 Research
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 Published:
Highly accelerated 4D flow cardiovascular magnetic resonance using a pseudospiral Cartesian acquisition and compressed sensing reconstruction for carotid flow and wall shear stress
Journal of Cardiovascular Magnetic Resonance volume 22, Article number: 7 (2020)
Abstract
Background
4D flow cardiovascular magnetic resonance (CMR) enables visualization of complex blood flow and quantification of biomarkers for vessel wall disease, such as wall shear stress (WSS). Because of the inherently long acquisition times, many efforts have been made to accelerate 4D flow acquisitions, however, no detailed analysis has been made on the effect of Cartesian compressed sensing accelerated 4D flow CMR at different undersampling rates on quantitative flow parameters and WSS.
Methods
We implemented a retrospectively triggered 4D flow CMR acquisition with pseudospiral Cartesian kspace filling, which results in incoherent undersampling of kt space. Additionally, this strategy leads to small jumps in kspace thereby minimizing eddy current related artifacts. The pseudospirals were rotated in a tiny goldenangle fashion, which provides optimal incoherence and a variable density sampling pattern with a fully sampled center. We evaluated this 4D flow protocol in a carotid flow phantom with accelerations of R = 2–20, as well as in carotids of 7 healthy subjects (27 ± 2 years, 4 male) for R = 10–30. Fully sampled 2D flow CMR served as a flow reference. Arteries were manually segmented and registered to enable voxelwise comparisons of both velocity and WSS using a BlandAltman analysis.
Results
Magnitude images, velocity images, and pathline reconstructions from phantom and in vivo scans were similar for all accelerations. For the phantom data, mean differences at peak systole for the entire vessel volume in comparison to R = 2 ranged from − 2.3 to − 5.3% (WSS) and − 2.4 to − 2.2% (velocity) for acceleration factors R = 4–20. For the in vivo data, mean differences for the entire vessel volume at peak systole in comparison to R = 10 were − 9.9, − 13.4, and − 16.9% (WSS) and − 8.4, − 10.8, and − 14.0% (velocity), for R = 20, 25, and 30, respectively. Compared to single slice 2D flow CMR acquisitions, peak systolic flow rates of the phantom showed no differences, whereas peak systolic flow rates in the carotid artery in vivo became increasingly underestimated with increasing acceleration.
Conclusion
Acquisition of 4D flow CMR of the carotid arteries can be highly accelerated by pseudospiral kspace sampling and compressed sensing reconstruction, with consistent data quality facilitating velocity pathline reconstructions, as well as quantitative flow rate and WSS estimations. At an acceleration factor of R = 20 the underestimation of peak velocity and peak WSS was acceptable (< 10%) in comparison to an R = 10 accelerated 4D flow CMR reference scan. Peak flow rates were underestimated in comparison with 2D flow CMR and decreased systematically with higher acceleration factors.
Background
3D phase contrast cine cardiovascular magnetic resonance (CMR) (4D flow CMR) [1] may help in risk stratification and followup of cardiovascular diseases, which is the leading cause of death worldwide [2]. Atherosclerosis is characterized by the accumulation of fatty deposits in the arterial walls, leading to inflammation, wall thickening, and reduced arterial elasticity [3,4,5] and is a main cause of cardiovascular disease. In relation to that, low wall shear stress (WSS), the tangential force of the blood flow on the vessel wall [6,7,8], was found to be an indicator for rearrangement of endothelial cells [9] and increased wall thickness [10]. Since atherosclerosis is a chronic disease that can stay asymptomatic for a long time, a great need exists for diagnostic tools that identify patients at high risk and at an early stage of the disease.
4D flow CMR enables comprehensive visualization and quantification of complex blood flow and the calculation of several relevant hemodynamic biomarkers, including WSS. However, 4D flow CMR acquisitions in general still remain challenging, mostly because of the long acquisition times involved. These can vary between 15 and 40 min [11,12,13], depending on the desired 3D spatial resolution, number of frames per cardiac cycle, the heart rate, the respiratory gating efficiency and (if applied) the use of acceleration techniques, such as sensitivity encoding (SENSE) or segmented kspace acquisitions. Overall, this seriously complicates its use in routine clinical practice, since apart from practical issues such as long waiting times and costs, it is difficult for patients to remain motionless in the scanner for such a long time. Also, physiological variations and movement during long scans may lead to artifacts and inaccuracies. Therefore, a clear need exists for scan time reduction in 4D flow CMR.
