## M1-Space Under-Sampling Fast Phase Contrast Magnetic Resonance Imaging

- Author(s): Wang, Da
- Advisor(s): Hu, Peng
- et al.

## Abstract

Phase Contrast Magnetic Resonance Imaging (PC-MRI) is one of the primary means for quantification of blood flow and velocity. In conventional PC-MRI, the Flow Compensated (FC) and the three-directional (3D) Flow Encoded (FE) images are acquired in an interleaved fashion, and each directional blood flow velocity is encoded in the phase difference between each directional FE and the FC data. This acquisition strategy often limits its achievable temporal sampling period and temporal footprint. Temporal sampling period and temporal footprint are two important indices govern the measurement accuracy of the maximum peak velocity. The underestimation of the maximum peak velocity due to long temporal sampling period and long temporal footprint may result in misdiagnosis of a number of clinical diseases, such as artery stenosis. In the conventional 4D flow PC-MRI, each cardiac phase requires four acquisitions (i.e. one FC and 3D FE, FC/3FE) to update the 3D velocity vector field. Thus, the temporal sampling period and temporal footprint of 4D flow PC-MRI equal to 4*TR*Views-per-segment. Using a small views-per-segment (VPS) can achieve a decreased temporal sampling period and temporal footprint but concomitantly increase the total scan time. So far, fast PC-MRI techniques are majorly implemented to compensate the increase of the total acquisition time. In this work, we first introduce the gradient first moment (M1) space under-sampling, which aims to reduce the number of the four samples (FC and 3D FE) required for 4D flow reconstruction. This is the unique advantage of M1-space under-sampling over conventional fast PC-MRI techniques. It can improve both the temporal sampling period and temporal footprint without increasing the total scan time or reduce the total scan time with fixed temporal sampling period and temporal footprint. Furthermore, the M1-space is a novel dimension to accelerate 4D flow scans, so it can be combined with K-space, K-t-space, temporal dimension fast PC-MRI techniques to achieve further acceleration.

In Chapter 2, we propose a technique to use sliding window temporal view sharing of the FC data (FCVS) to accelerate PC-MRI. The technique aims to accelerate certain PC-MRI applications, such as assessment of volumetric blood flow in the carotid arteries, intracranial vessels and peripheral vessels, where the physiological motion is minor and the FC background phase is not expected to change significantly over time. In this regard, the conventional PC-MRI acquisition strategy is redundant since it repetitively acquires the similar FC data for each cardiac phase. Especially the FC data does not contain dynamic flow velocity information. The FCVS technique achieves two-fold acceleration compared to standard through-plane encoding (FC/FE) PC-MRI. More importantly, the FCVS approach improves both the temporal sampling period and temporal footprint, which are very important for accurate velocity and flow quantification. Computational simulations and both retrospective and prospective in vivo studies demonstrated that the FCVS technique provides more accurate maximum peak velocity measurement while maintaining the measurement accuracy of total volumetric flow compared with conventional FCFE technique.

In Chapter 3, we propose a 4D flow PC-MRI strategy, which is completely free of FC data acquisition and achieves 4/3-fold acceleration. In this technique, we hypothesize that the velocity direction (not magnitude) remains relatively unchanged within two cardiac phases (~100-150ms) during the cardiac cycle. The velocity direction consistency constraint enables the FC background phase calculation based on 3D FE data. Thus, the four M1-space samples (FC/3FE) have been reduced to three samples (3FE). The HOTFEO achieves 4/3-fold acceleration. However, the velocity direction consistency constraint has two ill conditions: the two consecutive velocities equal to each other and they are along the diagonal direction in the logical encoding coordinate. To address these problems, we propose to use a hybrid one- and two-sided flow encoding only (HOTFEO) strategy. More specifically, that is to use FE acquisition pattern with alternating polarity (i.e. two-sided FE) in the Y-direction (FEy) in addition to using single polarity (i.e. one-sided) FEx and FEz. The HOTFEO pattern can address the two ill conditions by converting the underdetermined constraint into convex function optimizations. The HOTFEO technique can also significantly increase the accuracy of FC background calculation and result in more accurate maximum peak velocity and total volumetric flow measurement.

In Chapter 4, we propose a two-fold accelerated 4D flow PC-MRI technique with hybrid one- and two-sided flow encoding and velocity spectrum separation (HOTSPA). There are three components in the HOTSPA technique: 1) the two-sided FE has been applied in two of the three FE directions; 2) the one-sided FE has been applied in the remaining FE direction; 3) the FC data is not explicitly acquired. The two-sided FE strategy provides a 0/π linear phase modulation in the temporal dimension. In the Fourier velocity spectrum domain, the spectrum of temporal modulated velocity waveform will be shifted by half of the frequency support and separated from the spectrum of FC or one-sided FE waveform. The HOTSPA technique then separates the Fourier velocity spectra into components for FC background phase and 3D velocity waveforms. The combinations of the acquired data enable 3D velocity calculations based on two M1-space samples instead of four samples as conventional 4D flow PC-MRI. The HOTSPA technique can be used to either improve the temporal sampling period and temporal footprint or reduce the total scan time. The approach has been demonstrated to provide more accurate maximum peak velocity and total volumetric flow measurements.

The M1-space under-sampling is a novel and promising technique to accelerate PC-MRI. First, it can improve both temporal sampling period and temporal footprint by reducing the M1-space samples. Second, it can accelerate 4D flow independently or it can be applied on phase images after finishing other fast PC-MRI technique reconstructions, such as compressed sensing, parallel imaging, non-Cartesian trajectory, thus allowing their combination to achieve further acceleration. In Chapter 4, we will introduce the balanced four-point flow encoding strategy, which can achieve four-fold acceleration using HOTSPA technique. The M1-space under-sampling can significantly improve the measurement accuracy of velocity and flow quantifications or reduce the total scan time, especially for 4D flow applications.