GRASP reconstruction amplified with view‐sharing and KWIC filtering reduces underestimation of peak velocity in highly‐accelerated real‐time phase‐contrast MRI: A preliminary evaluation in pediatric patients with congenital heart disease

To develop a highly‐accelerated, real‐time phase contrast (rtPC) MRI pulse sequence with 40 fps frame rate (25 ms effective temporal resolution).


INTRODUCTION
2][3] Clinical standard 2D electrocardiograph (ECG)-triggered PC MRI with segmented k-space imaging is performed either during breath-holding or free-breathing with averaging.In both scenarios, patients with irregular heart rhythm will generate ghosting imaging artifacts; in breath-held imaging, patients with limited breath-hold capacity will generate motion-induced artifacts; in free-breathing imaging with averaging, the boundaries of vascular wall are typically blurred due to averaging of data from multiple respiratory states.Finally, in young pediatric patients, 2D PC MRI is often performed under general anesthesia, because of their inability to stay still inside the MRI bore and perform breathing instructions.Thus, there is a need to establish technical solutions to address such challenges.One approach to overcome the limitations of 2D PC MRI is performing real-time 2D PC (rtPC) MRI, [4][5][6][7][8][9][10][11][12][13] which has several advantages.First, rtPC is relatively insensitive to irregular heart rhythm and motion, enabling rapid scanning during free-breathing, and potentially reducing the need for general anesthesia in young pediatric patients. 14Second, as a real-time pulse sequence, it permits a beat-to-beat evaluation of hemodynamics, which may be useful for exercise stress testing, studying the impact of respiration on hemodynamics, and diagnosis of conditions such as cardiac tamponade. 15Third, compared with standard 2D PC, which has a scan time of approximately 20 s for breath-held scanning and 2 min for free-breathing scanning with averaging, 9 rtPC can be as short as two heartbeats, where the first heartbeat is necessary for playing a dummy scan to achieve a steady-state of magnetization.Conventional rtPC, however, produces relatively low spatial and temporal resolution compared with clinical standard PC MRI, which may result in quantification error, particularly the peak velocity derived from a single voxel.
There are several techniques for accelerating rtPC, including echo-planar imaging, 7,8 non-Cartesian sampling, [9][10][11][12] parallel imaging, 16,17 low-rank reconstruction, 13 and golden-angle radial sparse parallel (GRASP), 18 with each technique having advantages and disadvantages.It is very challenging for rtPC to match the 25 ms temporal resolution (40 fps frame rate) of transthoracic echocardiography (TTE), which is the first-line investigation for assessing blood flow. 3To realize 25 ms temporal resolution, we sought to achieve high acceleration by synergistically combining GRASP, view-sharing (VS), 19,20 and k-space weighted image contrast (KWIC) filtering. 21ur approach is similar to the vastly undersampled isotropic projection reconstruction (VIPR) technique 22 but amplified using GRASP and made more flexible with retrospective rebinning using golden angles. 23he aims of this study were to develop a highly accelerated rtPC to achieve 25 ms effective temporal resolution (40 fps frame rate) and test our methods in phantom experiments and a cohort of pediatric patients with congenital heart disease (CHD).

Study population
This study was conducted in accordance with protocols approved by our institutional review board and was compliant with the Health Insurance Portability and Accountability Act (HIPAA).We retrospectively identified raw k-space data of 17 pediatric patients with congenital heart disease (10 males and 7 females, mean age = 11.1 ± 3.2 y).All subjects and/or guardians consented in writing to participate in a study comparing clinical standard cardiovascular MRI and rapid research MRI.Table 1 summarizes the baseline characteristics of the patients.
For each patient, 2D PC MRI (clinical standard vs. real-time) was performed in up to four planes (aortic valve, pulmonary valve, left pulmonary artery, right pulmonary artery).In 10/17 (59%) patients who did not require general anesthesia, clinical 2D PC MRI was performed during free breathing for several minutes with averaging (either 2 or 3).In seven (41%) younger patients who required general anesthesia, clinical 2D PC MRI was performed during breath-holding by having the respirator suspended at end-expiration.In all patients, rtPC MRI was performed during free-breathing.As part of clinical routine, 12 (71%) patients received 0.15 mmol/kg of gadobutrol (Gadavist, Bayer HealthCare Pharmaceuticals, Whippany, New Jersey); three (18%) patients received 2 mg/kg of ferumoxytol (Feraheme, AMAG Pharmaceuticals, Waltham, Massachusetts); two (12%) patients did not receive any contrast agent.In all contrast-enhanced examinations, both clinical PC and research rtPC were performed after administration of contrast agent, and research rtPC was performed immediately after clinical PC.

