Peristaltic flow in nonlinear networks

Many biological systems, such as Physarum polycephalum, utilize peristaltic pumping to direct solutes through flow networks. When the fluid satisfies a linear pressure-flow relationship, pumping is optimized by coordinated peristalsis with a wavelength comparable to the system size. However, when a fluid interacts with flexible structures, such as the valves in the venous and lymphatic systems, pressure-flow relationships can be highly nonlinear. Interestingly, synchronous contractions can be more effective than peristaltic waves in driving flow through nonlinear edges. Another possibility in nonlinear edges is that flow may be induced opposite the peristalsis direction due to the rectification of oscillating flows by valves. These effects can persist in networks, but only if the valves are carefully placed throughout the network. A theory of peristaltic fluid flow through vessels with a nonlinear pressure-flow relationship is developed, and it is argued that coordination in valve placement is vital for the system to operate, while coordination between contractions is less important than in the linear network.