Highly-Accelerated, Real-Time Phase-Contrast MRI Using Radial k-Space Sampling and GROG-GRASP Reconstruction: A Feasibility Study in Pediatric Patients with Congenital Heart Disease

Abstract

Retrospective ECG-gated, 2D phase-contrast (PC) flow MRI is routinely used in clinical evaluation of valvular/vascular disease in pediatric patients with congenital heart disease (CHD). In patients not requiring general anesthesia, clinical standard PC is conducted with free-breathing for several minutes per slice with averaging. In younger patients under general anesthesia, clinical standard PC is conducted with breath-holding. One approach to overcome this limitation is using either navigator gating or self-navigation of respiratory motion, at the expense of lengthening scan times. An alternative approach is using highly-accelerated, free-breathing, real-time PC (rt-PC) MRI, which to date has not been evaluated in CHD patients. The purpose of this study was to develop a 38.4-fold accelerated 2D rt-PC pulse sequence using radial k-space sampling and compressed sensing with 1.5×1.5×6.0mm³ nominal spatial resolution and 40msec nominal temporal resolution and evaluate whether it is capable of accurately of measuring flow in 17 pediatric patients (aortic valve, pulmonary valve, right and left pulmonary arteries) compared with clinical standard 2D PC (either breath-hold or free-breathing). For clinical translation, we implemented an integrated reconstruction pipeline capable of producing DICOMS on the order of 2 minutes per time series (46 frames). In terms of association, forward volume, backward volume, regurgitant fraction, and peak velocity at peak systole measured with standard PC and rt-PC were strongly correlated (R²>0.76;P<0.001). Compared with clinical standard PC, in terms of agreement, forward volume (mean difference=1.4%[3.0% of mean]) and regurgitant fraction (mean difference=−2.5%) were in good agreement, whereas backward volume (mean difference=−1.1 mL[28.2% of mean]), and peak-velocity at peak systole (mean difference=−21.3 cm/s[17.2% of mean]) were underestimated by rt-PC. This study demonstrates that the proposed rt-PC with said spatial resolution and temporal resolution produces relatively accurate forward volumes and regurgitant fractions but underestimated backward volumes and peak velocities at peak systole in pediatric patients with CHD.

Graphical Abstract

This study describes development of a 38.4-fold accelerated, real-time 2D phase-contrast (rt-PC) pulse sequence using radial k-space sampling and compressed sensing with 1.5 × 1.5 × 6.0 mm³ nominal spatial resolution and 40 msec nominal temporal resolution, and implementation of an integrated GROG-GRASP reconstruction pipeline in the Yarra framework. The clinical motivation of this study is to enable rapid, free-breathing rt-PC MRI for assessment of valvular and vascular disease in pediatric patients with congenital heart disease. The mean image reconstruction time was approximately 2 min per time series with 46 cardiac frames. In 17 pediatric patients, compared with clinical standard 2D PC MRI, the proposed rt-PC method produced relatively accurate forward volumes and regurgitant fractions but underestimated backward volumes and peak velocities at peak systole in pediatric patients with congenital heart disease.

Introduction

Retrospective ECG-gated 2D phase-contrast (PC) flow MRI¹ is used routinely in clinical practice for imaging pediatric patients with congenital heart disease (CHD)^2,3 to diagnose valvular regurgitation^3,4, valvular and vascular stenosis³, and/or to quantify parameters such as Q_p/Q_s ratio^2,5. Despite its clinical utility, clinical standard PC MRI has several limitations due to its low data-acquisition efficiency. First, its scan time is long, typically greater than 20 sec for breath-hold scanning and 1 min for free-breathing scanning. Second, both free-breathing and breath-hold versions of clinical standard PC are sensitive to arrhythmia and/or bulk motion. Third, clinical standard free-breathing scans⁶ are performed without respiratory motion tracking and, thus, typically produce blurred boundaries of the valve apparatus and vessel wall due to respiratory motion. Fourth, in younger pediatric patients, general anesthesia is often necessary to suspend respiration during imaging. Fifth, segmented k-space PC MRI acquisitions are by nature incapable of assessing beat-to-beat variations in flow due to arrhythmia. Thus, there is a clinical need to overcome the aforementioned limitations associated with 2D clinical standard PC MRI for pediatric patients with CHD.

One approach to overcome these limitations associated with 2D clinical standard PC MRI is incorporating navigator echoes or self-navigation of respiratory motion⁷, at the expense of lengthening scan times and possibly losing retrospective ECG gating. An alternative approach is using real-time PC (rt-PC) MRI, defined as single-shot (or non-segmented) imaging. The advantages of rt-PC over non-real-time (i.e. segmented) acquisitions synchronized to cardiac and breathing rhythms are as follows: a) enables faster (< 5 sec per slice) scanning, b) enables free-breathing scanning, c) provides insensitivity to arrhythmia and/or bulk motion, d) provides a means to evaluate beat-to-beat variations in flow due to arrhythmia, and e) provides a means to perform rapid, real-time, free-breathing scanning without general anesthesia. While several research groups have proposed 2D rt-PC MRI using conventional imaging methods^8–10, they reported relatively low nominal spatial resolution (2.5 × 2.5 mm² to 2.7 × 2.7 mm²), nominal temporal resolution (55 to 124 ms), and/or relatively thick slice (8 mm to 10 mm), all of which may be inadequate for pediatric patients with smaller hearts and faster heart rates. Thus, there is a need to develop and evaluate an accelerated rt-PC for imaging pediatric patients with CHD.

