Reliable phase-contrast flow volume magnetic resonance measurements are feasible without adjustment of the velocity encoding parameter

Abstract.

Purpose: To show that adjustment of velocity encoding (VENC) for phase-contrast (PC) flow volume measurements is not necessary in modern MR scanners with effective background velocity offset corrections.

Approach: The independence on VENC was demonstrated theoretically, but also experimentally on dedicated phantoms and on patients with chronic aortic regurgitation ($n=17$) and one healthy volunteer. All PC measurements were performed using a modern MR scanner, where the pre-emphasis circuit but also a subsequent post-processing filter were used for effective correction of background velocity offset errors.

Results: The VENC level strongly affected the velocity noise level in the PC images and, hence, the estimated peak flow velocity. However, neither the regurgitant blood flow volume nor the mean flow velocity displayed any clinically relevant dependency on the VENC level. Also, the background velocity offset was shown to be close to zero ($<0.6\mathrm{cm}/\mathrm{s}$) for a VENC range of 150 to $500\mathrm{cm}/\mathrm{s}$, adding no significant errors to the PC flow volume measurement.

Conclusions: Our study shows that reliable PC flow volume measurements are feasible without adjustment of the VENC parameter. Without the need for VENC adjustments, the scan time can be reduced for the benefit of the patient.

1. Introduction

The diagnosis and management of patients with cardiac diseases requires assessment of parameters of cardiac morphology and function. Phase-contrast (PC) magnetic resonance imaging (MRI) has shown to be a versatile non-invasive imaging technique, providing accurate and reproducible quantification of blood flow volumes from velocity images.¹ Nonetheless, it has previously been pointed out that the technique needs careful optimization to enable reliable velocity measurements.² For example, the velocity encoding (VENC) parameter, i.e., the scan parameter that controls the velocity sensitivity of the PC measurement, has been shown to have an influence on the velocity values of the PC image.^3–9 That is, the background velocity offset error and velocity noise level are shown to increase in the PC images when the VENC level increases. Hence, PC measurements should benefit from lower VENC settings. The dependence of the velocity noise on the VENC level makes single velocity values in the PC images sensitive to the chosen VENC level. However, measures calculated from velocity-averaged data, e.g., flow volume measures, ought not to display any dependence on the velocity noise level. The summation of a large number of velocity values over the blood vessel and the time frames of the cardiac cycle should average out variations in the velocity values due to noise. Moreover, most modern MRI scanners have implemented dedicated tools based on gradient pre-emphasis and post-processing filters for automatic correction of background velocity offset errors in the PC images.^10,11 With the implementation of such effective background correction tools, it should be possible to lower the background velocity offset error to a value below the limit of acceptance ($<0.6\mathrm{cm}/\mathrm{s}$¹²), and hence, present reliable flow volume measurements of cardiac output, shunt flow, aortic, or pulmonary regurgitation, and indirectly, of mitral regurgitation without adjustment of the VENC level.

The aim of this study was to demonstrate that VENC adjustments are not necessary for modern scanners where PC flow volume measurements are performed with effective background correction.

2. Theory

2.1. Reconstruction of PC Images from the MRI Signal

To quantify flow volumes with the PC technique, signals originating from hydrogen nuclei are encoded with magnetic field gradients into spatial frequencies and sampled as real and imaginary parts in the frequency domain using quadrature detection.¹³ Images are then reconstructed from the quadrature detected signal using the inverse discrete Fourier transform. The PC technique maps, on a pixel-by-pixel-basis, the phase difference (PD) between two MR images with different VENC levels into velocity.¹⁴ From the resulting PC images, time-averaged flow volume measures are extracted and used for the diagnosis of different heart and vessel diseases.

