Fold-Over Oversampling Effects in the Measurements of Cerebral Cerebrospinal Fluid and Blood Flows with 2D Cine Phase-Contrast MRI

This prospective study investigated the effects of fold-over oversampling on phase-offset background errors with 2D-Cine phase contrast (Cine-PC) magnetic resonance imaging (MRI). It was performed on brain MRI and compared to conventional Full-field of view FOV coverage and it was tested with two different velocity encoding (Venc) values. We chose Venc = 100 mm/s to encode cerebrospinal fluid (CSF) flows in the aqueduct and 600 mm/s to encode blood flow in the carotid artery. Cine-PC was carried out on 10 healthy adult volunteers followed simultaneously by an acquisition on static agar-gel phantom to measure the phase-offset background errors. Pixel-wise correction of both the CSF and the blood flows was calculated through 32 points of the cardiac-cycle. We compared the velocity-to-noise ratio, the section area, the absolute and the corrected velocity (peak; mean and minimum), the net flow, and the stroke volume before and after correction. We performed the statistical T-test to compare Full-FOV and fold-over and Bland–Altman plots to analyze their differences. Our results showed that following phase-offset error correction, the blood stroke-volume was significantly higher with Full-FOV compared to fold-over. We observed a significantly higher CSF mean velocity and net flow values in the fold-over option. Compared to Full-FOV, fold-over provides a significantly larger section area and significantly lower peak velocity-offset in the aqueduct. No significant difference between the two coverages was reported before and after phase-offset in blood flow measurements. In conclusion, fold-over oversampling can be chosen as an alternative to increase spatial resolution and accurate cerebral flow quantification in Cine-PC.


Introduction
Flow-encoding 2D-Cine phase-contrast (Cine-PC) magnetic resonance imaging (MRI) has growing interest in cerebrospinal fluid (CSF) and blood flow assessment. It has the capability to measure the peak and mean flow velocities and volumes through the entire cardiac cycle. These underlying flow information and dynamic parameters can be used to grade the severity of hydrocephalus pathologies and cerebrovascular artero-venous dysfunctions. CSF and blood flow quantifications have been successfully performed in the aqueduct [1] and the artero-venous systems [2]. These measurements allow for a better understanding of the brain hydro/hemo dynamic related to hydrocephalus intracranial hypo/hypertension [3] and posterior fossa cystic mal-formations [4]. Recent Cine-PC study on healthy controls has demonstrated a regression of blood flow and velocity with age [2]. It has been successfully applied to reproduce the distribution of blood flow in the branches of the circle of Willis with age [5].  . ∆ . 2 (2) Flow mapping images or phase-differences ( Figure 1C) result from the subtraction of two datasets. The first dataset is acquired with bipolar phase-encoding gradients in a specific direction (inferior-superior, left-right, or anterior-posterior) and the second is obtained by toggling these bipolar gradients to acquire the same image in the opposite direction (respectively, superiorinferior, right-left, posterior-anterior). The axis of the bipolar direction is user defined, and it can be chosen in any of the three physical axes or all combined together. In this phase-difference technique, the term φ(n) cannot be merely neglected and must be accounted for. In fact, the unpredictable behavioral of phase-shift in each acquired image might affect the flow mapping dataset.

Image Acquisition
The study was performed on a 3T Achieva dStream scanner (Philips Healthcare, Best, The Netherlands) equipped with a gradient strength G0 = 40 mT/m and a slew-rate SR = 200 T/m/s. The imaging parameters were: Cine-PC fast-field-echo (FFE) sequence, Cartesian filling with flow-compensation, Sense = 1.5, flip angle = 30°, and a 2 mm slice thickness. A comparative list of the imaging parameters between the two schemes is given in Table 1. An axial oblique slice was prescribed perpendicular to the aqueduct with a through plane Venc value of 100 mm/s to encode CSF flow velocity ( Figure 1). For blood flow analysis, we chose the internal carotid artery (ICA) and Venc = 600 mm/s. The slice was prescribed perpendicular to the ICA at the level of the cervical spine C2-C3. Choosing either the jugular vein or the vertebral artery would answer the questions raised by this investigation. Since the main purpose of this study was to mimic the phase-offset errors on blood flow, there was no need to assess the total cerebral blood flow. The coverage-based Flow mapping images or phase-differences ( Figure 1C) result from the subtraction of two datasets. The first dataset is acquired with bipolar phase-encoding gradients in a specific direction (inferior-superior, left-right, or anterior-posterior) and the second is obtained by toggling these bipolar gradients to acquire the same image in the opposite direction (respectively, superior-inferior, right-left, posterior-anterior). The axis of the bipolar direction is user defined, and it can be chosen in any of the three physical axes or all combined together. In this phase-difference technique, The term ϕ(n) cannot be merely neglected and must be accounted for. In fact, The unpredictable behavioral of phase-shift in each acquired image might affect the flow mapping dataset.