A previous study by Joseph et al.¹¹ proposed highly-accelerated 2D rt-PC MRI using radial k-space sampling and non-linear inversion (NLINV) reconstruction, and demonstrated nominal spatial resolution of 1.3 × 1.3 × 6 mm³ and nominal temporal resolution of 40 msec. While this investigational technique is promising, it has not been evaluated in pediatric patients, and using regularly spaced radial angles does not lend itself to retrospective rebinning of data (i.e. rays per frame), which is useful for patient specific determination of temporal resolution. Therefore, we sought to build on the prior work by Joseph et al.¹¹ by incorporating the following three elements: (a) radial k-space sampling with golden-angle ordering¹² to increase temporal incoherence and permit flexible retrospective data binning of temporal frames, (b) reconstruction using the GRAPPA operator gridding (GROG) golden-angle radial sparse parallel (GROG-GRASP) framework¹³ with compressed sensing to jointly enforce multi-coil sparsity, and (c) clinical integration using an automated reconstruction pipeline that produces DICOMS and send them to a PACS server. Combined use of these advanced methods provides a means to image CHD patients with high nominal spatial (~1.5 × 1.5 × 6 mm³) and high nominal temporal resolution (~ 40 msec). The purposes of this study were to develop a 38.4-fold accelerated rt-PC pulse sequence using radial k-space sampling and GPU-accelerated GROG-GRASP reconstruction with the aforementioned spatial and temporal resolutions and evaluate its accuracy with respect to 2D clinical standard PC (see definition in the next paragraph) in pediatric patients with CHD.

Materials and Methods

Patient Selection

We evaluated the performance of the proposed 2D rt-PC in 17 pediatric patients with CHD (10 males and 7 females, mean age = 11.3 ± 3.2 years) undergoing a clinical cardiovascular MRI, which included retrospective ECG-gated 2D PC MRI at up to 4 locations (aortic valve, pulmonic valve, left pulmonary artery, right pulmonary artery; N = 60 planes in total). In our clinical practice, in patients not requiring general anesthesia, clinical standard PC is conducted with free-breathing for several minutes per slice with averaging. In younger patients under general anesthesia, clinical standard PC is conducted during breath-holding by having the respirator suspended. For convenience, clinical standard PC refers to either retrospective ECG-gated, free-breathing 2D PC scans with averaging or retrospective ECG-gated, breath-held 2D PC scans throughout.

Baseline characteristics of patients including congenital heart defects, age, sex, resting heart rate, left ventricular ejection fraction (LVEF), and right ventricular ejection fraction (RVEF) are summarized in Table 1. This study was conducted in accordance with the protocols approved by our institutional review board and was Health Insurance Portability and Accountability Act (HIPAA) compliant; all subjects and/or guardians provided informed consent in writing.

Table 1.

Baseline characteristics of pediatric CHD patients (N=17) including congenital heart defects, age, sex, resting heart rate, left ventricular ejection fraction (LVEF), and right ventricular ejection fraction (RVEF). s/p: status post; BAV: bicuspid aortic valve.

Characteristic
Age	11.1 ± 3.2 years
Females	7/17 (41.2%)
Resting Heart Rate	80.3 ± 9.6 bpm
LVEF	55.8 ± 5.4 %
RVEF	50.1 ± 8.7 %
Tetralogy of Fallot s/p repair	5 (29.4%)
Aortopulmonary window s/p repair	1 (5.9%)
Mitral stenosis s/p valvuloplasty	1 (5.9%)
Tetralogy of Fallot and pulmonary atresia s/p repair	1 (5.9%)
Transposition of the great arteries and coarctation s/p arterial switch and coarctation repair	1 (5.9%)
Ehler Danlos	1 (5.9%)
Partial anomalous pulmonary venous return	2 (11.8%)
Ebstein anomaly	1 (5.9%)
Supravalvar pulmonary stenosis	1 (5.9%)
Pulmonary valve stenosis	1 (5.9%)
Transposition of the great arteries s/p arterial switch	1 (5.9%)
BAV and coarctation	1 (5.9%)

Seven out of 17 (41.2%) patients received general anesthesia as part of the clinical routine; 12 out of 17 (70.6%) patients received 0.15 mmol/kg of gadobutrol (Gadavist, Bayer HealthCare Pharmaceuticals, Whippany, NJ) as part of clinical routine; 3 out of 17 (17.6%) patients received 2 mg/kg of ferumoxytol (Feraheme, AMAG Pharmaceuticals, Waltham, MA) as part of clinical routine; 2 out of 17 (11.8%) patients underwent cardiovascular MRI without contrast agent or general anesthesia. In all contrast-enhanced cases, PC scans were performed after administration of contrast agent, and clinical standard PC was performed immediately prior to research rt-PC.

