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

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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.