Sperm Pairing and Measures of Efficiency in Planar Swimming Models

Sperm of certain species engage in cooperative swimming behaviors which result in differences in velocity and efficiency of swimming, as well as ability to effectively fertilize the egg. In particular, Monodelphis domestica is a species of opossum whose sperm often swim cooperatively as a pair, with heads fused together. In order to understand the empirical effects of cooperative swimming behaviors, we propose a simple preferred-curvature-based model to model individual and paired sperm using the method of regularized Stokeslets to model the viscous fluid environment. The effects of swimming freely versus paired swimming, phase relationship, and the angle at which sperm heads are fused are investigated. Results are consistent with previous modeling work for free swimmers. Paired (fused) swimming results also compare well with experimental work, and provide evidence for optimal geometrical configurations. This indicates that there may be a fluid mechanical advantage to such cooperative motility behaviors in sperm swimming

A Model for Stokes Flow in Domains with Permeable Boundaries

We derive a new computational model for the simulation of viscous incompressible flows bounded by a thin, flexible, porous membrane. Our approach is grid-free and models the boundary forces with regularized Stokeslets. The flow across the porous membranes is modeled with regularized source doublets based on the notion that the flux velocity across the boundary can be viewed as the flow induced by a fluid source/sink pair with the sink on the high-pressure side of the boundary and magnitude proportional to the pressure difference across the membrane. Several validation examples are presented that illustrate how to calibrate the parameters in the model. We present an example consisting of flow in a closed domain that loses volume due to the fluid flux across the permeable boundary. We also present applications of the method to flow inside a channel of fixed geometry where sections of the boundary are permeable. The final example is a biological application of flow in a capillary with porous walls and a protein concentration advected and diffused in the fluid. In this case, the protein concentration modifies the pressure in the flow, producing dynamic changes to the flux across the walls. For this example, the proposed method is combined with finite differences for the concentration field