GPU acceleration of Volumetric Lattice Boltzmann Method for patient-specific computational hemodynamics

Volumetric Lattice Boltzmann Method (VLBM) has been recently developed for solving complex flow with arbitrary curved boundaries. The VLBM regards fluid particles are uniformly distributed in cells and distinguishes fluid, solid, and boundary cells by introducing a volumetric parameter P(x,t) defining the percentage of solid volume in each cell. The advantages of VLBM stem from the self-regulation of P(x,t) in the volumetric lattice Boltzmann equation (VLBE) for particle collision and streaming with no spatial interpolation when dealing with an arbitrarily curved boundary with or without motion. First, the VLBE satisfies mass conservation strictly. Second, the implementation of VLBM is rather simple after the solid volume percentages are determined in boundary cells. And third, no-slip boundary condition is integrated in the streaming formulation thus significantly enhances the capability of parallelization. In this paper, we perform GPU (Graphics Processing Unit) parallelization for VLBM using a uniform computing scheme for both fluid and boundary cells. In contrast to the traditional LBM acceleration, the boundary conditions have to be imposed over boundary nodes, where branching operations are required to identify boundary nodes from others, the VLBM implementation does not need to distinguish fluid and boundary cells in the computation so that branching is minimized and the GPU kernel execution is accelerated. Furthermore, the algorithmic steps are optimized to improve coalesced access of GPU memory and avoid race condition. An application study is on a pulsatile blood flow in a patient-specific carotid artery segmented from an anonymous clinical CT image and more than 30 times speedup over the serial counterpart. Simulations of fluid dynamics and wall shear stress (WSS) are presented and known velocity skewness and WSS distributions are captured. The GPU accelerated VLBM is promising to perform patient-specific computational hemodynamics within clinical accepted time frame and is expected to reveal quantitative real-time blood flow in living human arteries to aid clinical assessment of cardiovascular diseases.