Image Acquisition
The study was performed on a 3T Achieva dStream scanner (Philips Healthcare, Best, The Netherlands) equipped with a gradient strength G 0 = 40 mT/m and a slew-rate SR = 200 T/m/s. The imaging parameters were: Cine-PC fast-field-echo (FFE) sequence, Cartesian filling with flow-compensation, Sense = 1.5, flip angle = 30 • , and a 2 mm slice thickness. A comparative list of the imaging parameters between the two schemes is given in Table 1. An axial oblique slice was prescribed perpendicular to the aqueduct with a through plane Venc value of 100 mm/s to encode CSF flow velocity ( Figure 1). For blood flow analysis, we chose the internal carotid artery (ICA) and Venc = 600 mm/s. The slice was prescribed perpendicular to the ICA at the level of the cervical spine C2-C3. Choosing either the jugular vein or the vertebral artery would answer the questions raised by this investigation. Since the main purpose of this study was to mimic the phase-offset errors on blood flow, there was no need to assess the total cerebral blood flow. The coverage-based comparison involved: (1) a full coverage of the whole head, referred as Full-FOV, and (2) a small FOV referred to as fold-over oversampling to remedy for aliasing. The experiments were performed on ten healthy volunteers with informed consent. The group included Diagnostics 2020, 10, 387 4 of 13 ten controls (25-55 years of age, five females) recruited in our university hospital. The inclusion criteria were no history of any neurologic disorder, or neurological development, or head trauma, and could hold still in the scanner. For the purpose of our study, a static phantom was filled with 3 L of water solidified with commercial 16 g of agar powder and 1 kg of sugar. Simultaneously after each acquisition from the volunteers, The phantom was scanned using the same imaging parameters and slice positions to measure the static phase-offset errors.

Image Processing and Analysis
We analyzed the VNR, The mean, The peak, and the minimum velocity-offset measured on the static phantom (V peak offset , V mean offset , V min offset ). On each of the ten volunteers, we quantified the mean, peak, and minimum absolute (i.e., uncorrected) velocities (V peak , V mean , V min ). We extracted the aqueduct and the ICA section areas (mm 2 ), The absolute net flows (Q Net ), and the stroke volume (SVol). The final step aimed to correct the variables measured on the volunteers through baseline subtraction of the phase-offset errors measured on the static phantom. We calculated V peak corr , V mean corr , V min corr Q Net corr , and SVol corr as follows: where R stands for peak, mean, min, or Net; X stands for Velocity (V), net flow (Q), or stroke volume SVol. These flow measures were processed with a semi-automatic delineation of the section areas through the entire cardiac cycle.
The paired 2-tailed T-test statistical test was carried out to analyze the differences between Full-FOV and Fold-Over for each dynamic variable. The Pearson bivariate test (SPSS v22, IBM Chicago, IL) was performed to assess the correlations of these variables measured with the two coverage options. Bland-Altman plots were generated to test the lower and upper limit of differences and agreements between Full-FOV and fold-over. These statistical analyses were performed for the 2 prescribed Venc.

Results
Similar patterns of corrected mean velocity values (V mean corr ) were observed in both coverage modes (Full-FOV and fold-over) with the two Venc values ( Figure 2). Following phase-offset error correction, there were significant differences in the CSF flow mean velocity (V mean , p = 0.009) and the CSF net flow volume (Q Net , p = 0.02) with a fold-over option. These differences were not significant with Full-FOV coverage. No difference was recorded in the ICA blood flow ( Table 2). The main significant results and most important findings are detailed in Table 2.
Diagnostics 2020, 10, 387 5 of 13 with Full-FOV coverage. No difference was recorded in the ICA blood flow ( Table 2). The main significant results and most important findings are detailed in Table 2.