Phantom experiment
A flow phantom (a U-shaped PVC pipe with inner size 21 mm representing a simplified aorta) was scanned using both clinical PC and rtPC to estimate the effective temporal resolution.A pneumatically driven ventricular assist device (VAD) controlled by a pressure pump control unit (MEDOS, Germany) 24 was attached to the flow phantom and generated pulsatile flow through the phantom at a frequency of 90 beats per minute.Water doped with gadolinium-based contrast agent was used as fluid in the experiment.ECG-gating was performed using a synchronized trigger signal generated by the pump control unit.The same spatial resolution (1.5 × 1.5 × 6 mm 3 ) and similar temporal resolutions (29.16 ms for clinical PC and 25.5 ms for rtPC) were used in this experiment.A T1MES phantom was scanned using both clinical PC and rtPC to estimate the effective spatial resolution. 25or more details on analysis, see "Image sharpness assessment" subsection.

MRI hardware
MRI was performed on one 1.5T whole-body MRI scanner (MAGNETOM Aera, Siemens Healthineers, Erlangen, Germany) equipped with a gradient system capable of achieving a maximum gradient strength of 45 mT m −1 and a maximum slew rate of 200 T m −1 s −1 .A body coil was used for RF excitation, and standard body flex and spine coil arrays (30 elements) were used for signal reception.

Pulse sequence
Relevant  , TE/TR = 1.8/4.17ms, temporal resolution = 25.02ms, 3 native radial spokes per frame, free-breathing scan time = 2.75 s (835 ms of dummy scan +1.92 s), velocity encoding = 150-400 cm/s.While ECG triggering was unnecessary for rtPC acquisition, we used prospective ECG triggering for accurate determination of the start and end of each cardiac cycle during analysis, and to save cardiac cine specific information such as trigger time in the digital imaging and communications in medicine (DICOM) header.

View-sharing and KWIC filtering
Figure 1 shows radial spokes used for reconstructing each time frame and corresponding k-space trajectories in the conventional GRASP reconstruction and the proposed GRASP with VS and KWIC filtering (or GRASP + VS + KWIC).In GRASP, only three native spokes are used to reconstruct each time frame, leaving a large part of k-space not sampled; this results in low spatial resolution.In the proposed GRASP + VS + KWIC, we used a symmetric VS scheme along time to borrow k-space samples from neighboring time frames, specifically the edges of k-space defining spatial resolution.A previous study reported that velocity-induced phase shifts are primarily encoded in the center of k-space. 19Conventional VS in radial k-space sampling causes "averaging" hemodynamics between the native spokes and shared Diagrams of real-time phase contrast (rtPC) reconstruction using golden-angle radial sparse parallel (GRASP) alone (upper row) and GRASP + view-sharing (VS) + KWIC (lower row).Left column shows the radial spokes shared between adjacent time frames and the trapezoid-shaped KWIC filter; right column shows the resultant k-space sampling.Dark blue, native spokes; light blue, shared spokes.spokes.We used KWIC filtering to minimize the influence of shared k-space lines from contributing to the center of k-space, which dominates the hemodynamic information.We applied a trapezoid-shaped KWIC filter to remove the central part of the shared spokes.We elected to use a trapezoid-shaped KWIC filter with a narrow base of three-point width, in order to account for gradient delays (i.e., imperfect centering of radial spokes).For additional details describing the preliminary experiments and results for optimizing the parameters for VS and KWIC, see Figure S1 in Supporting Information.

