The rapid increase in computational power over the last decade has unlocked the possibility of providing patient-specific healthcare via simulation and data assimilation. In the past 2 decades, computational approaches to simulating cardiovascular flows have advanced significantly due to intense research and adoption of methods in medical device companies. A significant source of friction in porting these tools to the hospital and getting in the hands of surgeons is due to the expertise required to handle the geometry pre-processing and meshing of models. Meshless methods reduce the amount of corner cases which makes it easier to develop robust tools surgeons need. To accurately simulate modifications to a region of vasculature as in surgical planning, the entire system must be modeled. Unfortunately, this is computationally prohibitive even on today's machines. To circumvent this issue, the Radial-Basis Function Finite Difference (RBF-FD) method for solution of the higher-dimensional (2D/3D) region of interest is tightly-coupled to a 0D Lumped-Parameter Model (LPM) for solution of the peripheral circulation. The incompressible flow equations are updated by an explicit time-marching scheme based on a pressure-velocity correction algorithm. The inlets and outlets of the domain are tightly coupled with the LPM which contains elements that draw from a fluid-electrical analogy such as resistors, capacitors, and inductors that represent the viscous resistance, vessel compliance, and flow inertia, respectively. The localized RBF meshless approach is well-suited for modeling complicated non-Newtonian hemodynamics due to ease of spatial discretization, ease of addition of multi-physics interactions such as fluid-structure interaction of the vessel wall, and ease of parallelization for fast computations. This work introduces the tight coupling of meshless methods and LPMs for fast and accurate hemodynamic simulations. The results show the efficacy of the method to be used in building robust tools to inform surgical decisions and further development is motivated.
Alain Kassab, Committee Chair.
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