Modelling Vascular Blood Flow: From Hemorheology to Data Assimilation

Variational data assimilation (DA) provides a rigorous framework for the reconstruction of time-dependent, patient-specific arterial blood flows, enabling the consistent integration of clinical measurements into computational models and improving the fidelity of hemodynamic predictions.
In this talk, we present a variational DA approach coupled with the incompressible Navier–Stokes equations and four-dimensional flow magnetic resonance imaging (4D flow MRI) to assimilate noisy velocity data and personalise simulations of blood flow in cerebral aneurysms. The methodology is formulated as a PDE-constrained optimisation problem and is applied to the reconstruction of spatially varying viscosity fields associated with both Newtonian and non-Newtonian shear-thinning constitutive models for blood. In addition, the framework enables the computation of clinically relevant hemodynamic indicators that are not directly accessible from imaging data, including wall shear stress (WSS), time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI).
We begin with a concise review of hemorheological principles and commonly used constitutive models for blood. We then address the pathological hemodynamics of cerebral aneurysms, emphasising the role of shear-related indicators in aneurysm initiation, progression, and rupture risk. Finally, we describe the numerical implementation of the DA framework and present computational results demonstrating its effectiveness for shear-thinning flows under realistic noise levels.
Work in collaboration with J. Tiago and M. Adnan (Department of Mathematics, CEMAT-IST/Ulisboa)