Steady and pulsatile flow distribution in a multiple branching network with physiological applications

Flow rate of distribution in steady and pulsatile flow is investigated in a multiple branching network including six successive generations in the same plane. In this model, the geometry dependence of flow rate distribution has already been pointed out in steady flow (previous study) by observing the occurrence of non-uniform flow rate distribution at terminal orifices despite the symmetrical dichotomy, identical distance and cross-sectional profile of the 64 parallel pathways. In the present study, we point out two additional properties of the steady flow rate distribution. (i) The flow rate distribution is not markedly sensitive to a change in viscosity and therefore Reynolds number does not appear to be a determinant factor to modify the flow distribution. (ii) The effect of a branch obstruction on flow rate distribution is limited in space and its extension remains the same for the different Reynolds numbers tested. These properties also characterize the interdependence between the model geometry and the flow distribution in steady state. The results obtained in pulsatile flow show that the flow distribution remains similar to steady state as long as the parameter lambda = Qp/Qs (Qp = amplitude of flow oscillation, Qs = steady component of the total flow) is less than 1. When lambda is greater than 1, the flow distribution may become uniform, which means that contrary to the steady flow case, the velocity profiles become rapidly symmetrical downstream from the bifurcations. Physical explanations for this are proposed after considering the theoretical problem of pulsatile developed flow in a straight tube. In this case, the parameter lambda again plays a crucial role in the velocity distribution.