Image reconstruction
The custom-made GRASP image reconstruction code was implemented in MATLAB (R2020b, MathWorks, Natick, Massachusetts) running on a Linux operating system (Ubuntu20.04LTS) of a workstation (32 Xeon E5-2620 v4 384 GB memory, Intel, Santa Clara, CA, USA) equipped with two GPU cards (Tesla V100 GPU with 32 GB memory, NVIDIA, Santa Clara, California).We performed and compared the conventional GRASP reconstruction and the proposed GRASP + VS + KWIC reconstruction on the same raw k-space data.In GRASP + VS + KWIC, VS and KWIC filtering were implemented as pre-processing steps.Otherwise, the remaining reconstruction pipeline was identical to GRASP.Velocity-compensated and velocity-encoded data were reconstructed separately.
During preprocessing, we first rearranged the radial spokes according to VS.We then applied self-calibrated gradient delay correction for all spokes using the radial intersections (RING) method. 27GPU-based non-uniform fast Fourier transform (gpuNUFFT) 28 was used to convert radial k-space data to image data in Cartesian coordinates.GpuNUFFT regridding for time-average images was performed with geometrically-derived density compensation. 29Time-average images were used to derive auto-calibrated coil sensitivity profiles using the method described by Walsh et al. 26 No density compensation was used in gpuNUFFT regridding for producing time-resolved, coil-combined, zero-filled images, which was the initialization for GRASP reconstruction. 30The KWIC filter was applied as a radial k-space sampling mask, which was another input to the GRASP pipeline.Other inputs were the multi-coil radial k-space data and coil sensitivity maps.Our GRASP algorithm used temporal total variation (TTV) as the sparsifying transform and nonlinear conjugate gradient with back-tracking line search as the optimization algorithm with 50 iterations.In the reconstruction, we solved for where F is the NUFFT operator, S is the coil sensitivities, x is the image series to be reconstructed, y is the acquired k-space data, T is the TTV operator, and  is the normalized regularization weight that balances the tradeoff between data consistency and sparsity terms.With a KWIC filter, ∇f (x) in the conjugate gradient method for solving GRASP reconstruction 30 was modified to ∇f (x) = 2F * (KWIC × (Fx − y)) + ∇||Tx|| 1 .
The normalized regularization weight  for TTV was selected separately for GRASP and GRASP + VS + KWIC, Empirical determination of optimal TTV weight (λ) for GRASP alone (top half) and GRASP + VS + KWIC (bottom half).We swept through multiple λ to identify an optimal point that achieves a good balance between peak velocity accuracy and background phase stability.Because the overall effective acceleration factor differs between GRASP alone and GRASP + VS + KWIC, the optimal λ was determined separately.The images show one representative training case, whereas the curves show averaged results across three training cases.KWIC, k-space weighted image contrast; rtPC, real-time phase contrast; RT, real-time; STD, standard deviation; VS, view-sharing; TTV, temporal total variation.since the effective acceleration factor differs between them.We conducted a preliminary experiment on three training datasets to determine optimal regularization weights by sweeping over a range from 0.0005 to 0.01 to identify several regularization weights that achieve a good balance between visual assessment of aliasing artifacts (e.g., low variation in static tissue phase, as illustrated in Figure 2) and temporal fidelity of blood The stationary T1MES phantom experiment to estimate the effective spatial resolution of clinical PC, GRASP alone, and GRASP + VS + KWIC.All three images had identical nominal spatial resolution.Fifteen contiguous intensity profiles (see red on clinical image) were averaged to calculate the edge width, as shown.The measured edge width from clinical PC was 1.20 mm, from GRASP was 3.47 mm, and from GRASP + VS + KWIC was 1.22 mm.KWIC, k-space weighted image contrast; rtPC, real-time phase contrast; VS, view-sharing.flow (see Figure 2).The static tissue phase variation is important for maintaining high velocity-to-noise ratio, particularly for slow flow regions.As shown in Figure 2, we determined that  = 10e −4 and  = 5e −4 for GRASP and GRASP + VS + KWIC, respectively, produces a good balance between peak velocity accuracy and background aliasing artifact suppression.

