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

Lumped-parameter cardiovascular models are computationally efficient and physiologically interpretable, but many still represent arterial compliance as linear and pressure-independent. Here, we introduce a nonlinear extension of a classical closed-loop Windkessel model by defining aortic compliance as an exponential function of aortic pressure. The heart, systemic circulation, and pulmonary circulation are represented as an RLC network with time-varying ventricular elastances, yielding a twelve-state formulation derived from Kirchhoff's laws. Under nominal conditions, the nonlinear model recovers the linear baseline, with near-superimposable pressure and flow waveforms and physiologically plausible steady-state indices. Away from the nominal operating point, the pressure-dependent law selectively modulates proximal pulsatility, while mean arterial pressure, stroke volume, and cardiac output remain comparatively preserved. Targeted parameter changes produce qualitative waveform and index-level signatures consistent with aortic regurgitation and arterial stiffening. The proposed formulation provides a compact, physiologically grounded platform for sensitivity analysis, pathological emulation, and early-stage evaluation of cardiovascular modeling scenarios.