Combinations of three-dimensional (3-D), one dimensional (1-D) and lumped parameter (0-D) models have been proposed to model blood flow in vessels. Within the field of 1-D modeling there has been an upward trend in the total number of arterial vessels computed. However, as we increase the spatial dimensions of our models we require larger amounts of clinical data to determine all the model parameters for patient-specific simulations in the clinical setting.

Using a verified 55-vessel, nonlinear, 1-D model of pulse wave propagation in elastic vessels we systematically reduced the number of generations of bifurcations, while preserving the total compliance and net peripheral resistance of the system, to better understand the contributions of multiple reflections at each branching site to the pressure waveform measured along the upper aorta. This was achieved by reducing systematically 1-D model peripheral vessels to three-element 0-D Windkessel models that account for vessel tapering. When applied to the baseline 55-artery model we observed that a reduction in the generations of bifurcations from 5 to 1 resulted in a root-mean-square difference of aortic pressure and flow waveform shape of 0.3% and 17.9% respectively. We further assessed the methodology applied to four adaptations of the baseline model using generalised arterial stiffening, an iliac stenosis, carotid stent or abdominal aortic aneurysm.

Our study shows that a 1-D model can efficiently simulate the aortic pressure and flow waveforms with less than 20 arterial segments.