Question

at a bifurcation in an artery, you note that the cross-sectional area of each daughter artery is 20% of that for the parent artery. What is the ratio of the transmitted and reflected pressure wave magnitudes assuming the wave velocity co is the same in the parent and daughter arteries?

Answer 1

Any discontinuity in the properties of the artery will cause the wavefronts to produce reflected and transmitted waves according to the type of discontinuity. There are many types of discontinuities in the arterial system; changes in the area, local changes in the elastic properties of the arterial wall, bifurcations, etc.

We will mainly consider two types of discontinuity: changes in properties in single arteries and bifurcations.

For a symmetrical bifurcation that is well-matched in the forward direction, the area ratio for a wave travelling backwards in one of the daughter's vessels is approximately &alpha = 2.7. The reflection coefficient for this backward wave is approximately R = -0.5 which means that approximately half of the energy of the backward wave will be reflected back in the forward direction and that this wave will be of the opposite type as the incident wave (i.e. a compression wavefront will be reflected as an expansion wavefront and an expansion wavefront will be reflected as a compression wavefront.

This is reasonable physically because the backward wave approaching the bifurcation in one of the daughter's vessels (now the parent vessel) will see a bifurcation consisting of its twin vessel and the parent vessel with a net area much larger than its own. The bifurcation will, therefore, act more like an open-end tube and generate a negative reflection coefficient.