A one-dimensional computational model for blood flow in an elastic blood vessel with a rigid catheter

Area of Science:

• Biomedical Engineering
• Computational Fluid Dynamics
• Mathematical Modeling

Background:

• Strokes are a leading cause of death, requiring complex endovascular treatments.
• Current 3D computational fluid dynamics (CFD) solvers are too slow for planning patient-specific stroke interventions involving large arterial networks.

Purpose of the Study:

• To develop a novel, computationally efficient 1D mathematical model for simulating blood flow in elastic blood vessels with catheters.
• To enable systematic, patient-specific treatment planning for endovascular stroke interventions.

Main Methods:

• A 1D mathematical formulation using first-order hyperbolic partial differential equations was developed.
• The Discontinuous Galerkin method was employed to solve the hyperbolic system.
• The 1D model was validated against a 3D CFD solver using idealized and realistic arterial networks.

Main Results:

• The 1D model demonstrated clinically insignificant differences compared to 3D CFD in steady flow cases (variations <10%).
• Accurate capture of wave reflection phenomena was observed in unsteady flow simulations.
• The 1D model facilitates easier discretization of complex vasculatures with multiple branches.

Conclusions:

• The 1D computational model provides a good balance of accuracy and efficiency for simulating complex vascular geometries.
• This approach shows significant potential for advancing patient-specific simulation and planning of endovascular stroke interventions.