Towards patient-speci�fic modelling of cerebral blood flow using lattice-Boltzmann methods

Patient-specifi�c Computational fluid dynamics (CFD) studies of cerebral blood flow have the potential to help plan neurosurgery, but developing realistic simulation methods that deliver results quickly enough presents a major challenge. The majority of CFD studies assume that the arterial walls are rigid. Since the lattice-Boltzmann method (LBM) is computationally efficient on multicore machines, some methods for carrying out lattice-Boltzmann simulations of time-dependent fluid flow in elastic vessels are developed. They involve integrating the equations of motion for a number of points on the wall. The calculations at every lattice site and point on the wall depend only on information from neighbouring lattice sites or wall points, so they are suitable for efficient computation on multicore machines. The �first method is suitable for three-dimensional axisymmetric vessels. The steady-state solutions for the wall displacement and flow �fields in a cylinder at realistic parameters for cerebral blood ow agree closely with the analytical solutions. Compared to simulations with rigid walls, simulations with elastic walls require 13% more computational e�ffort at the parameters chosen in this study. A scheme is then developed for a more complex geometry in two dimensions, which applies the full theory of linear elasticity. The steady-state wall pro�files obtained from simulations of a Starling resistor agree closely with those from existing computational studies. I �find that it is essential to change the lattice sites from solid to fluid and vice versa if the wall crosses any of them during the simulation. Simple tests of the dynamics show that when the mass of the wall is much greater than that of the fluid, the period of oscillation of the wall agrees within 7% of the expected period. This method could be extended to three dimensions for use in cerebral blood ow simulations