Imaging Physics and Informatics| Volume 94, P93-102, February 2023

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# Real-time phase contrast MRI versus conventional phase contrast MRI at different spatial resolutions and velocity encodings

Open AccessPublished:December 01, 2022

## Highlights

• Compared to conventional phase-contrast MRI (Conv-PC), echo-planar phase-contrast MRI (EPI-PC) can provide flow rate in real-time.
• EPI-PC can accurately quantify flow rate and flow waveforms.
• Compared to Conv-PC, EPI-PC can adapt to lower spatial resolution.
• Excessive velocity encoding has a greater impact on the accuracy of EPI-PC compared to Conv-PC.

## Abstract

### Purposes

To compare the accuracy of real-time phase-contrast echo-planar MRI (EPI-PC) and conventional cine phase-contrast MRI (Conv-PC) and to assess the influence of spatial resolutions (pixel size) and velocity encoding on flow measurements obtained with the two sequences.

### Methods

Flow quantification was assessed using a pulsatile flow phantom (diameter: 9.5 mm; mean flow rate: 1150 mm3/s; mean flow velocity: 1.6 cm/s). Firstly, the accuracy of the EPI-PC was checked by comparing it with the flow rate in the calibrated phantom and the pulsation index from Conv-PC. Secondly, flow data from the two sequences were compared quantitatively as a function of the pixel size and the velocity encoding.

### Results

The mean percentage difference between the EPI-PC flow rate and calibrated phantom flow rate was −2.9 ± 2.1% (Mean ± SD). The pulsatility indices for EPI-PC and Conv-PC were respectively 0.64 and 0.59. In order to keep the flow rate measurement error within 10%, the ROI in Conv-PC had to contain at least 13 pixels, while the ROI in EPI-PC had to contain at least 9 pixels. Furthermore, Conv-PC had a higher velocity-to-noise ratio and could use a higher velocity encoding than EPI-PC (20 cm/s and 15 cm/s, respectively).

### Conclusions

The result of this in vitro study confirmed the accuracy of EPI-PC, and found that EPI-PC can adapt to lower spatial resolutions, but is more sensitive to velocity encoding than Conv-PC.

## 1. Introduction

Conventional phase-contrast magnetic resonance imaging (Conv-PC) is a non-invasive technique that can be used to measure blood and cerebrospinal fluid (CSF) velocities. Conv-PC was used by Moran in 1982 to study flow velocities in humans.
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Since then, Conv-PC has become a particularly important technique for in vitro studies and in vivo quantifications of blood and CSF flows.
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Unfortunately, Conv-PC is limited by its relatively poor time resolution; it can only provide flow measurements for an averaged heartbeat cycle, which is reconstructed from all the acquired heartbeat cycles and uses gating.
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Phase contrast cine magnetic resonance imaging.
It is now known that breathing can affect CSF and cerebral blood flows.
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Respiration-related cerebral blood flow variability increases during control-mode non-invasive ventilation in normovolemia and hypovolemia.
Consequently, the flow velocities measured with Conv-PC may be breathing-dependent. Furthermore, Conv-PC is difficult to reveal the effects of breathing on the dynamics of blood or CSF flows.
To overcome this limitation, several research groups have developed a fast acquisition method based on echo-planar imaging (EPI) in which a complete k-space can be acquired using one or a small number of pulse excitations.
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Eichenberger et al. in 1995 combined EPI with phase-contrast technique and thus introduced a novel sequence now commonly referred to as EPI-PC, using which they successfully quantified the blood flow of thoracic vessels at 20 mm diameter level in real-time with a spatial resolution of 5 × 5 mm2.
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Phase-contrast echo-planar MR imaging: real-time quantification of plow and velocity patterns in the thoracic vessels induced by valsalva's maneuver.
With improved hardware performance, higher spatial resolution and smaller velocity encoding (VENC) can recently be used in EPI-PC to quantify cerebrovascular blood flow with smaller cross-sectional areas and cerebrospinal fluid oscillations with slower flow rates in real-time. With a high time resolution (100 ms/image, or shorter), a freely determined acquisition time, and a simpler acquisition process (i.e. no need for synchronization), EPI-PC has clear advantages in the field of research but also opens new opportunities for clinical practice.
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Carotid artery flow as determined by real-time phase-contrast flow MRI and neurovascular ultrasound: a comparative study of healthy subjects.
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MetanbouC.CapelS.FallR.Bouzerar, 2021, May. Cerebro spinal fluid dynamic in front of cardiac and breathing influence.
An increasing number of researchers are using EPI-PC to quantify the effect of respiration on cerebral circulation.
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Quantifying the influence of respiration and cardiac pulsations on cerebrospinal fluid dynamics using real-time phase-contrast MRI.
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Use of real-time phase-contrast MRI to quantify the effect of spontaneous breathing on the cerebral arteries.
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Respiratory cerebrospinal fluid flow is driven by the thoracic and lumbar spinal pressures.
However, EPI-PC is more sensitive to eddy currents and has a longer readout window, resulting in a lower velocity-to-noise ratio (VNR) of the phase image than for Conv-PC.
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Increasing pixel size can increase VNR while improving imaging speed, but it is also more likely to produce partial volume effects.
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Accuracy of phase-contrast flow measurements in the presence of partial-volume effects.
Using a larger VENC can avoid the aliasing effects, but it will reduce the VNR and thus increase the segmentation difficulty. A better understanding of the effects of spatial resolution and VNR on EPI-PC allows us to further ensure quantification accuracy and improve imaging quality. However, to the best of our knowledge, there is a lack of specific literature on this field.
The objectives of this in vitro study were to quantitatively evaluate the accuracy of EPI-PC vs. Conv-PC and to assess the influence of pixel size and VENC on flow rate measurements.