Section Area
The ICA section area was not significantly different between the two coverage options (Full-FOV vs. fold-over). The aqueduct section area was significantly higher (p < 0.01) using fold-over (3.74 ± 1.30 mm 2 ) compared to Full-FOV (2.86 ± 0.98 mm 2 ) ( Table 3). There were strong correlations between the two coverage options in the ICA section areas (r = 0.80, p = 0.006) and the aqueduct section area (r = 0.91, p < 0.001) ( Table 4). Table 3. Differences between Full-FOV and fold-over. Results of the measurements achieved to compare Full-FOV and fold-over. Bilateral paired statistical t-test was performed to compare the two coverage options (threshold p < 0.05). The bold means p < 0.05. These are performed in the aqueduct (Venc = 100 mm/s) and the internal carotid artery (Venc = 600 mm/s) and are displayed by their mean and standard deviation values. The variables are: velocity-to-noise ratio (VNR), section area of the aqueduct and the internal carotid artery, phase-offset on phantom (mean velocity = V mean offset , peak or maximum velocity = V peak offset , minimum velocity = V min offset ), volunteers' native measures (mean = V mean , peak = V peak , minimum = V min , net flow = Q Net, stroke volume = SVol), volunteers' measures following phase-offset phantom correction (mean velocity = V mean corr , peak or maximum velocity = V peak corr , minimum velocity = V min corr , net flow = Q Net corr , stroke volume = SVol corr ).  The bias (B) was calculated as M x (variable differences between the two methods)/(variable)], r stands for the Pearson correlation coefficient and p refers to the significance threshold vale and was set to 0.05. The bold means p < 0.05. The variables are: velocity-to-noise ratio (VNR), section area of the aqueduct and the internal carotid artery, phase-offset on phantom (mean velocity = V mean offset , peak or maximum velocity = V peak offset , minimum velocity = V min offset ), volunteers' native measures (mean = V mean , peak = V peak , minimum = V min , net flow = Q Net, stroke volume = SVol), volunteers' measures following phase-offset phantom correction (mean velocity = V mean corr , peak or maximum velocity = V peak corr , minimum velocity = V min corr , net flow = Q Net corr , stroke volume = SVol corr ).

Velocity-to-Noise Ratio (VNR)
Higher, but non-significant VNR was measured in fold-over compared to Full-FOV with the two Venc values. The VNR measured in the aqueduct with fold-over correlates significantly with that of Full-FOV (r = 0.68, p = 0.03) ( Table 4).
3.3. V peak , V peak offset , and V peak corr Compared to Full-FOV, The fold-over option provided significantly lower CSF peak velocity offset (V peak offset ) (p = 0.03) (Figure 3). The absolute peak velocity (V peak ) measured in the aqueduct and in the ICA did not differ statistically (Table 3). Similarly, we did not observe any significant difference in the corrected peak velocity (V peak corr ), neither in the CSF nor in the blood flow (Table 3). V peak offset measured with fold-over correlated significantly ( Table 3) with that of Full-FOV in the ICA blood flow (r = 0.68, p = 0.030) and in the aqueduct CSF flow (r = 0.81, p = 0.005). A strong correlation between the two coverage options was observed in the V peak of the blood flow (r = 0.66, p = 0.039) ( Table 3) and V peak Corr in the CSF flow (r = 0.90, p < 0.001).
Diagnostics 2020, 10, 387 8 of 13 Figure 3. These comparative plots represent the measures for each volunteer. The graphs demonstrate the differences between Full-FOV and fold-over when we measured the peak velocity offset in the aqueductal CSF (A) and the internal carotid artery blood (B). We also show the difference in flow mean velocity following phase-offset correction in the aqueduct CSF (C) and internal carotid arterial blood (D).

Vmean, Vmean offset , and Vmean corr
Lower, but non-significant mean velocity offset (Vmean offset ) value was measured with the fold-over option and the two Venc values. The volunteers' mean velocity (Vmean) did not statistically differ in the CSF flow or blood flow. Following phase-offset correction, we did not observe any significant difference in the corrected mean velocity (Vmean corr ) in the CSF or in blood flow (Table 3). There were significant correlations (Table 3) between the two coverage options in the Vmean offset of ICA blood (r = 0.84, p = 0.002) and aqueduct CSF (r = 0.75, p = 0.012).

Vmin, Vmin offset , and Vmin corr
Lower, but non-significant minimum velocity offset (Vmin offset ) was measured with fold-over Figure 3. These comparative plots represent the measures for each volunteer. The graphs demonstrate the differences between Full-FOV and fold-over when we measured the peak velocity offset in the aqueductal CSF (A) and the internal carotid artery blood (B). We also show the difference in flow mean velocity following phase-offset correction in the aqueduct CSF (C) and internal carotid arterial blood (D).

V mean , V mean offset , and V mean corr
Lower, but non-significant mean velocity offset (V mean offset ) value was measured with the fold-over option and the two Venc values. The volunteers' mean velocity (V mean ) did not statistically differ in the CSF flow or blood flow. Following phase-offset correction, we did not observe any significant difference in the corrected mean velocity (V mean corr ) in the CSF or in blood flow (Table 3). There were significant correlations (Table 3) between the two coverage options in the V mean offset of ICA blood (r = 0.84, p = 0.002) and aqueduct CSF (r = 0.75, p = 0.012).