2.2. Probability Distribution Function of the Velocity Noise

The quadrature detected signal can be assumed to be contaminated with additive white Gaussian noise in both the real and imaginary parts.^15,16 The noise in the images can also be assumed to be additive and Gaussian since the Fourier transform used for the image reconstruction is a linear and orthogonal operator. Furthermore, the variance of the noise will be uniform over the image and the noise in the pixels can be assumed to be uncorrelated.¹⁷ Hence, the complex MRI signal can be written as

$$x(r)=m(r)+n(r),$$ (1)

where $m(r)=m_c(r)+i{m}_s(r)$ is the complex noise-free data that depends on the precession frequency, $\omega$, and time, $t$, with $m_c(r)=A\cos \omega t$ and $m_s(r)=A\sin \omega t$, and $n(r)=n_c(r)+i{n}_s(r)$ is the additive Gaussian noise contribution with $n_c(r)\sim N(0,{\sigma }^2)$, $n_s(r)\sim N(0,{\sigma }^2)$ and $\mathrm{cov}[n_c(r),n_s(r)]=0$. The signal magnitude in each pixel, $A$, and the variance of the signal in each coil element, ${\sigma }^2$, can be assumed to be equal in both the real and imaginary parts and not correlated between the quadrature channels. Then, it can be shown that the probability density function for all pixels can be written as^6,18

$$p_m(m)=\{\begin{array}{ll}\frac{2}{\sigma \sqrt{2\pi }}{e}^{(-\frac{(m^2-M^2)}{2{\sigma }^2})}{\cos }^{-1}\left(\frac{nM}{{\sigma }^2}\right)u(m)& \text{for}M>0\\ \frac{2}{\sigma \sqrt{2\pi }}{e}^{(-\frac{m^2}{2{\sigma }^2})}u(m)& \text{for}M=0\end{array},$$ (2)

where $m=2A\mathrm{\Delta }\varphi$ is the signal component of the PC image, $2\mathrm{\Delta }\varphi$ is the PD limited to $[-\pi ,\pi ]$, ${\sigma }^2=2{\sigma }^2$ is the variance, and $M$ is the magnitude mean. For $M=0$, i.e., when the image pixels are completely vitiated by noise, the phase noise displays a uniform probability density function within $[-\pi ,\pi ]$. As the signal component $M$ becomes large compared to the standard deviation (SD) $\sigma$ of the noise in each individual channel, i.e., $M\gg \sigma$, the deviation in the phase angle due to noise will be small and the probability density function can be regarded as zero-mean Gaussian distribution with variance ${(\sigma /A)}^2$.

The PC technique maps the difference in phase between two separate measurements with negative and positive VENCs into velocity according to

$$v=\frac{\mathrm{\Delta }\varphi }{\pi }·\mathrm{VENC},$$ (3)

where VENC is determined by the difference in the first gradient moment between the two different VENCs. Thus, the probability density function of the velocity can be written as

$$p_{\mathrm{v}}(v)\approx \frac{\sqrt{\pi }}{2}\frac{A}{\sigma \mathrm{VENC}}\exp [-\frac{{\pi }^2{A}^2{v}^2}{4·{\mathrm{VENC}}^2·{\sigma }^2}],$$ (4)

where the multiplicative factor $\mathrm{VENC}/\pi$ modifies the variance by the factor squared. That is, when $X$ and $Y$ are random variables, $k$ is a scaling constant, then $\mathrm{Var}\{k(X-Y)\}=k^2·\mathrm{Var}(X-Y)$ and the variance in the velocity noise, ${\sigma }_v^2$, can be described as

$${\sigma }_v^2={\left(\frac{\mathrm{VENC}}{\pi }\right)}^2\frac{2{\sigma }^2}{A^2}.$$ (5)

2.3. Effect of Velocity Averaging

The peak velocity can be extracted directly from the PC image. Moreover, measures of flow such as stroke volume, cardiac output, and aortic or pulmonary regurgitant flow volumes can be calculated based on the PC data.¹⁹ For calculation of these measures, a large number of velocity values are averaged in both space and time. When the stroke volume is calculated, for example, 100 pixels over the aorta cross-section and 40 time points over the cardiac cycle are generally averaged. Throughout the averaging process, random Gaussian errors, such as velocity noise, are dampened. It can be shown that the variance of the velocity noise decreases linearly with the numbers of measurements, $N$,

$${\sigma }_{\hat{v}}=\frac{1}{N}{\sigma }_v^2.$$ (6)

Hence, the velocity noise is expected to contribute only small errors to velocity-averaged measures, especially measures that are averaged both in space and time. To enable reliable quantification of velocity-averaged measures, however, the following condition needs to be fulfilled:

$$\mathrm{var}{[\widehat{v}-v]}^2=0,$$ (7)

but also

$$E[\widehat{v}-v]=0,$$ (8)

implying that potential velocity offsets in the PC images, e.g., due to eddy currents, should be close to zero. This further enhances the need for effective background correction.