## 2. Material and methods

### 2.1 Flow phantom

The phantom consisted of a series of four rigid, straight tubes (Tygon tubing, Saint-Gobain Performance Plastics, Akron, OH) with inner diameters of 9.5 mm (tube #1), 6.4 mm (tube #2), 4.4 mm (tube #3) and 2 mm (tube #4). We used water to simulate cerebrospinal fluid which has longer T1 and T2 relaxation times compared to blood.
• Bojorquez J.Z.
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• Lalande A.
What are normal relaxation times of tissues at 3 T?.
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• Odrobina E.E.
• Pun J.
• Escaravage M.
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The water flow was generated using a pulsatile flow pump. Six meters of tubing carried the water from the pump (located in the scanner control room) to the phantom's inlet. The phantom's outlet was connected to the tank that supplied water to the pump (Fig. 1a).
To validate our system's flow rates, the pump was calibrated to deliver a clinically relevant flow rate (pulsatile flow with 99 bpm), and the volume collected from the phantom's output was recorded as a function of time. The true (calibrated) phantom mean flow rate (1150 mm3/s) was obtained through repeated measurements and was used as the reference mean flow rate value for the present work. Both Conv-PC and EPI-PC were used to measure the flow rate of the first tube with 9.5 mm of diameter, its area of 70.8 mm2 was taken as reference for segmentation area. The flow waveform of Conv-PC was used as reference, the ratio of the amplitude flow rate (maximum flow rate minus minimum flow rate) and the mean flow rate was used as the reference pulsatility index.
The flow phantom was positioned in the center of a head coil. On the return tube, a gating-compliant balloon was used to capture the frequency of the oscillation and thus to synchronize the acquisition of the Conv-PC with the flow rate waveform. A water-filled tube (tube reference) was positioned beside the tubes, to define the static reference region.

