Nonlinear lumped-parameter models for blood flow simulations in networks of vessels

To address the issue of computational efficiency related to modelling blood flow in complex networks, we derive a family nonlinear lumped-parameter models for compliant vessels departing from well-established one-dimensional model. These 0D must preserve important properties original 1D model: nonlinearity pressure-area relation and pressure-dependent parameters characterizing models, resistance R inductance L , defined terms time-dependent cross-sectional area subject pressure changes. We introduce suitable coupling conditions join through junctions construct networks preserving network topology. The newly derived are then applied several arterial predicted results compared against (i) reference results, validate assess their ability reproduce good approximations waveforms all at much lower cost, measured CPU time, (ii) linear evaluate improvement gained by including certain nonlinearities agreement with results.