Pulsatile Flow Phantom Experiment

We scanned an MRI-compatible custom-made pulsatile flow phantom circuit with a U-shaped 3/4” SCH 40 PVC pipe representing a simplified aorta¹⁴. A pressure-pump control unit (MEDOS, Germany) in conjunction with a pneumatically-driven ventricular assist device (VAD) was used to generate pulsatile flow and generate a synchronized trigger signal for “ECG” gating. The VAD was directly attached to the simple U-phantom with 21 mm inner diameter to mimic pulsatile flow entering the ascending and descending thoracic aorta at a frequency of 60 beats per minute with regular heart rhythm. Water doped with gadolinium-based contrast material was used as fluid (T1 = 146 ms and T2 = 124 ms) in all experiments. For the flow phantom experiment, we adjusted the clinical standard PC protocol to match the spatial resolution (1.5 × 1.5 × 6 mm³) and temporal resolution (41.7 msec) of rt-PC used in vivo, in order to minimize confounders. For additional parameters, see the imaging parameters section.

MRI Hardware

All MRI examinations were conducted on a single 1.5T whole-body MRI scanner (MAGNETOM Aera, Siemens Healthcare, Erlangen Germany), which is equipped with a gradient system capable of creating a maximum gradient strength of 45 mT/m and a maximum slew rate of 200 mT/m/ms. A body coil was used for radio-frequency (RF) excitation, and standard body flex and spine coil arrays (30 elements) were used for signal reception.

Golden-Angle Radial k-Space Sampling, Net Acceleration, and Phase Correction

We implemented a rt-PC sequence with gradient-echo readout, RF and gradient spoiling, and golden-angle (111.2461°) radial k-space sampling¹². Our rt-PC MRI pulse sequence interleaved phase-reference and velocity-encoded acquisitions for each k-space line, as previously described¹⁵. At a repetition time of TR = 4.17 ms, we sought to reconstruct each image with 5 views per frame, resulting in a temporal resolution of 41.7 ms (=5 × 2 × TR). For an image reconstruction matrix of 192 × 192, this corresponds to an acceleration factor (R) = 38.4 relative to an equivalent Cartesian scan.

In any cine MRI acquisition, a dummy prep-scan on the order of 1 s is necessary to achieve a steady state of magnetization. As shown in Figure 1, we combined these dummy shots with trajectory-calibration scans^16,17 as a single pre-scan with 834 ms duration (200 × TRs, TR = 4.17 ms, last 120 TRs used for trajectory correction). Specifically, 200 calibration k-space lines in total (i.e. 100 for reference and 100 for velocity-encoding) were organized into 50 anti-parallel pairs (e.g., 0° and 180°, 3.6° and 183.6°) per type (reference or velocity-encoding) with equally spaced angles, ranging from 3.6° to 180° (3.6° steps). As described by Eq. 1, the gradient delay for a given azimuthal angle F(θ) was extracted from the phase of the cross-correlation function of two anti-parallel calibration views (R_θ and R_θ+180), after which they are fit to the model in Eq. 1^17,18, where Δk₁, Δk₂, and Δk₃ represent in-plane k-space trajectory errors due to x readout encoding, y readout encoding, and cross-talk between x and y readout encoding directions, respectively.

$$F\left(\theta \right)=\Delta k_1\ast co{s}^2\theta +\Delta k_2\ast si{n}^2\theta +\Delta k_3\ast sin\theta \ast cos\theta$$ Eq. 1

The delay estimated from the calibration data was then used to correct for trajectory errors in the radial views acquired with the golden-angle sequence.

Figure 1.

Schematic Diagram of ECG-triggered rt-PC pulse sequence. Prior to the acquisition of the first heartbeat for scanning, dummy and calibration scans totaling 834 ms duration (200 × TRs, TR = 4.17 ms, last 120 TRs used for trajectory correction) are played for 834 ms (200 × TRs, TR = 4.17 ms) to achieve a steady state of the magnetization and to correcting for k-space trajectory errors, respectively. Trajectory corrected phase reference and velocity-encoded k-space data are then sent to the GROG-GRASP reconstruction pipeline for de-aliasing as shown.

Imaging Parameters

The relevant imaging parameters for clinical standard PC MRI were as follows: image acquisition matrix size ranged from 176 × 132 (phase-encoding) to 256 × 208, field of view (FOV) ranged from 180 mm × 135 (phase-encoding) to 300 mm × 224 mm (depending on patient size), spatial resolution ranged from 1.1 × 1.1 mm² to 1.4 × 1.4 mm², slice thickness = 5 mm, Cartesian k-space sampling with GRAPPA (22) acceleration R = 1.8, receiver bandwidth = 445 Hz/pixel, flip angle = 20°, TE/TR = 2.45/4.8 ms, temporal resolution = 19.2 – 28.8 ms, velocity encoding = 150 – 400 cm/s (depending on valve/vessel type), k-space lines acquired per shot = 2–3 lines per shot. Ten out of seventeen patients underwent free-breathing scanning with averaging (2 or 3). Seven remaining patients underwent breath-hold scanning with the respirator suspended at end expiration.

