A coupling strategy for a first 3D-1D model of the cardiovascular system
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The bidirectional coupling of the circulatory system with the heart, which allows changes in the arterial system to adjust the pulsatile load on the heart, is a crucial aspect in the cardiac mechanical function. When contemplating coupling with anatomically accurate 3D electromechanical (EM) models, current image-based cardiac EM computer models use 0D representations of the vasculature. These, however, neglect significant effects related to pulse wave transmission. 1D models are necessary to account for these effects, although 3D-1D coupling is still challenging. In this talk, we present a novel and robust strategy for coupling a 3D cardiac EM model with 1D arterial blood flow model. In particular, a personalised coupled 3D-1D model of the left ventricle and artery system is developed for the first time and employed in numerical benchmarks to illustrate the accuracy and robustness of our method over a variety of time steps. The physiological response of the coupled system to alterations in the arterial system affecting pulse wave propagation, such as aortic stiffening, aortic stenosis, or bifurcations creating wave reflections, is studied in order to validate the coupled model. In terms of clinical application, we additionally present the results of a thorough variance-based sensitivity analysis for the new coupled 3D-1D model. The method under consideration is based on the employment of Gaussian process emulators to build precise surrogates for the coupled model and to efficiently perform sensitivity analyses to characterise the relative importance of the model input parameters to the model output.
