Fluid-structure interaction simulations of venous valves: A monolithic ALE method for large structural displacements

Area of Science:

• Biomedical Engineering
• Computational Fluid Dynamics
• Medical Simulation

Background:

• Venous valves are crucial for unidirectional blood flow, preventing backflow to the heart.
• Simulating venous valve dynamics involves fluid-structure interaction (FSI), which is prone to numerical instabilities due to large structural displacements.
• Existing simulation methods often suffer from mesh deterioration and solver divergence when modeling the complex behavior of venous valves.

Purpose of the Study:

• To develop and validate a robust arbitrary Lagrangian-Eulerian (ALE) scheme for accurate FSI simulations of venous valves.
• To address and overcome the numerical instabilities encountered in previous simulations of venous valve mechanics.
• To enable reliable reconstruction of venous valve opening and closing phases through advanced computational modeling.

Main Methods:

• A monolithic formulation for the FSI problem was employed, utilizing automatic differentiation for Jacobian matrix evaluation.
• The proposed ALE scheme incorporates a staggered-in-time velocity and fictitious springs to model leaflet contact forces, enhancing stability.
• A novel smoothing technique for fluid displacement, based on a distance scaling factor, prevents mesh entanglement in the fluid domain.
• The Streamline Upwind Petrov-Galerkin (SUPG) method was integrated to further improve simulation stability.

Main Results:

• The proposed ALE scheme effectively handles large structural displacements inherent in venous valve simulations.
• The method successfully prevents mesh entanglements and solver divergence, ensuring stable numerical solutions.
• Simulations accurately reconstructed the dynamic behavior of a two-dimensional venous valve model during both opening and closing phases.

Conclusions:

• The developed ALE scheme provides a stable and accurate approach for FSI simulations of venous valves.
• This method overcomes significant numerical challenges, enabling more reliable computational modeling of venous valve function.
• The findings facilitate better understanding and potential clinical applications related to venous valve mechanics.