3. Material and Methods

The study was conducted both in vitro and in vivo. The in vitro measurements were performed on a stationary phantom and on a flow phantom to demonstrate the efficiency of the background correction method, and the validity of the hypothesis. Patients with clear signs of aortic valve regurgitation (AR) were included to clinically demonstrate the validity of the hypothesis. Finally, PC measurements on one healthy subject were included in the study to visualize the effect of background velocity offset errors and the need for efficient background corrections.

3.1. Phantoms

The in vitro measurements were performed on the body phantom appurtenant to the MRI scanner for quality assurance purpose. The phantom container enclosed ${\mathrm{CuSO}}_4$-doped fluid. Using this stationary phantom, measurements of pixel values at the position of the aorta without true velocity information was enabled. Measurements were also performed on a flow phantom with a tube of diameter of 20 mm. Water with ${\mathrm{MnCl}}_2$-doping was pressed through the tube by means of a constant pressure head at different speeds, fulfilling the laminar condition $Re<2$, where Re = (flow volume rate $x$ tube diameter)/(fluid viscosity $x$ tube area). As a result, laminar velocity distributions were developed over the tube cross-section, enabling PC measurements of constant flow with well-known flow rates and velocity distributions. See Ref. 20 for more details.

3.2. Study Population

The in vivo study comprised 17 patients with chronic AR of age 32 years to 70 years (two with mild, six with moderate, and nine with severe AR, as determined by echocardiography according to guidelines²¹). Exclusion criteria were presence of an intra-cardiac shunt or any other form of cardiac disease and irregular heart rhythm. One healthy volunteer of age 24 years was also included in the study.

The study was conducted according to the Declaration of Helsinki. Ethical approval for the study protocol was given by the Regional Ethics Review Board at the region of Västra Götaland and oral and written informed consent was obtained from all participants.

3.3. MRI Scan Protocol for the in vivo Measurements

All PC measurements were performed on a 1.5 T MRI scanner (Achieva, Philips Healthcare, Best, Holland) with a dedicated cardiac coil. The measurements were performed during gentle breath-hold at end-expiration using an electrocardiography-gated through-plane gradient echo PC sequence. The scan parameters used in the PC measurements are given in Table 1. The image plane was positioned at the sino-tubular junction of the ascending aorta and all measurements were performed with the aorta and the image plane at the isocenter of the scanner.²² To demonstrate VENC insensitivity, two different VENC levels were used for each examination; one adjusted to the higher aortic flow during systole [hereafter referred to as high VENC (hVENC)] and the other adjusted to the lower aortic flow during diastole [referred to as low VENC (lVENC)]. In all hVENC measurements, the VENC level was higher than the peak blood flow velocity but did not exceed the peak velocity by more than 20%. This was ensured by the flow analysis tool implemented at the scanner console. Scans that did not fulfill the condition were rescanned after adjustment of the VENC level. The maximum diastolic velocity was also extracted from the flow analysis of the hVENC measurement and used as a reference to set the VENC level of the lVENC measurement. The VENC level of the lVENC measurement was set $10\mathrm{cm}/\mathrm{s}$ higher than the maximum diastolic velocity, accepting aliasing of the systolic flow but not of the diastolic flow. The VENC level of the lVENC measurements generally corresponded to one-third of the VENC level of the hVENC measurements. Both the hVENC and lVENC measurements were repeated twice, for determination of the inter-measurement variability.

Table 1.

Scan protocol for the different PC measurements, performed in vitro on the flow and body phantom and in vivo on the healthy volunteer and patients with chronic AR.

