAPPA and SENSE reconstruction with reduction factors of up to R=4. The assessment of the RF characteristics yielded a maximum noise correlation of 0.33. The baseline SNR advantage at 7.0T was put to use to acquire 2D CINE images of the heart with a spatial resolution of 1mm×1mm×4mm. The coil array supports 1D acceleration factors of up to R=3 without impairing image quality significantly. For un-accelerated 2D CINE FLASH acquisitions the results revealed an SNR of approximately 140 for the left ventricular blood pool. Blood/myocardium contrast was found to be approximately 90 for un-accelerated 2D CINE FLASH acquisitions. The proposed 8 channel cardiac transceiver surface coil has the capability to acquire high contrast, high spatial and temporal resolution in vivo images of the heart at 7.0T.

Multi-Channel Microstrip Transceiver Arrays Using Harmonics for High Field MR Imaging in Humans

Radio-frequency (RF) transceiver array design using primary and higher order harmonics for in vivo parallel magnetic resonance imaging imaging (MRI) and spectroscopic imaging is proposed. The improved electromagnetic decoupling performance, unique magnetic field distributions and high-frequency operation capabilities of higher-order harmonics of resonators would benefit transceiver arrays for parallel MRI, especially for ultrahigh field parallel MRI. To demonstrate this technique, microstrip transceiver arrays using first and second harmonic resonators were developed for human head parallel imaging at 7T. Phantom and human head images were acquired and evaluated using the GRAPPA reconstruction algorithm. The higher-order harmonic transceiver array design technique was also assessed numerically using FDTD simulation. Compared with regular primary-resonance transceiver designs, the proposed higher-order harmonic technique provided an improved g-factor and increased decoupling among resonant elements without using dedicated decoupling circuits, which would potentially lead to a better parallel imaging performance and ultimately faster and higher quality imaging. The proposed technique is particularly suitable for densely spaced transceiver array design where the increased mutual inductance among the elements becomes problematic. In addition, it also provides a simple approach to readily upgrade the channels of a conventional primary resonator microstrip array to a larger number for faster imaging.

SU‐E‐I‐131: Uniformity Evaluation of GRAPPA and MSENSE Parallel Imaging Reconstruction Algorithm

Purpose: Parallel Imaging (PI) MRI protocols lead to image characteristics that differ from conventional MR images. An accurate and simple method for determining image intensity uniformity in PI is lacking. This study examines five methods of uniformity measurement with PI. Accurate uniformity metrics decrease with increasing R‐value. Methods: A phantom was used in a 12 channel head coil and 3T MRI with TR 1200ms, TE 76 ms, 5 slices, 5 mm thickness, 1 mm gap, FOV 220×220 mm, 256×256 matrix, ETL 16, BW 122 Hz/pixel, axially. Non‐PI TSE sequence, PI method GRAPPA and PI method mSENSE with R: 2, 3 and 4 were inspected. Five uniformity measurement methods were investigated using equations involving: A) Minimum (Smin) and maximum signal pixels (Smax) calculated, PIUA B) Mean pixel value computed and each pixel grouped by: Group1=+/−10% of mean, Group2=+/−10%–20% of mean, Group3=more or less than 20% of mean. The number of pixels per group was used to compute: PIUB C) Same as A but Smax and Smin were 0.15% ROIs. D) This was the NAAD method E) The overall mean (S1) and the mean of 17, 7×7 square ROIs dispersed in the phantom were used. The average of each ROI was taken and PIUE was calculated. Two way ANOVA analysis evaluated reconstruction method and R‐value. Results: Methods D and E indicated increase in uniformity with R‐value at R=3. Two‐way ANOVA results indicated that uniformity measurements A–D were dependent on R‐ value. No uniformity method showed reconstruction method dependence. Conclusions: Methods A and C are similar, A is more sensitive. Methods E and D are inaccurate. Method B gives accurate information but is not as sensitive as A. Method A should be used to obtain the most precise uniformity measurement with PI protocols.

