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. Author manuscript; available in PMC: 2012 Apr 1.
Published in final edited form as: Magn Reson Med. 2011 Nov 14;67(4):1054–1064. doi: 10.1002/mrm.23088

Accelerated Phase-Contrast Cine MRI Using k-t SPARSE-SENSE

Daniel Kim 1,*, Hadrien A Dyvorne 1, Ricardo Otazo 1, Li Feng 1,2, Daniel K Sodickson 1, Vivian S Lee 1
PMCID: PMC3306497  NIHMSID: NIHMS355183  PMID: 22083998

Abstract

Phase-contrast (PC) cine MRI is a promising method for assessment of pathologic hemodynamics, including cardiovascular and hepatoportal vascular dynamics, but its low data acquisition efficiency limits the achievable spatial and temporal resolutions within clinically acceptable breath-hold durations. We propose to accelerate PC cine MRI using an approach which combines compressed sensing and parallel imaging (k-t SPARSE-SENSE). We validated the proposed 6-fold accelerated PC cine MRI against 3-fold accelerated PC cine MRI with parallel imaging (generalized autocalibrating partially parallel acquisitions). With the programmable flow pump, we simulated a time varying waveform emulating hepatic blood flow. Normalized root mean square error between two sets of velocity measurements was 2.59%. In multiple blood vessels of 12 control subjects, two sets of mean velocity measurements were in good agreement (mean difference = –0.29 cm/s; lower and upper 95% limits of agreement = –5.26 and 4.67 cm/s, respectively). The mean phase noise, defined as the standard deviation of the phase in a homogeneous stationary region, was significantly lower for k-t SPARSE-SENSE than for generalized autocalibrating partially parallel acquisitions (0.05 ± 0.01 vs. 0.19 ± 0.06 radians, respectively; P < 0.01). The proposed 6-fold accelerated PC cine MRI pulse sequence with k-t SPARSE-SENSE is a promising investigational method for rapid velocity measurement with relatively high spatial (1.7 mm × 1.7 mm) and temporal (~35 ms) resolutions.

Keywords: MRI, liver, PC MRI, velocity, compressed sensing, parallel imaging, blood flow

Abnormalities in vascular flow patterns frequently can provide useful insights into pathophysiology. For example, recent studies suggest that abnormal hepatic venous waveforms can be used to diagnose liver pathologies such as cirrhosis (1–3). Although ultrasound is typically used in these studies, phase-contrast (PC) cine MRI (4–9) is a promising modality for studying hemodynamics and can be performed in addition to conventional contrast-enhanced anatomic MR imaging. Also, unlike Doppler ultrasonography, which is sensitive to misalignment between the vessel axis and Doppler beam angle, PC cine MRI can acquire data in any orientation, regardless of the depth of the vessel or overlying bowel gas. A major disadvantage of PC cine MRI, however, is its low data acquisition efficiency, which may limit the achievable spatial and temporal resolutions within clinically acceptable breath-hold durations. In PC cine MRI, two data sets (e.g., phase reference and velocity-encoded) are acquired to subtract the background phase due to static magnetic field inhomogeneities and susceptibility. Typically, phase reference and velocity-encoded cine data sets are acquired in an interleaved fashion within the same heart beat and over multiple heart beats (7). As a result of this time-consuming acquisition approach, PC cine MRI studies are particularly in need of acceleration to achieve relatively high spatio-temporal resolution within clinically acceptable scan times.

Previous studies have incorporated acceleration methods into PC cine MRI, including spiral (10), radial (11), balanced steady-state free precession (12), view sharing (13,14), parallel imaging (15–17), and other spatio-temporal undersampling approaches (18,19), with each method having advantages and disadvantages. Among these acceleration methods, the most widely used method for PC cine MRI is parallel imaging (20–22). Most clinical MR scanners equipped with coil arrays are capable of performing generalized autocalibrating partially parallel acquisitions (GRAPPA) (22) or sensitivity encoding (SENSE) (21) accelerations with acceleration rates (R) of 2–3, but the achievable spatio-temporal resolution within a clinically acceptable breath-hold duration is still limited. Compressed sensing (CS) techniques, relatively recently introduced into the field of MRI (23), represent an alternative method to accelerate PC cine MRI (24–26). PC cine MRI is a good candidate for CS, because the background is in a steady state of magnetization, the temporal variation in signal is limited to blood vessel regions, and the resulting image data are sparse after applying an appropriate transform. Previous CS studies for dynamic MRI (27–32) have proposed temporal principal component analysis (PCA) as the sparsifying transform.

To date, only a few preliminary CS studies for PC cine MRI have been reported (24–26). The study by Yoon et al. (24) describes use of a nonconvex greedy algorithm for high acceleration in a simulated phantom. The study by Tao et al. (26) reports low acceleration in retrospectively undersampled carotid PC cine MRI data, using temporal fast Fourier transform (FFT) as the sparsifying transform. The study by Velikina et al. (25) describes high acceleration using second temporal difference as the sparsifying transform. These preliminary studies have been important developments, but they have not been validated in vivo. This study describes a method to accelerate PC cine MRI using a combination of k-t SPARSE (33) and SENSE (21) that exploits joint sparsity among all component coil datasets (k-t SPARSE-SENSE) (34). Although this approach can be used in all vascular systems, the motivation of our work was to study hepatic blood flow waveforms in liver diseases (1–3) using accelerated PC cine MRI. We describe an accelerated PC cine MRI pulse sequence with k-t SPARSE-SENSE and our results validating it against a reference PC cine MRI pulse sequence with GRAPPA in a flow phantom and human subjects.

MATERIALS AND METHODS

Hepatic and portal vein diameters in healthy subjects are on the order of 10 mm (35,36), and inferior vena cava (IVC) diameters are on the order of 20 mm (37). In patients with liver diseases, these vessel dimensions may vary, but typically not significantly. Based on these dimensions, our accelerated PC cine MRI pulse sequence was designed to achieve relatively high spatial resolution (1.7 mm × 1.7 mm) and temporal resolution (<40 ms) within a clinically acceptable breath-hold duration (11 s).