Relevant imaging parameters for rt-PC were as follows: matrix size = 192 × 192, FOV = 288 mm × 288 mm, spatial resolution = 1.5 × 1.5 mm², receiver bandwidth = 745 Hz/pixel, flip angle = 12°, TE/TR = 1.8/4.17 ms, prospective ECG triggering, free-breathing scan time = 2.75 s (835 ms of dummy scan + 1.92 s), slice thickness = 6 mm, temporal resolution of 41.7 ms, and 46 temporal frames. Velocity encoding strength was matched to the clinical standard PC MRI. For one patient we acquired an additional longer scan (~25 heartbeats) to illustrate its capability to assess beat-to-beat variations in hemodynamic. While ECG triggering was not necessary to acquire real-time PC data, we used it to save cardiac cine specific information (e.g. trigger time) in the DICOM header, in order to make the resulting DICOMS compatible with commercial analysis software.

Automated GROG-GRASP Reconstruction Pipeline

The integrated reconstruction pipeline was implemented using the Yarra framework (http://yarraframework.com), which is a user-friendly software that automatizes the transfer of the MRI raw k-space data to an external server for offline image reconstruction. For this project, we established a fast Ethernet connection to transfer raw k-space data from the MRI scanner to our GPU server (V100 Tesla GPU with 16GB memory, NVIDIA, Santa Carla, California, USA) equipped with Matlab (R2018b, The MathWorks Inc, Natick, MA, USA) running on a Linux operating system (Ubuntu16.04). After completing the reconstruction task, the reconstructed images in a DICOM format were sent directly to our PACS server and retrieved later for analysis.

As shown in Figure 2, GROG interpolation was used during pre-processing to translate radial k-space data onto a Cartesian grid for both time average multi-coil reference images, and time-resolved multi-coil reference k-space and velocity-encoding k-space data. Time average multi-coil reference images were used to derive auto-calibrated coil sensitivity profiles using the method described by Walsh et al.¹⁹. Coil-sensitivity profiles were subsequently inputted with density-compensated time-resolved multi-coil reference k-space and velocity-encoding k-space data to produce time-resolved zero-filled reference and velocity encoded images. After pre-processing, in the compressed sensing part, time-resolved zero-filled reference and velocity encoded images (Figure 2: red boxes), time resolved multi-coil reference k-space and velocity encoded k-space data (Figure 2: purple box), Cartesian k-space trajectories (Figure 2: orange box), density compensation matrix (Figure2: green box), and coil-sensitivity profiles (Figure 2: blue box) were fed into a nonlinear conjugate gradient optimization algorithm with back-tracking line search and temporal sparsity constraint (temporal total variation). Reference and velocity encoded images were reconstructed separately using a normalized regularization weight of 0.00321 and 22 iterations. The regularization weight was normalized using the maximum pixel intensity from the center 1/4 of time-averaged image, which avoided normalization to bright streaking signals and/or bright fat signals found in the outer portion of FOV. The central 1/4 of the imaging FOV was automatically selected, since we prescribed each acquisition with the heart centered in the FOV. Normalized regularization weight for temporal TV was set as 0.32% of the maximum signal of time average image based on visual inspection of image quality on training data of young patients (<12 years old), as previously described (23,24). We established the 0.32% as an optimal value by sweeping over a range from 0.25 to 1% (0.02% steps) and identifying the highest regularization weight that minimizes temporal blurring of voxels in the heart and distortion of the velocity-time curves. During post-processing, we applied a 1D median filter along time with a kernel size of 7 to the magnitude of reference images, in order to remove residual flickering artifacts, as previously described¹¹. To reduce reconstruction time, we applied coil compression using principal component analysis (PCA)²⁰ to produce 7 virtual coils, and we utilized the gpuArray functionality in Matlab to process on the GPU. For a more detailed description of the GROG-GRASP reconstruction algorithm, see reference¹³.

Figure 2.

In pre-processing, GROG translates radial k-space data onto a Cartesian grid for both time average multi-coil data and time-resolved multi-coil reference and velocity-encoding data (Figure 2: purple boxes). Time average multi-coil data were used to derive coil-sensitivity profiles (Figure 2: blue box) which were subsequently inputted with density-compensated (Figure 2: green box) reference and velocity-encoded multi-coil k-space into a SENSE operator to produce coil-combined zero-filled reference and velocity-encoded images (Figure 2: red boxes). After pre-processing, iterative nonlinear conjugate gradient optimization was used to reconstruct de-aliased reference and velocity-encoded images separately. In post-processing, magnitude images underwent an additional 1D temporal median filtering to remove residual flickering artifacts. After completing the reconstruction task, the resulting images in DICOMS format were sent directly to our PACS server.

Background Phase Correction

Clinical standard PC images were reconstructed inline using vendor’s processing pipeline including Maxwell term correction. We did not perform Maxwell term correction for our rt-PC images, because it is not straight forward to calculate concomitant gradient terms in radial k-space sampling with system imperfections such as gradient delays and eddy currents associated with golden angles. During post-processing, in both clinical standard and rt-PC images, background phase was corrected by using the method described by²¹. We elected to use second-order fitting for radial rt-PC, in order to account for the nonlinear phase offsets induced by non-Cartesian k-space sampling (see Supplementary Figure S1 which illustrates superior background phase correction with second-order compared to first-order fitting routine), whereas first-order fitting was adequate for clinical standard PC obtained with Cartesian k-space sampling.

