Zero-dimensional lumped approach to incorporate the dynamic part of the pressure at vessel junctions in a 1D wave propagation model

A benchmark study by Boileau et al tested 6 commonly used numerical schemes for 1D wave propagation, for their ability to capture the main features of pressure, flow, and area waveforms in large arteries. While all numerical schemes showed good agreement in pressure and flow waveforms for smaller arterial networks, the simplified trapezium rule method proposed by Kroon et al showed an overestimation for the systolic pressure of 1% in proximal regions and an underestimation of 3% in distal regions in comparison with the 5 other schemes when using a larger arterial network, published as the ADAN56 model. The authors attributed this difference to the neglection of the dynamic part of the pressure at vessel junctions. Carson et al resolved these differences by proposing 2 methods to implement the dynamic part of the pressure in the simplified trapezium rule method scheme. In the present study, an alternative method is introduced extending the work by Kroon et al. This alternative method consists of a new 0D element, which is placed at vessel junctions. The strength of this new element is the ease of implementation and its flexible coupling with other elements, without introducing additional degrees of freedom or the need of a penalty function. This new approach is compared with 5 other numerical schemes, which already have the dynamic part of the pressure incorporated. The new method shows excellent agreement with these schemes for the ADAN56 model.