### 2.2 Imaging procedure

All images were acquired on a 3T clinical scanner (Philips Achieva; maximum gradient: 80 mT/m; rate of gradient increase: 120 mT m−1 ms−1) using a 32-channel head coil.
The parameters of the imaging protocol for both sequences are shown in Table 1. The acquisition was repeated 10 times. The Conv-PC is a gradient echo based, blipped phase contrast sequence with a cartesian trajectory. During the acquisition of Conv-PC images, a finger pulse oximeter was posed on the gating balloon for retrospective cardiac gating. Typically, the velocity is encoded along the flow direction (A-P, in this study) by positioning a bipolar gradient (with opposite polarity) behind the slice selection gradient. The spins of flowing tissue are at different locations relative to the bipolar gradient's positive and negative lobes. These spins are then confronted with the magnetic field gradients and accumulate a residual phase difference, whereas the spins of stationary tissue do not produce phase differences. Phase data sets from before and after gradient reversal are subtracted to determine the “phase difference” of flowing spins, which is directly proportional to their underlying velocities. A description of the relationship between the measured phase and the velocities can be found in
• Bojorquez J.Z.
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• Acquitter C.
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• Walker P.M.
• Lalande A.
What are normal relaxation times of tissues at 3 T?.
.
Table 1Default parameters for Conv-PC and EPI-PC.
Conv-PCEPI-PC
FOV (F × P)100 × 60100 × 60
VENC (cm/s)55
ACQ pixel size (mm2)1.2 × 1.21.2 × 1.2
REC pixel size (mm2)0.31 × 0.310.78 × 0.78
Thickness (mm)44
Flip angle (degree)3030
EPI factorNA9
SENSE1.52.5
TR (ms)1115.2
TE (ms)7.79.1
Acquisition time (s)23.69.3
Number of images per cycle329.7
ACQ = acquisition; REC = reconstruction; FOV = field of view; VENC = velocity encoding; EPI = echo planar imaging; SENSE = sensitivity encoding; TE = echo time; TR = repetition time.
The EPI-PC sequence used in this experiment was a modified version of a standard, multi-shot
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Accuracy of MRI T2*-weighted sequences (GRE-EPI) compared to CTA for detection of anterior circulation large vessel thrombus.
with a Cartesian trajectory.
• DeLaPaz R.L.
Echo-planar imaging.
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• et al.
Multi-shot Echo planar imaging for accelerated cartesian MR fingerprinting: an alternative to conventional spiral MR fingerprinting.
EPI-factor is a parameter specific of EPI-PC that indicates the number of echoes acquired during a TR.
Each Conv-PC series contained 32 phase images after 23.6 s of acquisition, the interval between two images () during an average cycle was constant (∆t = 19 milliseconds). For EPI-PC series, the total number of acquired phase images was set to 150. The acquisition time was 9.3 s, and the ∆t was 62 milliseconds. The reconstructed images of the two sequences were obtained from the initial images by using interpolation algorithm (Table 1).
To assess the effects of pixel size and VENC on flow rate measurements for both sequences, the pixel size was set from 0.8 mm to 3.2 mm in increments of 0.4 mm, and VENC was set from 5 cm/s to 25 cm/s in increments of 5 cm/s. The acquisition was repeated four times for both sequences and for each parameter. Once the pixel size reached 2 × 2 mm2, the pixel size was increased by fixing the acquisition matrix and increasing the FOV.

### 2.3 Postprocessing procedure

To extract the flow rate curves, the MRI data were processed with in-house software (Flow
• Balédent O.
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A semi-automatic software for processing real-time phase-contrast MRI data.
). To minimize the effects of eddy current on the measurements, the velocity was calibrated by measuring the mean velocity in the tube reference (Fig. 2.a, green circle). Furthermore, to compare the two sequences, the EPI-PC flow rate signal was reconstructed over an average pulse cycle of 32 points with the same model as Conv-PC (Fig. 1.b). The post-processing procedure is as follows:

#### 2.3.1 Regions of interest

By using the software's segmentation function, a region of interest (ROI) within the tube #1 (ROI-Tube) can be automatically segmented on the phase image. The value of the segmented area can then be recorded. Likewise, a ROI within the static tube (ROI-Reference) was manually defined as the source of velocity noise (Fig. 2.a, green cycle). For each phase image, the mean (VRef) and standard deviation (SD) (σRef) velocity within ROI-Reference were calculated. The VRef and σRef values were used to define a reference signal and an uneven signal, respectively (Fig. 2.c & b).

#### 2.3.2 Calibration of the measured velocities

The calibration compensated for the noise error in the measurement of velocity. In theory, the measured velocity does not represent the true velocity, and the velocity in the ROI-Reference is null. To calculate the corrected (true) velocity, the measured velocity was subtracted from the VRef (Fig. 2.d).

#### 2.3.3 Calculation of the VNR

The mean uneven signal $σRef¯$ was used to calculate the VNR by dividing the mean velocity in the ROI-Tube by the mean uneven signal in ROI-Ref (Eq. (1)).
$VNR=V¯σRef¯$
(1)

#### 2.3.4 Reconstruction of the mean EPI-PC cycle

The steps in the segmentation and calibration of the EPI-PC data were the same as for the Conv-PC data (2.3.1, 2.3.2, 2.3.3). After the flow rate signal has been obtained from the EPI-PC data, the software's cropping tool can be used to extract all the single pulse cycles from the original signal (red points in Fig. 1.b). A spline interpolation algorithm was then used to increase the number of sampling points to 32 for each pulse cycle in the EPI-PC data. The sampling points at each position and each pulse cycles were then averaged to obtain the corresponding flow rate value for the reconstructed average pulse cycle. This average flow curve will be used for subsequent accuracy evaluations and analyses of the effects of pixel size and VENC.

