A Lattice Boltzmann Method for Non-Newtonian Blood Flow in Coiled Intracranial Aneurysms

TL;DR

The paper tackles the prediction of flow changes in intracranial aneurysms after coil embolization by integrating patient-specific geometry with a coil representation as an inhomogeneous porous medium. It couples volume-averaged Navier–Stokes equations for non-Newtonian blood with a lattice Boltzmann method that uses a variable relaxation rate to capture viscosity, enabling efficient simulations on voxelized geometries. A key contribution is the direct comparison between fully resolved coil geometry and a porous surrogate in a realistic aneurysm, showing good agreement and substantial flow and wall shear stress reductions with increasing packing density. The framework enables patient-specific flow assessment for treatment planning, though questions about parameter calibration and uncertainty quantification remain for future work.

Abstract

Intracranial aneurysms are the leading cause of hemorrhagic stroke. One of the established treatment approaches is the embolization induced by coil insertion. However, the prediction of treatment and subsequent changed flow characteristics in the aneurysm is still an open problem. In this work, we present an approach based on a patient-specific geometry and parameters including a coil representation as inhomogeneous porous medium. The model consists of the volume-averaged Navier-Stokes equations for a non-Newtonian blood rheology. We solve these equations using a problem-adapted lattice Boltzmann method and present a comparison between fully-resolved and volume-averaged simulations. The results indicate the validity of the model. Overall, this workflow allows for patient specific assessment of the flow due to potential treatment.

Figures (8)

• Figure 1: Cross-section of the resulting porosity field (color) for the three coils (3D shadow) with packing density of 15%, 20% and 25% (left to right).
• Figure 2: Velocity magnitude $\|\vec{u}\|$ [m/s] during systole ($t \approx 1.23$ s) in the aneurysm without coil plotted over a cross-section (left) and stream lines in the cut off aneurysm region (right).
• Figure 3: Velocity magnitude $\|\vec{u}\|$ [m/s] during systole ($t \approx 1.23$ s) in the aneurysm with fully resolved coil of 15% packing density (left) and with averaged porosity field (right).
• Figure 4: Velocity magnitude $\|\vec{u}\|$ [m/s] during systole ($t \approx 1.23$ s) in the aneurysm with fully resolved coil of 20% packing density (left) and with averaged porosity field (right).
• Figure 5: Velocity magnitude $\|\vec{u}\|$ [m/s] during systole ($t \approx 1.23$ s) in the aneurysm with fully resolved coil of 25% packing density (left) and with averaged porosity field (right).

Theorems & Definitions (1)

• remark 1: Velocity solution for anisotropic permeability