School of Electrical Engineering, Shandong University, Jinan 250061, China.
Math Biosci Eng. 2020 Oct 30;17(6):7519-7543. doi: 10.3934/mbe.2020384.
The mathematical modeling of the cardiovascular system is a simple and noninvasive method to comprehend hemodynamics and the operating mechanism of the mechanical circulatory assist device. In this study, a numerical model was developed to simulate hemodynamics under different conditions and to evaluate the operating condition of continuous-flow left ventricular assist device (LVAD). The numerical model consisted of a cardiovascular lumped parameter (CLP) model, a baroreflex model, and an LVAD model. The CLP model was established to simulate the human cardiovascular system including the left heart, right heart, systemic circulation, and pulmonary circulation. The baroreflex model was used to regulate left and right ventricular end-systolic elastances, systemic vascular resistance, and heart rate. The centrifugal pump HeartMate III used as an example to simulate the rotary pump dynamics at different operating speeds. Simulation results show that hemodynamics under normal, left ventricular failure and different levels of pump support conditions can be reproduced by the numerical model. Based on simulation results, HeartMate III operating speed can be maintained between 3600 rpm and 4400 rpm to avoid pump regurgitation and ventricular suction. Additionally, in the simulation system, the HeartMate III operating speed should be between 3600 rpm and 3800 rpm to provide optimal physiological perfusion. Thus, the developed numerical model is a feasible solution to simulate hemodynamics and evaluate the operating condition of continuous-flow LVAD.
心血管系统的数学建模是一种理解血液动力学和机械循环辅助装置工作机制的简单、非侵入性方法。本研究开发了一个数值模型,以模拟不同条件下的血液动力学,并评估连续流左心室辅助装置(LVAD)的工作状态。数值模型由心血管集总参数(CLP)模型、压力反射模型和 LVAD 模型组成。CLP 模型用于模拟包括左心、右心、体循环和肺循环在内的人体心血管系统。压力反射模型用于调节左、右心室收缩末期弹性、体循环阻力和心率。以 HeartMate III 离心泵为例,模拟不同工作速度下的旋转泵动力学。模拟结果表明,数值模型可以再现正常、左心室衰竭和不同程度泵支持条件下的血液动力学。基于模拟结果,HeartMate III 的工作速度可以保持在 3600 rpm 到 4400 rpm 之间,以避免泵反流和心室抽吸。此外,在模拟系统中,HeartMate III 的工作速度应在 3600 rpm 到 3800 rpm 之间,以提供最佳的生理灌注。因此,开发的数值模型是一种模拟血液动力学和评估连续流 LVAD 工作状态的可行方法。