Nonlinear Lumped-Parameter Cardiovascular Modeling Using Time-Varying Elastance for Pressure–Volume Loop and Cuffless Blood Pressure Analysis

Abstract

This study presents a mathematical model of cardiovascular dynamics based on a lumped-parameter approach for analyzing left ventricular pressure–volume (PV) relationships. The model employs a time-varying elastance formulation to represent ventricular mechanics during systole and diastole and introduces a pressure-dependent nonlinear vascular resistance term to improve physiological realism. The governing differential equations are solved numerically using the fourth-order Runge–Kutta (RK4) method with a fixed time step. Simulations were conducted under several physiological conditions, including normal conditions, increased and decreased afterload, and increased heart rate. The results show that the proposed model successfully reproduces physiologically realistic Pressure–volume (PV) loopand stable ventricular volume waveforms. Under increased afterload, the nonlinear resistance term becomes more significant, leading to elevated systolic pressure and reduced stroke volume. In contrast, under normal and low-pressure conditions, the nonlinear contribution remains relatively small, causing the system to behave similarly to linear models. In addition, waveform analysis indicates that afterload variations mainly affect waveform amplitude, whereas heart rate influences temporal spacing between cycles. These findings demonstrate that the proposed model provides improved sensitivity to pressure variations and offers a more realistic representation of cardiovascular dynamics, supporting potential applications in cuffless blood pressure estimation using photoplethysmography (PPG).