The aortic sinus vortex

Area of Science:

• Cardiovascular fluid dynamics
• Computational fluid dynamics
• Biomechanical modeling

Background:

• The aortic sinus plays a critical role in cardiovascular function, particularly in aortic valve closure.
• Understanding the fluid dynamics within the aortic sinus is essential for diagnosing and treating related pathologies.

Purpose of the Study:

• To develop and validate analytical and numerical methods for simulating blood flow in the aortic sinus.
• To investigate the formation and stability of vortices within the aortic sinus.
• To elucidate the role of these vortices in aortic valve closure.

Main Methods:

• Utilized point vortex dynamics and conformal mapping for analytical modeling.
• Employed Chorin's vortex method combined with conformal mapping for numerical simulations, incorporating fluid viscosity.
• Developed explicit formulas for vortex velocities and resolved domain singularities.

Main Results:

• The analytical model provided insights into vortex stability and valve closure mechanisms but had limitations in predicting vortex formation.
• The numerical method successfully modeled vortex formation and confirmed the analytical model's predictions regarding the vortex's role in valve closure.
• Conformal mapping effectively handled singularities and provided explicit velocity calculations.

Conclusions:

• A hybrid analytical-numerical approach using point vortex dynamics and conformal mapping offers a robust framework for aortic sinus flow analysis.
• The developed methods enhance the understanding of vortex dynamics crucial for aortic valve function.
• This research provides a foundation for more accurate biomechanical modeling of cardiovascular flows.