Various methods have been presented to accelerate 4D flow CMR [12, 14,15,16,17], which are commonly based on undersampling kspace (e.g. acquiring a reduced amount of data at a subNyquist rate) and performing reconstructions at full image quality using advanced reconstruction algorithms. 4D flow CMR and other timeresolved cardiac imaging techniques are highly correlated in time. Therefore, these data are very suitable for applying undersampling, particularly in the time dimension. The use of nonCartesian radial [14], spiral [15] and coneshaped [16] undersampling techniques has been demonstrated, enabling highly accelerated and motionrobust scans. Nevertheless, nonCartesian scans can be challenging with respect to implementation, postprocessing, and reconstruction time. Cartesian kt undersampling techniques, such as kt SENSE [18] or kt PCA [12] have shown to be successful with acceleration factors up to R = 8. EPI accelerated 4D flow CMR scans provided acceleration factors of R = 5 [19]. More recently, compressed sensing (CS) accelerated 4D flow techniques have been introduced, which facilitated even higher acceleration factors (R = 8–27) [17].
However, no comprehensive evaluation has been made on how highly (prospectively) Cartesian undersampling with CS reconstruction in 4D flow CMR affects quantitative flow parameter estimates like WSS in vivo.
For this study, we therefore aimed to firstly implement a highly accelerated 4D flow acquisition based on a Cartesian pseudospiral sampling trajectory. This resulted in incoherent undersampling patterns for each individual cardiac frame, enabling CS reconstructions using temporal constraints. We secondly evaluated the performance of this CS 4D flow CMR technique over a range of acceleration factors (R = 2–30) for estimating quantitative flow and WSS parameters in a carotid flow phantom, as well as in the carotid arteries of healthy subjects.
Methods
Sampling strategy and implementation
Our specific method of accelerating 4D flow CMR using pseudospiral Cartesian sampling is schematically depicted in Fig. 1. 3D kspace consists of two phase encoding directions (k_{y},k_{z}) and one fully sampled frequency encoding (readout) direction (k_{x}). In regular Cartesian sampling (k_{y},k_{z})profiles (a combination of k_{y} and k_{z} coordinates) would be acquired linebyline (Fig. 1a). Additionally, in traditional cine imaging each (k_{y},k_{z})profile would be sampled multiple times during each heartbeat (regular profile change) to ensure complete filling of ktspace and a fully sampled time dimension for each (k_{y},k_{z})profile (Fig. 1b). However, highly undersampling kspace in a random order on a Cartesian grid is not preferred since it would involve large steps in kspace. Regular linebyline undersampling would complicate interleaving kspace sampling of multiple cardiac frames.
We implemented a pseudospiral filling strategy which was proposed earlier by Liu and Saloner [20] and also used in a similar fashion in GCASPR [21], VDRad [17], ROCKMUSIC [22] and GOCART [23] to create a randomly undersampled ktspace. The pseudospiral trajectory has a couple of advantages. First, it involves only small jumps in kspace thereby minimizing eddy current related artifacts. Secondly, the pseudospirals can be rotated in a tiny goldenangle fashion, which provides optimal incoherence and a variable density sampling pattern with a fully sampled center (Fig. 1c), which is highly beneficial for CS reconstruction. Finally, despite the pseudospiral acquisition, the kspace points are still located on a Cartesian grid (hence the name pseudospiral), as shown in Fig. 1d, which improves the reconstruction as no regridding interpolation is required.
The second important mechanism in our approach is related to the cardiac triggering strategy (Figs. 1e, f). By using retrospective gating and a continuous update of the (k_{y},k_{z})profile throughout the cardiac cycle, each separate cardiac frame will have its unique random kspace filling, but with preservation of the variable density pattern. This maximizes randomness in both the spatial and temporal (i.e. cardiac frames) domain. Note that first all four flowencoding directions are sampled (4xTR) before changing the (k_{y},k_{z})profile number.
The pseudospiral sampling trajectory in (k_{y},k_{z})plane can be described in more detail as a spiral with radius r and linearly increasing angle φ gridded on the scan matrix size:
with n the number of Cartesian readouts per pseudospiral (φ_{0}φ_{n}) and l the number of turns. In all experiments n =100 and l =3 were used. After one pseudospiral arm was sampled a new arm was acquired in a tiny goldenangle increment of 23.63 degrees relative to the previous pseudospiral. The number of pseudospirals depends on the desired acceleration factor. For asymmetric matrix size the pseudospiral was rescaled according to the ratio k_{y,max}/k_{z,max}.
