4D flow MRI allows visualization and quantification of blood flow and enables comprehensive analysis of cardiovascular hemodynamics in vivo [1]. However, total scan time is still a major limitation of 4D flow MRI. Reconstruction techniques using spatiotemporal correlations such as kt-GRAPPA and kat-ARC are highly promising methods to accelerate 4D flow MRI [2,3]. Nevertheless, when the acceleration factor is high, k-t acceleration degrades temporal resolution and can impact the accuracy of the velocity, especially peak velocities. The purpose of this study is to improve the performance of kt-ARC reconstruction by exploiting the correlations between different velocity encoding samples, therefore called ktv-ARC, and to evaluate performance with respect to velocity accuracy.

In balanced four-point velocity encoded 4D flow MRI, each cardiac phase consists of four velocity encoding steps and each step simultaneously encodes v_x, v_y, and v_z with different polarity [4]. Conventional kt-ARC reconstructs the data of each velocity encoding step separately. For kt-ARC reconstruction kernel in temporal dimension, neighboring cardiac phases with same velocity encoding are used. Here, we proposed a modification, ktv-ARC, by including the different velocity encoded directions in the reconstruction kernel as show in Fig. 1. In other words, we add a dimension through velocity encodings for the reconstruction kernel to use the correlations between different velocity encoding steps. It means that the proposed kernel dimension becomes 5 (three spatial, temporal and velocity encoding).

To evaluate the proposed method, healthy adult volunteers were scanned on MR750 3T (GE Healthcare, Waukesha, WI) using a 32-channel cardiac coil without contrast agent injection. Fully sampled, retrospectively ECG gated and free breathing 4D flow MRI was performed as described previously [5]. Imaging parameters were: FOV=380×260×180 mm², spatial resolution=2.11×2.11×2.4 mm², venc=150 cm/s, FA=8°, TR/TE=4.28/2.13 ms and temporal resolution=45 ms. To analyze the performance of the proposed method with the conventional kt-ARC method, the fully sampled Cartesian data was retrospectively undersampled (along k_y, k_z and t dimensions) with different acceleration factors (R = 6, 8, 10 and 12). For computational efficiency, uniform undersampling pattern and geometric coil compression methods were used [6,7]. Number of N_ACS(z) and N_ACS(y) lines for both methods were 16×12 and reconstruction kernel sizes for kt-ARC and ktv-ARC were [3×7×5×3] and [3×7×5×3×4], respectively. For the comparisons, different error metrics including velocity Normalized Root Mean Squared Error (NRMSE), speed NRMSE and direction errors (Fig. 2) were used in masked regions of blood flow identified in the fully sampled data as reference. Background phase correction was performed and color-coded velocity images were generated with Arterys (Arterys, San Francisco, CA, USA).

Fig. 3 shows the reconstructions of ktv-ARC in end systolic phase (R=8). Moreover, error behavior of the methods with acceleration factors between 6 and 12 were analyzed in end systole and end diastole, as show in Fig. 4. For all acceleration factors the ktv-ARC method had lower errors in velocity and speed NRMSE, as well as velocity direction. In this work, a new method for 4D flow reconstruction which uses the correlations between velocity encodings is proposed and evaluated with different acceleration factors. As kt-ARC methods induce temporal and spatial blurring, ktv-ARC may additionally induce blurring along the velocity encodings, especially when the acceleration factor is high. Since the reconstruction kernel of ktv-ARC is higher than kt-ARC, computation time could be longer however computation time can be decreased significantly with data decoupling method in calibration [8]. Performance of the ktv-ARC can be improved with an optimized sampling pattern and adaptive time (kat-ARC) which is the topic of further investigation. ktv-ARC is a promising technique for achieving the same data quality as kt-ARC with higher acceleration, therefore enabling further scan time reductions. Also, this ktv approach can be applied for other k-space based reconstruction methods.