4D flow magnetic resonance imaging (MRI) is a reliable, non-invasive approach for estimating blood flow velocities, vital for cardiovascular diagnostics. Unlike conventional MRI focused on anatomical structures, 4D flow MRI requires high spatiotemporal resolution for early detection of critical conditions such as stenosis or aneurysms. However, achieving such resolution typically results in prolonged scan times, creating a trade-off between acquisition speed and prediction accuracy. Recent studies have leveraged physics-informed neural networks (PINNs) for super-resolution of MRI data, but their practical applicability is limited as the prohibitively slow training process must be performed for each patient. To overcome this limitation, we propose PINGS-X, a novel framework modeling high-resolution flow velocities using axes-aligned spatiotemporal Gaussian representations. Inspired by the effectiveness of 3D Gaussian splatting (3DGS) in novel view synthesis, PINGS-X extends this concept through several non-trivial novel innovations: (i) normalized Gaussian splatting with a formal convergence guarantee, (ii) axes-aligned Gaussians that simplify training for high-dimensional data while preserving accuracy and the convergence guarantee, and (iii) a Gaussian merging procedure to prevent degenerate solutions and boost computational efficiency. Experimental results on computational fluid dynamics (CFD) and real 4D flow MRI datasets demonstrate that PINGS-X substantially reduces training time while achieving superior super-resolution accuracy. Our code and datasets are available at https://github.com/SpatialAILab/PINGS-X.

翻译：四维血流磁共振成像（MRI）是一种可靠、无创的血流速度估计方法，对心血管疾病诊断至关重要。与专注于解剖结构的传统MRI不同，四维血流MRI需要高时空分辨率以早期检测诸如狭窄或动脉瘤等危重病症。然而，实现此类分辨率通常会导致扫描时间延长，从而在采集速度与预测精度之间形成权衡。近期研究利用物理信息神经网络（PINNs）进行MRI数据的超分辨率重建，但其实际应用受限，因为针对每位患者都需进行极其耗时的训练过程。为克服此限制，我们提出了PINGS-X，一种利用坐标轴对齐时空高斯表示对高分辨率血流速度进行建模的新型框架。受三维高斯泼溅（3DGS）在新视角合成中有效性的启发，PINGS-X通过多项非平凡创新扩展了这一概念：（i）具有形式化收敛保证的归一化高斯泼溅，（ii）坐标轴对齐高斯函数，可在保持精度和收敛保证的同时简化高维数据训练，（iii）防止退化解并提升计算效率的高斯合并流程。在计算流体动力学（CFD）和真实四维血流MRI数据集上的实验结果表明，PINGS-X在显著减少训练时间的同时，实现了更优的超分辨率精度。我们的代码与数据集公开于 https://github.com/SpatialAILab/PINGS-X。