Pulse Sequence

A prospectively electrocardiogram-triggered PC cine MRI pulse sequence was used to acquire phase reference and velocity-encoded data in an interleaved fashion within the same cardiac cycle (see Fig. 1). This pulse sequence was modified to use a different random k-space under-sampling pattern through all cardiac phases (see “Incoherence” section). The sequence was implemented on a whole-body 3 T MRI scanner (Tim Trio, Siemens Health-care, Erlangen, Germany) equipped with a gradient system capable of achieving a maximum gradient strength of 45 mT/m and a slew rate of 200 T/m/s. The radio-frequency excitation was performed using the body coil, and a 32-element cardiac coil array (Invivo, Orlando, FL) was used for signal reception. Relevant imaging parameters for the reference PC cine MRI with GRAPPA and accelerated PC cine MRI with k-t SPARSE-SENSE were: field of view = 320 mm × 320 mm, acquisition matrix 192 × 192, spatial resolution = 1.7 mm × 1.7 mm, slice thickness = 7 mm, k-space lines per cardiac phase = 3, flip angle = 20°, and receiver bandwidth = 500 Hz/pixel. For portal and hepatic vein imaging, we used velocity encoding (venc) = 50 cm/s, TE = 4.05 ms, TR = 6.35 ms, and effective temporal resolution = 38.25 ms (due to interleaved acquisition). For IVC imaging, we used venc = 80 cm/s, TE = 3.42 ms, TR = 5.72 ms, and effective temporal resolution = 34.5 ms (due to interleaved acquisition). Reference PC cine MRI with GRAPPA was performed with R = 3.1 and breath-hold duration = 21 heart beats (1 heart beat to acquire dummy scans to approach steady state of magnetization, and 20 heart beats to acquire data). Accelerated PC cine MRI with k-t SPARSE-SENSE was performed with R = 6.3 and breath-hold duration = 11 heart beats (1 heart beat to acquire dummy scans to approach steady state of magnetization, and 10 heart beats to acquire data). For each subject, the acquired number of cardiac frames depended on the subject's heart rate.

FIG. 1.

FIG. 1

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a: Electrocardiogram-triggered, interleaved phase reference and velocity-encoded acquisitions. b: Individual reconstruction method, where the phase reference and velocity-encoded data are processed separately before phase subtraction. A 6-fold accelerated ky-t sampling pattern based on 20 cardiac phases, as well as exemplary k-space representations of the phase reference and velocity-encoded data. c: Joint reconstruction method, where the phase reference and velocity-encoded data are interleaved as shown, reconstructed jointly, and then separated for phase differencing. In our implementation of the interleaved reconstruction method, the same ky-t sampling pattern (b) was used for both phase reference and velocity-encoded acquisitions, for ease of implementation. The corresponding k-space representations of interleaved phase reference and velocity-encoded data are actual depictions of the zero-padded k-space data.

Compressed Sensing

The two key components for high performance in CS are incoherent aliasing artifacts and image sparsity. In this study, a variable density random k-space undersampling pattern is used to generate incoherent aliasing artifacts, and temporal PCA transform is used to sparsify the data. In a preliminary analysis of fully sampled PC cine MRI data, we determined that temporal PCA is a superior sparsifying transform than temporal FFT (data not shown). The following two subsections (Incoherence and Sparsity) describe the methods and results of preliminary experiments which were needed for the acceleration strategy.

Incoherence

A ky-t random undersampling pattern was used for k-t SPARSE-SENSE, to minimize the resulting incoherent aliasing artifacts (pseudo-noise) by distributing them along two dimensions, phase-encoding ky and time t (33,34). We used various realizations of an eighth-ordered polynomial distribution function, defined as (1 – k)^8 + d, to generate a different variable-density random undersampling pattern along ky for each cardiac frame, where k is the magnitude of ky, where the first ky and last ky lines are normalized to –1 and 1, respectively, and d is the minimum sampling density. The proposed variable density function was computed using an iterative bisection method, where at each iteration the previous value of d is divided by two and the variable density function values larger than 1 are set to 1 until the sum of variable density function values is equal to the number of reduced ky lines (i.e., total number of ky steps/R). An iterative bisection method was used to ensure a higher density at the center of k-space than the edges of k-space, and the final k-space pattern is constructed after the iterative process has been completed. Sampling more densely at the center of ky-space provides a better starting point for the iterative reconstruction algorithm than uniform random sampling, as previously described (33,34).

Image Sparsity

Conventionally, PC cine MR images are generated via individual reconstruction of the phase reference data and the velocity-encoded data. We hypothesized that combining phase reference and velocity-encoded data together, as shown in Fig. 1, presents better reconstruction performance, because sorting the data in this way increases sparsity due to effective expansion of the temporal dimension. Figure 1b shows a 6.3-fold accelerated ky-t sampling pattern for a typical heart rate with 20 cardiac frames, as well as exemplary k-space representations of the phase reference and velocity-encoded data. In this study, the same ky-t sampling pattern (Fig. 1b) was used for both phase reference and velocity-encoded acquisitions (Fig. 1c), for ease of implementation. Note that the phase reference and velocity-encoded data sets are correlated and that combining the data in this way doubles the time dimension (Fig. 1d).

To validate this hypothesis, we performed a theoretical analysis to compare the data sparsity of two different reconstruction approaches (see Fig. 2): (i) two individual reconstructions of phase reference and velocity-encoded data and (ii) joint reconstruction of interleaved phase reference and velocity-encoded data. We acquired a PC cine MRI data set with GRAPPA acceleration (R = 3.1) as a reference, reconstructed the complex raw data off line and performed temporal PCA transformation of the time series data for the two reconstruction methods. Figure 2 shows, for the individual reconstruction case, the magnitude of the phase reference and velocity-encoded data sets in the x-y-PCA domain, and, for the joint reconstruction case, the magnitude of the interleaved data in the x-y-PCA domain. For histogram analysis, we normalized the data sets by their corresponding maximum signal. On the histograms with the same number of voxels, the joint reconstruction case showed 12.6% higher incidence of absolute normalized signal values <0.01 than the individual reconstruction case, confirming that the joint interleaved data are sparser than the sum of two individual datasets in the x-y-PCA domain.

FIG. 2.