#### 2.3.5 The pulsatility index

Calculate the pulsatility index of flow curve of Conv-PC and the pulsatility index of average flow curve of EPI-PC using Eq. (2).
$Pulsatility index=Maxflow−MinflowMean flow$
(2)

### 2.4 Accuracy assessment of EPI-PC

The accuracy of EPI-PC was evaluated by comparing the quantified results of EPI-PC with the reference flow rate and reference area of calibrated phantom, and with the pulsatility index of the flow curve of Conv-PC.

### 2.5 The influence of pixel size and VENC

The measured average flow, segmentation area and VNR of the two sequences at different pixel sizes and velocity encodings were compared to analyze the effect of these two parameters on Conv-PC and EPI-PC. Based on literature procedures for measuring the accuracy of phase contrast sequences,
• Tang C.
• Blatter D.D.
• Parker D.
Accuracy of phase-contrast flow measurements in the presence of partial-volume effects.
• Greil G.
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• Maier S.E.
• Powell A.J.
Effect of acquisition parameters on the accuracy of velocity encoded cine magnetic resonance imaging blood flow measurements.
we considered that the acceptable confidence intervals (CIs) for the segmentation error and the flow rate error were ± 10%.

### 2.6 Statistical analysis

The influence of pixel size and VENC on flow rate was evaluated using a regression analysis. Pearson's test was used to analyze the correlation between variables. Values are expressed as the mean ± standard deviation (SD). All statistical analyses were performed with R software (version 3.2.3, R Foundation for Statistical Computing, Vienna, Austria, www.r-project.org). The threshold for significance was set to p < 0.05.

## 3. Results

After several manual measurements, it was verified that the average flow rate of the phantom was 1150 mm3/s. The Reynolds number of the tube #1 is 1260 and so was <2100, the flow was considered to be laminar.

### 3.1 Comparison of EPI-PC and Conv-PC sequences

The EPI-PC and Conv-PC sequences were applied to tube #1 with the default parameters.
After 10 measurements, the distributions of the average flow rate, segmentation area and pulsatility index of EPI-PC and Conv-PC are shown in Fig. 3. The mean flow rates for EPI-PC and Conv-PC were 1116 ± 25 mm3/s and 1239 ± 26 mm3/s respectively, and the associated coefficient of variation was 2.2% in both cases (Fig. 3.b). The segmentation areas of EPI-PC and Conv-PC were 70.1 ± 1 mm2 and 70 ± 0.9 mm2 respectively, and their coefficient of variations were 1.5% and 1.3% respectively (Fig. 3.c). The pulsatility indices for EPI-PC and Conv-PC were respectively 0.64 ± 0.03 and 0.59 ± 0.01 respectively, and their coefficient of variations were 2.5% and 4% respectively (Fig. 3.d).