Volume and Peak Velocity Quantification

We quantified the forward volume, backward volume, regurgitant fraction²², and peak velocity per location by manually drawing regions of interest (ROIs) using custom software built in Matlab. Volumes and regurgitant fraction values reflect the entire cardiac cycle, whereas peak velocity was measured at peak systole. For rt-PC, we analyzed the first full heartbeat in all subjects, but expanded this analysis to 20 seconds (~25 heartbeats) for one subject, in order to demonstrate capability to assess beat-to-beat variations in hemodynamics.

Statistical Analysis

Two-tailed, paired t-test was used to compare results between clinical standard PC and rt-PC. Bland-Altman and linear-regression analyses were conducted on volume and velocity values to assess the level of agreement and association, respectively. A value of P < 0.05 was considered statistically significant. All differences were calculated as real-time minus clinical standard.

Results

Figure 3 shows phase contrast images of our pulsatile phantom obtained with clinical standard PC and rt-PC acquisitions with matching spatial and temporal resolutions, as well as their corresponding flow and peak-velocity curves. As shown in Figure 3, the flow and peak velocity time curves obtained by clinical standard and rt-PC acquisitions were closely on top of each other. The normalized root-mean-square-error (NRMSE) of all time points was 4.0% for ascending forward volume, 6.3% for descending forward volume, 4.9% for ascending peak velocity at peak systole, and 6.7% for descending peak velocity at peak systole. For dynamic display of magnitude and phase-contrast images, see Supplementary Video S1 and S2 for clinical standard PC and rt-PC, respectively.

Figure 3.

Pulsatile phantom results produced by clinical standard and rt-PC MRI acquisitions with matching spatial and temporal resolutions: magnitude and phase-contrast images (upper left), flow and peak velocity values (lower left), and flow and peak velocity time curves (right). Note, for descending flow there is swirling complex flow pattern visible in both clinical standard PC and rt-PC MRI acquisitions. The table reports forward volume through the entire cardiac cycle and peak velocity at peak systole. The normalized root-mean-square-error (NRMSE) of all time points was 4.0% for ascending forward volume, 6.3% for descending forward volume, 4.9% for ascending peak velocity at peak systole, and 6.7% for descending peak velocity at peak systole. For dynamic display, see corresponding Supplementary Video S1 and S2.

All 17 patients successfully underwent both clinical standard PC and rt-PC MRI. Our rt-PC (2.75 sec, fixed scan time for all patients) was acquired 15.0-fold faster than breath-hold clinical standard PC (41.2 ± 1.6 sec), and 25.9-fold faster than free-breathing clinical standard PC (71.2 ± 21.0 sec). The mean image reconstruction time clocked by our Yarra serve was 128.9 ± 7.1 sec per time series with 46 frames. Figure 4 shows phase difference images and corresponding flow and peak-velocity curves of 3 representative pediatric patients with visible regurgitation (see Supplementary Video S3–5 for dynamic display of magnitude of reference and phase difference images for clinical standard [odd] and rt-PC [even]).

Figure 4.

Representative magnitude and phase-contrast images, and corresponding flow and peak velocity time curves of three patients with measurable regurgitant fraction: 10-year-old patient (top row), 12-year-old patient (middle row), and 16-year-old patient. The percent error in regurgitant fraction and peak velocity at peak systole was less than 16.4% and 13.9%, respectively. Regurgitant fraction reported in the table represents value over the entire cardiac cycle, whereas peak velocity represents value at peak systole. For dynamic display, see corresponding Supplementary Video S3–8.

Summarizing the results over all patients, there was a non-significant (P = 0.22) difference in forward volume, whereas there were statistically significant differences (P< 0.001) in backward volume, regurgitant fraction, and peak velocity at peak systole. It should be noted that the percent difference in regurgitant fraction was only −2.5%, which is clinically insignificant. According to the linear regression analysis, forward volume, backward volume, regurgitant fraction, and peak velocity measured by standard PC and rt-PC were strongly correlated (Figure 5A; R² > 0.76; P < 0.001). According to the Bland-Altman analysis (Figure 6A), there was good agreement in forward volume (mean = 46.1 mL; mean difference = 1.4 mL [3.0% relative to mean], limits of agreement [LOA] = 17.3 mL [37.4% relative to mean]) and regurgitant fraction (mean difference = −2.5%, LOA= 8.9%), whereas moderate agreement in backward volume (mean = 3.9 mL; mean difference = −1.1 mL [28.2% relative to mean], LOA = 3.7 mL [94.9% relative to mean]) and peak velocity at peak systole (mean = 124.0 cm/s; mean difference = −21.3 cm/s [17.2% relative to mean], LOA = 42.6 cm/s [34.3% relative to mean]).

Figure 5.

Scatter plots resulting from linear regression for all patients (A), a subgroup of patients who underwent free-breathing clinical standard PC (B), and remaining subgroup of patients who underwent breath-hold clinical standard PC (C): forward volume (first column), backward volume (second column), regurgitant fraction (third column), and peak velocity (fourth column). Volume and regurgitant fraction values represent values computed over the entire cardiac cycle, whereas peak velocities represent values at peak systole. Planar locations are color coded: aortic valve (black), pulmonic valve (red), right pulmonary artery (blue), and left pulmonary artery (green).