FIG. 2

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Reference GRAPPA PC cine MRI data in the x-y-PCA domain, (a) with phase reference and velocity-encoded data displayed separately or (b) as a single interleaved time series. Both image sets (a–b) are displayed with identical grayscale ranging from 0 to 1 in arbitrary units. For histogram analysis, we normalized the data sets by their corresponding maximum signal. c,d: On the histograms with the same number of voxels, the joint reconstruction method showed 12.6% higher incidence of absolute signal values <0.01 than the individual reconstruction method, confirming that the joint interleaved data are sparser than the sum of two individual datasets in the x-y-PCA domain.

Phantom Imaging

For in vitro validation, we used a CompuFlow 1000 MR flow pump (Shelley Medical Imaging Technologies, Toronto, Ontario, Canada), which was programmed to receive an external trigger pulse and generate a time-varying flow wave pattern. The phantom tube was aligned near the magnet isocenter to minimize phase errors due to concomitant gradients. The inner diameter of the phantom tube was 10 mm, and diluted glycerol (2:3; glycerol: distilled water) was used as the fluid. To account for the small diameter of the tube, we imaged the phantom with a reduced field of view of 200 mm × 200 mm. Both GRAPPA and k-t SPARSE-SENSE acquisitions were repeated 16 times. For each measurement, the mean velocity within the phantom tube was computed for each time point. Reported values represent the mean ± standard deviation over 16 measurements.

Liver Imaging

Twelve adult volunteers (nine males and three females; mean age = 28.7 ± 4.3 years) were imaged with electrocardiogram triggering. In all subjects, through-plane velocity was encoded for the vessels of interest and imaging planes were oriented orthogonal to the vessels of interest. In seven of 12 volunteers, portal vein and hepatic veins were imaged with venc = 50 cm/s. In five of 12 volunteers, the portal vein was imaged with venc = 50 cm/s and the IVC was imaged with venc = 80 cm/s. PC cine MRI was performed near the magnet isocenter to minimize phase errors due to concomitant gradients. Human imaging was performed in accordance with protocols approved by our Institutional Review Board; all subjects provided written informed consent.

To assess inter-scan variability, we repeated both the GRAPPA and k-t SPARSE-SENSE acquisitions in all 12 subjects. For each subject, the two vessels of interest were imaged in no particular order. For each vessel of interest, both GRAPPA and k-t SPARSE-SENSE acquisitions were repeated without repositioning, and GRAPPA was always performed before k-t SPARSE-SENSE.

To assess the influence of differences in breath-hold durations between GRAPPA and k-t SPARSE-SENSE acquisitions, in five volunteers, both GRAPPA and k-t SPARSE-SENSE acquisitions were performed with similar breath-hold durations (21–22 heart beats) by acquiring two k-t SPARSE-SENSE acquisitions within the same breath-hold: scan 1 (first 11 heart beats) and scan 2 (last 11 heart beats). Results from scan 1 were compared with scan 2 to examine possible changes in hemodynamics during the breath-hold duration. Additionally, the aver aged results from scans 1 and 2 were then compared with the GRAPPA results.

We elected to use the 32-element cardiac coil in this study to optimize the GRAPPA performance. In addition, we performed a separate experiment in one volunteer to compare the performances of GRAPPA and k-t SPARSE-SENSE using a Siemens 12-element body matrix coil array as an alternative to the 32-element cardiac coil array. For the 12-element matrix coil array, we performed two acquisitions, one in “CP” mode with four effective coil elements, and the other in “triple” mode using all 12 elements.

Image Reconstruction

GRAPPA image reconstruction was performed using the Siemens inline reconstruction algorithm on our VB13 scanner. The k-t SPARSE-SENSE reconstruction was performed off-line using customized software developed in MATLAB® (R2009b software; Mathworks, Natick, MA) running on Windows Server 2003 Standard 64-bit Edition (Microsoft Corporation, Redmond, WA). Coil sensitivity maps were self-calibrated by averaging under-sampled k-space data over time and computed using the adaptive array combination method, as previously described (38,39; Fig. 3). For details on the general k-t SPARSE-SENSE reconstruction, see Ref. 34.

FIG. 3.

FIG. 3

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Schematic flowchart of the two-step image reconstruction method. a: Coil sensitivity maps were self calibrated by averaging undersampled k-space data over time and computed using the adaptive array combination method. b: For the two-step reconstruction method, in step 1, multicoil, zero-filled k-space data, along with the corresponding coil sensitivity maps, were reconstructed using temporal FFT as the sparsifying transform, and the reconstruction was iterated 10 times. In step 2, results from step 1 (which contains less artifacts), along with the corresponding coil sensitivity maps, were used to derive the temporal principal components, and the reconstruction was iterated 30 times, thereby updating the temporal PCA basis 30 times.

Given the proposed undersampling pattern shown in Fig. 1, in the first iteration, an accurate PCA basis cannot be directly estimated from the zero-filled data matrix because the central portion of k-space was not fully sampled. Therefore, as described in the previous work (28,40), we implemented a two-step bootstrap reconstruction approach to derive the temporal principal coefficients after performing an initial k-t SPARSE-SENSE reconstruction with temporal FFT as the sparsifying transform (Fig. 3). In step 1, multicoil, zero-filled k-space data, along with the corresponding coil sensitivity maps, were reconstructed using temporal FFT as the sparsifying transform, and the reconstruction was iterated 10 times. In step 2, results from step 1 (which contains less artifacts), along with the corresponding coil sensitivity maps, were used to derive the temporal principal components, and the reconstruction was iterated 30 times, thereby updating the temporal PCA basis 30 times. In each iteration of step 2, by concatenating each time signal vector along column direction, a matrix V is constructed, and then, by conducting eigen-decomposition of the covariance matrix C of V, a basis set for PCA is estimated. In our implementation, the L1-norm minimization problem is solved with 40 iterations (e.g., 10 FFT iterations and 30 PCA iterations). In each k-t SPARSE-SENSE iteration (Eq. 3 in (34)), the L1-norm minimization problem is solved using a nonlinear conjugate gradient with backtracking line search, as proposed in (23). Using a computer equipped with an Intel Xeon CPU at 2.27 GHz with 16 GB global memory, the total computational time was 75 min.

Numerical Simulation

In this subsection, we describe the methods and results of a preliminary numerical experiment, which was needed to empirically determine a weighting factor (λ) that achieves a good balance between SENSE data consistency and PCA sparsity, before selecting a reconstruction strategy for phantoms and human volunteer studies. In this study, λ was normalized as a fraction of the maximum signal.

