Recent advances on the Immersed Structural Potential Method for fluid-structure interaction haemodynamic applications

In this presentation, the new Immersed Structural Potential Method (ISPM) [3], based on the original Immersed Boundary Method [1], is presented with the purpose of modelling highly complex 2D/3D Fluid-Structure Interaction (FSI) haemodynamics problems. The defining characteristic of “immersed methods” is the numerical treatment of any solid structure within the fluid as a field of body forces via convolution with smoothed approximations (kernels) of the Dirac delta distribution. Immersed techniques posses many attractive features, particularly when large deformation of thin structures in three dimensions is considered. Unfortunately, the original IBM method is restricted to massless fibre-like (one dimensional) structures immersed within the fluid and the discrete convolution with these kernels induces diffusive effects at the solid boundaries. Some of its extensions (EIBM, IFEM [2]) have tried to palliate the aforementioned limitations, but still present several shortcomings[2]. The IFEM, for instance, relies on an embedded finite element space to perform interpolation and computation of interaction forces, which poses a challenge under large deformations, as extreme mesh distortion requires remeshing, defeating the original purpose of immersed techniques. In this work, it will be shown how the ISPM overcomes these limitations by using a more sophisticated formulation, considering the structure as an elastic potential that is integrated within the fluid. This approach allows not only for a far more computationally efficient and accurate modelling of cardiovascular applications, particularly for heart-valve problems, but also more versatile and robust, since integration can be performed preserving the inherent features of the problem, such as incompressibility, a constant source of problems for many existing methods in the literature. In addition, this method creates a much more natural framework to model the viscoelastic and anisotropic material behaviour of cardiovascular tissues. Figure 1: Deformation of a thin elastic leaflet under 3D pulsatile flow. REFERENCES[1] C. Peskin, Flow patterns around heart valves: a numerical method, JCP, 10, 252-271, 1972.[2] W. K. Liu, et al., Immersed finite element method and its applications to biological systems,CMAME, 195, 1722-1749, 2006.[3] A.J. Gil, A. Arranz-Carreño, J. Bonet, O. Hassan, The Immersed Structural PotentialMethod for haemodynamic applications, Journal of Computational Physics, CJP, 229,8613-8641, 2010, doi:10.1016/j.jcp.2010.08.005.