  We propose an arterial network model based on 1D blood hemodynamic equations
to study the behavior of different vascular surgical bypass grafts in case of
an arterial occlusive pathology: an obliteration or stenosis of the iliac
artery. We investigate the performances of three different bypass grafts
(Aorto-Femoral, Axillo-Femoral and cross-over Femoral) depending on the degree
of obliteration of the stenosis. Numerical simulations show that all bypass
grafts are efficient since we retrieve in all cases the normal hemodynamics in
the stenosed region while ensuring at the same time a global healthy
circulation. We analyze in particular the Axillo-Femoral bypass graft by
performing hundreds of simulations by varying the values of the Young's modulus
[0.1--50 MPa] and the radius [0.01--5 cm] of the bypass graft. We show that the
Young's modulus and radius of commercial bypass grafts are optimal in terms of
hemodynamic considerations. The numerical findings prove that this approach
could be used to optimize or plan surgeries for specific patients, to perform
parameter's statistics and error propagation evaluations by running extensive
simulations, or to characterize numerically specific bypass grafts.