Physiological noise and signal-to-noise ratio in fMRI with multi-channel array coils

Sensitivity in BOLD fMRI is characterized by the signal to noise ratio (SNR) of the time-series (tSNR), which contains fluctuations from thermal and physiological noise sources. Alteration of an acquisition parameter can affect the tSNR differently depending on the relative magnitude of the physiological and thermal noise, therefore knowledge of this ratio is essential for optimizing fMRI acquisitions. In this study, we compare image and time-series SNR from array coils at 3T with and without parallel imaging (GRAPPA) as a function of image resolution and acceleration. We use the “absolute unit” SNR method of Kellman and McVeigh to calculate the image SNR (SNR0) in a way that renders it comparable to tSNR, allowing determination of the thermal to physiological noise ratio, and the pseudo-multiple replica method to quantify the image noise alterations due to the GRAPPA reconstruction. The Kruger and Glover noise model, in which the physiological noise standard deviation is proportional to signal strength, was found to hold for the accelerated and non-accelerated array coil data. Thermal noise dominated the EPI time-series for medium to large voxel sizes for single-channel and 12-channel head coil configurations, but physiological noise dominated the 32-channel array acquisition even at 1mm×1mm×3mm resolution. At higher acceleration factors, image SNR is reduced and the time-series becomes increasingly thermal noise dominant. However, the tSNR reduction is smaller than the reduction in image SNR due to the presence of physiological noise.

Preliminary study of 3.0 T contrast-enhanced whole heart coronary MR angiography using 32-channel coils with high acceleration factor

Objective To evaluate the diagnostic accuracy of 3.0 T contrast enhanced (CE) whole heart coronary MRA ( CE MRA ) using 32-channel coils with high acceleration factor. Methods Sixty patients with suspected coronary artery disease who were scheduled for coronary angiography (CAG)underwent CE CMRA at 3.0 T MRI scanner. A 32-channel receiver coil was used for data acquisition. For image acquisition, an ECG-triggered, navigator-gated, inversion-recovery prepared, segmented gradient-echo sequence was used with an acceleration factor of three in the phase-encoding direction using GRAPPA reconstruction. Gd-BOPTA (0.15 mmol/kg body weight) was intravenously administered at a rate of 0. 3 ml/s. The diagnostic accuracy in detecting significant stenoses ( ≥50% of vessel lumen) was evaluated using χ2 test with X-ray angiography as the reference. Results Whole-heart CE CMRA was successfully completed in 56 patients who were scheduled for CAG. The averaged imaging time was ( 6. 0 ± 1.3 ) min.3.0 T CE CMRA using 32 channel coils correctly identified significant CAD in 28 patients and correctly ruled out CAD in 23 patients. The sensitivity and specificity were 93. 3% and 88.5% respectively.Conclusion Combined with dedicated 32-channel coils, 3.0 T CE CMRA allows significant reduction in imaging speed and reduced dose of the contrast agent. These improvements resulted in substantially improved overall accuracy of CE CMRA in detecting coronary artery disease. Key words: Magnetic resonance angiography; Coronary disease; Contrast media

Independent slab‐phase modulation combined with parallel imaging in bilateral breast MRI

Independent slab-phase modulation allows three-dimensional imaging of multiple volumes without encoding the space between volumes, thus reducing scan time. Parallel imaging further accelerates data acquisition by exploiting coil sensitivity differences between volumes. This work compared bilateral breast image quality from self-calibrated parallel imaging reconstruction methods such as modified sensitivity encoding, generalized autocalibrating partially parallel acquisitions and autocalibrated reconstruction for Cartesian sampling (ARC) for data with and without slab-phase modulation. A study showed an improvement of image quality by incorporating slab-phase modulation. Geometry factors measured from phantom images were more homogenous and lower on average when slab-phase modulation was used for both mSENSE and GRAPPA reconstructions. The resulting improved signal-to-noise ratio (SNR) was validated for in vivo images as well using ARC instead of GRAPPA, illustrating average SNR efficiency increases in mSENSE by 5% and ARC by 8% based on region of interest analysis. Furthermore, aliasing artifacts from mSENSE reconstruction were reduced when slab-phase modulation was used. Overall, slab-phase modulation with parallel imaging improved image quality and efficiency for 3D bilateral breast imaging.

