A model of Stokesian peristalsis and vesicle transport in a three-dimensional closed cavity

The complexity of the mechanics involved in the mammalian reproductive process is evident. Neither an ovum nor an embryo is self-propelled, but move through the oviduct or uterus due to the peristaltic action of the tube walls, imposed pressure gradients, and perhaps ciliary motion. Here we use the method of regularized Stokeslets to model the transport of an ovum or an embryo within a peristaltic tube. We represent the ovum or the embryo as a spherical vesicle of finite volume - not a massless point particle. The outer membrane of the neutrally buoyant vesicle is discretized by nodes that are joined by a network of springs. The elastic moduli of these springs are chosen large enough so that a spherical shape is maintained. For simplicity, here we choose an axisymmetric tube where the geometry of the two-dimensional cross-section along the tube axis reflects that of the sagittal cross-section of the uterine cavity. Although the tube motion is axisymmetric, the presence of the vesicle within the tube requires a fully three-dimensional model. As was found in Yaniv et al. (2009, 2012) for a 2D closed channel, we find that the flow dynamics in a 3D peristaltic tube are strongly influenced by the closed end and the manner in which the peristaltic wave damps out towards the closure. In addition, we demonstrate that the trajectory of a vesicle of finite volume can greatly differ from the trajectory of a massless fluid particle initially placed at the vesicle׳s centroid.