We conducted the numerical experiment by retrospectively undersampling a fully sampled PC cine MRI data set to simulate the k-t SPARSE-SENSE reconstruction. To minimize the ghosting artifacts associated with free breathing and bowel peristalsis, we acquired a fully sampled PC cine MRI data set in an axial plane of the thigh station of a 28-year old male volunteer, with venc = 100 cm/s and scan time = 1 min (see “Pulse Sequence” section for other imaging parameters). For pulsatile velocity, we analyzed a femoral artery as a surrogate for a hepatic blood vessel. We performed the two-step k-t SPARSE-SENSE reconstruction with several λ values: 0.1, 0.05, 0.01, and 0.005. Figure 4 shows the magnitude and phase difference images, as well as the corresponding fem-oral artery velocity curves, for the fully sampled and k-t SPARSE-SENSE images with different λ values. Compared with the fully sampled data, the velocity root mean square error (RMSE) was 5.46, 4.49, 2.22, and 2.03 cm/s for λ = 0.1, 0.05, 0.01, and 0.005, respectively; the corresponding normalized RMSE (NRMSE) was 4.89, 4.03, 1.99, and 1.82 %, respectively. Although the velocity RMSE was lowest for λ = 0.005, we also observed more residual aliasing artifacts than for other λ values. As such, we elected to use λ = 0.01 to achieve a good balance between data consistency and artifact suppression.

FIG. 4.

FIG. 4

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The (left column) magnitude and (middle column) phase difference images, as well as the (right column) corresponding femoral artery velocity curves: (row 1) fully sampled and (rows 2–4) k-t SPARSE-SENSE images with different λ values, as noted. Compared with the fully sampled data, the velocity RMSE was 5.46, 4.49, 2.22, and 2.03 cm/s for λ = 0.10, 0.05, 0.01, and 0.005, respectively; the corresponding NRMSE was 4.89, 4.03, 1.99, and 1.82%, respectively. Although the velocity RMSE was lowest for λ = 0.005, we also observed more residual aliasing artifacts than for other λ values. As such, we elected to use λ = 0.01 to achieve a good balance between data consistency and artifact suppression.

Image Analysis

Image analysis was performed using customized software developed in MATLAB. For the phantom, a region-of-interest (ROI) was manually drawn to cover as much of the entire lumen of the tube as possible, and the mean velocity was calculated. For in vivo vessels, a magnitude-weighted mask was used to segment partially the vessel of interest, and a ROI was manually drawn to calculate the mean velocity per time point. Some of the portal vein data sets were acquired with “negative” velocity, and, for convenience, we flipped the sign of the phase difference images in these data sets. The noise in phase difference images, defined as the standard deviation of the phase in a homogeneous stationary region, is inversely proportional to the signal-to-noise ratio in the corresponding magnitude images (41,42). To assess the differences in phase noise, another ROI was manually drawn, adjacent to the vessel of interest, to include a homogenous region with no flow or motion. For each time series, the mean phase noise was calculated. Care was taken to minimize partial volume effects and reproduce the same ROIs between multiple acquisitions per vessel per subject.

Statistical Analysis

To validate the resulting flow measurements, PC cine MRI data sets were randomized and blinded for flow quantification. We performed both Pearson correlation and Bland-Altman analyses to compare the velocity results. Intra and inter-breath-hold acquisition agreements were assessed using Pearson's correlation and Bland-Altman analyses. In this study, velocity measurement at each cardiac phase was considered to be an independent sample. The mean phase noise measurements within the ROI adjacent to the vessels of interests were compared using the paired-sample t-test (two-tailed). A P < 0.05 was considered to be statistically significant. Reported values represent mean ± standard deviation.

RESULTS

With the programmable flow pump, we simulated a time varying waveform emulating hepatic blood flow. Figure 5 shows representative phase difference images of the phantom, as well as the corresponding mean phantom velocity curves obtained from the GRAPPA and k-t SPARSE-SENSE data sets. These two velocity curves were in good agreement, and the RMSE and NRMSE were 0.81 cm/s and 2.58%, respectively.

FIG. 5.

FIG. 5

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Representative phase difference images of the flow phantom: (upper left) GRAPPA and (bottom left) k-t SPARSE-SENSE. (Right) The corresponding mean velocity vs. time curves from GRAPPA and k-t SPARSE-SENSE data. Reported values represent the mean and standard deviation over 16 measurements. The velocity RMSE and NRMSE were 0.81 cm/s and 2.58%, respectively.

To compare the performances of individual and joint k-t SPARSE-SENSE reconstruction methods, we retrospectively performed two different reconstructions from the same accelerated data set of 20 cardiac frames. Figure 6 shows phase difference images using the individual and joint reconstruction methods. The joint reconstruction method yielded 33% lower phase noise than the individual reconstruction method (0.045 vs. 0.067 radians, respectively). These experimental results are consistent with the theoretical analysis illustrated in Fig. 2 and confirm that the proposed joint reconstruction method increases sparsity.

FIG. 6.

FIG. 6

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Phase difference images reconstructed with the (left column) individual and (middle column) joint reconstruction methods. The joint reconstruction method yielded 33% lower phase noise than the individual reconstruction method (0.045 vs. 0.067 radians, respectively).

In all 12 subjects, k-t SPARSE-SENSE reconstruction consistently yielded good image quality. Figure 7 shows representative GRAPPA and k-t SPARSE-SENSE phase difference images of the portal vein of the same volunteer using the 4-element, 12-element, and 32-element coil arrays. For GRAPPA, the phase noise was high and decreased with increasing number of coil elements (0.480 vs. 0.246 vs. 0.098 radians; 4-element vs. 12-element vs. 32-element, respectively). For k-t SPARSE-SENSE, the phase noise was low and decreased with increasing number of coil elements (0.068 vs. 0.065 vs. 0.039 radians; 4-element vs. 12-element vs. 32-element, respectively), suggesting that k-t SPARSE-SENSE can generate good image quality with even the 4-element coil array. Figure 8 shows representative magnitude and phase difference images acquired using the 32-element cardiac coil array, mean velocity vs. time curves, and phase noise comparisons for the GRAPPA and k-t SPARSE-SENSE data sets. In this subject, compared with GRAPPA PC MRI, k-t SPARSE-SENSE PC MRI produced similar mean velocity curves, while yielding 70.6% lower phase noise (0.05 vs. 0.17 radians).

