Simulation of blood flow in complex bifurcations of the cerebral arteries is critical to understanding patient-specific vascular conditions (such as the occurrence, growth, and rupture of aneurysms) and optimizing medical treatments. This study presents a novel computational approach to simulate 3D blood flow in brain artery bifurcations using the Lattice-Boltzmann method (LBM).
 

Patients’ acquisitions of Time-of-Flight Magnetic Resonance Angiography (ToF MRA) images were used to reconstruct the vascular geometries to preserve high anatomical precision. The vascular geometries were stored as a surface mesh in STL format. A 3D structured mesh grid has been created to limit the geometry of the vascular artery, including its bifurcation area. The grid was constructed by identifying the geographic extents of the geometry in all three dimensions to ensure complete coverage of the area of interest. The developed solver used a ray casting approach to identify internal fluid points located inside the bifurcation geometry within the domain, which are then stored using a hash table-based adaptive method that retains only essential fluid simulation data, analogous to selectively populating cells in traditional grid-based solvers.
 

The numerical part of the solver for blood flow simulation is written using the CUDA C programming language, a parallel computation platform, and a programming model that allows execution on NVIDIA GPUs. In addition to the numerical part of this work, the ray-casting algorithm that identifies fluid points in the vascular region was also parallelized on the GPU, to optimize the detection to be more efficient and faster in the 3-D grid. This significantly improves performance, especially in patient-specific vascular geometry with a large number of grid points. The hash table approach was also used to classify neighbor indices in the streaming step of the LBM. This allows the solver to pull distribution functions from neighboring indices in O(1) time complexity, which represents a substantial gain in efficiency over linear search-based methods that are of O(n) complexity. Two simulations were performed on a realistic patient-specific vascular model with single and multiple bifurcations to analyze flow behavior under increasingly complex hemodynamic conditions. The study presents results related to blood flow velocity within the vascular region, as well as wall shear stress distribution along the vascular surface.