Figure 6.

Scatter plots resulting from Bland-Altman analyses for all patients (A), a subgroup of patients who underwent free-breathing clinical standard PC (B), and remaining subgroup of patients who underwent breath-hold clinical standard PC (C): Forward volume (first column), backward volume (second column), regurgitant fraction (third column), and peak velocity (fourth column). Volume and regurgitant fraction values represent values computed over the entire cardiac cycle, whereas peak velocities represent values at peak systole. By convention, difference is defined as rt-PC minus clinical standard PC. Planar locations are color coded: aortic valve (black), pulmonic valve (red), right pulmonary artery (blue), and left pulmonary artery (green).

A sub-analysis comparing rt-PC with free-breathing clinical standard PC produced the following results. According to linear regression analysis, the forward volume, backward volume, regurgitant fraction, and peak velocity at peak systole were strongly correlated (Figure 5B; R² > 0.87; P < 0.01). According to the Bland-Altman analysis (Figure 6B), there was good agreement in forward volume (mean = 53.2 mL; mean difference = 0.6 mL [1.1% relative to mean], LOA = 18.9 mL [35.5% relative to mean]) and regurgitant fraction (mean difference = −1.2%, LOA = 9.6%), whereas moderate agreement in backward volume (mean = 4.6 mL; mean difference = −0.8 mL [17.4% relative to mean], LOA = 4.3 mL [93.5% relative to mean]) and peak velocity at peak systole (mean = 129.2 cm/s; mean difference = −20.9 cm/s [16.2% relative to mean], LOA = 32.5 cm/s [25.1% relative to mean]).

A sub-analysis comparing rt-PC with breath-hold clinical standard PC produced the following results. According to the linear regression analysis, the forward volume, backward volume, and regurgitant fraction were strongly correlated to rt-PC (Figure 5C; R² ≥ 0.89; P < 0.01), whereas the association in peak velocity at peak systole was comparatively less (Figure 5C; R2 = 0.61; P < 0.01). According to the Bland-Altman analysis (Figure 6C), there was good agreement in forward volume (mean = 36.3 mL; mean difference = 2.6 mL [7.2% relative to mean], LOA = 14.8 mL [40.7% relative to mean]) and regurgitant fraction (mean difference = −4.4%, LOA = 6.5%), whereas moderate agreement in backward volume (mean = 2.9 mL; mean difference = −1.5 mL [51.7% relative to mean], LOA = 2.5 mL [86.2% relative to mean]) and peak velocity at peak systole (mean = 116.8 cm/s; mean difference = −22.0 cm/s [18.8% relative to mean], LOA= 54.4 cm/s [46.6% relative to mean]).

Figure 7 shows plots of peak-velocity time curves over 20 sec obtained with rt-PC MRI in-vitro and in-vivo. As shown, the coefficient of variation (CV) in peak velocity at peak systole was 43.5% less in the pulsatile phantom (4.5%) than in a patient with CHD (7.9%), reflecting variations in physiology.

Figure 7.

Magnitude and phase-contrast images of the phantom (top row) and a 5-year-old patient (middle row), as well as the corresponding peak velocity time curves over 20 s. Peak-to-peak variations were greater for the patient (pulmonic valve) than for the phantom. Descriptive statistics of peak velocity are summarized in the table (bottom row).

Discussion

The proposed rt-PC has several advantages over clinical standard PC. First, as a real-time technique, it is insensitive to irregular heart rhythm and/or bulk motion. Second, real-time, free-breathing methods provide a means to perform rapid pediatric cardiovascular MRI without general anesthesia, which is important for reducing potential neurotoxic changes in the developing brain from general anesthetics. Third, rt-PC provides a means to assess beat-to-beat variations in flow due to arrhythmia. To our knowledge, this is the first study to report on the performance of highly-accelerated (R > 30) rt-PC MRI with relatively high nominal spatial and temporal resolutions in pediatric patients with CHD. In terms of agreement, forward volume (mean difference = 1.4 mL [3.0% of mean]) and regurgitant fraction (mean difference = −2.5%) were in good agreement, whereas backward volume and peak-velocity at peak systole were in moderate agreement. Our GROG-GRASP reconstruction pipeline implemented on a Yarra framework is capable of producing the resulting DICOMS to our clinical PACS system within approximately 2 min per time series with 46 frames, suggesting clinical translatability.