FIG. 7.

FIG. 7

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Representative phase difference images acquired using the (first column) 4-element, (middle column) 12-element, and (right column) 32-element coil arrays: (top row) GRAPPA and (bottom row) k-t SPARSE-SENSE. For GRAPPA, the phase noise was high and decreased with increasing number of coil elements (0.480 vs. 0.246 vs. 0.098 radians; 4-element vs. 12-element vs. 32-element, respectively). For k-t SPARSE-SENSE, the phase noise was low and decreased with increasing number of coil elements (0.068 vs. 0.065 vs. 0.039 radians; 4-element vs. 12-element vs. 32-element, respectively), suggesting that k-t SPARSE-SENSE can generate good image quality with even the 4-element coil array.

FIG. 8.

FIG. 8

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Representative (left column) magnitude and (right column) phase difference images acquired using the 32-element cardiac coil array: (top row) GRAPPA and (middle row) k-t SPARSE-SENSE. The corresponding (bottom row, left column) mean velocity vs. time curves in the right hepatic vein (arrows) from two repeated scans show good agreement. The corresponding (bottom row, right column) phase noise within an ROI was 70.6% lower for the k-t SPARSE-SENSE than GRAPPA images (0.05 vs. 0.17 radians; k-t SPARSE-SENSE vs. GRAPPA, respectively).

Figure 9 shows Pearson's correlation and Bland-Altman scatter plots of pooled data from 12 subjects (n = 512; 7 hepatic, 12 portal, and 5 IVC vessels; 21.3 ± 1.6 cardiac frames per vessel); the mean velocity measurements by GRAPPA and k-t SPARSE-SENSE acquisitions were strongly correlated (Pearson correlation coefficient, R = 0.95; P < 0.05) and in good agreement (mean = 14.5 cm/s; mean difference = –0.29 cm/s; lower and upper 95% limits of agreement = –5.26 and 4.67 cm/s, respectively). The RMSE and NRMSE were 2.55 cm/s and 5.67%, respectively. As summarized in Table 1, the inter-breath-hold repeatability of the same pulse sequence was similar between GRAPPA and k-t SPARSE-SENSE acquisitions. Overall the reproducibility of portal vein and IVC measurements was higher than for hepatic vein measurements (Table 1).

FIG. 9.

FIG. 9

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a: Pearson correlation and (b) Bland-Altman scatter plots. For pooled data (n = 512; 7 hepatic, 12 portal, and 5 IVC vessels; 21.3 ± 1.6 cardiac frames per vessel), the mean velocity measurements by GRAPPA and k-t SPARSE-SENSE acquisitions were strongly correlated (R = 0.95; P < 0.05) and in good agreement (mean difference = –0.29 cm/s [gray line]; lower and upper 95% limits of agreement = –5.26 and 4.67 cm/s [black lines], respectively). HV: hepatic vein; IVC: inferior vena cava; PV: portal vein.

Table 1.

Bland-Altman and Pearson's Correlation Statistics Comparing Mean Velocity Measurements Obtained Using GRAPPA and k-t SPARSE-SENSE

Bland-Altman
Vessel type Difference pair Mean (cm/s) Difference (cm/s) Lower 95% limit (cm/s) Upper 95% limit (cm/s) Pearson R
Hepatic (n = 146) k-t SPARSE-SENSE vs. GRAPPA 11.2 0.80 –5.54 7.13 0.89
GRAPPA vs. GRAPPA 11.6 –1.54 –10.10 7.03 0.88
k-t SPARSE-SENSE vs. k-t SPARSE-SENSE 11.8 –0.44 –7.39 6.51 0.91
Portal (n = 250) k-t SPARSE-SENSE vs. GRAPPA 13.3 –0.39 –3.79 3.02 0.92
GRAPPA vs. GRAPPA 13.6 0.25 –2.28 2.77 0.96
k-t SPARSE-SENSE vs. k-t SPARSE-SENSE 12.9 –0.37 –3.50 2.75 0.93
IVC (n = 116) k-t SPARSE-SENSE vs. GRAPPA 21.6 –0.14 –3.44 3.16 0.99
GRAPPA vs. GRAPPA 22.0 –0.69 –5.78 4.40 0.97
k-t SPARSE-SENSE vs. k-t SPARSE-SENSE 21.9 –0.76 –6.77 5.24 0.96
Overall (n = 512) k-t SPARSE-SENSE vs. GRAPPA 14.5 –0.29 –5.26 4.67 0.95
GRAPPA vs. GRAPPA 15.0 –0.48 –6.15 5.19 0.94
k-t SPARSE-SENSE vs. k-t SPARSE-SENSE 14.6 –0.48 –5.65 4.68 0.95
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Intra- and inter-pulse-sequence agreements for mean velocity measurements. Each pulse sequence acquisition was performed with a separate breath hold. For each difference pair, the difference is defined as the first method minus second method, as shown.

For intra-breath-hold repeatability of k-t SPARSE-SENSE (Table 2), the mean velocity measurements by two repeated acquisitions were strongly correlated (R = 0.97; P < 0.05) and in good agreement (mean = 17.6 cm/s; mean difference = –0.51 cm/s; lower and upper 95% limits of agreement = –4.97 and 3.96 cm/s, respectively). These statistics were similar to those for inter-breath-hold repeatability. For comparison between the GRAPPA acquisition (22 heart beats) and average of two repeated k-t SPARSE-SENSE acquisitions (scan 1: first 11 heart beats; scan 2: last 11 heart beats), the mean velocity measurements were strongly correlated (R = 0.98; P < 0.05) and in good agreement (mean = 17.7 cm/s; mean difference = –0.72 cm/s; lower and upper 95% limits of agreement = –5.05 and 3.61 cm/s, respectively, see Table 3). These statistics are similar to those for inter-breath-hold agreements (see Table 1). The two sub-analyses (Tables 2 and 3) suggest that the differences between breath-hold durations had a negligible contribution to variability in measured velocities.

Table 2.

