  An improved one-dimensional mathematical model based on Pulsed Flow Equations
(PFE) is derived by integrating the axial component of the momentum equation
over the transient Womersley velocity profile, providing a dynamic momentum
equation whose coefficients are smoothly varying functions of the spatial
variable. The resulting momentum equation along with the continuity equation
and pressure-area relation form our reduced-order model for physiological fluid
flows in one dimension, and are aimed at providing accurate and fast-to-compute
global models for physiological systems represented as networks of quasi
one-dimensional fluid flows. The consequent nonlinear coupled system of
equations is solved by the Lax-Wendroff scheme and is then applied to an open
model arterial network of the human vascular system containing the largest
fifty-five arteries. The proposed model with functional coefficients is
compared with current classical one-dimensional theories which assume steady
state Hagen-Poiseuille velocity profiles, either parabolic or plug-like,
throughout the whole arterial tree. The effects of the nonlinear term in the
momentum equation and different strategies for bifurcation points in the
network, as well as the various lumped parameter outflow boundary conditions
for distal terminal points are also analyzed. The results show that the
proposed model can be used as an efficient tool for investigating the dynamics
of reduced-order models of flows in physiological systems and would, in
particular, be a good candidate for the one-dimensional, system-level component
of geometric multiscale models of physiological systems.
