A lumped parameter model to evaluate the fluid dynamics of different coronary bypasses

Coronary bypass grafting is a surgical procedure frequently performed to obtain myocardial reperfusion downstream from severe coronary stenoses. Different surgical techniques may be adopted which include the use of graft made of internal mammary artery or saphenous vein, and the adoption of multiple or sequential bypasses for more than one stenosis. The haemodynamics of the surgically reconstructed coronary bed is strongly dependent on the bypass configuration and may induce atherogenic processes affecting the long-term potency of the bypass. We have improved a closed-loop mathematical model of the cardiovascular system including a more detailed description of the coronary tree which allows the calculation of the flow rate and pressure curves in all the vessels considered. Pathological situations, such as stenoses, have been simulated and investigated. Models of the internal mammary artery and of the saphenous vein have also been developed in order to simulate coronary artery bypasses. The four simulated bypass configurations have been the single saphenous vein, the sequential saphenous vein, the single internal mammary artery and the sequential internal mammary artery. Results of the simulations of the different bypass grafting configurations indicate that between single saphenous vein and single internal mammary artery the latter shows better haemodynamics both for the flow rate pattern and for the calculated wall shear stress. The sequential bypasses show better haemodynamics in comparison with the single bypass in the proximal segments and worse performance in the distal ones. The models may be applied as an investigative tool to evaluate actual cases of surgically treatable coronary stenoses. They can predict the modification in blood flow waveforms, mean velocities, shear stress and distribution of blood flow in the coronary branches as a function of the adopted bypass configuration.