Parameters	Flow phantom	Body phantom	In vivo
FOV (${\mathrm{mm}}^2$)	$150\times 150$	$320\times 260$	$320\times 260$
Slice orientation	axial	oblique	oblique
Scan pixel (${\mathrm{mm}}^2$)	$2.5\times 2.5$	$2.5\times 2.5$	$2.5\times 2.5$
Reconstructed pixel (${\mathrm{mm}}^2$)	$1.25\times 1.25$	$1.25\times 1.25$	$1.25\times 1.25$
TR/TE (ms)	4.8/2.9	4.8/2.9	4.8/2.9
Bandwidth (Hz/pixel)	477.8	477.8	477.8
RF flip angel (deg)	12	12	12
Time frames/cardiac cycle	40	40	40
Acceleration factor	2	2	2
TFE factor	4	4	4
# Shots	13	13	13
NEX	1	1	1
# Scan repetitions	2: $\mathrm{VENC}=250\mathrm{cm}/\mathrm{s}$; 1: else	1: all	2: all
LPC-filter	On: all; off: all	On: all	On: all; off: one healthy and one patient

Note: FOV = field of view; TR = repetition time; TE = echo time; TFE = turbo field echo; NEX = number of excitations; LPC = local phase correction

3.4. Post Processing of the in vivo Measurements

The analysis of the in vivo PC images was performed on the dedicated workstation of the MRI scanner (Easy Vision, Philips Healthcare, Best, Holland). The analysis was performed in two steps. First, the aortic blood flow rate, i.e., the volume of flow passing through the aorta per time unit, was determined in all image frames (Fig. 1). Then, the regurgitation volume (RVol) through the insufficient aortic valve of the AR patients was calculated from the diastolic phases of the cardiac cycle. The background velocity offset error was assessed directly from the in vivo images as the mean velocity estimated in four regions of interests (ROIs) including $\sim 100\text{pixels}$ per ROI. The ROIs were drawn in stationary muscle tissue at each corner of the image (Fig. 1).

Fig. 1.

PC measurement shown as magnitude and velocity images displaying the position of the ROIs that were used for the quantification of the RVol (ROI1: at the sino-tubular junction of the aorta approximately at the isocenter of the scanner) and for the in vivo assessment of the background velocity offset (ROI2, ROI3, ROI4, and ROI5: positioned in stationary muscle at approximately 80, 90, 80, and 60 cm from the isocenter of the scanner).

3.5. MRI Scan Protocol for the in vitro Measurements

Directly following the in vivo PC measurements, in vitro measurements were performed on the stationary body phantom to determine the background velocity offset error and the velocity noise level at the position of the aorta. For this purpose, the same study protocol as in the preceding in vivo measurement was used (Table 1), including the same image slice angulation and position. An artificial heart pulse triggered the scanner during the in vitro measurements.

Flow phantom measurements were performed separately to investigate the influence of VENC in more detail. The image slice was positioned at the isocenter of the MRI scanner, orthogonal to the tube using the same scan parameters as in the in vivo measurements (Table 1), but with a smaller field of view (FOV) ($260\times 260{\mathrm{mm}}^2$) and a larger range of VENC levels (150 to $500\mathrm{cm}/\mathrm{s}$). For reproducibility estimation, one of the PC measurements ($\mathrm{VENC}=250\mathrm{cm}/\mathrm{s}$) was repeated six times. Also, phantom measurements without flow were performed to determine the background velocity offset error and velocity noise level at the position of the tube.

3.6. Post Processing of the in vitro Measurements

The analysis of the in vitro images was also performed on the dedicated workstation of the MRI scanner.

To estimate the background velocity offset error at the position of the aorta in the in vivo measurement, a circular ROI was drawn with size and position similar to the aorta in the corresponding in vitro measurement. The mean velocity within the ROI, i.e., the background velocity offset error, was then estimated. Additionally, the SD of the mean velocity within the ROI was used as an estimate of the velocity noise level.

From the flow phantom measurements, both a single velocity measure, peak flow velocity, and a velocity averaged measure, mean flow velocity, were determined. The peak flow velocity was determined as the maximum velocity value in an ROI, encircling the flow through the tube and the mean flow velocity was determined as the average of all velocity values inside the ROI. The flow volume per second through the tube area was also determined. Finally, the background velocity offset error and the velocity noise level in the flow phantom measurements were extracted from phantom images without flow using three circular ROIs; two ROIs in the stationary media to the left and right of the tube and one encircling the stationary media in the tube.