Image sharpness assessment
From the T1MES images, 15 contiguous intensity profiles were measured across one sharp edge of a tube and then averaged.The edge width, defined as the distance between the 25th and 75th percentiles of the maximum intensity value, was measured.To improve the precision, we interpolated each intensity profile by a factor of 150 using linear interpolation (see Figure 3).For in-vivo assessment, we calculated the blur metric (0-1: sharp-blur) 31 to quantify the overall image sharpness of GRASP and GRASP + VS + KWIC reconstruction in magnitude images from one heartbeat for each plane.

Phase unwrapping and background phase correction
We applied the ROMEO technique 32 to unwrap phase aliasing as needed.For all clinical PC and rtPC images, background phase was corrected using the method described by Walker et al. 33 We used first-order fitting for clinical 2D PC sampled with Cartesian k-space sampling, whereas second-order fitting for rtPC to account for the nonlinear phase offsets induced by non-Cartesian k-space sampling.

Velocity and volume quantification
For analysis of velocity and volume from rtPC data, we used the ECG time stamp information to extract one full cardiac cycle.For both clinical PC and rtPC, regions of interest (ROIs) were contoured manually with custom software written in MATLAB.For fair comparisons, the same set of ROI masks was used for GRASP and GRASP + VS + KWIC.Peak velocities at peak systole, forward and backward volumes through one full cardiac cycle, and regurgitation fraction were measured for both clinical PC and rtPC.The peak velocity was defined as the 95-percentile, instead of the maximum, of all velocities within the ROI at peak systole to avoid inaccuracies caused by spurious voxels.
To evaluate the ability of rtPC for assessing beat-to-beat variations, we used the semi-automatic tools in Circle cvi42 (v5.14, Circle Cardiovascular Imaging, Calgary, Canada) to contour the ROIs in the time frames corresponding to peak systole for all cardiac cycles and all cases.Variations in peak velocity at peak systole across different cardiac cycles were analyzed.In one case, ROIs were contoured in all time frames with cvi42 to visualize the change of peak velocity with time.

Statistical analysis
The statistical analyses were conducted by one investigator (H.Y.).We tested for variable normality using the Shapiro-Wilk test.Bland-Altman and linear regression analyses were performed on peak velocity, forward volume, backward volume, and regurgitation fraction values to assess the level of agreement and correlation between clinical PC and each reconstruction method for rtPC.One-way analysis of variation (Kruskal-Wallis if not normally distributed) with Bonferroni correction was conducted to detect any significant differences among results from clinical PC and reconstruction methods of rtPC.A p-value <0.05 was considered statistically significant for all tests performed.

RESULTS
The dataset from one patient was excluded due to a mismatch in imaging plane between rtPC and clinical PC.The total number of planes used in this study was N = 58.According to the Shapiro-Wilk test, the blur metric values were normally distributed (p > 0.51) while all hemodynamic parameters for clinical PC and rtPC were not normally distributed (p < 0.04).Thus, we used parametric statistical tests (one-way analysis of variation) for blur metric and non-parametric statistical tests (Kruskal-Wallis) for hemodynamic parameters.
The mean reconstruction time was 16.6 s/frame for GRASP and 22.7 s/frame for GRASP + VS + KWIC.

Image sharpness
Figure 3 shows images of the T1MES phantom tubes, the average normalized intensity profiles, and the measured edge widths from clinical PC, GRASP, and GRASP + VS + KWIC rtPC.The regularization weights were the same as in-vivo conditions.GRASP + VS + KWIC produced better image sharpness than GRASP.The edge width was 1.20, 1.22 (1.7% higher than clinical PC), and 3.47 mm (189.2% higher than clinical PC) for clinical PC, GRASP + VS + KWIC, and GRASP, respectively.Figures 4 and 5 show representative rtPC magnitude and phase images from the flow phantom experiment and from in-vivo data, respectively.As shown in Figure 4, GRASP reconstruction resulted in phantom structures appearing larger than the true size due to blurring, whereas GRASP + VS + KWIC reconstruction produced similar size as the clinical PC.As shown in Figure 5, GRASP + VS + KWIC provides shaper in-vivo images compared with GRASP.For dynamic display of images in Figures 4 and 5, see Videos S1-S3.