A text file containing all (k_{y},k_{z})profiles was created in MATLAB (MathWorks Inc., Natick, Massachusetts, USA) and imported in the scanner software (Philips Healthcare, Best, the Netherlands; software release 5.1.8 CDAS). A custom patch was used (PROspective Undersampling in multiple Dimensions (PROUD) patch [24,25,26]), which allows sampling of predefined trajectories. PROUD also enables continously updating the (k_{y},k_{z})profiles within each cardiac cycle. Moreover, PROUD controls the acquisition in real time by bitmasking the ktspace filling and prevents duplicate acquisitions of profiles of the same cardiac frame.
In continuous pseudospiral sampling, the acceleration factor R can be chosen in reference to the number of readouts of a fully sampled scan N_{fully} and the number of readouts of an undersampled scan N_{undersampled}. Hereby N_{fully} depends on the number of phase encoding steps \( {\mathrm{N}}_{k_y} \) and \( {\mathrm{N}}_{k_z} \), the desired number of cardiac frames N_{card} and the number of flow encoding segments N_{flow}.
Compressed sensing reconstruction
All image reconstruction steps, including phaseoffset corrections, were done offline using MRecon and GTFlow (Gyrotools, Zurich, Switzerland). For each measured kline, the time distance to the ECG R top was available from the raw data. This allowed binning of the data into a specific number of cardiac frames (N_{card}) using an ‘absolute’ binning approach. The last cardiac frames at enddiastole receive less data due to RR variabilities and were discarded during flow curve analysis (phantom: last 2 frames see Fig. 3b, in vivo: last 3 frames due to larger RR variability). Data from each flowencoding direction was binned independently. After cardiac binning, the undersampled data was reconstructed with a nonlinear CSPI (compressed sensing and parallel imaging) algorithm available from the Berkeley Advanced Reconstruction Toolbox (BART) [27] according to
using a sparsifying TV operator performed along the time dimension. F_{U} denotes the undersampling Fourier operator, y the measured data, and m the reconstructed data. While the left term ensures data consistency, the right term enforces sparsity, regularized by parameter λ. Reconstructions were tested for different regularization parameters and number of iterations i. Heuristically, by reconstructing the data using different settings (ranging from 0.001< λ < 1, and 2 < i < 100) λ =0.01 and i = 10 were found to lead to the best match in peak flow values in comparison to the 2D flow reference scan, and were thus used for all reconstructions.
Flow phantom experiments
A flow phantom was designed (LifeTec, Eindhoven, The Netherlands) (Fig. 2) consisting of a distensible silicon carotid artery embedded in water. A pulsatile water flow was applied at a simulated heart rate of 60 bpm and a random variability with 5% standard deviation. At the inlet of the phantom a peak flow rate of 10 ml/s and a mean flow rate of 3 ml/s was established.
4D flow CMR was performed with a 3 T CMR scanner (Ingenia, Philips Healthcare) using a 32channel head coil and a referenced fourpoint flow encoding method (as explained in detail in [28]). Scan parameters were: TR = 8.9 ms, TE = 4.5 ms, FA = 8°, VENC = 150 cm/s (in all three flow encoding directions), matrix size = 160 × 160 × 40, FOV = 128 × 128 × 32 mm^{3}, bandwidth = 713 Hz/pixel, spatial resolution = 0.8 × 0.8 × 0.8 mm^{3}, and 19 reconstructed cardiac frames. No segmented kspace was used. As a flow reference, fully sampled 2D flow CMR scans with identical scan settings (except FA = 20° and bandwidth = 217 Hz/pixel) and spatial resolution = 0.8 × 0.8 × 3 mm^{3} were acquired in two planes perpendicular to the tubes. No contrast agent was used. The 4D flow scans were accelerated R = 2, 4, 6, 8, 10, 12, 15, and 20 times, with corresponding scan times decreasing from 45:57, 22:59, 15:18, 11:28, 9:08, 7:32, 5:45, to 4:30 min. The nonaccelerated scan time for the given heart rate and number of cardiac frames amounted to 1:32 h.
In vivo experiments
The acceleration technique was applied in the carotid arteries of 7 healthy subjects (27 ± 2 y, 4 male) using an 8channel neck coil. Using the same settings as for the phantom, the 4D flow scans were accelerated R = 10, 20, 25 and 30 times (scan times: 9:08, 4:16, 3:14 and 2:32 min, respectively). Left and right carotid arteries were analyzed separately. 2D flow CMR reference scans were acquired using the same settings as for the phantom.
Flow rate and WSS calculation
To calculate flow rates, regionsof interest (ROIs) in common, internal, and external carotid artery (CCA, ICA and ECA) were drawn using GTFlow in the same slice as the 2D flow reference scans for each artery and each acceleration factor separately. The time resolved flow rate Q was calculated as: Q(t) = ∫_{ROI}v(r, t) d^{2}r, with v(r, t) the absolute velocity at position r and cardiac phase t.
