Mechanics of wave reflections in a coronary bypass loop model: the possibility of partial flow cut-off

Local hemodynamics in a bypass loop model with dimensions typical of those in the human coronary circulation are studied, particularly with regards to the effects of wave reflections. While in a single vessel of such dimensions and a single source of wave reflections the effects would be insignificant, in a bypass loop the combination of a narrowed vessel with a converging junction and several reflection sites may produce wave reflections with significant effects on the pressure and flow distributions within the vessels forming the loop. Calculations to test this possibility were performed, based on D'Alembert's solutions of the wave equation and with a proposed matching scheme to deal with the converging junction. The results indicate that there are very large wave reflection effects at a frequency of 10 Hz, smaller but significant effects at 5 Hz, and some insignificant effects at 1 Hz. The results also indicate that partial flow cut-off may occur within the loop under some singular circumstances, whereby certain harmonic components of the incident wave are totally reflected. In the clinical setting these effects would detract from the efficiency of the bypass as a conduit, to a degree dependent on the degree of occlusion of the bypassed vessel. The choice of a larger diameter for the bypass appears to diminish this dependence and is thus on the whole favorable despite the contribution it makes to impedance mismatch at the junction.