V min , V min offset , and V min corr
Lower, but non-significant minimum velocity offset (V min offset ) was measured with fold-over option using the two Venc values. The volunteers' minimum velocity (V min ) did not statistically differ in CSF flow or in blood flow. Following phase-offset correction, we did not observe any significant difference in the corrected minimum velocity (V min corr ) in CSF flow or in blood flow (Table 3). There were significant correlations between the two coverage options (Table 4)

Q Net and Q Net corr
The comparison between the two coverage modes did not record any significant difference in the net flow volume (Q Net ) in CSF or in blood (  (Table 4).

SVol, and SVol corr
In the aqueduct CSF flow, The comparison between Full-FOV and fold-over demonstrated that there was no significant difference in the stroke volume before or after phase-offset correction (SVol, SVol corr ). The ICA blood SVol and SVol corr were not significantly different when comparing the two coverage options. Significant correlations between Full-FOV and fold-over were observed in the ICA blood flow SVol and SVol corr (Table 4).

Discussion
This study aimed to investigate the effects of fold-over oversampling compared to Full-FOV coverage in the assessment of CSF and blood flow dynamics with Cine-PC MRI. We demonstrated that the VNR, The mean velocities, The net flows, and the stroke volumes were not significantly different. This was observed with two different Venc values (100 and 600 mm/s) prescribed respectively at the level of the aqueduct and the internal carotid artery. Following phase-offset corrections, we recorded significantly higher blood flow stroke volume with Full-FOV mode. In the CSF flow, we noticed that following phase-offset correction, The net flow volume and the mean flow velocity were significantly higher. The fold-over option provides a significantly lower V peak offset in the aqueduct CSF flow.
However, V peak and V peak corr were not significantly different. Given the important contribution of concomitant gradient fields and eddy-current induced offsets to overall phase errors, particularly with low Venc and oversampling coverage, there is a need to explicitly subtract these from Cine-PC data.
In cardiovascular MRI, phantom corrections of blood flow measurements often resulted in clinically significant changes. Following phase-offset correction, The flow measurements in patients with known or suspected congenital heart disease have shown that up to 12% of Fallot patients have been reclassified according to the severity of the pulmonary regurgitation [12]. Another study pointed out that 13% to 48% of flow measurements were sufficiently affected by phantom correction, enough to potentially alter clinical management [13]. Intracranial blood and CSF flow velocities were lower than those of cardiovascular systems and they require reduced velocity sensitivity compared to that prescribed in CMR (>2000 mm/s), hence stronger flow encoding gradients are needed. This involves more contribution of eddy-currents and Maxwell-effects in the inaccuracy and the oscillation of the measured values. It has been shown that velocities measured with lower Venc are more susceptible to errors from intra-voxel dephasing and are of concern when quantifying CSF or cerebrovascular flows [14][15][16]. The lower values reported by non-corrected measures resulted from an increased noise, which led to erroneous velocity measurements, particularly in regions of slow flow. This is in line with previous studies showing that an automatic phase unwrapping often failed to correct for phase errors with a low Venc [13,17]. Compared to Full-FOV, fold-over oversampling significantly increased CSF V peak offset . The impact of velocity-offset correction led to higher CSF and blood net flow values (Q Net corr > Q Net ). This highlights the importance of such correction to better rate patients with altered cerebral hydrodynamic and/or hemodynamic. Recent studies on idiopathic normal pressure hydrocephalus have shown that there was a reversed Q Net direction compared to the healthy controls [18], or patient following surgical shunt [19]. Other studies have shown no difference in terms of Q Net magnitude and directions [20]. An error of approximately ±10% in Q Net in aqueductal flow rate was reported as acceptable [21], nevertheless a decrease of such errors is mandatory. The outcome is a better evaluation of complex cerebrovascular diseases such as arteriovenous malformations and alteration of the CSF hydrodynamic seen in hydrocephalus. Overall, The measurements of blood and CSF Q Net showed a good correlation between Full-FOV and fold-over and the values were within acceptable limits of agreements. Many errors influence the quantification of Cine-PC parameters. These could be generated by any of the following: VNR, inflow effects, changes in the pulsatility, physiological factors, and partial volume effects. A caveat of these quantifications is that inter-variability might be larger than intra-variability in both patients and healthy control subjects [22]. Higher spatio-temporal resolution is critical for such applications to better delineate the ROI and to enhance the accuracy of these measurements over the entire cardiac cycle [19,20]. The trade-off is an increase of eddy-currents effects and gradient non-linearities that result from gradient field inhomogeneity. These small systematic