Pulsatile flow through an idealized arterial bypass graft: an application of the constructal design method

Bypass grafts promote blood flow impaired by a partial obstruction (stenosis) of arteries by fat accumulation. This type of system’s computational modeling is used to understand the flow characteristics and look for reasons and solutions for postoperative failures. The present work deals with the effects of changes in geometry in the performance of a system consisting of an idealized partially obstructed artery and a bypass graft. The constructal design method has been employed in previous works in the analysis of such system assuming steady-state flow. In the present work, blood flow is modeled as transient and pulsatile. The constructal design method is used to determine the performance indicator (dimensionless pressure drop), constraints (system volume and stenosis degrees–50% and 75%) and degrees of freedom: junction angle (30º ≤ α ≤ 70º) and diameter ratio (0.5 ≤ D1/ D ≤ 1). The response surface methodology was used to evaluate the conditions of minimum pressure drop in transient conditions. As the junction angle decreased to 30º, and the diameter ratio increased to 1, the pressure drop decreased, and there was a considerable dependence of pressure drop on the stenosis degree. The effects of the diameter ratio were more pronounced than those of the junction angle. A resistance model based on an analogy with an electronic circuit was introduced, resulting in a correlation for the pressure drop due to the bypass. This correlation confirmed that the point (, D1∕D) = (30◦, 1) is a point of minimization of flow resistance. The application of the constructal design method in hemodynamics might be an excellent alternative to configuring enhanced performance and providing valuable results to the understanding of biological flows.