Project proposal

Flow in blood vessels, or Data assimilation using adjoint optimization and the time-dependent Navier-Stokes equations

Supervisor: Vladimir Kozlov (MAI)
Co-supervisors: Matts Karlsson (IMT), Per Weinerfelt (Saab), Fredrik Berntsson (MAI)

This is a multidisciplinary project which deals with reconstruction of time-dependent three-dimensional velocity fields using techniques and theory from computational fluid dynamics, optimization, inverse problems and magnetic resonance imaging (MRI). The main objective is to use sparse data from MRI measurements and suitable mathematical models to compute the field with a much higher resolution. In meteorology the procedure is known as data assimilation.

Important application areas are meteorology, medicine, for example visualizing the flow of blood in the human heart and in larger vessels with a high resolution. In particular, an important objective in medicine is to be able to compute accurately the so called wall shear stress (WSS) of blood vessels. This can be done by computing the velocity gradient at the wall of the blood vessel, using a high resolution velocity field.

The aim of the project is to develop methods for computing dense velocity fields in space and time from sparse measured velocity fields assuming that the velocity fulfills the Navier-Stokes equations. This problem can be reduced to finding the initial state of the fluid. When the initial state is found, a velocity field with high accuracy can be computed on a dense computational grid.

The assimilation problem in question is ill posed and therefore sensitive to noise, measurement errors and the choice of numerical solution method. The case, when the model is described by the Euler equations, was treated in PhD dissertation no. 1121 of Johan Lundvall in 2007.

Page responsible: luba.kulesh@liu.se
Last updated: 2011-06-07