Flow networks of length-changing vessels

From the human lymphatic system to the slime mold, vessel contractions play a pivotal role in driving fluid flows through biological networks. Typically, these contractions are modeled as a changing radius which induces flow by mass continuity. However, a change in vessel length can also drive flow. For the jellyfish gastrovascular system, these length changes may be just as important in determining the flow through the network. Longitudinal contractions have more subtle geometric properties, especially when considered in networks, since the node positions and edge lengths become time dependent. We will demonstrate how to incorporate longitudinal contractions in networks of elastic fluid-carrying vessels that relies only on the Lagrangian coordinates of the deforming material. This description allows one to incorporate properties of the elastic vessels to determine how longitudinal deformations, radial deformations, and fluid properties are coupled. We will begin by demonstrating the properties of longitudinal contractions in single vessels, then apply the theory to complex networks inspired by the jellyfish.