Isotropic Sub-Millimeter fMRI of V5 in Human at 7T

Introduction: Recently a combination of a zoomed approach (reduced FOV) with parallel imaging was proposed, to improve the image quality of single-shot EPI acquisitions [1]. For high resolution single-shot EPI at high field strength the use of parallel imaging is mandatory to address the problems of susceptibility induced geometric distortions and blurring due to T2* decay. However, imperfect parallel image reconstruction can result in remaining aliasing artifacts. The combination of parallel imaging with a zoomed approach can eliminate this specific problem, enabling high resolution fMRI acquisitions at ultra-high field strength [2]. Since human cortex is convoluted, the use of isotropic resolution is essential to identify specific areas, as for example V5, within the layer structure. The goal of this study is to demonstrate the feasibility of sub-millimeter isotropic resolution fMRI at ultra-high field strength. Methods: All experiments were performed on a 7T whole-body MR scanner (MAGNETOM 7T, Siemens Healthcare Sector, Erlangen, Germany). An 8element phased array head coil (RAPID, Wurzburg, Germany) was used. Eight healthy volunteers were included in the study; informed consent was obtained before each study. A functional paradigm with blocks of 40s stimulus-on and stimulus-off was used with 8 epochs for a total acquisition time of 20 min. For stimulus-on an expanding and contracting star field and for stimulus-off a static star field was shown to the subjects to activate the motion sensitive area V5. The experiments were performed with a zoomed EPI sequence (TR=5000ms, TE=27, FOV=43x128mm, 15 slices, voxel size=0.7x0.7x0.7mm) with OVS using a SKEWED pulse as proposed in [3,4] and a GRAPPA reconstruction with a 2D convolution kernel [5] with 3 source points along the readout direction and four source points along phase encoding direction and an acceleration factor of three. Results and Discussion: Fig.1 shows the mean EPI image from two different fMRI acquisitions, acquired within a time frame of one month from the same subject. The activation pattern is overlaid onto the mean EPI images. The zoomed EPI acquisition with an isotropic resolution of 0.8 mm is shown in Fig. 1a, while Fig. 1b shows nearly the same slice with an isotropic resolution of 0.7 mm acquired a month later. Enlarged sections of those images are shown in Fig. 2 with the activation pattern (Fig. 2a and 2b) and without the activation pattern (Fig. 2c and 2d). Normally the activation pattern is overlaid onto an anatomical scan with good gray/white matter contrast. In this study the activation pattern is overlaid onto the mean images from the EPI raw images. Due to this, there is no potential error in the registration as might occur whenever the activation pattern is overlaid onto anatomical images from a separate scan. As can be seen in Fig. 2, the activation is mostly concentrated above and below the vein but not within the vein. Conclusion: Sub-millimeter isotropic resolution fMRI is feasible at ultra-high field strength using a combination of parallel imaging and a zoomed approach. The open question, whether gradient echo EPI acquisitions at ultra-high field strength mostly show activations arising from oxygenation changes in larger veins, is not fully answered. However, in this case it is clear that the V5 activation does not come from the big adjacent vein. Further studies should allow studying cortical layer-specific activations.

3T contrast-enhanced whole heart coronary MRA using 32-channel cardiac coils for the detection of coronary artery disease

Introduction: The development of contrast enhanced whole heart coronary MR angiography (CMRA) at 3T has shown promising results in clinical studies for the detection of significant coronary artery stenoses. However, the imaging time (~ 9 minutes) and spatial resolution (1.3 × 1.3 × 1.3 mm) remain major limitations. Newly available 32-channel cardiac coils allow greater acceleration factors, and thus reduced imaging time, reduced contrast agent dose and higher spatial resolution. Purpose: To evaluate the diagnostic accuracy of 3T contrast enhanced whole-heart CMRA with an optimized protocol for improved spatial resolution and reduced scan time using a 32-channel cardiac coils. Imaging time, image quality score, and diagnostic accuracy are evaluated in 32 consecutive patients with suspected coronary artery disease using conventional x-ray coronary angiography (CAG) as reference standard. Methods and Materials: 32 patients with suspected coronary artery disease who were scheduled for coronary angiography (CAG) (mean age 62 ± 12 y) underwent MRCA at 3T (MAGNETOM Tim Trio, Siemens) after informed consent was obtained. A 32-channel receiver coil was used for data acquisition (Invivo, Gainesville, FL). For image acquisition an ECG-triggered, navigator-gated, inversion-recovery prepared, segmented gradient-echo sequence was used with an acceleration factor of three in the phase-encoding direction using GRAPPA reconstruction. Imaging parameters included: voxel size 0.55x0.55x0.65 mm (interpolated from 1.1x1.1x1.3 mm), TR/TE = 3.3/1.5 msec, flip angle = 20°, bandwidth = 700 Hz/pixel, TI=200 msec. Contrast agent (0.15 mmol/kg body weight, MultiHance, Bracco, Italy) was intravenously administered at a rate of 0.3 ml/sec. For image analysis, standard 15-segment AHA classification system was used and only segments with a reference diameter of ≥ 1.5 mm were included, excluding those segments distal to complete occlusions. The diagnostic accuracy in detecting significant stenoses (≥50% of vessel lumen) was evaluated on the assessable segments only, as well as on all segments. Both non-assessable segments and the segments of the patients where the scan failed were considered to have a stenosis. Results: Whole-heart CMRA was successfully completed in 30 of 32 (94%) patients who were scheduled for CAG. The averaged imaging time was 5.9 ± 1.2 min. 40 of 392 segments (10%) with a reference luminal diameter > 1.5 mm on QCA were determined as non-assessable. On assessable segments only, the sensitivity, specificity, and accuracy of coronary MRA for detecting significant stenoses were 93% (78-99%), 99% (97-99%), 98%