Velocity and volume quantification
In the flow phantom experiment (see Figure 4), where the overall sparsity is considerably higher than in vivo condition and the spatial resolution is matched between clinical PC and rtPC, the underestimation in peak Flow phantom images produced by clinical standard PC, rtPC with GRASP, and rtPC with GRASP + VS + KWIC.The magnitude images are displayed with a narrow intensity scale to bring out the edge definition.The corresponding peak velocity and flow curves are also shown.Compared with clinical PC, the peak velocity was underestimated by 5.4% and 8.1% for GRASP alone and proposed, respectively.For the corresponding video display, see Video S1 in Supporting Information.KWIC, k-space weighted image contrast; ROI, region of interest; rtPC, real-time phase contrast; VS, view-sharing.

F I G U R E 5
Two example images of two different patients produced by clinical PC, rtPC with GRASP alone, and rtPC with GRASP + VS + KWIC.The corresponding peak velocity and flow curves are also shown.For the corresponding video display, see Videos S2 (part A) and S3 (part B) in Supporting Information.AV, aortic valve; KWIC, k-space weighted image contrast; PV, pulmonary valve; rtPC, real-time phase contrast; VS, view-sharing.velocity was relatively low for both GRASP (5.4%) and GRASP + VS + KWIC (8.1%).In contrast, in patients (see Figure 5), where the overall sparsity is considerably lower than flow phantoms and the spatial resolution is higher for clinical PC than rtPC, the underestimation in peak velocity was lower for GRASP + VS + KWIC than GRASP.Both GRASP and GRASP + VS + KWIC achieved good agreement with clinical PC in flow measurements, which are less influenced by spatial resolution.
Figure 6 shows scatter plots illustrating the linear regression analysis on hemodynamic parameters.For peak velocity, GRASP + VS + KWIC was strongly correlated with clinical PC (the coefficient of determination [R 2 ] = 0.71), whereas GRASP had moderate correlation with clinical PC (R 2 = 0.55).For forward volume, backward volume, and regurgitant fraction, GRASP + VS + KWIC and GRASP had similarly strong correlation with clinical PC (R 2 ≥ 0.88).

F I G U R E 6
Scatter plots representing the linear regression analysis on hemodynamic parameters (in-vivo, single heartbeat), where clinical PC is the reference.AV, aortic valve; LPA, left pulmonary artery; PV, pulmonary valve; RPA, right pulmonary artery.According to the Kruskal-Wallis test, GRASP produced significantly lower peak velocity than clinical PC (p < 0.007), whereas all other pair-wise comparisons of hemodynamic parameters were not significantly different (p > 0.17).