A 3D segmentation of the carotid bifurcation was created per 4D flow scan using Mimics (Materialise, Leuven, The Netherlands) for both phantom and in vivo scans. The peak systolic time frame was defined as the time frame with the highest absolute velocity averaged over the segmented volume. WSS vectors τ were calculated in MATLAB (Mathworks) as described in Potters et al. [29]:
With η the blood viscosity of 3.2·10^{− 3} Pa·s, n the inward normal vector on the vessel wall and \( \dot{\upvarepsilon\ } \) the rate of the deformation tensor
By selecting a local coordinate system for each point on the vessel wall such that the z′ axis aligns with the inward normal, and by assuming no flow through the vessel wall, i.e. n · v = 0, this equation simplifies to
Spatial derivatives of the velocity on the vessel wall were derived from fitted splines. After transforming back to the original coordinate system, the (time resolved) magnitude of the WSS vector is reported throughout the manuscript. The segmented volume of each scan was rigidly registered on the segmented carotid of the scan with the lowest acceleration factor (MATLAB) [30]. For in vivo scans this was done per subject. WSS and velocity values at peak systole were interpolated on the reference volume, to facilitate voxelwise comparisons. Pathlines were visualized using GTFlow.
Statistical analysis
BlandAltman analysis was used to determine the mean difference and the limits of agreement. Orthogonal regression was used to determine the slope, intercept and Pearson correlation coefficient ρ.
Results
Phantom
Figure 3 shows typical ktspace filling patterns in spatial and temporal direction with from left to right increasing acceleration factors of R = 2–20. For all the accelerations the resulting kspaces after cardiac binning had quasirandom filling with a densely sampled center. The undersampling patterns were also incoherent over time (Fig. 3b), which is important for the CS reconstruction with TV constraint.
Reconstructed magnitude and feethead (FH) velocity images of the phantom visually were very comparable for all acceleration factors (Fig. 4ad). With increasing acceleration factor some spatial blurring became apparent, particularly for the tube walls. More importantly however, the flow curves for ROIs in CCA, ICA and ECA were comparable for all acceleration factors and in comparison to the fully sampled 2D flow CMR scan (Fig. 5a). More variations in peak flow rate were observed in the smaller vessels (ICA and ECA), than in the CCA.
The largest deviation in flow rate as compared to the 2D reference was observed at peak systole in the CCA, with 0.5 ml/s (4.4%) less for the R = 12 times accelerated 4D flow CMR scan (Additional file 7: Table S1). The R = 20 times accelerated scan had a deviation in peak systolic flow rate of only 0.2 ml/s (1.7%). Pathlines, through plane velocity and WSS of the phantom at peak systole are shown in Fig. 5b, c (pathline movies are available online, see Additional file 1: Video S1). Only minor visual differences were observed for WSS values and pathlines at peak systole for scans with varying acceleration factors.
For a quantitative assessment of the influence of high accelerations on the hemodynamic parameters at peak systolic, velocity and WSS values in the phantom and per acceleration factor (R = 4–20) were compared voxelwise within the segmented volume against the values of the lowest acceleration factor (R = 2) in a BlandAltman analysis (Fig. 6).
The mean differences and the limits of agreement (LOA) of the BlandAltman analysis for all acceleration factors, shown in Fig. 6, are summarized and visualized in Fig. 7. The maximum mean difference for WSS at peak systole was 5.3% for R = 20. The maximum mean difference for velocity was − 2.4% for R = 10. The LOA increased slightly with increasing acceleration factor. Slope and Pearson correlation coefficients are summarized in Fig. 7c, d. The slope of the correlation for both WSS and velocity at peak systole essentially stayed the same with increasing acceleration, whereas the Pearson correlation coefficients ρ slightly decreased for higher acceleration factors. Figure 7e, f depicts the mean WSS and mean velocity of the vessel volume not only at peak systole, but for every time point in the cardiac cycle, demonstrating no variation in other cardiac frames. A summarizing table of the BlandAltman analyses for peak systolic WSS and velocity values of the phantom experiment is found in Additional file 7: Table S2.
In vivo
Similar to the phantom scans, the magnitude and velocity images of the in vivo scans were visually of good quality up to the highest acceleration factors (Fig. 8). Some blurring occurred with increasing acceleration.
