Hemodynamics of Ventricular-Arterial Coupling under Enhanced External Counterpulsation: An Optimized Dual-Source Lumped Parameter Model

Background and Objective Enhanced external counterpulsation (EECP) is a mechanically assisted circulation technique widely used in the rehabilitation and management of ischemic cardiovascular diseases. It contributes to cardiovascular functions by regulating the afterload of ventricle to improve hemodynamic effects, including increased diastolic blood pressure at aortic root, increased cardiac output and enhanced blood perfusion to multiple organs including coronary circulation. However, the effects of EECP on the coupling of the ventricle and the arterial system, termed ventricular-arterial coupling (VAC), remain elusive. We aimed to investigate the acute effect of EECP on the dynamic interaction between the left ventricle and its afterload of the arterial system from the perspective of ventricular output work. Methods A neural network assisted optimization algorithm was proposed to identify the ordinary differential equation (ODE) relation between aortic root blood pressure and flow rate. Based on the optimized order of ODE, a lumped parameter model (LPM) under EECP was developed taking into consideration of the simultaneous action of cardiac and EECP pressure sources. The ventricular output work, in terms of aortic pressure and flow rate cooperated with the LPM, was used to characterize the VAC of ventricle and its afterload. The VAC subjected to the principle of minimal ventricular output work was validated by solving the Euler-Poisson equation of cost function, ultimately determining the waveforms of aortic pressure and flow rate. Results A third-order ODE can precisely describe the hemodynamic relationship between aortic pressure and flow rate. An optimized dual-source LPM with three energy-storage elements has been constructed, showing the potential in probing VAC under EECP. The LPM simulation results demonstrated that the VAC in terms of aortic pressure and flow rate yielded to the minimal ventricular output work under different EECP pressures. Conclusions The ventricular-arterial coupling under EECP is subjected to the minimal ventricular output work, which can serve as a criterion for determining aortic pressure and flow rate. This study provides insight for the understanding of VAC and has the potential in characterizing the performance of the ventricular and arterial system under EECP.