  Using analytical expressions for the pressure and velocity waveforms in
tapered vessels, we construct a linear 1D model for wave propagation in
stenotic vessels in the frequency domain. We demonstrate that using only two
parameters to approximate the exact geometry of the constriction (length and
degree of stenosis), we can construct a model that can be solved analytically
and can approximate with excellent accuracy the response of the original vessel
for a wide range of physiologically relevant frequencies. We then proceed to
compare the 1D results with full 3D FSI results from the literature for
parameters corresponding to an idealized stenotic carotid artery. We find
excellent matching with the volume flow rate over the cardiac cycle (less than
$1\%$ error). Using results from DNS simulations to parametrize the velocity
profile in the stenotic region, we manage to predict also the pressure
distribution with small error (a few percentage points). The method proposed in
the paper can be used to approximate vessels of arbitrary shape profile and can
be extended to cover the whole cardiovascular tree. Recursive expressions make
the solution very fast and open the possibility of carrying out sensitivity and
uncertainty quantification studies that require thousands (or even millions) of
simulations with minimal cost.

Fluid Dynamics