We also considered the impact of intrathoracic pressure on flow measurements. Sub-analyses comparing rt-PC with two different types of clinical standard PC (breath-hold vs. free-breathing) revealed noticeable trends. Free-breathing rt-PC showed better agreement with free-breathing clinical standard PC than breath-hold clinical standard PC for forward volume (mean difference = 0.6 mL with respect to free-breathing vs. 2.6 mL with respect to breath-hold), backwards volume (mean difference = −0.8 mL with respect to free-breathing vs. −1.5 mL with respect to breath-hold), regurgitation fraction (mean difference = −1.2 mL with respect to free-breathing vs. −4.4 mL with respect to breath-hold), and peak velocity at peak systole (mean difference −20.9 cm/s with respect to free-breathing vs. −22.0 cm/s with respect to breath-hold). This discrepancy may be due to physiologic variations in patients (e.g., beat-to-beat variations in heart rhythm, free-breathing vs. breath-holding, valve motion), which were absent in the phantom. Our rt-PC sequence was performed during free-breathing for approximately 2 s (excluding dummy scan), and we used the first full heartbeat for analysis. As such, our rt-PC data were obtained randomly over the patients’ breathing cycles, and the impact of intrathoracic pressure on flow values varied among patients. While we observed underestimated peak velocities at peak systole in patients, such was not the case in the flow phantom. The effect of physiologic variations on peak velocity was characterized by 20 sec rt-PC acquisitions. As shown in Figure 7, the peak velocity at peak systole showed higher variability in the patient (mean = 175.2 ± 13.9 cm/s) than the flow phantom (mean = 102.2 ± 4.6 cm/s), suggesting that physiologic changes may have contributed to the observed discrepancy between clinical standard-PC and rt-PC MRI. Our inference is further supported by better agreement with clinical standard PC in peak-systolic peak velocity for averaging (19.8 % difference) than single heartbeat (28.3% difference) in one patient scanned with rt-PC over 20 sec.

With respect to other accelerated 2D rt-PC techniques, our rt-PC technique with 1.5 × 1.5 × 6 mm³ nominal spatial resolution, 41.7 ms nominal temporal resolution, and R = 38.4 at 1.5 Tesla has relative advantages and disadvantages compared with prior rt-PC techniques. Compared with the Cartesian k-space sampling method with 1.8 × 1.8 × 5 mm³ nominal spatial resolution and 18 msec nominal temporal resolution at 3 Tesla proposed by Sun et al.²³, our method has the advantage of not requiring training data. This may be particularly important for intracardiac and vessels/valves near the heart, where there is considerable nonlinear motion. Compared with the radial k-space sampling method with 1.5 × 1.5 × 6 mm³ nominal spatial resolution, 35.7 msec nominal temporal resolution, and R = 30.3 using asymmetric echoes at 3 Tesla proposed by Untenberger et al.¹⁷, our method has 16.8% worse temporal resolution but 26.7% higher R. Compared with the echo-planar imaging method with 2.9 × 2.8 × 10 mm³ nominal spatial resolution and 39.7 msec nominal temporal resolution at 1.5 Tesla proposed by Traber et al.²⁴, our method has 90% higher spatial resolution but 5.0% worse temporal resolution. Compared with two prior studies which examined ascending and descending aorta only^17,23 and one prior study which examined ascending aorta, mean pulmonary artery, and superior vena cava²⁴, our study examined more challenging anatomy (pulmonary arteries, aortic valve, pulmonic valve) with smaller anatomy with faster heart hearts in pediatric patients. Compared with prior studies conducted at 3 Tesla^17,23, out study was conducted at 1.5 Tesla, which has two-fold lower magnetization strength. We elected to not discuss in detail the relative accuracy described by each of these studies, because the clinical and technical contexts vary widely among them. A future study is warranted to directly compare and contrast our method to these investigational methods in pediatric patients with CHD at both 1.5 and 3 Tesla MRI scanners.

This study contains several interesting points worth emphasizing. First, in-vitro, the NRMSE was less for ascending volume and peak velocity at peak systole than for descending values. This is likely due to the swirling complex pattern in the descending flow (see Supplementary Video S1 and S2). Nevertheless, the NRMSE was less than 10% for both. Second, 41.2% of patients received gadolinium-based contrast agent, 17.6% of patients received ferumoxytol, and 41.2% of patients received general anesthesia. Our sample size was not large enough to statistically adjust for the confounding influence by general anesthesia, patient age, sex, gadolinium-based contrast agent, and type of clinical standard PC sequence. A larger study is warranted to investigate the impact of general anesthesia (hemodynamics), intrathoracic pressure (breath holding vs. free breathing), and contrast agent (signal-to-noise ratio) on the accuracy of rt-PC with respect to clinical standard PC. Third, despite the limited sample size, we observed trends towards better association and agreement with respect free-breathing clinical standard PC than breath-hold clinical standard PC. These trends may be due to similar intrathoracic pressure conditions during free breathing and/or more favorable anatomy in older patients (larger hearts and slower heart rate) who underwent free-breathing clinical standard PC. Fourth, our GPU-accelerated GROG-GRASP reconstruction pipeline was able to reconstruct each time series with 46 frames in approximately 2 min, which may be adequate for initial clinical translation. One potential solution to further reduce the reconstruction time is incorporating deep-learning techniques²⁵. Fifth, our phantom experiment was conducted with 60 beats per minute, whereas the mean heart rate of our patient cohort was approximately 80 beats per minute. We elected to run our phantom experiment with 60 beats per minute due to the mechanical refractory period of our VAD pump, because increasing the frequency (i.e. heart rate) would considerably shorten the tail end (i.e. diastole) of the flow curve (Figure 3).