Flow rate was calculated for the accelerated 4D flow CMR scans and compared to the fully sampled 2D flow CMR scan. The flow curves through the cardiac cycle, averaged over all subjects, and left and right carotid, plotted per acceleration factor, are shown in Fig. 9a. The typical carotid flow curves through the cardiac cycle could be appreciated for all the accelerated scans, with consistent flow rate values, albeit with lower flow rate values than for the 2D reference scan. The subjectaveraged flow rate at peak systole with respect to the 2D flow reference was lower by − 5.0 ± 2.1 ml/s (− 24.4 ± 10.4%) for R = 20 and − 6.6 ± 3.4 ml/s (− 32.6 ± 16.7%) for R = 30 in the CCA (Additional file 7: Table S3). Flow rates in ICA and ECA were lower in accelerated 4D flow scans than in the 2D flow scan.
Calculated pathlines, through plane velocities, and WSS during peak systole of one exemplary in vivo scan are shown in Fig. 9be. Pathlines movies during the cardiac cycle are also available online in Additional file 2: Video S2. Peak systolic WSS at all acceleration factors for all volunteers can be found in Additional file 3: Figure S3. Visually, peak systolic WSS spatial patterns, pathline movies, and through plane velocities were similar. However, in contrast to the phantom experiment, the mean WSS during peak systole from voxelwise BA analysis decreased slightly for higher acceleration factors. WSS values decreased by − 9.9, − 13.4% and − 16.9% for acceleration factors of R = 20, 25 and 30, respectively (Fig. 10). Also, the slopes of the correlation plots and the Pearson correlation coefficients ρ slightly decreased for higher acceleration factors. The velocities within the vessel volume of the carotid arteries showed a similar trend. Velocities decreased by − 8.4, − 10.8%, and − 14.0% for acceleration factors of R = 20, 25 and 30, respectively (these results can also be found in Additional file 7: Table S4).
Discussion
In this work we demonstrated the feasibility of accelerating 4D flow CMR of the carotids up to 30 times using a pseudospiral Cartesian sampling strategy. We recommend an acceleration factor of R = 20 to facilitate fast 4D flow CMR with an acceptable (< 10%) [31] underestimation of in vivo peak velocities (− 8.4 ± 9.9%) and WSS (− 9.9 ± 10.9%) in comparison to the R = 10 4D flow CMR reference scan. In comparison to 2D flow CMR, R = 20 times accelerated 4D flow CMR however may result in a peak flow rate underestimation of − 24.4 ± 10.4%. We developed and evaluated the protocol using a carotid flow phantom for acceleration factors up to R = 20 and in the carotid arteries of seven healthy subjects for acceleration factors up to R = 30. For high accelerations, we observed a trend of increased spatiotemporal blurring and decreased image quality in vivo. This resulted in a progressive decrease in the hemodynamic velocity and WSS values at systole.
Acceleration of 4D flow CMR has been an important topic since years. Experts in the field have published a consensus paper [32] in which different acceleration strategies for 4D flow CMR are advised. Papers from leading experts in accelerated 4D flow CMR [11, 12, 17, 33], as discussed one by one below, typically use a SENSE R = 2 acceleration (sometimes with a segmented kspace factor of 2–3) as a reference scan when validating a new acceleration technique. However, there exists no clear consensus on how to validate a 4D flow CMR acceleration techniques and which parameters to report in order to estimate accuracy [32]. Peak velocity or peak flow rate seem important parameters however peak velocity underestimation was not mentioned as an exclusion criterion in the consensus paper, as e.g. also kspace segmentation limits the temporal resolution of the scan, leading to peak underestimation. Nevertheless, peak velocity is important and should be considered when using acceleration. Generally, the accuracy of 4D flow CMR is also highly dependent on spatiotemporal resolution and SNR. There might also be a general bias between 4D and 2D flow CMR [32].
In Additional file 4: Figure S4A, we have repeated our experiments in vivo in N = 1 subject, including a SENSE (R = 2) 4D flow CMR acquisition with a kspace segmentation factor of 2. Our CS acceleration performs equally well to this reference method for acceleration factors up to R = 20. However both CS and SENSE accelerated 4D flow CMR scans underestimate peak flow rate values as compared to 2D flow CMR, which is likely associated with lower SNR (see also magnitude images in Additional file 4: Figure S4A, left). In a phantom setting (Additional file 4: Figure S4B) both methods perform evenly good up to an acceleration factor of R = 30. Phantom flow curves up to an acceleration factor of R = 100 are shown. This shows, that R = 10 CS accelerated scans serve as a good reference for scans with higher acceleration factors. It also demonstrates, that very high acceleration factors (> 50) can be achieved, in which reasonable flow curves can still be recognized.