### 3.2 The influence of pixel size

Table 2 shows the parameters and measurement results of Conv-PC and EPI-PC at different pixel sizes.
Table 2Parameters and quantification results of Conv-PC and EPI-PC at different pixel sizes.
ParametersACQ pixel size (mm2)
0.8 × 0.81.2 × 1.21.6 × 1.62.0 × 2.02.4 × 2.42.8 × 2.83.2 × 3.2
REC Pixel (mm2)
Conv-PC0.31 × 0.310.31 × 0.310.39 × 0.390.52 × 0.520.58 × 0.580.75 × 0.750.86 × 0.86
EPI-PC0.78 × 0.780.78 × 0.780.78 × 0.780.78 × 0.780.78 × 0.780.75 × 0.750.98 × 0.98
Average Flow rate (mm3/s)
Conv-PC1007 ± 71035 ± 171101 ± 101128 ± 61189 ± 181278 ± 51446 ± 46
EPI-PC971 ± 241064 ± 131117 ± 231140 ± 81143 ± 101177 ± 81394 ± 40
Area ROI (mm2)
Conv-PC55.7 ± 1.258.8 ± 2.864.0 ± 1.166.5 ± 1.173.4 ± 2.273.2 ± 0.674.8 ± 3.3
EPI-PC54.3 ± 2.756.8 ± 1.161.4 ± 3.067 ± 2.372.2 ± 4.179.3 ± 6.276.2 ± 4.6
Maximum flow rate (mm3/s)
Conv-PC1333142214671541162217051854
EPI-PC1200135814671558161416701865
Maximum flow velocity (mm/s)
Conv-PC36393939383533
EPI-PC37373840403332
ACQ time (second)
Conv-PC3322.617.120.217.115.915.3
EPI-PC16.99.38.27.77.47.16.8
VNR
Conv-PC91613.91514.315.918.8
EPI-PC1.93.34.66.79.513.620.6
Flow with fixed ROI (mm3/s)
Conv-PC1044109811161140117212521380
EPI-PC1104111411801157110011251363
ACQ = acquisition; REC Pixel = reconstruction pixel size; Area ROI = Segmented area of Tube #1; VNR = velocity-to-noise ratio; Flow with fixed ROI = using the amplitude image for segmentation to lock the ROI at the standard value (70.8 mm2). The flow rate data in bold indicates values outside the cofidence interval.
In Fig. 4, the segmentation area (blue points) and the flow rate (red points) are shown as a function of pixel size. Each variable was measured four times. The blue shading corresponds to the CI for the reference segmentation area (70.8 mm2 ± 10%) and the red shading corresponds to the CI for the reference flow rate (1150 mm3/s ± 10%). The flow rates measurements obtained with EPI-PC were within the CI for pixel sizes of 1.2 mm to 2.8 mm. For Conv-PC, only pixel sizes of 1.2 mm to 2.4 mm provided flow rates within the CI.
The distributions of the segmentation area (on the x axis) and flow rate (on the y axis) of the two sequences are shown in Fig. 5. The purple and green shadings correspond to the CI of the segmentation area and the flow rate, respectively.
Fig. 6 shows the VNR of EPI-PC and Conv-PC with different pixel sizes. For a pixel size of 1.2 mm to 2.8 mm, the VNR increased for EPI-PC but did not change for Conv-PC. For each pixel size, the VNR was higher for Conv-PC than for EPI-PC.

### 3.3 The influence of VENC

Table 3 shows the parameters and measurement results of Conv-PC and EPI-PC at different VENC.
Table 3Parameters and quantification results of Conv-PC and EPI-PC at different VENC.
ParametersVENC (cm/s)
510152025
Velocity reference (cm/s)
Conv-PC−3.20.373.21.42.2
EPI-PC−1.2−1.4−1.30.730.73
SD reference (cm/s)
Conv-PC0.540.9221.882.26
EPI-PC4.99.413.817.721.7
Average flow rate (mm3/s)
Conv-PC1230 ± 101112 ± 31118 ± 61072 ± 14996 ± 24
EPI-PC1145 ± 121212 ± 181139 ± 34803 ± 4
Area ROI (mm2)
Conv-PC62.9 ± 1.969.7 ± 1.869 ± 0.961.6 ± 5.656.0 ± 4.4
EPI-PC65.3 ± 2.262.6 ± 1.554.5 ± 3.846.4 ± 0.6
Maximum flow rate (mm3/s)
Conv-PC16741607153515041416
EPI-PC1535160514611251
Maximum flow velocity (mm/s)
Conv-PC4345403838
EPI-PC38384242
ACQ time (second)
Conv-PC23.622.422.422.422.4
EPI-PC9.38.58.28.07.9
VNR
Conv-PC27.217.48.19.37.9
EPI-PC3.62.11.51.00.8
Flow with fixed ROI (mm3/s)
Conv-PC12141115104010701034
EPI-PC1207123111741028983
Velocity reference = average velocity within the ROI of reference tube; SD reference = standard deviation of velocity within the ROI of reference tube; Area ROI = segmented area of Tube #1; ACQ = acquisition; VNR = velocity-to-noise ratio; Flow with fixed ROI = using the amplitude image for segmentation to lock the ROI at the standard value (70.8 mm2).
Fig. 7 shows the influence of VENC on EPI-PC and on Conv-PC. As the VENC increased, the accuracy decreased more rapidly for EPI-PC than for Conv-PC. With a VENC of 15 cm/s, the segmentation area for EPI-PC was outside the CI. Moreover, with a VENC of 20 cm/s, the flow rate for EPI-PC was also outside of the CI. For a VENC of 25 cm/s or more, the software was not able to segment the ROI. In contrast, with a VENC below 20 cm/s, the flow rates for Conv-PC were within the CI.
Fig. 8 gives the VNR for EPI-PC and Conv-PC with different VENC values. As the value of VENC increased, the VNR for EPI-PC fell from 3.6 to 0.8. For Conv-PC, the VNR fell from 27.2 to 8.1 as the VENC value increase from 5 cm/s to 15 cm/s. For VENC values of 15 cm/s to 25 cm/s, the VNR varied less (8.4 ± 0.76). Overall, the VNR with different VENC values was much greater for Conv-PC than for EPI-PC.