inaccuracies seen in individual cardiac phase might be of concern when they propagate to the entire cardiac cycle. The fold-over option might be a compromise between higher spatial resolution and phase-offset errors. When Cine-PC is performed to measure CSF flow in the aqueduct (diameter~2 mm), The fold-over oversampling option provides significantly a larger section area compared to Full-FOV. A better delineation of the aqueduct section area achieves accurate CSF measurements through a reduction in the partial volume effects, while inaccurate delineation of the aqueductal section area might lead to ±23.1% variations in Q Net using high spatial resolution [23]. For cerebrovascular blood flow assessment, The fold-over option is similar to Full-FOV with regard to the section area and does not impact the delineation.
VNR is inversely proportional to the magnitude of Venc, hence when Cine-PC is performed to measure flow with a low velocity dynamic range (cerebrovascular blood or CSF), The prescribed Venc produces relatively high VNR in the targeted flow region [24]. In this investigation, The two different coverages demonstrated that there was no statistical difference in VNR, thus fold-over should not be selected solely for the purpose of increasing VNR value.
The higher CSF SVol corr recorded with fold-over in the aqueduct resulted from an increase in both the section area and the V mean corr . Previous study by Yoshida et al. (2009) pointed out that low spatial resolution overestimated SVol due to partial volume effects and larger section area [21]. Other investigators stipulated that aqueductal SVol was more sensitive to inaccuracies from the calculation of V mean , rather than manual delineation of the section area [19]. In our study, we showed that the fold-over option provided a larger (respectively smaller) section area, and SVol was higher (respectively lower).
Our results demonstrated that fold-over overcomes wrap-around artifact and decreases inaccuracy [23], thus it can be activated with the need for background phase-offset compensation.
The trade-off is a slight increase in both TE and TR. The difference reported between fold-over and Full-FOV is mainly related to the acquisition mode and not the imaging parameters. The activation of this mode is questionable for Cine-PC, even if a specific protocol optimization is required to increase SNR and VNR.
Our results showed a complex behavior of phase-offsets depending on Venc, scan time, first order moments, gradient amplitude, and slew-rate. As such, velocities measured with lower Vencs are more susceptible to errors from intra-voxel dephasing [14]. Knowing the interaction between hemodynamics and hydrodynamics, a modification of any variable generates a derivative change in intracranial volume that leads to a temporal modification of intracranial pressure [25]. These small variabilities might draw a line between low-to-mild, or mild-to-severe alteration in idiopathic intracranial hypertension, Chiari malformation, normal pressure hydrocephalus, or cerebrovascular stenosis [26]. Future clinical works are required to determine the effect of phantom corrections on these pathologies. Future research directions might be an extension of this study to involve other centers to include all major vendors and different gradient strengths. By achieving this, we will have a broader approach to phase-wraparound artifact and the effects on the quantification of brain hemodynamics with PC-MRI.
The present study has few limitations. First, we assumed constant SNR value over the cardiac cycle, hence the effect of the phase dispersion and noise level in the measurement of VNR was neglected, which is a potential limitation. Our aims were to assess the differences between Full-FOV coverage and fold-over using two Venc values to encode the CSF and the blood flow dynamics and not to study the overall cerebrovascular system. For this reason, we included the background phase correction for a single artery and not for all of them. We only included a group of 10 healthy controls. Statistical analysis of the fold-over effect using two Venc values requires a larger cohort. Finally, The lack of a gold standard technique to measure true flow values on healthy control subjects, to which the Cine-PC values with and without phantom correction could be compared, is another significant limitation to this study.

Conclusions
We showed that spatiotemporal phase differences vary significantly depending on structure area and Venc values. This underlies the needs for protocol-specific calibration measurements and phase-offset correction. The clinically available gradient mode runs with standard derating of gradient performance in order to decrease inaccuracies, and both coverage options still suffer from spatially varying background phase-offset due to eddy-currents and concomitant magnetic field that deteriorate the quantification of cerebral flow in Cine-PC. Compared to full coverage, fold-over oversampling is an alternative to increase spatial resolution and provides comparable flow quantification values. This option can be selected with Cine-PC phase-difference reconstruction when low Venc values are prescribed for the assessment of cerebral brain flows.

Acknowledgments:
We would like to express our acknowledgments to David Chechin from Philips Healthcare France for setting the sequences.

Conflicts of Interest:
The authors declare no conflict of interest.