Intra-Breath-Hold Repeatability of k-t SPARSE-SENSE: Scan 1 (First 11 Heart Beats) vs. Scan 2 (Last 11 Heart Beats)

Bland-Altman
 Pearson R
Vessel type Mean (cm/s) Difference (cm/s) Lower 95% limit (cm/s) Upper 95% limit (cm/s)
Portal (n = 106) 13.1 0.18 –3.09 3.44 0.82
IVC (n = 116) 21.7 –1.13 –6.17 3.91 0.98
Overall (n = 222) 17.6 –0.51 –4.97 3.96 0.97
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Difference is defined as scan 2 minus scan 1.

Table 3.

Pearson Correlation and Bland-Altman Statistics Comparing Mean Velocity Measurements Using GRAPPA and Averaged k-t SPARSE-SENSE (Two Repeated Scans Within the Same Breath-Hold)

Bland-Altman
 Pearson R
Vessel type Mean (cm/s) Difference (cm/s) Lower 95% limit (cm/s) Upper 95% limit (cm/s)
Portal (n = 106) 13.3 –0.56 –2.89 1.77 0.95
IVC (n = 116) 21.8 0.23 –3.71 4.17 0.99
Overall (n = 222) 17.7 –0.72 –5.05 3.61 0.98
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Difference is defined as k-t SPARSE-SENSE minus GRAPPA.

The mean phase noise was 73.7% lower for the k-t SPARSE-SENSE data than for the GRAPPA data (0.05 ± 0.01 vs. 0.19 ± 0.06 radians, respectively; P < 0.01).

DISCUSSION

We have developed a 6-fold accelerated PC cine MRI pulse sequence using k-t SPARSE-SENSE that results in an acquisition time of 11 s for images with true temporal resolution (no view sharing) of 34.5–38 ms and spatial resolution of 1.7 mm × 1.7 mm. Joint reconstruction of interleaved phase reference and velocity-encoded data produced lower phase noise than the individual reconstruction method (Fig. 6). Accelerated PC cine MRI acquisition with k-t SPARSE-SENSE produced results in vivo of comparable accuracy to those obtained with the reference PC cine MRI acquisition using GRAPPA (Table 1). The intra- and inter-breath-hold agreements for mean velocity measurements were also good (Table 2).

This study demonstrates that the proposed 6-fold accelerated PC cine MRI pulse sequence is a promising investigational method for hepatic blood flow measurement with relatively high spatial resolution (1.7 mm × 1.7 mm × 7 mm). Nonetheless, these initial studies have limitations that warrant discussion. First, GRAPPA (21 s) and k-t SPARSE-SENSE (11 s) acquisitions have significantly different durations and changes in physiology could contribute to differences in flow measurements in the liver and IVC. However, we did perform experiments to assess the effects of breath-holding differences, and our results (see Tables 1–3) from a substudy of five subjects showed that the difference in breath-hold duration contributed no appreciable bias. Second, our study was carried out in a small number of healthy subjects. Further studies in a larger number of patients are necessary to evaluate fully the clinical utility of the 6-fold accelerated PC MRI pulse sequence and to establish the intra- and inter-instrumental and study variability of the pulse sequence. Third, we used the proposed ky-t sampling pattern (Fig. 1) based on prior experience with accelerated first-pass cardiac perfusion MRI with k-t SPARSE-SENSE (34). Although there may be other superior k-space sampling patterns, we believe that the proposed k-space sampling pattern does provide adequate results. Fourth, the reconstruction time is approximately 75 min using MATLAB® on a 64-bit workstation for the imaging parameters used in this work. One approach to accelerate the reconstruction time is to use a coil array with fewer elements (Fig. 7). Another approach is to use a GPU (graphics processing unit) platform with CUDA (Compute Unified Device Architecture) programming, or optimized code programmed using C++. Fifth, in this study, we used the same k-space undersampling pattern for both the phase reference and the velocity-encoded data acquisitions, for ease of implementation. Varying the k-space undersampling pattern for the interleaved phase reference and velocity-encoded data acquisitions should further increase incoherence and improve results.

Previously reported k-t acceleration methods such as k-t GRAPPA (43), k-t SENSE (18), and PEAK-GRAPPA (44) also exploit spatio-temporal correlations in the time series data in combination with coil sensitivity information. However, sparsity and coil sensitivity encoding are exploited in a different way than in k-t SPARSE-SENSE. These k-t acceleration methods take advantage of sparsity to reduce signal overlap in the sparse domain due to regularly undersampled data and perform a linear reconstruction to unfold the sparse representation using prior information on this sparse representation and coil sensitivity information. These linear algorithms are computationally less demanding. Acceleration is achieved at the expense of signal-to-noise ratio and residual coherent aliasing artifacts, and additional training data are needed to learn the sparse representation. In contrast, in k-t SPARSE-SENSE, the specific sparse representation is not needed and a nonlinear reconstruction is used to recover the sparse signal coefficients contaminated by incoherent aliasing artifacts produced by an irregular (pseudo-random) undersampling pattern. This nonlinear reconstruction is computationally more demanding. Acceleration is achieved at the expense of residual incoherent aliasing artifacts and loss of low signal coefficients in the sparse domain.

According to the Bland-Altman analysis, the mean difference between k-t SPARSE-SENSE and GRAPPA was slightly negative; suggesting that k-t SPARSE-SENSE has a slight tendency to underestimate velocity. This finding is not surprising, because, with even λ as low as 0.01, small coefficients in the temporal PCA domain may not be recovered during the k-t SPARSE-SENSE reconstruction. Loss of small coefficients in the temporal PCA domain will lead to temporal blurring (Fig. 4). However, it should be noted that the magnitude of the mean difference was small, and the Bland-Altman statistics were comparable with other pairs: GRAPPA vs. GRAPPA, k-t SPARSE-SENSE vs. k-t SPARSE-SENSE pair. Furthermore, in our phantom experiment with a pulsatile flow (Fig. 5), k-t SPARSE-SENSE accurately matched GRAPPA.

In conclusion, the proposed 6-fold accelerated PC cine MRI pulse sequence can be used to perform rapid blood flow measurement with relatively high spatiotemporal resolution and is a promising investigational method for quantitative assessment of hemodynamics. Further application in patients with liver disease and in measurement of other vascular territories remains to be explored.

