4D Flow phase contrast MRI acquisitions inherently require an estimate of background phase to remove phase contributions from non-velocity based components. Traditionally, this measurement is acquired once during each cycle of velocity encoding steps, or every 4 TRs (~20-30ms), however many modern methods have been introduced that sample background phase much less frequently^1-3. This assumes that the background phase does not change by a significant amount during each velocity encoding cycle, but that it does change substantially over the cardiac cycle. The temporal dynamics of background phase are not well understood for 4D Flow acquisitions. Consequently, the background phase may be measured too infrequently or too often for accurate and/or time efficient measurements.

From results seen in 2D through plane PC-MRI⁴, it is expected that background phase does not change as rapidly as velocity phase, and 4D Flow sequences could be potentially accelerated by sampling background phase less frequently. The purpose of this work was to measure the temporal dynamics of the background phase with high temporal resolution, and demonstrate methods of selecting time optimal background phase sampling strategies to improve the measurement efficiency of 4D Flow acquisitions.

Blood-mimicking fluid was pumped (CardioFlow 5000, Shelley Medical) through a straight tube phantom with three different programmed waveforms: sinusoidal, femoral, and carotid. Two healthy human volunteers were also scanned covering the carotid arteries and the middle cerebral artery (MCA).

4D Flow MR imaging was performed at 3.0T (Skyra, Siemens) with: FOV=24x18x4cm, 1.25mm isotropic, TE/TR=2.7/6.25ms, flip angle=10°, venc=70-100cm/s, and BW=800Hz/pixel. The temporal resolution of the phantom experiments was 25ms (27 cardiac phases) and the temporal resolution of the volunteer scans was 50ms (18-20 cardiac phases). High temporal resolution sampling of the background phase was acquired with identical sequence parameters, but without flow-encoding gradients. Consequently, the number of acquired phases was quadrupled to 108 (phantoms) and 72-80 (humans).

Flow values were extracted from the regular 4D Flow measurements using standard post-processing methods. For the background phase measurements, all phases were offset by the negative of the first cardiac phase, to mitigate phase wrapping. Spectral decomposition of the background phase was analyzed after mean detrending. The high temporal resolution background phase data was used to estimate peak and mean velocity errors for various background sampling rates, effectively varying the number of TRs (i.e. velocity encodes) between background phase measurements.

Figure 1 shows representative velocity waveforms and the underlying background phase for a phantom waveform and a volunteer. For phantom experiments, the total change in background phase (max-min of a vessel ROI mean) was 0.14±0.05 radians (1.8±0.6cm/s) for the 3 waveforms. For in vivo experiments the total change in background phase was 0.29±0.001 radians (4.7±1.2cm/s) for the 2 volunteers. Figure 2 shows the frequency components of the background phase for all experiments. Figure 3 shows the results of simulating different sampling rates on velocity error. Analysis of the potential velocity error (Figure 3) shows increasing error with slower sampling rates, however even the peak velocity errors seen with the slowest sampling rate (12 TR, 68.75ms) would only amount to a velocity error of roughly 10%, as compared to the roughly 5% error seen with traditional 4 TR sampling rates.

This work shows how background phase can be measured with high temporal resolution and used to evaluate the requirements of background phase sampling in 4D flow. The results confirm that the background phase is a small, but significant source of potential error in 4D Flow MRI.

This study demonstrated methods of selecting sampling rates by looking at the frequency components of the background phase variation as well as simulating the effect of different sampling rates on the mean and peak error in velocity measurements. It was seen that the frequency components of the background phase contained significant low frequency components on top of noise. From analyzing the potential error due to changes in background phase, it was seen that mean and max phase errors tended to increase with less sampling, though the scale of the error was small (<0.1 radian or 2-3 cm/s). Depending on the nature of the measurement, this additional error could be made up for with more efficient measurements of velocity components, leading to net VNR improvements.

This study is limited in the number of volunteers/territories examined. Ideally all vascular regions could be classified by the scale of their respective background phase dynamics. Additionally, this work only looks at periodic changes in background phase over the cardiac cycle, however other sources of motion (e.g. respiratory) or temperature changes were not investigated.