3.7. Background Velocity Offset Corrections of the PC Measurements

All phase images that were used in the reconstruction of the PC image were automatically corrected for phase offset errors due to eddy currents, Maxwell terms, and gradient field nonlinearities using the built-in methods of the MRI scanner. The pre-emphasis circuit^23,24 was used to prospectively correct for eddy-current-induced gradients.²⁵ Remaining offsets in the phase images were corrected for using a local phase correction (LPC) method with a workflow as follows. First, a weighted image, $w$, was calculated according to

$$w=\frac{12{*N}^2}{|c1|*|c2|*[{(|c1|-|c2|)}^2+6N]+12*N^2},$$ (9)

where $c1$ and $c2$ are the complex based images acquired with different flow encoding gradients before correction, and $N^2$ denotes the noise power. Second, the PD between $c1$ and $c2$ was multiplied by the weighted image, i.e., $[c1*\mathrm{conj}(c2)]*w$. Third, a complex-phase corrected image was calculated by averaging the local phase for each pixel with a two-dimensional uniform convolution operator with window size comparable to the width of the blood vessel. Finally, the PD was obtained as

$$\mathrm{PD}=\arg [c1*\mathrm{conj}(c2*I)],$$ (10)

where $c2*I$ is the phase-corrected image for $c2$. Finally, the background velocity offset error was calculated only from phase offsets in a pixel that was expected to be part of the static background using higher weights on pixels that were expected to contain flow, assuming that pixels with flow have $|c1|\ne |c2|$.

To determine the effectivity of the LPC method in reducing the background velocity offset errors in the PC measurements, the flow phantom measurements were performed also with the LPC filter switched off. Moreover, one of the patients and one of the healthy volunteers were scanned without application of the LPC filter to demonstrate the effectivity of the correction method in vivo.

3.8. Statistical Data Analysis

All statistical analyses were performed using MATLAB. For the in vivo data, significant differences between the hVENC and lVENC measurements in RVol and in the coefficient of variation (CV) of RVol were determined using the Wilcoxon signed-rank test, where $p<0.05$ was considered significant. Agreement between the hVENC and lVENC measurements in RVol was evaluated using the Bland–Altman method. The background velocity offset level, determined in stationary muscle at four different positions were compared statistically for the hVENC and lVENC measurements using the Friedman test to determine the overall $p$-value ($p<0.05$ was considered significant) followed by a post-hoc analysis using a Wilcoxon signed-rank test where the initial null hypothesis was rejected. After adjustments for multiple test using the Bonferroni correction, $p<0.013$ was considered significant.

Linear regression analysis of the flow phantom data was performed to determine the correlation between the VENC level and the peak and mean flow velocity. Correlation analyses between the VENC level and the background velocity offset error and velocity noise level were also performed. The significance of the correlations was determined with post-hoc analysis using the Wilcoxon signed-rank test where the initial null hypothesis was rejected ($p<0.05$ was considered significant). Significant differences between the hVENC and lVENC measurements in the estimated background velocity offset were determined using the Wilcoxon signed-rank test, where $p<0.05$ was considered significant.

4. Results

4.1. In vitro Measurements

Figure 2 shows the velocity noise level, given as the SD of the velocity for different VENC levels. For comparison, the peak and mean flow velocity, and the flow volume are plotted in the same figure. The velocity noise level, measured in the flow phantom, scaled linearly with the VENC level [Fig. 2(a): $y=0.06x+1.7$, $R=0.9996$, $p<0.001$]. This was also confirmed by the body phantom measurements [Fig. 2(b)]. That is one-third reduction in VENC level between the hVENC and lVENC measurements corresponded to one-third reduction in the SD of the velocity ($p<0.001$). Due to its intrinsic sensitivity to velocity noise, the peak flow velocity increased with increased VENC level [Fig. 2(a): $y=0.07x+73.8$, $R=0.87$, $p<0.001$] and displayed poor reproducibility ($\mathrm{CV}=17\%$), as shown by the large error bar in Fig. 2(a). However, the mean flow velocity and the flow volume, which is a scaled version of the mean velocity, did not show any dependence on the VENC level and displayed high reproducibility [CV 3%; Fig. 2(a)].