## 4. Discussion

In the present study, we validated the accuracy of EPI-PC and evaluated the effects of spatial resolution and VENC on EPI-PC and Conv-PC.
The effects of magnetic field inhomogeneity must be taken account, since the reference tube was not positioned around the flow tube in the FOV.
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Therefore, there may be errors in the background field correction, and it will be increased with the increase of VENC (Figs. S5, S6, Table S1). Moreover, since EPI-PC is more susceptible to eddy currents, in clinical applications, stationary tissue close to the target vessel should be selected as much as possible for background field correction.
The estimated VNR in this study was a pseudo-VNR averaged across all images. This measurement method is likely to be more conveniently and might be sufficient for comparing the VNRs from several different sequences.
These results are not directly transferred to single-shot EPI-PC as this sequence is more sensitive to geometric distortion and has a lower VNR,
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and does not apply on non-laminar or asymmetrical flow profiles. The multi-shot EPI-PC is less sensitive to geometric distortions, given the shorter readout time.
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This is why we used a multi-shot EPI-PC in this study.

### 4.1 Comparison of EPI-PC and Conv-PC

Using default parameters, the respective flow rate and segmentation area measurements for the two sequences were both within the CIs and did not exceed 8%
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• Westenberg J.J.M.
• et al.
Comparison of fast acquisition strategies in whole-heart four-dimensional flow cardiac MR: two-centre, 1.5 Tesla, phantom and in vivo validation study.
(flow rate error: −2.9% for EPI-PC vs. 7.8% for Conv-PC; segmentation area error: −1% for EPI-PC vs. -1.1% for Conv-PC). Difference in the pulsatility index between EPI-PC and Conv-PC was <10%.
There are many other factors that influence the flow quantification. Even with the same imaging protocol, differences in the placement of the water pipes in the magnetic field can affect the results. Therefore, it is acceptable with a quantification error of no more than 10%.
The Conv-PC sequence was able to complete several phase encodings during each pulse cycle and to fill them into the different phase images' K-space; even though the acquisition time increased, it did not therefore affect the pseudo-sampling interval ∆t. However, for the real-time imaging with EPI-PC, the acquisition time was directly related to ∆t. The EPI-PC continue flow rate signal with default parameters, only 9 or 10 characteristic points were used to describe a pulse cycle. Therefore, EPI-PC is more suitable for flows with gentle fluctuations, such as venous blood and CSF. However, EPI-PC has limitations for reconstructing high-frequency fluctuations, such as certain arterial waveforms. Increasing the EPI-PC sampling frequency is likely to improve the accuracy of the corresponding reconstructed curve (Fig. S1).