A number of 4D flow CMR studies have reported on the accuracy of acceleration techniques. Cheng et al. demonstrated 4D flow in pediatric congenital heart disease patients, using a prospective pseudospiral sampling strategy with total variation CS reconstruction (VDRad). Effective acceleration factors ranged from R = 15–27. This resulted in clinically acceptable image quality, as rated by a radiologist. However, no quantitative comparisons with 2D flow were available. 4D flow CMR scans were compared against a CS reconstruction using spatial wavelets after (temporally constant) Poisson disk sampling [17], which had been demonstrated to lead to 12% flow rate underestimation in comparison to 2D flow at R = 5 in a previous study [34]. Valvano et al. prospectively accelerated 4D flow CMR in the aorta using a lowrank+sparse reconstruction algorithm. Errors in the aortic peak flow rate were reported in comparison to a standard SENSE = 2 acquisition (segmented kspace factor = 3). The peak flow rate was underestimated at an acceleration factor of R = 8 by 2.5 ± 4.6% in the ascending and by 3.6 ± 8.4% in the descending aorta [33]. Knobloch et al. [11] investigated the effects of kt PCA acceleration on 4D flow CMR in the carotids (spatial resolution 1.2 × 1.2 × 1.2 mm^{3} vs. 0.8 × 0.8 × 0.8 mm^{3} in our study). Errors in peak flow rate were smaller than 4.9 ± 7%. However, the accelerated scans resulted from retrospective undersampling of a 4D flow CMR reference (75% Fourier sampling in k_{y} and k_{z}, 23 min scan time), which likely will result in a better agreement between accelerated and reference scans than would be obtained for true prospective acceleration [11]. In Giese et al., prospectively kt PCA accelerated aortic 4D flow CMR was compared to 2D flow [12]. The authors introduced an error metric E_{SV} for the stroke volume (SV) to compare 4D flow with 2D flow CMR (eq. 2 from [12]) and found E_{SV} = 2.5 ± 8.4 ml (5.6 ± 14.9%) for R = 8 in the aorta. Applying this metric to our in vivo carotid artery measurements, we find E_{SV} = 0.2 ± 0.7 ml (1.8 ± 10.9%) for R = 10, E_{SV} = 0.3 ± 0.5 ml (4.6 ± 7.0%) for R = 20, E_{SV} = 0.4 ± 0.4 ml (5.7 ± 6.7%) for R = 25 and E_{SV} = 0.4 ± 0.5 ml (5.6 ± 7.8%) for R = 30 in comparison to 2D flow. This timeaveraged error metric can therefore partially obscure peak velocity differences. Taken together, the above studies show that there is no consensus on how to assess flow errors for accelerated 4D flow CMR protocols. The numbers will depend on whether the scans were retrospectively or prospectively undersampled and the choice of reference scan, being another accelerated 4D flow technique or 2D flow CMR.
In our study we found an underestimation of the in vivo carotid peak systolic flow rate for high acceleration factors in the CCA (− 24.4% for R = 20 and − 32.6% for R = 30) when compared to a 2D phasecontrast reference scan. This underestimation was less in phantoms, in which we found only − 1.7% peak flow rate underestimation (R = 20) in comparison to the 2D flow scan. The difference between in vivo and phantom scans might be explained by smoother flow profiles in the phantom, which might lead to better results when using a total variation operator in the CS reconstruction algorithm. The phantom curves, although very consistent between scans, showed slight variations due to partial volume effects with the tube wall, which had a noisy velocity due to lack of signal (Fig. 4). Differences between 2D flow and 4D flow CMR might be affected by higher SNR in 2D flow scans. Also, the high contrast of blood vessels in the 2D flow scan, created by inflow enhancement at high flip angles, might result in different partial volume effects and phase offsets than in 4D flow CMR [31, 35]. This might also explain deviations in smaller vessels like the ICA and ECA. Within the set of accelerated 4D flow CMR scans, volumetric velocity differences between R = 10 and higher accelerated scans were much more acceptable (8.4% for R = 20 and 14.0% for R = 30) than the results from the flow analysis. For peak systolic WSS, a similar behavior was observed. As the overall trend was to underestimate WSS at very high acceleration factors (similar to velocity), this could conceal small changes in WSS patterns that might be important for disease characterization. Overall we can conclude that, although hemodynamic parameters seem systematically underestimated if we consider the 2D phase contrast scan as a gold standard, the accuracy of WSS and velocity values with decreasing scan time in 4D flow is maintained within acceptable limits for R = 20. This can also be appreciated in the pathline movies, which remain