3.3
Beat-to-beat variation

DISCUSSION
This study describes our solution to achieve high spatial and temporal resolution in rtPC MRI.We incorporated VS and KWIC filtering into GRASP to achieve 25 ms effective temporal resolution (40 fps frame rate) and 1.5 × 1.5 mm 2 spatial resolution.Our solution provides a means to address the challenges associated with pediatric cardiovascular MRI.
][10]34,35 Kowalik et al. 14 combined perturbed spiral k-space sampling with compressed sensing and achieved 1.76 × 1.76 mm 2 spatial resolution, 26.6 ms temporal resolution, and acceleration rate of 18.In comparison, our method is 17.3% better in spatial resolution and 6.4% better in temporal resolution.Compared with Scatter plots representing the Bland-Altman analysis on hemodynamic parameters (in-vivo, single heartbeat), where clinical PC is the reference.AV, aortic valve; LPA, left pulmonary artery; PV, pulmonary valve; RPA, right pulmonary artery.radial k-space sampling, spiral k-space sampling is more susceptible to geometric distortion due to longer readout.Compared with the Cartesian k-space sampling method proposed by Sun et al. 13 with 1.8 × 1.8 mm 2 spatial resolution and 18 ms temporal resolution, our method is 20% better in spatial resolution and 38.9% worse in temporal resolution.The method by Sun et al. 13 is sensitive to potential mismatch between the training and imaging data for temporal interpolation, whereas our method does not rely on training data.Compared with the model-based radial k-space sampling method proposed by Tan et al. 36 with 1.5 × 1.5 mm 2 spatial resolution and 25.6 ms temporal resolution, our method provides similar spatio-temporal resolution without special assumptions or approximations required for model development.In these prior studies, the temporal resolution was fixed during acquisition, whereas in our study, the golden angle sampling scheme enabled retrospective rebinning for arbitrary or patient-specific temporal resolution based on heart rate.Compared with two previous studies performed on adult subjects, 13,36 our study was validated on pediatric CHD patients, which is a more challenging clinical context due to higher heart rates and smaller patient size.Compared with previous studies examining only the aortic flow, 13,14,36 we examined more challenging planes such as the pulmonary valve and pulmonary arteries.A direct head-to-head comparison study Representative magnitude image, phase-contrast image, and the resulting peak velocity curve over multiple heartbeats of rtPC with GRASP + VS + KWIC.The maximum peak velocity was 211.4 cm/s and the median peak velocity was 186.8 cm/s.KWIC, k-space weighted image contrast; rtPC, real-time phase contrast; VS, view-sharing.

T A B L E 2
Peak velocity results per vessel over 17 patients from clinical PC and from rtPC with GRASP + VS + KWIC reconstruction.involving multiple developers and/or vendors is warranted to evaluate the relative accuracies in a pediatric patient cohort.

Imaging
We systematically tested different levels of VS and KWIC filtering.Sharing a sufficient number of radial spokes improved accuracy in velocity measurements, but sharing too many radial spokes worsened the accuracy compared with no VS.This was due to the "averaging" effect from all the spokes contributing equally to the central part of k-space, in effect worsening temporal resolution.KWIC filtering mitigated the "averaging" effect from shared k-space lines and retained high accuracy, but excessively large KWIC filters resulted in reduced accuracy.We optimized the level of VS and the shape of KWIC filtering to maintain high accuracy in peak velocity, since it is influenced by spatial resolution.
We demonstrated the ability of rtPC with GRASP + VS + KWIC reconstruction to assess beat-to-beat variation in hemodynamics.Clinical scenarios in which beat-to-beat variations would be meaningful include, cardiac rhythm disorders, exercise stress testing, and Valsalva maneuver.This feature afforded by rtPC is not available in clinical PC due to the averaging nature with segmented k-space imaging.
Our study has several limitations.First, our sample size was insufficient for adjusting for factors such as age, sex, CHD type, contrast agent, intrathoracic pressure (breath-hold or free-breathing in clinical PC), general anesthesia, and imaging plane.Second, the impact of heart rate on the accuracy of hemodynamic measurements was not investigated.The proposed technique enables retrospective adjustment of temporal resolution that could be personalized according to heart rate.Theoretically, a higher heart rate could benefit more from better temporal resolution.A future study involving more subjects with a wider range of heart rates is warranted to verify the benefit of patient specific temporal resolution.Third, the ability to assess beat-to-beat variations was not fully explored, because in this study we focused on improving the spatial and temporal resolution of rtPC MRI and the accuracy of peak velocity measurements in pediatric CHD patients.Future studies will investigate beat-to-beat variations in patients with arrhythmias.Fourth, the time-consuming nature of reconstruction based on GRASP was not addressed.The term "real-time" in this study refers to "single-shot" sampling of all requisite k-space lines per frame (i.e., no repetition) 37 ; it does not indicate "real-time" inline display of image with low latency. 38Several studies 39,40 have used deep learning to shorten the reconstruction time in rtPC MRI.A future study is warranted to apply deep learning to accelerate the reconstruction of our rtPC images, which may support "real-time" inline display of image with low latency.
In conclusion, the synergistic combination of GRASP, VS, and KWIC achieves 25 ms effective temporal resolution (40 fps frame rate), while minimizing the underestimation of peak velocity compared with conventional GRASP.