A one-dimensional fluid dynamic model of the systemic arteries

Area of Science:

• Biomedical Engineering
• Computational Fluid Dynamics
• Cardiovascular Physiology

Background:

• Systemic arteries are complex, branching networks.
• Accurate modeling of blood flow and pressure is crucial for cardiovascular research.
• Full Navier-Stokes simulations of the entire arterial tree are computationally prohibitive.

Purpose of the Study:

• To develop a computationally feasible model for predicting blood flow and pressure in the systemic arterial tree.
• To introduce a novel outflow boundary condition based on physiological principles.
• To accurately represent wave propagation and phase lag in arterial dynamics.

Main Methods:

• Modeling the systemic arteries as a structured, bifurcating tree of compliant, tapering vessels.
• Truncating the arterial tree after a limited number of generations.
• Calculating root impedance using a semi-analytical approach.
• Linearizing fluid dynamic equations to obtain a solvable wave equation for each vessel.
• Applying a dynamical outflow boundary condition derived from physiological principles.

Main Results:

• The proposed model provides a computationally feasible method for predicting blood flow and pressure.
• The model accurately captures the phase lag between flow and pressure.
• Wave propagation effects throughout the systemic arterial tree are accommodated.
• Comparison with a standard Windkessel model shows comparable or improved results.

Conclusions:

• The structured tree model with a semi-analytical root impedance and dynamical boundary condition is a viable approach for simulating systemic arterial hemodynamics.
• This method offers a balance between physiological accuracy and computational efficiency.
• The model enhances our understanding of cardiovascular dynamics and wave propagation.