Time-resolved three-dimensional flow MRI (4D flow MRI) provides a unique non-invasive solution to visualize and quantify hemodynamics in blood vessels such as the aortic arch. However, most current analysis methods for arterial 4D flow MRI use static artery walls because of the difficulty in obtaining a full cycle segmentation. To overcome this limitation, we propose a neural fields-based method that directly estimates continuous periodic wall deformations throughout the cardiac cycle. For a 3D + time imaging dataset, we optimize an implicit neural representation (INR) that represents a time-dependent velocity vector field (VVF). An ODE solver is used to integrate the VVF into a deformation vector field (DVF), that can deform images, segmentation masks, or meshes over time, thereby visualizing and quantifying local wall motion patterns. To properly reflect the periodic nature of 3D + time cardiovascular data, we impose periodicity in two ways. First, by periodically encoding the time input to the INR, and hence VVF. Second, by regularizing the DVF. We demonstrate the effectiveness of this approach on synthetic data with different periodic patterns, ECG-gated CT, and 4D flow MRI data. The obtained method could be used to improve 4D flow MRI analysis.

翻译：时间分辨三维血流磁共振成像（4D血流MRI）为主动脉弓等血管内的血流动力学可视化与量化提供了一种独特的无创解决方案。然而，由于难以获得完整心动周期的分割结果，目前大多数针对动脉4D血流MRI的分析方法均使用静态动脉壁。为克服这一局限，我们提出一种基于神经场的方法，可直接估计整个心动周期内连续的周期性壁变形。针对三维+时间成像数据集，我们优化了一个隐式神经表示（INR），该表示用于描述一个时间依赖的速度矢量场（VVF）。通过使用常微分方程求解器将VVF积分得到变形矢量场（DVF），该DVF可随时间对图像、分割掩码或网格进行变形，从而实现局部壁运动模式的可视化与量化。为恰当反映三维+时间心血管数据的周期性本质，我们通过两种方式施加周期性约束：首先，对输入INR（进而VVF）的时间变量进行周期性编码；其次，对DVF施加正则化。我们在具有不同周期模式的合成数据、心电图门控CT以及4D血流MRI数据上验证了该方法的有效性。所获得的方法可用于改进4D血流MRI分析。