A coupling strategy for a 3D-1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function

The impact of increased stiffness and pulsatile load on the circulation and their influence on heart performance have been documented not only for cardiovascular events but also for ventricular dysfunctions. For this reason, computer models of cardiac electromechanics (EM) have to integrate effects of the circulatory system on heart function to be relevant for clinical applications. Currently it is not feasible to consider three-dimensional (3D) models of the entire circulation. Instead, simplified representations of the circulation are used, ensuring a satisfactory trade-off between accuracy and computational cost. In this work, we propose a novel and stable strategy to couple a 3D EM model of the heart to a one-dimensional (1D) model of blood flow in the arterial system. A personalised coupled 3D-1D model of LV and arterial system is built and used in a numerical benchmark to demonstrate robustness and accuracy of our scheme over a range of time steps. Validation of the coupled model is performed by investigating the coupled system's physiological response to variations in the arterial system affecting pulse wave propagation, comprising aortic stiffening, aortic stenosis or bifurcations causing wave reflections. Our results show that the coupled 3D-1D model is robust, stable and correctly replicates known physiology. In comparison with standard coupled 3D-0D models, additional computational costs are negligible, thus facilitating the use of our coupled 3D-1D model as a key methodology in studies where wave propagation effects are under investigation.