GPU accelerated volumetric lattice Boltzmann model for image-based hemodynamics in portal hypertension

Abstract

We are developing a new technique for monitoring portal hypertension by the pressure gradient between the portal vein and the inferior vena cava (PPG) based on non-invasive measurements (MRI images). Massive parametrization and classification are required to investigate the underlying relationship between the porosity and the stages of liver cirrhosis numerically, and the hepatic-portal venous system is a multi-scale system. Both of them need high computational costs. The suitability of the lattice Boltzmann method for GPU (Graphics Processing Unit) parallel computation provides an opportunity to overcome it. In this paper, we perform GPU parallelization and optimization for the volumetric lattice Boltzmann method with arbitrary geometry based on images. Three application cases, including pipe flow, hemodynamics in the portal venous system, and hemodynamics in a simple hepatic-portal venous system, are employed to prove the method can be applied in the hepatic-portal venous system based on accuracy and efficiency. The reliability of the model is qualitatively validated by the analytical solution of velocity and pressure difference distribution of pipe flow and quantitatively confirmed by the pulsatility of velocity and pressure difference that can be neglected in the portal venous system. The performance of the application cases is examined with Intel Broadwell E5-2683 v3@ 2.30 GHz (CPU) and NVIDIA Tesla V100 16GB (GPU). It shows the GPU algorithm for sparse geometry (SPARSE) has a similar speed to the regular GPU algorithm for dense geometry (DENSE) when the fluid volume fraction (q) is close to 1. And SPARSE speeds up to 2.2 times compared with DENSE when q is in the range of 0.19∼0.27. Meanwhile, the saving ratio of memory cost depends on q. For a numerical case in the hepatic-portal venous system, i.e., a large-scale system, parallel execution can be converged around half an hour with SPARSE, while the memory spills the limitation with DENSE with a single GPU. Hence, multi-GPU implementation is applied to release the limitation, and it can improve performance by increasing the number of GPU cards. In summary, the method presented in the paper is feasibility applied in the hepatic-portal venous system, laying the foundation of the new technique development.