Peristaltic pumping in vessels of changing length*

The radial and longitudinal contractions of biological vessels can drive instantaneous fluid flows in an organism. When these contractions propagate as peristaltic waves, net volume can be transported throughout the system, as is the case, for example, with peristaltic pumping in the human esophagus. However, traditional models of peristaltic pumping only account for changes in radius. For some networks, such as the gastrovascular system of the jellyfish, length changes of vessels may be just as important in determining flow properties. We will outline a method of incorporating longitudinal peristalsis that relies only on the Lagrangian coordinates of the deforming material. This description of contractions can be coupled to mechanical properties of the deforming solid boundary such as the Poisson ratio. We explore the results of this model in some simple single-vessel examples. We then demonstrate a novel way of studying flow networks of length-changing vessels using time-dependent node positions.