visually of good quality up to the highest acceleration. Therefore, also clinical 4D flow CMR scans with acceleration factors of up to R = 20 can be used. However, depending on the purpose of the clinical examination, lower (for accurate peak velocity estimation) or higher (for mean flow, stroke volume or streamline visualization) acceleration factors could be considered. Moreover, regional differences in hemodynamic parameters are consistent for all accelerations, as for example shown in Fig. 9d (e.g. low WSS in the carotid bulb vs. high WSS in the rest of the vessel). More advanced pulsatile flow phantoms of the (diseased) carotid artery, with a sharp, systolic peak flow will help to investigate on the effects of 4D flow CMR acceleration in carotid pathology in the future.
Using a repeated scan protocol in vivo (repeated 2 times for R = 10, 20, 25 and 30) and in the phantom (repeated 3 times for R = 10, 15, 20, 25 and 30) as summarized in Additional file 5: Figure S5 we could demonstrate, that there was almost no deviation between repeated scans in both cases. The SD of paired differences (scanrescan) per time frame was in vivo SD = 0.6, 0.6, 0.6, 0.6 ml/s and in the phantom SD = 0.4, 0.4, 0.4, 0.5 and 0.6 ml/s, for each acceleration factor respectively.
The comparison between in vivo and phantom experiments has some limitations. Although flow rate and mean velocities were similar, maximum velocities of 120 cm/s were achieved in the phantom in comparison to maximum velocities of 80 cm/s in vivo (see Additional file 6: Figure S6BC). Because excessively long scan times are an issue in vivo, it was not possible to acquire 4D flow CMR data with low or no acceleration and consequently an in vivo 4D flow CMR dataset of for example R = 2 was not available. Another limitation to the study is that only a low number of N = 7 participants were included.
The here reported acceleration factors are calculated before the data acquisition in reference to the scan time of a fully sampled scan acquired with the same acquisition strategy. Effective acceleration factors can be calculated retrospectively to the scan from the ratio of the number of klines in a fully sampled kspace versus the actually sampled klines, i.e. N_{undersampled} in eq. [2] can vary slightly retrospectively to the scan. For in vivo scans R_{effective} (±SD) was on average R = 12.2 ± 0.8, R = 22.6 ± 0.9, R = 27.9 ± 0.9, and R = 32.9 ± 0.9, for scans with target acceleration R = 10, R = 20, R = 25, and R = 30, respectively. The effective acceleration factor would also vary slightly with the heart rate of each subject. This behavior is however similar in fully sampled scans, which are only optimal when the number of reconstructed cardiac frames times 4xTR (4 flow encoding steps used) approximately matches the average acquired heart cycle length. If the number of reconstructed cardiac frames is higher, undersampling would be the consequence, which in practice is compensated for by a retrospective interpolation. If the number of reconstructed cardiac frames is lower, oversampling occurs, which results in averaging and higher SNR, but which also leads to a lower temporal resolution. Reporting effective acceleration factors and their variations is similar to variations in regular cardiac triggered scans and therefore not further discussed in this paper.
Potential other applications for the here presented methodology are cine CMR scans and 4D flow CMR scans in other anatomical regions, such as the circle of Willis, the heart, the aorta and for assessing venous flow return. Other, cutting edge algorithms, such as lowrank [33] reconstruction, could be integrated in the current reconstruction to push the acceleration factors even further or mitigate the spatiotemporal blurring. The pseudospiral sampling strategy can be combined with breathing navigators or selfgating, which allows for sorting the data in respiratory bins [21, 36].
Conclusion
We achieved highly accelerated 4D flow CMR of the carotid arteries using pseudospiral Cartesian undersampling and a CS reconstruction. At an acceleration factor of R = 20 the underestimation of peak velocity and peak WSS was acceptable (< 10%) in comparison to an R = 10 accelerated 4D flow CMR reference scan. Peak flow rates were underestimated in comparison with 2D flow CMR and decreased systematically with higher acceleration factors. However, even at an acceleration factor of R = 30, the highly CS accelerated 4D flow CMR scans allowed reconstructions of the 4D velocity field and velocity pathlines, at only 2:30 min scan time.
Availability of data and materials
All data was scanned using our inhouse developed AMC ‘PROspective Undersampling in multiple Dimensions’ (PROUD) patch. A compiled version of this patch as well as all data and PWV analysis code are is available on reasonable request.
Abbreviations
 2D:

