In vitro assessment of real-time phase contrast MRI accuracy

Pan LIU (  liupanronald@hotmail.com ) CHU Amiens-Picardie: Centre Hospitalier Universitaire Amiens-Picardie https://orcid.org/0000-00030559-6432 Sidy FALL University of Picardy Jules Verne: Universite de Picardie Jules Verne Maureen AHIATSI University of Picardy Jules Verne: Universite de Picardie Jules Verne Olivier BALEDENT CHU Amiens-Picardie: Centre Hospitalier Universitaire Amiens-Picardie


Background
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 [26]. In 1984, Bryant et al. used Conv-PC to produce flow velocity map [7]. The synchronization of cardiac movements with velocity measurements has been applied to MR velocity imaging [14,34]. Since then, Conv-PC has become a very important technique for in vitro studies and in vivo quantifications of blood and CSF flows [27,16,1,2,25,20,37].
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. It is now known that breathing can affect CSF and cerebral blood flows [31,33]. Consequently, the flow velocities measured with Conv-PC may be breathing-dependent. Furthermore, Conv-PC is not able 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 [24,11].
In order to speed up data acquisition, Chen et al. combined EPI with a phase-contrast technique and thus introduced a novel sequence now commonly referred to as EPI-PC. This technique can be used to map CSF movements and demonstrate that CSF dynamics are influenced by breathing as well as by the cardiac cycle [8].
With a high time resolution (a sampling frequency of ~10 Hz), a shorter 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. Recently, some researchers have used EPI-PC to quantify the influence of cardiac and respiratory pulses on the CSF and cerebral blood flow rates in the cranial system [39]. However, EPI-PC is more sensitive to eddy currents and has a longer readout window, resulting in a lower signal-to-noise ratio (SNR) than for Conv-PC [22,38]. Moreover, EPI-PC data is impacted by high-frequency, high-intensity gradient switching and by differences in magnetic susceptibility between blood and bone/air [35]. To the best of our knowledge, there are no published data on the accuracy of EPI-PC vs. Conv-PC.

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The objectives of the present study were to quantitatively evaluate the accuracy of EPI-PC vs. Conv-PC and to assess the influence of pixel size and velocity encoding (VENC) on flow rate measurements. The acquisition parameters had to be optimized before EPI-PC could be validly compared with Conv-PC.

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). The fluid flow was generated using a pulsatile flow pump. Six meters of tubing carried the fluid 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. 1 a).

Figure 1
The flow phantom and the flow curve for the two sequences. a A realistic pulse-based model of the craniospinal system (left). An amplitude image for four tubes and a static tube in the acquisition plane (right), b An EPI-PC phase image (left) and its calibrated flow curve (middle) with the minimum (trough) points (in red) in each cycle found automatically by the software, which are used to separate the cycles. All the EPI-PC pulse cycles were used to reconstruct an average pulse cycle (right), c The Conv-PC phase image (left) and its calibrated flow curve. 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 flow rate was obtained through repeated measurements and was used as the reference value for calculation of the EPI-PC's accuracy. The present work covered measurements obtained with the first tube (diameter: 9.5 mm) only.
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 was positioned around the tubes, to define the static reference region.
Imaging procedure and method of comparison 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 ). A 32-channel head coil was used to detect signals.
The EPI-PC sequence used in this experiment was a modified version of a standard, multi-shot, gradient-echo EPI sequence [30] with a Cartesian trajectory [4,9]. Typically, the velocity is encoded along the flow direction 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 stationary tissue does not experience a variation in the magnetic gradient. 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 [28].
One of the objectives of the present study was to ensure that the optimized EPI-PC protocol could be applied in the clinic. Based on our clinical experience of Conv-PC, the imaging parameters are set to the initial values (field of view (FOV), VENC, etc.), except that the pixel size, flip angle and slice thickness (i.e., variable parameters) were set to different values within a small range; this improved the speed of imaging while maintaining image quality (Table 1). For each set of parameters, the EPI-PC and Conv-PC sequences were compared in terms of the segmentation error (expressed as a percentage of the difference between the segmented area and theoretical area), flow error (expressed as a percentage of the difference between the phantom flow rate and the measured flow rate), velocity-noise ratio (VNR), acquisition time, and sampling interval. This step was based on literature procedures for measuring the accuracy of phase contrast sequences [17,35]. We considered that the acceptable confidence intervals (CIs) for the segmentation error and the flow error were ±10%.