Comprehensive quantification of signal‐to‐noise ratio and g‐factor for image‐based and k‐space‐based parallel imaging reconstructions

Parallel imaging reconstructions result in spatially varying noise amplification characterized by the g-factor, precluding conventional measurements of noise from the final image. A simple Monte Carlo based method is proposed for all linear image reconstruction algorithms, which allows measurement of signal-to-noise ratio and g-factor and is demonstrated for SENSE and GRAPPA reconstructions for accelerated acquisitions that have not previously been amenable to such assessment. Only a simple "prescan" measurement of noise amplitude and correlation in the phased-array receiver, and a single accelerated image acquisition are required, allowing robust assessment of signal-to-noise ratio and g-factor. The "pseudo multiple replica" method has been rigorously validated in phantoms and in vivo, showing excellent agreement with true multiple replica and analytical methods. This method is universally applicable to the parallel imaging reconstruction techniques used in clinical applications and will allow pixel-by-pixel image noise measurements for all parallel imaging strategies, allowing quantitative comparison between arbitrary k-space trajectories, image reconstruction, or noise conditioning techniques.

Discrepancy‐based adaptive regularization for GRAPPA reconstruction

To develop a novel regularization method for GRAPPA by which the regularization parameters can be optimally and adaptively chosen. In the fit procedures in GRAPPA, the discrepancy principle, which chooses the regularization parameter based on a priori information about the noise level in the autocalibrating signals (ACS), is used with the truncated singular value decomposition (TSVD) regularization and the Tikhonov regularization, and its performance is compared with the singular value (SV) threshold method and the L-curve method, respectively by axial and sagittal head imaging experiments. In both axial and sagittal reconstructions, normal GRAPPA reconstruction results exhibit a relatively high level of noise. With discrepancy-based choices of parameters, regularization can improve the signal-to-noise ratio (SNR) with only a very modest increase in aliasing artifacts. The L-curve method in all of the reconstructions leads to overregularization, which causes severe residual aliasing artifacts. The 10% SV threshold method yields good overall image quality in the axial case, but in the sagittal case it also leads to an obvious increase in aliasing artifacts. Neither a fixed SV threshold nor the L-curve are robust means of choosing the appropriate parameters in GRAPPA reconstruction. However, with the discrepancy-based parameter-choice strategy, adaptively regularized GRAPPA can be used to automatically choose nearly optimal parameters for reconstruction and achieve an excellent compromise between SNR and artifacts.

Multiple-acquisition parallel imaging combined with a transceive array for the amelioration of high-field RF distortion: A modeling study

A new method for ameliorating high-field image distortion caused by radio frequency/tissue interaction is presented and modeled, The proposed method uses, but is not restricted to, a shielded four-element transceive phased array coil and involves performing two separate scans of the same slice with each scan using different excitations during transmission. By optimizing the amplitudes and phases for each scan, antipodal signal profiles can be obtained, and by combining both images together, the image distortion can be reduced several-fold. A hybrid finite-difference time-domain/method-of-moments method is used to theoretically demonstrate the method and also to predict the radio frequency behavior inside the human head. in addition, the proposed method is used in conjunction with the GRAPPA reconstruction technique to enable rapid imaging. Simulation results reported herein for IIT (470 MHz) brain imaging applications demonstrate the feasibility of the concept where multiple acquisitions using parallel imaging elements with GRAPPA reconstruction results in improved image quality. (c) 2006 Wiley Periodicals, Inc.

Parallel magnetic resonance imaging using the GRAPPA operator formalism

In this article it is shown that GRAPPA reconstruction can be reformulated as a matrix operator, similar to ladder or propagator operators used in quantum mechanics, that shifts data in k-space. Using this formalism, it is shown that there exists an infinitesimal GRAPPA operator that shifts data in k-space by arbitrarily small amounts. Other desired k-space shifts can then be accomplished through repeated applications of this infinitesimal GRAPPA operator. Implications of these ideas are described.