Fig. 2.

(a) The velocity noise level (blue), given as the standard deviation of the velocity (SDv), and the peak velocity (peakv; red), mean velocity (meanv; green), and flow volume (Q; gray) measured in the flow phantom, for different VENC levels before (crosses) and after application of the LPC-filter (circles). Error bars represent the SD of the mean for six repeated measurements. (b) The velocity noise level, given as SDv at the position of the aorta in the body phantom, for the high (hVENC) and lVENC measurements.

The background velocity offset error displayed a dependence on the VENC level (Fig. 3). With application of the LPC-filter, however, the increase in the background velocity offset error was very small and not clinically significant. Even for the highest selectable VENC setting ($500\mathrm{cm}/\mathrm{s}$), both the flow and body phantom measurements showed an error ($0.5\mathrm{cm}/\mathrm{s}$) below the limit of acceptance ($<0.6\mathrm{cm}/\mathrm{s}$¹²).

Fig. 3.

(a) The background velocity offset, assessed in the flow phantom without flow, before (crosses) and after application of the LPC-filter (circles) for different VENC levels and measurement positions (green = at the center of the image; red = to the left; yellow = to the right; and blue = mean ± SD for all positions). (b) The background velocity offset (circles), assessed in the stationary body phantom for the hVENC and lVENC measurements. (c) The in-vivo-assessed background velocity offset levels for the lVENC and hVENC measurements measured in ROI2 (green diamond), ROI3 (blue square), ROI4 (yellow triangle), and ROI5 (purple circle), where the ROI positions are given in Fig. 1.

4.2. In vivo Measurements

Figure 4 shows the importance of effective background correction for reliable flow volume quantification, demonstrated by the PC measurements on one healthy volunteer and one of the AR patients. The large error contribution from the background velocity offset without correction resulted in an unrealistic flow rate curve for the healthy volunteer with a clearly visible systematic flow rate bias at the diastolic phases of the cardiac cycle. After correction, a more realistic flow rate curve with no systematical bias was found, demonstrating the effectivity of the LPC method. Without the correction, the background velocity offset error was large ($\sim 2.5\mathrm{cm}/\mathrm{s}$) and added a positive bias to the measurement that resulted in an overestimation of the systolic blood flow volume of $\sim 7\mathrm{ml}$ and an underestimation of RVol of $\sim 10\mathrm{ml}$ in the AR patient.

Fig. 4.

Visualization of the background velocity offset in the PC images (a) before and (b) after application of the LPC-filter. The flow-rate-versus- time-curves for (c) a healthy volunteer and (d) a patient with severe chronic AR (crosses) and after application of the LPC-filter (circles).

When the background velocity offset error was determined in vivo in muscle tissue at some distance from the aorta [Fig. 3(c)], it was slightly higher than the limit of acceptance ($0.6\mathrm{cm}/\mathrm{s}$) and showed an increment with the distance from the aorta. The highest value was obtained in ROI3 at the largest geometrical distance from the aorta and the lowest value was obtained in ROI5 at the shortest distance. Subsequent head to head comparisons of background phase offset errors between different ROI positions gave for the hVENC measurements; ROI3-ROI2: $p<0.001$, ROI3-ROI5: $p<0.001$, lVENC ROI3-ROI5: $p=0.002$.

Figure 5 shows the estimated RVol in patients with chronic AR for different VENC levels. A large spread in RVol was seen between individual patients, but no significant differences in RVol and in CV of RVol regarding the choice of VENC level were detected ($p>0.05$). The RVol was $57.2\pm 3.4$ and $53.7\pm 1.1\mathrm{ml}$ for hVENC and lVENC, respectively. The CV of RVol was $22.2\pm 20.1$ and $16.0\pm 21.3\%$ for hVENC and lVENC, respectively. Similarly, Bland–Altman plots showed only a small discrepancy in RVol between the hVENC and lVENC measurements and no dependence on RVol (Fig. 6).

