A nonlinear windkessel model for cardiovascular dynamics: Variable compliance and pathological simulations

Area of Science:

• Cardiovascular Physiology
• Computational Modeling
• Biomedical Engineering

Background:

• Traditional lumped-parameter cardiovascular models often assume linear arterial compliance.
• Pressure-independent arterial compliance limits physiological interpretability and accuracy.
• There is a need for more sophisticated models that capture nonlinear arterial dynamics.

Purpose of the Study:

• To introduce a nonlinear extension of the Windkessel model incorporating pressure-dependent aortic compliance.
• To develop a physiologically grounded cardiovascular model for improved simulation accuracy.
• To provide a platform for analyzing cardiovascular pathologies and model sensitivity.

Main Methods:

• A nonlinear extension of the closed-loop Windkessel model was developed.
• Aortic compliance was defined as an exponential function of aortic pressure.
• A twelve-state formulation using an RLC network and time-varying ventricular elastances was derived from Kirchhoff's laws.

Main Results:

• The nonlinear model accurately reproduced linear model results under nominal conditions.
• Pressure-dependent compliance selectively modulated proximal pulsatility away from nominal operating points.
• Mean arterial pressure, stroke volume, and cardiac output were largely preserved across conditions.
• Simulations showed distinct signatures for aortic regurgitation and arterial stiffening.

Conclusions:

• The proposed nonlinear cardiovascular model offers enhanced physiological realism and interpretability.
• This compact model serves as a valuable tool for cardiovascular research, including pathological emulation and sensitivity analysis.
• The formulation advances lumped-parameter modeling by incorporating key nonlinear arterial mechanics.