Two dimensional
 CCA:

Common carotid artery
 CMR:

Cardiovascular magnetic resonance
 CS:

Compressed sensing
 ECA:

External carotid artery
 ECG:

Electrocardiography
 FA:

Flip angle
 FH:

Foothead direction
 FOV:

Field of view
 ICA:

Internal carotid artery
 LOA:

Limits of agreement
 PC:

Phase contrast
 PROUD:

Scanner patch to PROspective Undersampling in multiple Dimensions
 ROI:

Region of interest
 SD:

Standard deviation
 SNR:

Signal to noise ratio
 SV:

Stroke volume
 TE:

Echo time
 TR:

Repetition time
 TV:

Total variation
 VENC:

Velocity encoding gradient
 WSS:

Wall shear stress
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Acknowledgements
We thank Maarten Versluis (Philips), Gérard Crelier (Gyrotools) and Martin Bührer (Gyrotools) for their support.
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Funding
This research was partly supported by the Dutch Technology Foundation STW (Stichting voor de Technische Wetenschappen) Grant HTSM2014 (grant number #13928).
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All authors contributed significantly to this manuscript. All authors read, reviewed, and approved the final manuscript. EP, LG: study design, method development, CMR scanning, data analysis, manuscript writing; QZ, BC: method development, data analysis; PvO, AN, GS: study design, method development, data analysis.
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Correspondence to Pim van Ooij.
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Peper, E.S., Gottwald, L.M., Zhang, Q. et al. Highly accelerated 4D flow cardiovascular magnetic resonance using a pseudospiral Cartesian acquisition and compressed sensing reconstruction for carotid flow and wall shear stress. J Cardiovasc Magn Reson 22, 7 (2020). https://doi.org/10.1186/s129680190582z
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Keywords
 Compressed sensing
 4D flow MRI
 Undersampling
 Pseudospiral sampling
 Cartesian
 Incoherent sampling
 Total variation
 Acceleration