This study has several limitations that warrant further discussion. First, this study did not include test and re-test of our rt-PC MRI technique in the same patients. While it would be scientifically worthwhile to conduct such a reproducibility study, it is difficult in practice to recruit pediatric patients for a second visit. Second, our rt-PC method underestimated backward volume with respect to clinical standard PC MRI. One possible reason for these observed discrepancies might be due to differences in physiology (intrathoracic pressure, heart rate variation) and ECG gating scheme (prospective rt-PC vs. retrospective ECG-gated clinical standard). However, it should be noted that an underestimation of 1.1 mL in backward volume translates into a mean difference of −2.5% for regurgitant fraction, which is clinically insignificant. Future investigation includes rebinning the quiescent period of the cardiac cycle (between late diastole of the current heartbeat and early systole of the next heartbeat) with fewer rays per frame, at the expense of increased aliasing artifacts. This strategy achieves higher temporal resolution for the quiescent period and, thus, increases the likelihood of capturing true end diastole. Third, another possible reason for the observed discrepancies might be due to differences in imaging and reconstruction parameters. Of note, the spatial and temporal resolutions, slice thickness, and flip angles did not match between rt-PC and clinical standard PC pulse sequences, and it is likely that GROG-GRASP reconstruction of 38.4-fold accelerated data produced temporal blurring due to regularization. Fourth, patients examined in this study were imaged under different contrast agent conditions. In two patients, no contrast agent was administered. In twelve patients, gadobutrol was administered. In three patients, ferumoyxtol was administered. As such, the signal-to-noise ratio varied among these three conditions. As a reference, the phantom experiment was conducted with gadolinium-doped water. Fifth, we did not fully explore rt-PC’s capability to assess beat-to-beat variations in hemodynamics due to arrhythmia, because the purpose of this study is evaluate the effectiveness of a rapid pediatric rt-PC protocol. A future study is warranted to investigate pediatric applications where beat-to-beat variations in flow are clinically relevant. Sixth, we applied different background phase correction methods for clinical standard PC and rt-PC data. For clinical standard PC data, Maxwell terms were corrected inline by the vendor’s reconstruction pipeline, and a first-order fitting routine was used during post-processing to remove the residual background phase. For rt-PC data, we did not correct for the Maxwell terms, and a second-order fitting routine was used during post-processing to remove the background phase. Note, it is not straight forward to calculate concomitant gradient terms in radial k-space sampling with system imperfections such as gradient delays and eddy currents associated with golden angles. Seventh, peak velocity measured with rt-PC was underestimated by 17% relative to clinical standard PC. While this limitation may be acceptable for assessment of flow volume and shunt quantification in pediatric patients with CHD, further refinement is warranted for applications where peak velocity is clinically paramount.

In summary, this study describes the development and evaluation of a 38.4-fold accelerated, rt-PC pulse sequence with 1.5 × 1.5 × 6.0 mm³ nominal spatial resolution and 41.7 msec nominal temporal resolution and automated GROG-GRASP reconstruction pipeline capable of achieving clinically-translatable reconstruction times (~ 2 min per time series). Our proposed method produces relatively accurate forward volumes and regurgitant fractions but underestimated backward volumes and peak velocities at peak systole in pediatric patients with CHD.

Supplementary Material

Supp videoS1

Supplementary Video S1. Dynamic display of magnitude (left) and PC (right) images shown in Figure 1. These images were acquired using the clinical standard PC pulse sequence.

Supp videoS2

Supplementary Video S2. Dynamic display of magnitude (left) and PC (right) images shown in Figure 3. These images were acquired using the rt-PC pulse sequence.

Supp videoS3

Supplementary Video S3. Dynamic display of magnitude (left) and PC (right) images of the 10-year-old patient shown in Figure 4. These images were acquired using the clinical standard PC pulse sequence.

Supp videoS4

Supplementary Video S4. Dynamic display of magnitude (left) and PC (right) images of the 10-year-old patient shown in Figure 4. These images were acquired using the rt-PC pulse sequence.

Supp videoS5

Supplementary Video S5. Dynamic display of magnitude (left) and PC (right) images of the 12-year-old patient shown in Figure 4. These images were acquired using the clinical standard PC pulse sequence.

Supp videoS6

Supplementary Video S6. Dynamic display of magnitude (left) and PC (right) images of the 12-year-old patient shown in Figure 4. These images were acquired using the rt-PC pulse sequence.

Supp videoS7

Supplementary Video S7. Dynamic display of magnitude (left) and PC (right) images of the 16-year-old patient shown in Figure 4. These images were acquired using the clinical standard PC pulse sequence.

Supp videoS8

Supplementary Video S8. Dynamic display of magnitude (left) and PC (right) images of the 16-year-old patient shown in Figure 4. These images were acquired using the rt-PC pulse sequence.

List of Abbreviations in Alphabetical Order

CHD

congenital heart disease

CV

coefficient of variability

DICOM

Digital imaging and Communications in Medicine

ECG

electrocardiogram

FOV

field of view

GRAPPA

Generalized Autocalibrating Partially Parallel Acquisitions

GROG-GRASP

GRAPPA operator gridding golden-angle radial sparse parallel

HIPPA

health insurance portability and accountability act

LOA

limits of agreement

LVEF

left ventricular ejection fraction

NLINV

non-linear inversion

NRMSE

normalized root-mean-square-error

PC

phase contrast

PCA

principal component analysis

R

acceleration factor

R²

coefficient of determination

RF

radio-frequency

ROI

region of interest

RVEF

right ventricular ejection fraction

SENSE

sensitivity encoding