To develop and evaluate a fast phase-contrast MRI (PC-MRI) technique with Hybrid One- and Two-sided Flow Encoding Only (HOTFEO) for accurate blood flow and velocity measurements using 4D-flow PC-MRI.4D-flow PC-MRI is widely used clinically for visualization and quantification of blood flow and velocity. In conventional 4D-flow, each cardiac phase acquires the flow-compensated (FC) and three-directional (3D) flow-encoded (FE) echoes (FC/3FE), which often limits the achievable temporal resolution and temporal footprint. This can result in under-estimation of maximum peak velocity (1). Herein, we propose a 4D-flow strategy that eliminates acquisition of the FC echo using hybrid one- and two-sided flow encoding only (HOTFEO), as shown in Fig. 1a. The FC background phase is derived from 3D FE data based on a velocity direction constraint that assumes the velocity direction, not the magnitude, changes very little between two cardiac phases. To validate our technique, we compare flow and velocity measurements between 4D HOTFEO and conventional 4D-flow in a cohort of healthy volunteers retrospectively and prospectively.

In many vascular territories, such as the common carotid arteries (CCAs) and the circle of Willis, the blood flow tends to be laminar flow. We hypothesize that, in the same spatial voxel, the blood flow velocity direction (not magnitude) remains relatively unchanged between two cardiac phases (~140ms). Assuming consistency of the FC data (1), we have the following velocity direction constraint for cardiac phases n and n+1:

$$$\phi_{FC,n}=arg\min_{\phi_{FC,n}}\mid|\overrightarrow{V}_{n}\cdot\overrightarrow{V}_{n+1}|-|\overrightarrow{V}_{n}|\times|\overrightarrow{V}_{n+1}|\mid$$$ [1]

In Eq. [1], $$$\phi_{FC,n}(=\phi_{FC,n+1})$$$ represents the FC background phase, $$$\overrightarrow{V}_{n}=\frac{VENC}{\pi}\cdot(\phi_{FEx,n}-\phi_{FC,n},\pm(\phi_{FEy,n}-\phi_{FC,n}),\phi_{FEz,n}-\phi_{FC,n})$$$ and $$$\overrightarrow{V}_{n+1}=\frac{VENC}{\pi}\cdot(\phi_{FEx,n+1}-\phi_{FC,n},\mp(\phi_{FEy,n+1}-\phi_{FC,n}),\phi_{FEz,n+1}-\phi_{FC,n})$$$ are velocity vectors of cardiac phases n and n+1, respectively, as a function of the FC background phase $$$\phi_{FC,n}$$$ and $$$\phi_{FEx/y/z}$$$ is the FE data in x/y/z-direction. The optimization problem in Eq. [1] solves for the $$$\phi_{FC,n}$$$ that yields the smallest angle between the blood flow velocity vectors between two successive cardiac phases. In HOTFEO, the polarity of FE gradient in the y-direction is alternated between successive cardiac phases. This two-sided y-directional FE acquisition is necessary to ensure a more robust solution compared with a recently proposed one-sided FE Only (FEO) technique (2). HOTFEO addresses the ill-conditioning of FEO when $$$\overrightarrow{V}_{n}=\overrightarrow{V}_{n+1}$$$. As shown in Fig. 1b, Eq. [1] of FEO is underdetermined (blue), but Eq. [1] of HOTFEO is a quadratic function that ensures a unique FC solution (red).

Six volunteers (N=6) were recruited for a retrospective and prospective in vivo study. The CCAs were scanned using a standard 4D-flow protocol and the proposed HOTFEO sequence using a 3T scanner (Skyra, Siemens) with a 4-channel neck coil. Reference 4D-flow data were also used to simulate a HOTFEO acquisition for retrospective comparisons of flow and velocity. Both sequences were implemented with Velocity ENCoding (VENC)=100-105cm/s, flip angle=20°, readout bandwidth=815Hz/Pixel, TE=3.35ms, views-per-segment=3(FC/3FE) and 4(HOTFEO), temporal resolution=68ms, acquired matrix=256x176x10, FOV=256x176x18.2mm³. All scans were acquired during free breathing with prospective ECG gating.

Figure 2a shows the difference between the acquired FC background phase and the background phase calculated using Eq. [1] from a healthy volunteer. Figure 2b-c show a comparison between the through-plane mean flow velocity and peak magnitude velocity ($$$=\sqrt{V_x^2+V_y^2+V_z^2}$$$) calculated using conventional 4D-flow and the retrospectively simulated HOTFEO data. Compared with reference 4D-flow, the simulated HOTFEO strategy was able to accurately calculate the FC background phase (<3.4° difference). Based on retrospective data from six volunteers, the through-plane mean flow velocity and peak magnitude velocity based on HOTFEO were in good agreement with the reference. The average RMSE of mean flow velocity waveform was 1.22(range:0.65-2.07)cm/s and peak magnitude velocity was 3.23(range:1.68-5.09)cm/s. The Bland-Altman plot of the total volumetric flow measurement (Fig. 3a) shows a bias of -0.06mL (-1.2% error) and the 95% confidence interval (CI) is [-0.2, 0.1] mL. The Bland-Altman plot of maximum peak magnitude velocity (Fig. 3b) shows a bias of -0.2cm/s (-0.2% error) and the 95% CI is [-4.7, 4.4] cm/s.

For the prospective in vivo study, Fig. 4a-b shows examples of through-plane mean flow velocity and peak magnitude velocity waveform comparisons between reference 4D-flow (gray) and HOTFEO (blue). The two techniques have good agreement. The Bland-Altman plots of total volumetric flow between HOTFEO and conventional 4D-flow is shown in Fig. 5a. The bias is -0.1mL (-3.4% error) with the 95% CI [-0.6, 0.3]mL. The Bland-Altman plots of maximum peak magnitude velocity (Fig. 5b) shows that the bias is -1.8cm/s (-2.0% error) with 95% CI [-9.7, 6.1] cm/s.

HOTFEO can accelerate 4D-flow PC-MRI by 4/3-fold while maintaining the measurement accuracy of total volumetric flow and peak magnitude velocity measurements.