### 4.2 The influence of pixel size

The EPI-PC sequence was less sensitive to pixel size than Conv-PC. Due to the characteristics of laminar flow, the velocity is lower at the boundary of the tube than in its center. When the resolution is high, the flow at the tube wall did not produce a large phase difference. Hence, this area can be considered to be non-flowing on the phase contrast image, and so the true segmented area is smaller than the theoretical area (Fig. 5).
Accurate segmentation area and flow rate measurements were possible with a range of pixel sizes: from 1.8 to 2.8 mm for EPI-PC and from 1.8 to 2.4 mm for Conv-PC. Within these ranges, the measured flow rate was slightly influenced by the segmentation area. As the pixel size continued to increase (above 2.8 mm for EPI-PC and above 2.4 mm for Conv-PC), the flow rate of the two sequences began to exceed the boundaries of the CI (Fig. 5). We hypothesize that a partial volume effect led to overestimation of the velocity.
• Tang C.
• Blatter D.D.
• Parker D.
Accuracy of phase-contrast flow measurements in the presence of partial-volume effects.
• Bouillot P.
• Delattre B.M.A.
• Brina O.
• et al.
3D phase contrast MRI: partial volume correction for robust blood flow quantification in small intracranial vessels.
As a result, the flow rate error was too large - even though the segmentation region was within the CI.
A larger acquisition pixel size can effectively improve the VNR of EPI-PC and reduce the difficulty of image post-processing (Fig. 6); it can also improve the temporal resolution and increase the accuracy of flow waveform quantification (Fig. S1). Moreover, to a certain extent, it avoids the aliasing effect since larger acquisition pixels can average the high velocity area with the surrounding area and thus reduce the maximum flow velocity (Fig. S7).
Therefore, in order to measure the flow rate accurately, the pixel size for Conv-PC should be <25% of the target ROI diameter; in other words, the ROI of Conv-PC should comprise at least 13 pixels. Our result is in line with those obtained by Greil et al. and Tang et al.,
• Tang C.
• Blatter D.D.
• Parker D.
Accuracy of phase-contrast flow measurements in the presence of partial-volume effects.
• Greil G.
• Geva T.
• Maier S.E.
• Powell A.J.
Effect of acquisition parameters on the accuracy of velocity encoded cine magnetic resonance imaging blood flow measurements.
who confirmed that a minimum of 16 pixels within the Conv-PC ROI was required to keep the flow rate error within 10%. For the EPI-PC sequence, the pixel size should be <30% of the diameter of the target ROI diameter; in other words, the ROI of EPI-PC should have at least 9 pixels. On the other hand, while ensuring accuracy, larger pixel sizes can increase the VNR and improve imaging speed (Fig. S1), which is essential for EPI-PC.

### 4.3 The influence of VENC

The EPI-PC was more sensitive to VENC. Without aliasing, the VNR is inversely proportional to the VENC.
• Lee A.T.
• Pike G.B.
• Pelc N.J.
Three-point phase-contrast velocity measurements with increased velocity-to-noise ratio.
• Ha H.
• Kim G.B.
• Kweon J.
• et al.
Multi-VENC acquisition of four-dimensional phase-contrast MRI to improve precision of velocity field measurement.
This sensitivity was also reflected in our experiments by the pseudo-VNR (Figs. 8 & S2). Compared to EPI-PC, Conv-PC can provide accurate flow rate with a larger VENC. Firstly, this was because the Conv-PC can use multiple cycles to fill a phase image, and so the influence of noise on the echo signal is smaller. For EPI-PC, multiple phase encodings are needed to complete the K-space during a TR, so the SNR of the echo signal is much smaller and the VNR of the phase image is relatively low. Secondly, in order to increase the sampling frequency in the EPI-PC sequence, the SENSE
• Pruessmann K.P.
• Weiger M.
• Scheidegger M.B.
• Boesiger P.
SENSE: sensitivity encoding for fast MRI.
value in this study as set to 2.5 which is 66% greater than that of Conv-PC (1.5), and a larger SENSE value decreases the VNR of phase image.
Since the VNR of Conc-PC was higher than that of EPI-PC, the increase in VENC had relatively little influence on the accuracy of Conv-PC flow rate measurements. Even when the VENC increased from 5 cm/s to 20 cm/s, the flow rate measured with Conv-PC was still within the CI. In contrast, the maximum value for VENC in the EPI-PC sequence was 10 cm/s; above this value, the segmentation was inaccurate.
The decrease in VNR mainly affects the segmentation of phase images; segmentation errors can arise when the pixel intensity in the phase image of the target vessel is close to that of the surrounding (non-flowing) tissue. This effect can be reduced if the magnitude image is used for segmentation, because the effect of VENC on the SNR of the magnitude image is much smaller than the effect on the VNR on the phase image.
On the other hand, a smaller VENC can increase the VNR, but at the same time slightly increasing the TR, leading to an increase in the Δt of EPI-PC (Fig. S3). Therefore, it is also feasible to improve the imaging speed by increasing the VENC in clinical applications while ensuring accurate quantification.

