A one-dimensional arterial network model for bypass graft assessment

We propose an arterial network model based on one-dimensional hemodynamic equations to study the behavior of different vascular surgical bypass grafts in the case of an arterial occlusive pathology: a stenosis of the Right Iliac artery. We investigate the performances of three different bypass grafts (Aorto-Femoral, Axillo-Femoral and cross-over Femoral) depending on the degree of obstruction of the stenosis. Numerical simulations show that all bypass grafts are efficient since we retrieve in each case the healthy hemodynamics downstream of the stenosed region while ensuring at the same time a global healthy circulation. We analyze in detail the behavior of the Axillo-Femoral bypass graft by performing hundreds of simulations where we vary the values of its Young's modulus [0.1-50 MPa] and radius [0.01-5 cm]. Our analysis shows that Young's modulus and radius of commercial bypass grafts are optimal in terms of hemodynamic considerations. Our numerical findings prove that this model approach can be used to optimize or plan patient-specific surgeries, to numerically assess the viability of bypass grafts and to perform parametric analysis and error propagation evaluations by running extensive simulations.