Integrated lumped parameter modeling of cardiac–vascular interaction with valve dynamics and ventricular pressure–volume

Figures

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  FIGURE 1. Lumped parameter model of the closed-loop cardiovascular system illustrating the coupling between cardiac chambers, valve dynamics, and vascular compartments. The left and right hearts are represented by time-varying elastance models for the atria and ventricles, where chamber pressures depend on instantaneous volume and elastance. Cardiac valves (mitral, aortic, tricuspid, and pulmonary) regulate flow between adjacent compartments and are modeled using pressure-driven nonlinear flow relations with a dynamically varying effective opening area. The pulmonary and systemic circulations are represented using interconnected resistance (R), compliance (C), and inertance (L) elements, corresponding to viscous losses, vascular elasticity, and blood inertia, respectively. Arterial segments incorporate R–L–C configurations to capture pulsatile flow dynamics and pressure wave propagation, whereas venous and capillary compartments are modeled primarily using R–C elements due to negligible inertial effects. Pressure (P), flow rate (Q), and volume (V) variables are defined at each compartment, ensuring continuity and full coupling across the network. The closed-loop structure enables…

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  FIGURE 2. Time-resolved hemodynamic waveforms of the left heart over one complete cardiac cycle and comparison with the reference model of Korakianitis and Shi (2006). (a) Left ventricular pressure (Plv) and systemic aortic sinus (Psas), demonstrating isovolumetric contraction, systolic ejection, and diastolic decay with clear identification of the dicrotic notch. (b) Aortic (Qao) and mitral (Qmi) flow rates, illustrating systolic ejection through the aortic valve and biphasic diastolic filling (E-wave and A-wave) through the mitral valve. (c) Left ventricular volume variation, showing end-diastolic and end-systolic volumes, stroke volume, and distinct isovolumetric phases. Solid lines represent the present model, and dashed lines indicate the reference data.

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  FIGURE 3. Hemodynamic characteristics of aortic valve dynamics and ventricular pumping behavior under three simulated conditions: aortic stenosis (AS), aortic stenosis with increased left ventricular stiffness (AS + LV stiffness), and aortic stenosis with reduced vascular compliance (AS + VC↓). (a) Temporal variation of the transvalvular pressure difference during the ejection phase, defined as ΔPt=Plvt−Psast , evaluated only when the aortic valve flow Qaot > 0. This parameter represents the instantaneous pressure load across the aortic valve that the left ventricle must overcome during blood ejection. (b) Left ventricular pressure–volume (PV) loop illustrating the relationship between ventricular pressure and volume over one complete cardiac cycle. The loop describes the sequential phases of ventricular filling, isovolumetric contraction, ejection, and isovolumetric relaxation, and reflects the mechanical work performed by the ventricle. (c) Aortic valve flow waveform Qaot showing the instantaneous blood flow rate through the aortic valve during systole. The waveform indicates the onset of valve opening, peak ejection flow, and the deceleration of flow associated with valve closure…

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  FIGURE 4. Sensitivity of model outputs to variations in key cardiovascular parameters under three operating > conditions (S1–S3). (a) Effect of arterial compliance (Csat, ±SD), (b) effect of minimum elastance (Emin, ±SD), and (c) effect of stenosis severity (θmax, adjacent levels) on stroke volume (SV) and peak pressure difference (ΔPpeak). Positive (+) and negative (−) perturbations indicate increases and decreases, respectively, in the corresponding input parameters. The results showed that arterial compliance had a relatively small influence on both outputs; minimum elastance produced moderate changes, with increasing sensitivity from S1 to S3; and stenosis severity had a dominant effect on ΔPpeak with minimal impact on SV.