Data Assimilation for Mathematical Modelling of Blood Flow - A Study Interlacing CFD with MRI.

What is it about?

The frictional forces or wall shear stresses (WSSs) induced by the blood flow at arterial vessels have long been hypothesised to play a major role in the onset and progress of endothelial disorders. The endothelial cell function depends on different flow conditions and the WSSs have an impact in the development of atherosclerosis. Through the paradigm of data assimilation, the work remarkably improves the evaluation of WSSs induced by the blood flow at the arterial walls of the aortic root.

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Why is it important?

Optimisation problems can be addressed through the use of gradient-based methods, which require, in a Lagrangian framework, the solution of a forward problem, an adjoint problem and the evaluation of the cost functional sensitivity. Most of the studies first discretise the forward problem and use it to derive the adjoint problem based on this approximation. This makes the adjoint solution sub-optimal. Only a few studies considered deriving the adjoint problem first in a continuous level and discretising it thereafter. However due to the computational burden and challenges in the implementation, such strategies were applied mostly in 2D and for very simple geometries using artificially generated flow data. This work applies the optimise-then-discretise approach in computational haemodynamics for the first time using both a 3D geometry and real flow MRI acquisitions. The accuracy of wall shear stresses is remarkably improved, especially in the regions around the aortic root.

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