Development of a discrete fluid-structure interaction method for cardiovascular applications

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Abstract

The interaction between blood and cardiovascular tissue is known to play a significant role in the development cardiovascular diseases and associated conditions. With the ever increasing availability and performance of computational resources, in conjunction with improved understanding of the disease mechanisms, the integration of numerical analysis into in silico tools has become more prevalent. Once viewed as emerging technology, these tools are now being routinely utilised in clinical practice. However, the majority of these tools consider the fluid or structure in isolation. This is due to the added complexity of coupling the methods and the computational cost incurred through modelling fluid-structure interaction using traditional continuum methods. As a result, discretisations of the structure used in fluid-structure interaction (FSI) methods tend to be simpler representations and offer limited potential to model complex non-linear material properties and discrete effects such as rupture. The purpose of this work is to develop an efficient fluid-structure interaction method capable of modelling complex phenomena. The inherent parallel performance of discrete numerical methods is explored, with a long-term view to developing the method for use in clinical tools; where speed, robustness and adaptability are paramount. In the present work, the fluid is represented via the lattice Boltzmann method and the structure via the vector-based discrete element method, known as the V-model. These solvers are strongly coupled using a version of the immersed boundary method based on direct forcing in a block Gauss-Seidel scheme, where the time step size of the fluid and structure are to be kept independent. Validation results for the V-model show good agreement with analytical and numerical solutions for static and dynamic cantilever beam cases with constant and time-varying external loads. This demonstrates the V-model's ability to accurately capture the mechanical response of a material before extending the method to model more complex physics. GPU implementation of the V-model demonstrated speed-ups of x50 relative to an optimised serial CPU implementation. The FSI method demonstrated good agreement with numerical benchmark data while stochastic modelling of the structure material properties demonstrated the V-model's potential to model variation in cardiovascular tissue that occurs naturally and due to disease. The major original contributions of this work include the implementation and elucidation of a recently developed structure model; which is used here for the first time with a lattice Boltzmann scheme. The work also provides first steps towards the use of stochastic modelling using the V-model, the first GPU implementation of the V-model, and development of the first strongly coupled fluid-structure interaction method to include the V-model.

Keyword(s)

GPU; discrete element method; fluid-structure interaction; immersed boundary method; lattice Boltzmann method; numerical modelling

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