Lumped Parameter Outflow Models for 1-D Blood Flow Simulations: Effect on Pulse Waves and Parameter Estimation (Communications in Computational Physics, 2018)
Several lumped parameter, or zero-dimensional (0-D), models of the microcirculation are coupled in the time domain to the nonlinear, one-dimensional (1-D)equations of blood flow in large arteries. A linear analysis of the coupled system, together with in vivo observations, shows that: (i) an inflow resistance that matches thecharacteristic impedance of the terminal arteries is required to avoid non-physiologicalwave reflections; (ii) periodic mean pressures and flow distributions in large arteriesdepend on arterial and peripheral resistances, but not on the compliances and inertias of the system, which only affect instantaneous pressure and flow waveforms; (iii)peripheral inertias have a minor effect on pulse waveforms under normal conditions;and (iv) the time constant of the diastolic pressure decay is the same in any 1-D modelartery, if viscous dissipation can be neglected in these arteries, and it depends on allthe peripheral compliances and resistances of the system. Following this analysis, wepropose an algorithm to accurately estimate peripheral resistances and compliancesfrom in vivo data. This algorithm is verified against numerical data simulated usinga 1-D model network of the 55 largest human arteries, in which the parameters of theperipheral windkessel outflow models are known a priori. Pressure and flow waveforms in the aorta and the first generation of bifurcations are reproduced with relativeroot-mean-square errors smaller than 3%.