Fig. 5.

The RVol in patients with chronic AR for the hVENC and lVENC measurements. Gray dots visualize the mean of the repeated measurements of each subject and black dots visualize the mean of all subjects. Error bars, showing the SD of the mean propagated from repeated measurements in individual subjects, was smaller than the symbols.

Fig. 6.

Bland–Altman comparison of the RVol in patients with chronic AR for the hVENC and lVENC measurements. Dashed lines represent 95% limits of agreement and the solid line represents the mean difference between the hVENC and lVENC measurement.

5. Discussion

This study clearly demonstrated that reliable PC flow volume MRI measurements are feasible on modern scanners without adjustment of the VENC parameter. Consequently, there is no need for multiple adjustments of the VENC level as long as VENC is chosen somewhat higher than the actual peak flow velocity, ensuring no artifacts due to velocity aliasing are present in the images.

With the use of PC MRI, information about the blood flow is obtained from subtracted scans with different flow encoding gradients. The scan subtraction eliminates phase errors due to magnetic field inhomogeneities and susceptibilities. However, Eddy currents,^5,26,27 Maxwell terms,²⁵ and gradient field nonlinearities²⁸ can still give residual phase offsets after subtraction. Such offsets can be detected in static background tissue as they display a spatially flat behavior with slowly varying offset over the image. If uncorrected, the velocity errors can significantly distort the flow volume estimation. That is, even small systematic inaccuracies in the velocity can propagate into large errors when calculating the flow volume.^12,29,30 Eddy currents are induced by the rapid switching of the VENC gradient. The switching changes the magnetic flux and induces currents in the conducting parts of the MR scanner, including the gradient coils. As a result, linear or higher-order velocity offsets will be distributed over the PC image.^27,29 In this study, the PC measurements with hVENC level utilized stronger VENC gradients per time unit, resulting in a larger eddy current effect and thus larger velocity offsets as shown by Fig. 3.

The phase error of a pixel can be estimated from the phase of the neighboring pixels. The slowly varying phase behavior of eddy currents, Maxwell terms, and gradient field nonlinearities was exploited by the LPC method to correct for these background errors (see “background velocity offset corrections of the PC measurements”). The effectivity of the background correction method was validated quantitatively both in vitro and in vivo. The effectiveness of the method was also displayed qualitatively as flow rate curves for an AR-patient and a healthy volunteer, where more realistic curves with no visible systematical biases were shown after correction.

While comparisons with other background correction methods were out of scope of this study, concluding that VENC adjustments are not needed as long the method provides sufficient velocity offset correction, it is worth mentioning that similar post-processing methods previously have been presented by others.^27,31–33 Walker et al.²⁷ presented a semi-automatic method that utilizes a linear surface fit for estimation of the phase-offset error in non-stationary pixels. Moreover, Rigsby et al.³² showed improvement in the quantification of the main pulmonary artery flow relative to the combined right and left pulmonary artery flow using an optimized method for automatic correction of linear offset effects based on the work by Lankhaar et al.³¹ Furthermore, Tan et al.³⁴ presented a promising self-calibrated, nonlinear PC correction method that provides superior results compared to linear-only correction. In comparison to linear methods, their method seemed to display a larger number of accurate pixels at a longer distance from the great vessels of the heart and, hence, seems to be promising for PC measurements in more distal blood vessels.

It is well known that the PC measurement is sensitive to background velocity offsets caused by eddy currents, Maxwell terms, and gradient field nonlinearities resulting in severe degradation of the PC image and inaccurate velocity quantification. Therefore, methods for correction of background velocity offset errors are implemented in most modern MRI scanners. In older scanners, however, methods for effective correction of velocity offsets are lacking or even absent, leading to inaccurate flow volume quantifications and subsequently to false conclusions regarding the disease severity.^7–9,12 This is of course serious as it may result in inappropriate patient care. Hence, quality control procedures and validation activities are of great importance to assure diagnostic reliability of PC measurements.