Acknowledgments

Grant sponsor: National Institutes of Health (NIH); Grant numbers: R01-HL092439, R01-EB000447-07A1, R01-DK069373; Grant sponsor: American Heart Association; Grant number: 0730143N

REFERENCES

  • 1.Ohnishi K, Saito M, Nakayama T, Iida S, Nomura F, Koen H, Okuda K. Portal venous hemodynamics in chronic liver disease: effects of posture change and exercise. Radiology. 1985;155:757–761. doi: 10.1148/radiology.155.3.3890004. [DOI] [PubMed] [Google Scholar]
  • 2.Lebrec D. Methods to evaluate portal hypertension. Gastroenterol Clin North Am. 1992;21:41–59. [PubMed] [Google Scholar]
  • 3.Baik SK, Kim JW, Kim HS, Kwon SO, Kim YJ, Park JW, Kim SH, Chang SJ, Lee DK, Han KH, Um SH, Lee SS. Recent variceal bleeding: Doppler US hepatic vein waveform in assessment of severity of portal hypertension and vasoactive drug response. Radiology. 2006;240:574–580. doi: 10.1148/radiol.2402051142. [DOI] [PubMed] [Google Scholar]
  • 4.Bryant DJ, Payne JA, Firmin DN, Longmore DB. Measurement of flow with NMR imaging using a gradient pulse and phase difference technique. J Comput Assist Tomogr. 1984;8:588–593. doi: 10.1097/00004728-198408000-00002. [DOI] [PubMed] [Google Scholar]
  • 5.Constantinesco A, Mallet JJ, Bonmartin A, Lallot C, Briguet A. Spatial or flow velocity phase encoding gradients in NMR imaging. Magn Reson Imaging. 1984;2:335–340. doi: 10.1016/0730-725x(84)90200-5. [DOI] [PubMed] [Google Scholar]
  • 6.Nayler GL, Firmin DN, Longmore DB. Blood flow imaging by cine magnetic resonance. J Comput Assist Tomogr. 1986;10:715–722. doi: 10.1097/00004728-198609000-00001. [DOI] [PubMed] [Google Scholar]
  • 7.Axel L, Morton D. MR flow imaging by velocity-compensated/uncompensated difference images. J Comput Assist Tomogr. 1987;11:31–34. doi: 10.1097/00004728-198701000-00006. [DOI] [PubMed] [Google Scholar]
  • 8.Firmin DN, Nayler GL, Kilner PJ, Longmore DB. The application of phase shifts in NMR for flow measurement. Magn Reson Med. 1990;14:230–241. doi: 10.1002/mrm.1910140209. [DOI] [PubMed] [Google Scholar]
  • 9.Bernstein MA, Shimakawa A, Pelc NJ. Minimizing TE in momentnulled or flow-encoded two- and three-dimensional gradient-echo imaging. J Magn Reson Imaging. 1992;2:583–588. doi: 10.1002/jmri.1880020517. [DOI] [PubMed] [Google Scholar]
  • 10.Pike GB, Meyer CH, Brosnan TJ, Pelc NJ. Magnetic resonance velocity imaging using a fast spiral phase contrast sequence. Magn Reson Med. 1994;32:476–483. doi: 10.1002/mrm.1910320409. [DOI] [PubMed] [Google Scholar]
  • 11.Thompson RB, McVeigh ER. Flow-gated phase-contrast MRI using radial acquisitions. Magn Reson Med. 2004;52:598–604. doi: 10.1002/mrm.20187. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 12.Markl M, Alley MT, Pelc NJ. Balanced phase-contrast steady-state free precession (PC-SSFP): a novel technique for velocity encoding by gradient inversion. Magn Reson Med. 2003;49:945–952. doi: 10.1002/mrm.10451. [DOI] [PubMed] [Google Scholar]
  • 13.Foo TK, Bernstein MA, Aisen AM, Hernandez RJ, Collick BD, Bernstein T. Improved ejection fraction and flow velocity estimates with use of view sharing and uniform repetition time excitation with fast cardiac techniques. Radiology. 1995;195:471–478. doi: 10.1148/radiology.195.2.7724769. [DOI] [PubMed] [Google Scholar]
  • 14.Markl M, Hennig J. Phase contrast MRI with improved temporal resolution by view sharing: k-space related velocity mapping properties. Magn Reson Imaging. 2001;19:669–676. doi: 10.1016/s0730-725x(01)00386-1. [DOI] [PubMed] [Google Scholar]
  • 15.Beerbaum P, Korperich H, Gieseke J, Barth P, Peuster M, Meyer H. Rapid left-to-right shunt quantification in children by phase-contrast magnetic resonance imaging combined with sensitivity encoding (SENSE). Circulation. 2003;108:1355–1361. doi: 10.1161/01.CIR.0000087603.97036.C2. [DOI] [PubMed] [Google Scholar]
  • 16.Beerbaum P, Korperich H, Gieseke J, Barth P, Peuster M, Meyer H. Blood flow quantification in adults by phase-contrast MRI combined with SENSE—a validation study. J Cardiovasc Magn Reson. 2005;7:361–369. doi: 10.1081/jcmr-200053538. [DOI] [PubMed] [Google Scholar]
  • 17.Thunberg P, Karlsson M, Wigstrom L. Accuracy and reproducibility in phase contrast imaging using SENSE. Magn Reson Med. 2003;50:1061–1068. doi: 10.1002/mrm.10634. [DOI] [PubMed] [Google Scholar]
  • 18.Baltes C, Kozerke S, Hansen MS, Pruessmann KP, Tsao J, Boesiger P. Accelerating cine phase-contrast flow measurements using k-t BLAST and k-t SENSE. Magn Reson Med. 2005;54:1430–1438. doi: 10.1002/mrm.20730. [DOI] [PubMed] [Google Scholar]
  • 19.Jung B, Kozerke S. Comparison of kt-SENSE and kt-GRAPPA applied to cardiac cine and phase contrast imaging.. Proceedings of the 17th Annual Meeting of ISMRM; Honolulu, Hawai'i, USA. 2009. p. 4559. [Google Scholar]
  • 20.Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magn Reson Med. 1997;38:591–603. doi: 10.1002/mrm.1910380414. [DOI] [PubMed] [Google Scholar]
  • 21.Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med. 1999;42:952–962. [PubMed] [Google Scholar]
  • 22.Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med. 2002;47:1202–1210. doi: 10.1002/mrm.10171. [DOI] [PubMed] [Google Scholar]
