A novel mono-physics particle-based approach for the simulation of cardiovascular fluid-structure interaction problems

Background and objective: Fluid-structure interaction (FSI) is required in the study of several cardiovascular engineering problems were the mutual interaction between the pulsatile blood flow and the tissue structures is essential to establish the biomechanics of the system. Traditional FSI methods are partitioned approaches where two independent solvers, one for the fluid and one for the structure, are asynchronously coupled. This process results into high computational costs. In this work, a new FSI scheme which avoids the coupling of different solvers is presented in the framework of the truly incompressible smoothed particle hydrodynamics (ISPH) method. Methods: In the proposed FSI method, ISPH particles contribute to define both the fluid and structural domains and are solved together in a unified system. Solid particles, geometrically defined at the beginning of the simulation, are linked through spring bounds with elastic constant providing the material Young's modulus. At each iteration, internal elastic forces are calculated to restore the springs resting length. These forces are added in the predictor step of the fractional-step procedure used to solve the momentum and continuity equations for incompressible flows of all particles. Results: The method was validated with a benchmark test case consisting of a flexible beam immersed in a channel. Results showed good agreement with the system coupling approach of a well-established commercial software, ANSYS®, both in terms of fluid-dynamics and beam deformation. The approach was then applied to model a complex cardiovascular problem, consisting in the aortic valve operating function. The valve dynamics during opening and closing phases were compared qualitatively with literature results, demonstrating good consistency. Conclusions: The method is computationally more efficient than traditional FSI strategies, and overcomes some of their main drawbacks, such as the impossibility of simulating the correct valve coaptation during the closing phase. Thanks to the incompressibility scheme, the proposed FSI method is appropriate to model biological soft tissues. The simplicity and flexibility of the approach also makes it suitable to be expanded for the modelling of thromboembolic phenomena.