Patient-specifi�c Computational fluid dynamics (CFD) studies of cerebral blood flow haveudthe potential to help plan neurosurgery, but developing realistic simulation methods thatuddeliver results quickly enough presents a major challenge. The majority of CFD studiesudassume that the arterial walls are rigid. Since the lattice-Boltzmann method (LBM) isudcomputationally 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. Theudcalculations at every lattice site and point on the wall depend only on information fromudneighbouring lattice sites or wall points, so they are suitable for efficient computation on multicore machines.udThe �first method is suitable for three-dimensional axisymmetric vessels. The steady-stateudsolutions for the wall displacement and udflow �fields in a cylinder at realistic parameters forudcerebral blood udow agree closely with the analytical solutions. Compared to simulationsudwith rigid walls, simulations with elastic walls require 13% more computational e�ffort atudthe parameters chosen in this study.udA scheme is then developed for a more complex geometry in two dimensions, which appliesudthe full theory of linear elasticity. The steady-state wall pro�files obtained from simulationsudof a Starling resistor agree closely with those from existing computational studies. I �findudthat it is essential to change the lattice sites from solid to fluid and vice versa if the walludcrosses any of them during the simulation. Simple tests of the dynamics show that whenudthe mass of the wall is much greater than that of the udfluid, the period of oscillation of theudwall agrees within 7% of the expected period. This method could be extended to threeuddimensions for use in cerebral blood udow simulations.
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