Conv
To compare the two sequences, a set of default parameters was obtained by selecting those for which (i) the segmentation error and flow error were within the CI, and (ii) the acquisition was the shortest. Once the default parameters had been selected, we evaluated the accuracy of the EPI-PC flow rate curve and also assessed the effects of pixel size and VENC on flow rate measurements for both sequences. To this end, the pixel size ranged from 0.8 mm to 3.2 mm in increments of 0.4 mm, whereas the VENC ranged from 5 cm/s to 25 cm/s in increments of 5 cm/s.

Statistical analysis
The reconstructed flow rate curves for the EPI-PC data and the Conv-PC data were compared in a Bland & Altman plot [5]. The influence of pixel size on flow rate was evaluated using a regression analysis. Pearson's test was used to analyze the correlation between variables. 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.

Software and postprocessing
To extract the flow rate curves, the MRI data were processed with in-house software (Flow [3,12]). Each Conv-PC series contained 32 phase images that were acquired to obtain a representative flow rate cycle (duration: 606 ms).
Even though the acquisition time ranged from 13 to 33 s (depending on the spatial resolution), the interval between two images (∆ ) during an average cycle was constant (∆ = 19 ms). For EPI-PC series, the total number of acquired phase images was constant (n=150). The acquisition time ranged from 7 to 17 s, leading to a ∆ that ranged from 46.7 ms to 113 ms. Six to 13 phase images were then reconstructed per cycle.
To minimize the effects of eddy current on the measurements, the velocity was calibrated by measuring the mean velocity in the static tube. 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.1b); the reconstruction method is described below.

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

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.2d).

Calculation of the VNR
The mean uneven signal ̅̅̅̅̅̅̅ was used to calculate the VNR by dividing the mean velocity in the ROI-Tube by the mean uneven signal in ROI-Ref (equation 1).

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. 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.1b). 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.

The pulsatility index
The pulsatility index was defined as follows [32]:

Default parameters
After several repeated measurements, the phantom flow rate was found to be 1150 mm 3 /s. The Reynolds number for the four tubes (calculated with the maximum velocity) ranged from 399 to 1260 and so was less than 2100; the flow was considered to be laminar. Table 2 shows how the main sequence parameters influenced the quality of the acquisition in Conv-PC and EPI-PC. As the pixel size increased, the Conv-PC acquisition time shortened but the segmentation area and flow rate were still accurate. For EPI-PC, an increase in the pixel size from 0. As expected, the flip angle had no effect on the imaging time but did influence the VNR. An increase in the flip angle from 10° to 30° was associated with a 123% relative increase in the VNR. Increasing the EPI factor decreased the acquisition time: changing the EPI factor from 7 to 9 reduced the acquisition time by 25% but barely impacted the segmentation area and flow rate measurements.
On the basis of these results, we selected the default parameters for comparing the two sequences (

Comparison of EPI-PC and Conv-PC sequences
The EPI-PC and Conv-PC sequences were applied to tube #1 with the selected default parameters.
After 10 measurements, the reconstructed EPI-PC and Conv-PC data were postprocessed to reconstruct the two average flow rate curves (Fig.3). The two curves were superimposed so that the peaks of the flow rates coincided on the time axis. The mean flow rates for EPI-PC and Conv-PC were 1116±25 mm 3 /s and 1239±26 mm 3 /s respectively, and the associated coefficient of variation was 2.3% in both cases. The pulsatility indices for EPI-PC and Conv-PC were respectively 0.64 and 0.59.      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.   The VNR for EPI-PC and Conv-PC sequences, as a function of the VENC.

Discussion
In the present study, a pulse-based phantom model was used to generate a constant pulse wave with velocities similar to those of CSF and venous blood flows. Our objective was not only to check the accuracy of the mean flow rate measured with EPI-PC but also to compare the shape of the flow rate curve with that determined by Conv-PC, which had a smaller sampling interval (i.e. the gold standard). In order to compare EPI-PC and Conv-PC, the real-time flow rate signal for the EPI-PC curve was reconstructed to give the same 32-point flow rate curve as for Conv-PC.