The validation of the background velocity offset correction method can preferably be performed with a static body phantom, similarly to the body phantom used in the present study. With such phantom, the background velocity offset error can be estimated at the position of the aorta. The background velocity offset error was also extracted from in vivo measurements and was determined in terms of mean velocity in stationary muscle tissue. This quality control procedure has been recommended by Ref. 35 and is commonly used for assessment of the background velocity offset error in clinical routine. In this study, however, the measured background velocity offset in muscle tissue at some distance from the aorta was shown to be slightly higher than the offset at the position of the aorta and, hence, did not reflect the relevant background velocity phase offset error. In MRI scanners displaying non-conservative results, significant background velocity phase offset errors could be undetected using such quality control procedure. We, therefore, encourage phantom quality control measurements to validate the performance of a background correction method at the region of interest.

As expected, present work demonstrated high dependence of the VENC level on the peak flow velocity (Fig. 2). This can be explained by its dependence on the velocity-to-noise-ratio. Provided that the maximum velocity of the blood flow is lower than the VENC level, the SNR of the PD is shown to be proportional to the SNR of the corresponding modulus image and the peak velocity in relation to the VENC level, as shown by Eq. (5). This implies that a hVENC level will give rise to a lower phase SNR, i.e., a smaller PD with the same phase variation and, thus, a larger variation in the estimated velocity, which, in turn, will result in a higher peak velocity estimate. Hence, individual adjustments of the VENC level for increased velocity-to-noise-ratio are beneficial when PC measurements are used for peak velocity estimations. The same requirement also applies to quantifications based on single velocity values, such as stream-line and vessel strain quantifications. For that purpose, variable VENC methods, which adapt the VENC level to the variation of the flow velocity over the cardiac cycle and thereby optimizes the velocity-to-noise ratio for all cardiac phases should be used.^36–38 On the other hand, our findings demonstrate that high velocity-to-noise-ratio is of less importance for the quantification of velocity averaged measures [Fig. 2(a)]. Averaging of all velocities over the vessel area for calculation of the mean velocity and also over the time frames of the cardiac cycle for calculation of the flow volume reduces the variations in the velocity values due to noise. As a result, individual adjustment of the VENC level is not a requirement for reliable assessments of cardiac output, shunt flow, aortic or pulmonary regurgitation, and indirectly, of mitral regurgitation. Also, the VENC level can be chosen somewhat higher than what is conventionally done in the clinic, ensuring that no velocity aliasing artifacts are present in the PC images. This is of value in the clinical setting as VENC adjustments are rather time-consuming and prolong an already extensive examination protocol. In our clinic, we estimate that the reduction in acquisition time as compared to acquisitions with VENC adjustment would be $\sim 4\min$ for a conventional cardiovascular evaluation and up to 15 min for a functional hemodynamic aortic coarctation evaluation, including several PC measurements at the ascending aorta, and at the thoraco descending aorta, abdominal aorta, and pulmonary artery. Also, minimizing the examination time and thereby reducing the load on the patient may be of value from an image quality perspective as the PC measurements are performed at the end of the cardiac examination when the patient usually is tired and less cooperative. However, this remains to be confirmed in future studies.

Present study was limited by the small number of patients. Also, only individuals with chronic AR were included in the patient cohort. However, the patient cohort was suitable to validate the in vitro findings and to strengthen the conclusions of the study. The AR patients displayed a large variation in flow rate values over the cardiac cycle, from large positive systolic flow to small negative diastolic flow and, thus, enabled investigation of both large and small VENC-to-velocity conditions for quantification of relevant flow volumes, i.e., RVol.

6. Conclusions

This study shows that reliable PC flow volume measurements are feasible without adjustment of the VENC parameter. The background correction methods implemented in the present scanner gave PC images with background velocity offsets close to zero. With such effective correction methods, the velocity-averaged measures, i.e., mean flow velocity and regurgitant flow volume, showed no dependence on the VENC level. Without the need for VENC adjustments, scan times can be reduced for the benefit of the patient.

Biography

Biographies of the authors are not available.

Disclosures

No conflicts of interest, financial or otherwise, are declared by the authors.