Physics-based enhancement of flow biomarkers quantification from 4D flow imaging

Four-dimensional magnetic resonance imaging ("4D flow") holds great promise towards the development of actionable flow-related biomarkers of disease and their implementation into clinical practice. Nonetheless, many of the flow metrics that have so far demonstrated correlation with pathophysiology have also shown severe sensitivity to the coarse 4D flow spatial/temporal resolution, and cannot be reliably estimated. In this work, we leverage the analogy between 4D flow imaging and unresolved computations of multi-scale flows to: i) propose a mathematical framework for the description of the evolution equations of the measured velocity fields, and ii) exploit this framework to augment the reconstruction of 4D flow velocity fields via physics-inspired modeling paradigms. Particularly, we focus on enhancing the quantification of two well-established flow metrics: the viscous dissipation rate (aka viscous energy losses), and the wall shear stress. The novel concepts are qualitatively and quantitatively demonstrated in the context of right-heart flow dynamics, and validated against synthetic datasets generated using computational fluid dynamics. The impact of the uncertainties related to the proposed methodology is also briefly discussed.