Creating digital twins of flows from noisy and sparse flow-MRI data

4D流动磁共振成像（flow-MRI）是一种非侵入性的流动成像技术，广泛应用于医学和工程领域，用于测量三维空间和一维时间（4D）的速度场。例如，它用于测量心脏和周围血管中的血液速度，以识别动脉瘤和狭窄等异常。然而，随着空间分辨率的增加，速度测量变得越来越嘈杂。为了达到可接受的信噪比（SNR），扫描往往是重复和平均，导致较长的采集时间。该提案旨在使用贝叶斯物理约束算法扩展flow-MRI的功能，该算法可以从嘈杂和稀疏的4D flow-MRI数据中自动生成最有可能的流的数字孪生。这些方法将flow-MRI的准确度和时空分辨率提高了10至100倍，提供了难以测量的导出流量的定量估计，并且能够对使用最先进的flow-MRI技术无法捕获的短长度和/或时间尺度的流进行成像。例如，在多孔介质流动中，这些方法将提供速度场、应力张量和导出的量，其精度远远超过当前最先进的流动MRI，从而获得更好的理解和新的发现。在医学成像中，这些方法还将实现患者特定的建模，如果成功，将导致临床医生更多地采用4D flow-MRI。这将减少患者扫描时间，取代心脏导管插入术等侵入性技术，并允许对新生儿和胎儿心脏病学中发现的较小血管进行成像。在我的博士论文中，我开发了这些方法，并表明，为了在轴对称和2D平面流动中获得给定的精度，它们将所需的流动MRI数据减少了10到100倍。该奖学金的目的是将我在博士期间开发的方法从刚性几何形状的2D和3D稳态流动扩展到柔性几何形状的4D流动，以确定体内心血管血液动力学所带来的挑战，并广泛传播这些方法。在本提案中，我将重点关注流动MRI，但请注意，这些方法可以扩展到其他测速方法，如PIV。

4D flow Magnetic Resonance Imaging (flow-MRI) is a non-invasive flow imaging technique widely used in medicine and engineering to measure velocity fields in three spatial and one time dimension (4D). For example, it is used to measure the velocity of blood in the heart and surrounding vessels to identify anomalies such as aneurysms and stenoses. The velocity measurements become increasingly noisy, however, as the spatial resolution is increased. To achieve acceptable signal-to-noise ratio (SNR), scans are often repeated and averaged, leading to long acquisition times. This proposal is to extend the capabilities of flow-MRI using Bayesian physics-constrained algorithms that automatically generate the most likely digital twin of a flow from noisy and sparse 4D flow-MRI data. These methods increase the accuracy and the spatiotemporal resolution of flow-MRI by 10 to 100 times, provide quantitative estimates of derived flow quantities that are difficult to measure, and enable the imaging of flows whose short length and/or time scales cannot be captured using state-of-the-art flow-MRI techniques. In porous media flows, for example, these methods will provide velocity fields, stress tensors, and derived quantities far beyond the accuracy of current state-of-the-art flow-MRI, leading to better understanding and new discoveries. In medical imaging, these methods will also enable patient-specific modelling and, if successful, will lead to increased adoption of 4D flow-MRI by clinicians. This would reduce patient scan times, replace invasive techniques such as cardiac catheterization, and permit the imaging of smaller vessels such as those found in neonatal and fetal cardiology. In my PhD I developed these methods and showed that, to obtain a given accuracy in axisymmetric and 2D planar flows, they reduce the required flow-MRI data by 10 to 100 times. The aim of this fellowship is to extend the methods I developed during my PhD from 2D and 3D steady flows in rigid geometries to 4D flows in flexible geometries, to scope out challenges posed by in-vivo cardiovascular haemodynamics, and to disseminate these methods widely. In this proposal I will focus on flow-MRI, but note that these methods could be extended to other velocimetry methods such as PIV.