  • 23.Lustig M, Donoho D, Pauly JM. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med. 2007;58:1182–1195. doi: 10.1002/mrm.21391. [DOI] [PubMed] [Google Scholar]
  • 24.Yoon D, Fessler J, Nielsen J, Gilbert A, Noll D. Non-convex greedy compressed sensing for phase contrast MRI.. Proceedings of the 18th Annual Meeting of ISMRM; Stockholm, Sweden. 2010. p. 4852. [Google Scholar]
  • 25.Velikina J, Johnson K, Block W, Samsonov A. Design of temporally constrained compressed sensing methods for accelerated dynamic MRI.. Proceedings of the 18th Annual Meeting of ISMRM; Stockholm, Sweden. 2010. p. 4865. [Google Scholar]
  • 26.Tao A, Rilling G, Davies M, Marshall I. Compressed sensing reconstruction with retrospectively gated sampling patterns for velocity measurement of carotid blood flow.. Proceedings of the 18th Annual Meeting of ISMRM; Stockholm, Sweden. 2010. p. 4866. [Google Scholar]
  • 27.Jung H, Sung K, Nayak KS, Kim EY, Ye JC. k-t FOCUSS: a general compressed sensing framework for high resolution dynamic MRI. Magn Reson Med. 2009;61:103–116. doi: 10.1002/mrm.21757. [DOI] [PubMed] [Google Scholar]
  • 28.Feng L, Otazo R, Jung H, Jensen JH, Ye JC, Sodickson DK, Kim D. Accelerated cardiac T2 mapping using breath-hold multi-echo fast spin-echo pulse sequence with compressed sensing and parallel imaging. Magn Reson Med. 2011;65:1661–1669. doi: 10.1002/mrm.22756. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 29.Tsao J, Tarnavski O, Privetera M, Shetty S. k-t denoising—exploiting spatiotemporal correlations for signal-to-noise improvement in dynamic imaging.. Proceedings of the 14th Annual Meeting of ISMRM; Seattle, Washington, USA. 2006. p. 690. [Google Scholar]
  • 30.Liang Z. Spatiotemporal imaging with partially separable functions.. Proceedings of IEEE International Symposium on Biomedical Imaging:; From Nano to Macro, Arlington. 2007. pp. 988–991. [Google Scholar]
  • 31.Pedersen H, Kozerke S, Ringgaard S, Nehrke K, Kim W. k-t PCA: temporally constrained k-t BLAST reconstruction using principal component analysis. Magn Reson Imaging. 2009;63:706–716. doi: 10.1002/mrm.22052. [DOI] [PubMed] [Google Scholar]
  • 32.Ding Y, Chung YC, Jekic M, Simonetti OP. A new approach to auto-calibrated dynamic parallel imaging based on the Karhunen-Loeve transform: KL-TSENSE and KL-TGRAPPA. Magn Reson Imaging. 2011;65:1786–1792. doi: 10.1002/mrm.22766. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 33.Lustig M, Santos J, Donoho D, Pauly J. k-t SPARSE: high frame rate dynamic MRI exploiting spatio-temporal sparsity.. Proceedings of the 14th Annual Meeting of ISMRM; Seattle, Washington, USA. 2006. p. 2420. [Google Scholar]
  • 34.Otazo R, Kim D, Axel L, Sodickson D. Combination of compressed sensing and parallel imaging for highly accelerated first-pass cardiac perfusion MRI. Magn Reson Med. 2010;64:767–776. doi: 10.1002/mrm.22463. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 35.Abu-Yousef MM. Duplex Doppler sonography of the hepatic vein in tricuspid regurgitation. AJR Am J Roentgenol. 1991;156:79–83. doi: 10.2214/ajr.156.1.1898574. [DOI] [PubMed] [Google Scholar]
  • 36.Weinreb J, Kumari S, Phillips G, Pochaczevsky R. Portal vein measurements by real-time sonography. AJR Am J Roentgenol. 1982;139:497–499. doi: 10.2214/ajr.139.3.497. [DOI] [PubMed] [Google Scholar]
  • 37.Prince MR, Novelline RA, Athanasoulis CA, Simon M. The diameter of the inferior vena cava and its implications for the use of vena caval filters. Radiology. 1983;149:687–689. doi: 10.1148/radiology.149.3.6647844. [DOI] [PubMed] [Google Scholar]
  • 38.Walsh DO, Gmitro AF, Marcellin MW. Adaptive reconstruction of phased array MR imagery. Magn Reson Med. 2000;43:682–690. doi: 10.1002/(sici)1522-2594(200005)43:5<682::aid-mrm10>3.0.co;2-g. [DOI] [PubMed] [Google Scholar]
  • 39.Griswold MA, Walsh DO, Heidemann RM, Haase A, Jakob PM. The use of an adaptive reconstruction for array coil sensitivity mapping and intensity normalization.. Proceedings of the 10th Annual Meeting of ISMRM; Honolulu, Hawai’i, USA. 2002. p. 2410. [Google Scholar]
  • 40.Jung H, Ye JC. Motion estimated and compensated compressed sensing dynamic magnetic resonance imaging: what we can learn from video compression techniques. Int J Imaging Syst Technol. 2010;20:81–98. [Google Scholar]
  • 41.Pelc NJ, Sommer FG, Li KC, Brosnan TJ, Herfkens RJ, Enzmann DR. Quantitative magnetic resonance flow imaging. Magn Reson Q. 1994;10:125–147. [PubMed] [Google Scholar]
  • 42.Andersen AH, Kirsch JE. Analysis of noise in phase contrast MR imaging. Med Phys. 1996;23:857–869. doi: 10.1118/1.597729. [DOI] [PubMed] [Google Scholar]
  • 43.Huang F, Akao J, Vijayakumar S, Duensing GR, Limkeman M. k-t GRAPPA: a k-space implementation for dynamic MRI with high reduction factor. Magn Reson Med. 2005;54:1172–1184. doi: 10.1002/mrm.20641. [DOI] [PubMed] [Google Scholar]
  • 44.Jung B, Ullmann P, Honal M, Bauer S, Hennig J, Markl M. Parallel MRI with extended and averaged GRAPPA kernels (PEAK-GRAPPA): optimized spatiotemporal dynamic imaging. J Magn Reson Imaging. 2008;28:1226–1232. doi: 10.1002/jmri.21561. [DOI] [PubMed] [Google Scholar]

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