title: A fully three-dimensional model of the interaction of driven elastic filaments in a Stokes flow with applications to sperm motility.
abstract: In many animals, sperm flagella exhibit primarily planar waveforms. An isolated sperm with a planar flagellar beat in a three-dimensional unbounded fluid domain would remain in a plane. However, because sperm must navigate through complex, three-dimensional confined spaces along with other sperm, forces that bend or move the flagellum out of its current beat plane develop. Here we present an extension of previous models of an elastic sperm flagellar filament whose shape change is driven by the pursuit of a preferred curvature wave. In particular, we extend the energy of the generalized elastica to include a term that penalizes out-of-plane motion. We are now able to study the interaction of free-swimmers in a 3D Stokes flow that do not start out beating in the same plane. We demonstrate the three-dimensional nature of swimming behavior as neighboring sperm swim close to each other and affect each others' trajectories via fluid-structure coupling.
authors.affiliation: Center for Computational Science and Mathematics Department, Tulane University, 6823 St. Charles Ave., New Orleans, LA 70118, USA. Electronic address: jsimons@tulane.edu.
authors.forename: Julie
authors.initials: J
authors.lastname: Simons
authors.affiliation: Center for Computational Science and Mathematics Department, Tulane University, 6823 St. Charles Ave., New Orleans, LA 70118, USA. Electronic address: fauci@tulane.edu.
authors.forename: Lisa
authors.initials: L
authors.lastname: Fauci
authors.affiliation: Center for Computational Science and Mathematics Department, Tulane University, 6823 St. Charles Ave., New Orleans, LA 70118, USA. Electronic address: rcortez@tulane.edu.
authors.forename: Ricardo
authors.initials: R
authors.lastname: Cortez
mesh_terms: D000465:Algorithms; D000818:Animals; D001696:Biomechanical Phenomena; D003198:Computer Simulation; D003599:Cytoskeleton / Q000502:physiology*; D006801:Humans; D021621:Imaging, Three-Dimensional; D008297:Male; D008954:Models, Biological; D013081:Sperm Motility; D013082:Sperm Tail / Q000502:physiology*
keywords: Planar waveforms; Regularized Stokeslets; Sperm motility; Stokes equations; Three-dimensional flagellum