Study of a Lattice–Boltzmann Immersed Boundary Coupled Method for Fluid-Structure Interactions in Hemodynamics

The development of most cardiovascular diseases can be associated with certain specific hemodynamic conditions. Hence, a detailed description of such conditions is an important information for the medical community. With this goal in mind, we propose in this work a lattice-Boltzmann Immersed Boundary coupled method to model two and three-dimensional blood flows in deformable vessels. The lattice-Boltzmann (LB) method is a mesoscale method that deals with micro-particles distributions on a regular lattice and approximates the incompressible Navier-Stokes equations under some hypothesis. In the cardiovascular system, besides a detailed blood dynamics description, it is also important to represent the phenomena of pressure wave propagations (by fluid-structure interactions). When coupled, for instance, to an Immersed Boundary (IB) method, the LB method can model the fluid dynamics and its interaction with an immersed structure. Here, the structure represents the arterial walls and the blood is represented by the fluid inside the closed domain defined by the structure. The LB method with BGK approximation is explicit and efficiently parallelizable, therefore, suitable to be implemented in a parallel environment in order to reduce the computing time of complex simulations. In that direction, it is important to point that the use of an IB method has the advantages of permitting the description of different constitutive laws for the wall arteries and also of preserving the efficiency of the parallelization of the LB method, without having to create and destroy nodes as the structure moves. We validate this implementation by simulating an elastic stretched membrane oscillating towards an equilibrium state. In addition, we present the pressure wave propagation phenomena in two and three-dimensional vessels. These last two cases are used to study the sensitivity of the problem to changes in some of the new parameters introduced by the coupled method.