Background and Objective: Time resolved three-dimensional phase contrast magnetic resonance imaging (4D-Flow MRI) has been used to non-invasively measure blood velocities in the human vascular system. However, issues such as low spatio-temporal resolution, acquisition noise, velocity aliasing, and phase-offset artifacts have hampered its clinical application. In this research, we developed a purely data-driven method for super-resolution and denoising of 4D-Flow MRI.

Methods: The flow velocities, pressure, and the MRI image magnitude are modeled as a patient-specific deep neural net (DNN). For training, 4D-Flow MRI images in the complex Cartesian space are used to impose data-fidelity. Physics of fluid flow is imposed through regularization. Creative loss function terms have been introduced to handle noise and super-resolution. The trained patient-specific DNN can be sampled to generate noise-free high-resolution flow images. The proposed method has been implemented using the TensorFlow DNN library and tested on numerical phantoms and validated in-vitro using high-resolution particle image velocitmetry (PIV) and 4D-Flow MRI experiments on transparent models subjected to pulsatile flow conditions.

Results: In case of numerical phantoms, we were able to increase spatial resolution by a factor of 100 and temporal resolution by a factor of 5 compared to the simulated 4D-Flow MRI. There is an order of magnitude reduction of velocity normalized root mean square error (vNRMSE). In case of the in-vitro validation tests with PIV as reference, there is similar improvement in spatio-temporal resolution. Although the vNRMSE is reduced by 50%, the method is unable to negate a systematic bias with respect to the reference PIV that is introduced by the 4D-Flow MRI measurement.

Conclusions: This work has demonstrated the feasibility of using the readily available machinery of deep learning to enhance 4D-Flow MRI using a purely data-driven method. Unlike current state-of-the-art methods, the proposed method is agnostic to geometry and boundary conditions and therefore eliminates the need for tedious tasks such as accurate image segmentation for geometry, image registration, and estimation of boundary flow conditions. Arbitrary regions of interest can be selected for processing. This work will lead to user-friendly analysis tools that will enable quantitative hemodynamic analysis of vascular diseases in a clinical setting.

背景与目的：时间分辨三维相衬磁共振成像（4D-Flow MRI）已被用于非侵入性地测量人体血管系统中的血流速度。但是，诸如时空分辨率低，采集噪声，速度混叠和相位偏移伪影之类的问题阻碍了其临床应用。在这项研究中，我们开发了一种纯数据驱动的4D-Flow MRI超分辨率和去噪方法。

方法：将流速，压力和MRI图像大小建模为患者特定的深层神经网络（DNN）。为了进行训练，在复杂的笛卡尔空间中使用4D流MRI图像来施加数据保真度。流体的物理学是通过规则化来施加的。引入了创新的损失函数术语来处理噪声和超分辨率。可以对受过训练的患者特定的DNN进行采样，以生成无噪声的高分辨率流图像。拟议的方法已使用TensorFlow DNN库实施，并在数字体模上进行了测试，并在高分辨率模型中通过高分辨率粒子图像测速（PIV）和4D-Flow MRI实验在脉动流动条件下的透明模型上进行了体外验证。

结果：在数字幻象的情况下，与模拟的4D-Flow MRI相比，我们能够将空间分辨率提高100倍，将时间分辨率提高5倍。速度归一化均方根误差（vNRMSE）降低了一个数量级。在以PIV为参考的体外验证测试中，时空分辨率也有类似的提高。尽管vNRMSE降低了50％，但该方法无法消除相对于4D-Flow MRI测量引入的参考PIV的系统偏差。

结论：这项工作证明了使用简单易用的深度学习机制通过纯数据驱动方法增强4D流MRI的可行性。与当前的最新技术不同，所提出的方法与几何形状和边界条件无关，因此无需繁琐的任务，例如对几何形状进行精确的图像分割，图像配准和边界流动条件的估计。可以选择任意感兴趣的区域进行处理。这项工作将导致用户友好的分析工具，这些工具将在临床环境中对血管疾病进行定量血液动力学分析。