  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.
