Physics-enhanced velocimetry of Flow-MRI

Over the past decade, 4D-Flow MRI has become a routine diagnostic for cardiovascular disorders. This non-invasive imaging technique provides highly detailed, time-resolved visualisations of the blood flow velocity with full volumetric coverage. However, conventional 4D-Flow MRI images are inherently 'noisy' and have low resolution in space

and time. As a result, they often require extensive post-processing. This spells practical challenges for clinical assessments of the cardiovascular system. Aortic valve pathologies in particular have been found to trigger transition to turbulent flow, characterised by structures smaller than a few millimetres. Due to the trade-off that

exists between signal-to-noise ratio and image resolution, these small scales of motion cannot be measured directly and must instead be modelled. Most of the research effort devoted to MRI image reconstruction and super-resolution to date has focused on the laminar regime. Of key interest, therefore, is the joint physics-based reconstruction and

segmentation of turbulent flow fields. A particularly promising approach consists in the solution of an inverse Navier-Stokes problem, in which the boundary conditions, blood vessel boundaries and flow parameters are inferred directly from the 4D-Flow MRI data. The problem is regularised using a Bayesian framework with Gaussian random fields. An

adjoint formulation is also adopted to accelerate the reconstruction and segmentation processes. This method produces quantitatively accurate, physics-constrained models tuned specifically to each patient, along with uncertainty estimates of the model predictions. The proposed framework has been successfully applied to (i) sparse and

noisy acquisitions of laminar, Newtonian flows through vascular geometries, and (ii) laminar, non-Newtonian flows through simple geometries. The aim of the present research is to extend this approach to turbulent blood flows by assimilating experimental data into well-established closure models in a Bayesian setting. The calibrated model

with the highest evidence will then be selected. By accounting for turbulence, this work will raise the accuracy with which key biomarkers, such as wall shear stress and turbulent kinetic energy, are predicted. This information is of great value in clinical evaluations of aortic valve diseases like stenosis. A distinct advantage of the Bayesian formulation lies

in its ability to extract these hidden flow quantities without any additional computation. Moreover, the quality of the reconstructed images can be attained in a substantially shorter timeframe relative to the state-of-the-art, thus enabling order of magnitude reductions in patient examination time. This work will open new opportunities for aortic

valve replacement. It will also inform the timing and nature of medical interventions, which will help improve the quality and accessibility of healthcare in the long-term.