Oscillatory Flow Networks with Valves

To first approximation, fluidic networks are modeled as linear resistor networks, allowing for a straightforward calculation of the flows depending on the driving pressures, which can be steady or oscillating. However, when valves are present, the flow response is nonlinear such that the flow along one direction is prefered. This mechanism is utilized by the lymphatic system, which consists of a network of contracting lymphangions and one-way valves that allow the lymph to incrementally overcome a negative pressure gradient even when the peristaltic pumping direction is opposite that of the mean flow. Modeling a chain of lymphangions in series allows one to understand the cooperation between peristalsis and valves. However, this alone is insufficient to study complications that arise at the network level, when the network contains loops and branches. The orientation induced by valves must compete with the orientation given by the sign of the mean pressure drop. In order to achieve positive flow in a network with unfavorable pressure conditions, the placement of the valves in the network becomes important.