Turbulent finite element model applied for blood flow calculation in arterial bifurcation

Due to the relatively low fluid velocities in major arteries and veins, blood flow is by default laminar, however, turbulence can occur as a result of stenosis or other obstacles. Hemodynamic parameters like Wall Shear Stress or Oscillatory Shear Index can be used for plaque formation prediction, and these parameters are depended on the nature of the flow. Implementation of the k-ω turbulent flow in the Finite Element solver aims to improve numerical analysis of cardio-vascular condition development and progression. Calculation of turbulent fluid flow in this paper is performed using a two-equation turbulent finite element model that can calculate values in the viscous sublayer.

Implicit integration of the equations is used for determining the fluid velocity, turbulent kinetic energy and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of the incremental-iterative procedure. Developed turbulent finite element model with the customized generation of finite element meshes is used for calculating complex blood flow problems.

Turbulent model is verified on an example of fluid flow in the backward-facing step channel and analysis results correspond well with the experimental ones from the literature. Further, a turbulent model is applied for the simulation of blood flow through artery bifurcation. Verification of numerical examples obtained using different commercial software packages (Ansys, COMSOL Multiphysics) ensuring usage and accuracy of PAK in-house solver.

Analysis results show that turbulence cannot be neglected in the modelling of cardio-vascular conditions and that cardiologists can use the proposed tools and methods for investigating the hemodynamic conditions inside the bifurcation of arteries. Appropriate agreement between experimental results, and results obtained using commercial solutions and the k-ω turbulent flow in the Finite Element solver PAK, validate methodology presented in this paper. However, small deviations between the results underline the importance of the proper boundary condition prescription and mesh size and node distribution, which is also discussed in this paper. Due to the implicit integration implemented in PAK solver, time step size has an insignificant influence on the analysis results, assuming the initial time increments are sufficiently small to ensure proper discretization of velocity and pressure pulsatile functions.