Definition of default parameters
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 pseudosampling interval ∆ . However, for the real-time imaging with EPI-PC, the acquisition time was directly related to ∆ ; hence, increasing the sampling frequency could improve the accuracy of the reconstructed curve. The protocol's default parameters were chosen to achieve a higher sampling frequency while maintaining the accuracy of the segmentation area and flow rate measurements.
The effects of magnetic field inhomogeneity must also be taken account, since the reference tube was not positioned around the flow tube in the FOV [19,10]. Therefore, the estimated VNR in this work 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.
In single-shot EPI, all the lines in K-space are filled by switching the frequency-encoding gradient after a single excitation pulse. In contrast, for multi-shot EPI, the k-space is segmented into multiple shots, which are filled through multiple TR periods. The number of lines per segment is called the "EPI factor " or the "echo train length" and has a great influence on the sampling frequency. The single-shot EPI has a higher sampling frequency and a lower VNR, and so is more likely to be sensitive to geometric distortion [13]. The multi-shot EPI is less sensitive to geometric distortions, given the shorter readout time [21]. This is why we used a multi-shot EPI in the present study.
When the EPI factor is fixed and the number of phase-encoding lines is reduced, the sampling frequency can still be increased. With sensitivity encoding (SENSE), the reduction in phase-encoding lines depends on the number of coils used for parallel data acquisition [29]. In our experiment, the SENSE value was 2.5 for EPI-PC and 1.5 for Conv-PC.

Comparison of EPI-PC and Conv-PC
Using the default parameters, the respective flow rate measurements for the two sequences were both within the CIs and did not exceed 8% [15] (flow rate error: -2.9% for EPI-PC vs. 7.8% for Conv-PC).
With the default protocol, each EPI-PC cycle contained 10 sampling points. By comparing the reconstructed flow rate curves for EPI-PC and Conv-PC and considering a waveform similar to that observed for venous blood and CSF, the difference in the pulsatility index between EPI-PC and Conv-PC was less than 10%. The errors for the corresponding 32 points in the two curves were all within the limits of agreement (Fig. 4). Furthermore, the Conv-PC technique could use multiple pulse cycles to gradually fill a K-space for 32 phase images; hence, the flow rate curve for Conv-PC was described by only 32 characteristic points. For EPI-PC with the default parameters, only 9 or 10 characteristic points were used to describe a pulse cycle, and the reconstructed flow rate curve was smoother than that for Conv-PC.
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.

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.6).
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 and above 2.4 mm for Conv-PC), the flow rate of the two sequences began to exceed the boundaries of the CI (Fig.6). We hypothesize that a partial volume effect led to overestimation of the velocity [35,6]. As a result, the flow rate error was too large -even though the segmentation region was within the CI.
Therefore, in order to measure the flow rate accurately, the pixel size for Conv-PC should be less than 25% of the  [23,28,18]. This sensitivity was also reflected in our experiments by the pseudo-VNR (Fig.10). Using different VENC values, the VNR was much greater for Conv-PC than for EPI-PC. 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, and in order to increase the sampling frequency in the EPI-PC sequence, the SENSE value in our experiment was set to 2.5; this was 66% greater than the value for Conv-PC (1.5).
Since the VNR was higher for Conv-PC than for 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 segmented.

Limitations and perspectives
Firstly, the phantom waveform in our study was sinusoidal, whereas there are two higher-frequency harmonics (2)(3)(4) Hz) in the cerebral arterial waveform. Hence, the ability of EPI-CP to accurately quantify the arterial waveform will now have to be demonstrated in in vivo studies. Secondly, 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.

Conclusion
We used a segmentation algorithm and flow rate curve reconstruction to determine the accuracy of EPI-PC. When using the selected default parameters, the calculated error between the reconstructed EPI-PC curve and the Conv-PC curve was small. Increasing the sampling frequency gave a more detailed view of the EPI-PC sequence's curve.
Compared with Conv-PC, EPI-PC can be adapted to increase the spatial resolution but is more sensitive to VENC. An excessively small pixel size reduced the VNR and the sampling frequency, while an excessively large pixel size produced partial-volume effects and an overestimation of the flow rates.
Our study shows that setting the pixel size of the EPI-PC to 33% 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). These results provided reference values for the clinical application of EPI-PC.