### 4.4 Limitations and perspectives

There are also some potential limitations in our study that should be noted.
Although the acquisition pixel size is the main influence on the measurement accuracy, the difference in reconstructed pixel size still affects the fairness of comparing two sequences and should be considered in subsequent studies.
The phantom in our study presents a sinusoidal waveform with only one frequency component, which is used to simulate the CSF or cerebral vein waveform, whereas there are two higher-frequency harmonics (2–4 Hz) in the cerebral arterial waveform.
• Maier I.L.
• Hofer S.
• et al.
Carotid artery flow as determined by real-time phase-contrast flow MRI and neurovascular ultrasound: a comparative study of healthy subjects.
The results of this study are only applicable to demonstrate the accuracy of EPI-PC in quantifying CSF and cerebral veins. Hence, the ability of EPI-PC to accurately quantify more pulsatile arterial waveforms (e.g., aorta) with a temporal resolution of 62 ms/image needs further evaluation.
The phantom model did not take account of arrhythmic and respiratory effects, for which the EPI-PC sequence is advantageous because (in contrast to Conv-PC) it does not require synchronization with the cardiac cycle. Including these influences allows a more comprehensive comparison of the characteristics of the two sequences.

## 5. Conclusion

Our study shows that the calculated error between the reconstructed EPI-PC flow curve and the Conv-PC flow curve was small. Compared with Conv-PC, EPI-PC can be adapted to a lower spatial resolution but is more sensitive to VENC.
In this study, setting the pixel size of the EPI-PC to 30% of the diameter of the water tube gives the best VNR and temporal resolution without causing partial volume effects; and to obtain a higher VNR, VENC should be set small (aliasing needs to be avoided). With the imaging speed of 62 ms/image can accurately represent the venous or cerebrospinal flow rate waveform at 99 bpm.
EPI-PC is more susceptible to eddy currents, so when performing background field correction for clinical applications, the stationary tissue should be selected as close to the target vessel as possible, and a small VENC should be used.
These results provided reference values for the clinical application of EPI-PC.

## Abbreviations

Conv-PC
conventional cine phase-contrast MRI
CI
confidence interval
CSF
cerebrospinal fluid
EPI
echo-planar imaging
EPI-PC
phase-contrast echo-planar MRI
FOV
field of view
ROI
region of interest
ROI-Reference
ROI within the static tube
VRef
mean velocity within ROI-Reference
σRef
standard deviation velocity within ROI-Reference
VENC
velocity encoding
VNR
velocity-noise ratio
SD
standard deviation
SENSE
sensitivity encoding
SNR
signal-to-noise ratio
time interval between two images

## Availability of data and materials

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

## Funding

This research was funded by the French National Research Agency (reference: Hanuman ANR-18-CE45-0014 and EquipEX FIGURES 10-EQPX-0001) and INTERREG France (Channel) England Programme (REVERT project).

## CRediT authorship contribution statement

LP designed the study, developed the post-processing software, and wrote the initial draft of the manuscript. SF performed statistical analysis of the data and revised the manuscript. MA collected and analyzed the in vitro data. Ob developed the post-processing software and revised the manuscript. All authors approved the final version of the manuscript for submission. All authors read and approved the final manuscript.

## Declaration of competing interest

The authors declare that they have no conflicts of interest with respect to the research, authorship, and/or publication of this article. The figures are original and have not been published previously.

## Acknowledgements

The authors thank David Chechin for scientific support and the staff members at the Facing Faces Institute (Amiens, France) for technical assistance.

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## Biography

Dr Pan Liu received his PhD in Radiological and Medical Physics from the Jules Verne University of Picardy (Amiens, France) in 2021. He is currently funded as a postdoctoral fellow through the CHIMERE-UR7516 research group. His main research interests are MRI image processing algorithms and image processing software development.
Dr Sidy Fall received a PhD in Biomedical Engineering from the Jules Verne University of Picardy (Amiens, France) in 2009. He is currently an engineer at the university's Preclinical MRI Facility. His main research interests are MRI and physiological data processing and especially functional MRI, DTI, and vascular imaging.
Maureen Ahiatsi received a Master's Degree in Neurosciences – Neurobiology from the University of Grenoble Alpes (Grenoble, France) in 2020. She is currently studying for a Master's Degree in Artificial Intelligence and Digital Transformation at the AI & Digital Transformation School (Paris, France). Her research interests include brain pathophysiology, and medical imaging data processing and analysis.
Dr Olivier Baledent received a PhD on the MRI-based imaging of CSF and blood flow using at the Jules Verne University of Picardy (Amiens, France) in 2001. He is currently an assistant professor at the university and also heads the Medical Image Processing Department at Amiens University Medical Center (Amiens, France), where he is developing flow MRI techniques in the CHIMERE-UR7516 research group. In 2020, he helped to create ‘neurofluid imaging’ as a new section in the International Society of Magnetic Resonance Imaging.