Hydrodynamic interactions of actuated elastic filaments near a planar wall with applications to sperm motility

Huang, Jianjun; Carichino, Lucia; Olson, Sarah D.

doi:10.1166/jcsmd.2018.1166

Cited by 11 publications

(12 citation statements)

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“…The trajectories of the first point during this time frame (blue and black solid lines) show the hydrodynamic attraction of the two sperm cells; the top sperm starts to go down and attract to the bottom sperm, which is swimming with an upward trajectory. We classify this movement as yaw since these motions remain within the plane z 0, which has been observed in other modeling work for a single swimmer [29,30,34]. A solo swimmer has an upward yaw [34], but attraction dominates and…”

Section: Free Spacementioning

confidence: 86%

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A Computational Study of Hydrodynamic Interactions Between Pairs of Sperm With Planar and Quasi-Planar Beat Forms

2021

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Although hydrodynamic interactions and cooperative swimming of mammalian sperm are observed, the key factors that lead to attraction or repulsion in different confined geometries are not well understood. In this study, we simulate the 3-dimensional fluid-structure interaction of pairs of swimmers utilizing the Method of Regularized Stokeslets, accounting for a nearby wall via a regularized image system. To investigate emergent trajectories of swimmers, we look at different preferred beat forms, planar or quasi-planar (helical with unequal radii). We also explored different initializations of swimmers in either the same plane (co-planar) or with centerlines in parallel planes. In free space, swimmers with quasi-planar beat forms and those with planar beat forms that are co-planar exhibit stable attraction. The swimmers reach a maintained minimum distance apart that is smaller than their initial distance apart. In contrast, for swimmers initialized in parallel beat planes with a planar beat form, we observe alternating periods of attraction and repulsion. When the pairs of swimmers are perpendicular to a nearby wall, for all cases considered, they approach the wall and reach a constant distance between swimmers. Interestingly, we observe sperm rolling in the case of swimmers with preferred planar beat forms that are initialized in parallel beat planes and near a wall.

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Section: Free Spacementioning

confidence: 86%

“…To date, there have been many studies that have investigated the 3-dimensional (3D) dynamics of a single sperm near a wall [10,19,34]. Wall attraction was observed when approaching at specific angles, including perpendicular to the wall.…”

Section: Introductionmentioning

confidence: 99%

A Computational Study of Hydrodynamic Interactions Between Pairs of Sperm With Planar and Quasi-Planar Beat Forms

2021

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“…This tendency of boundaries serving to reduce non-planar components of beating has also be affirmed by more recent observations (Su et al, 2012 ; Bukatin et al, 2015 ; Nosrati et al, 2015 ). From a theoretical perspective, elastohydrodynamic studies have sought to investigate this phenomenon (Fauci and McDonald, 1995 ; Elgeti et al, 2010 ; Huang et al, 2018 ; Ishimoto and Gaffney, 2018a ), concluding that the flagellar waveform can be modified by hydrodynamic interactions with boundaries, though further experimental investigation is required in order to clarify the effects of boundaries on the flagellar gait.…”

Section: The Evolving Methodological Landscapementioning

confidence: 99%

Modelling Motility: The Mathematics of Spermatozoa

Gaffney

Ishimoto

Walker

2021

Front. Cell Dev. Biol.

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In one of the first examples of how mechanics can inform axonemal mechanism, Machin's study in the 1950s highlighted that observations of sperm motility cannot be explained by molecular motors in the cell membrane, but would instead require motors distributed along the flagellum. Ever since, mechanics and hydrodynamics have been recognised as important in explaining the dynamics, regulation, and guidance of sperm. More recently, the digitisation of sperm videomicroscopy, coupled with numerous modelling and methodological advances, has been bringing forth a new era of scientific discovery in this field. In this review, we survey these advances before highlighting the opportunities that have been generated for both recent research and the development of further open questions, in terms of the detailed characterisation of the sperm flagellum beat and its mechanics, together with the associated impact on cell behaviour. In particular, diverse examples are explored within this theme, ranging from how collective behaviours emerge from individual cell responses, including how these responses are impacted by the local microenvironment, to the integration of separate advances in the fields of flagellar analysis and flagellar mechanics.

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“…The swimming speed and efficiency of micro-swimmers has been extensively studied through both analysis and model simulations [3,12]. To date, in the case of a homogeneous fluid governed by the incompressible Stokes equations, computations have explored a single to thousands of swimmers with varying levels of complexity with respect to accurate geometries of the flagellum, regulation of the beat form, and coupling to chemical concentrations [13][14][15][16][17][18][19][20][21][22][23]. Early pioneering work by Taylor focused on an infinite-length swimmer with a beat form that was prescribed [24,25], where swimming speeds and propulsive efficiency were derived as a function of beat form parameters in the case of a Stokesian fluid.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Swimmers in Fluids with Resistance

Jeznach

Olson

2020

Fluids

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Micro-swimmers such as spermatozoa are able to efficiently navigate through viscous fluids that contain a sparse network of fibers or other macromolecules. We utilize the Brinkman equation to capture the fluid dynamics of sparse and stationary obstacles that are represented via a single resistance parameter. The method of regularized Brinkmanlets is utilized to solve for the fluid flow and motion of the swimmer in 2-dimensions when assuming the flagellum (tail) propagates a curvature wave. Extending previous studies, we investigate the dynamics of swimming when varying the resistance parameter, head or cell body radius, and preferred beat form parameters. For a single swimmer, we determine that increased swimming speed occurs for a smaller cell body radius and smaller fluid resistance. Progression of swimmers exhibits complex dynamics when considering hydrodynamic interactions; attraction of two swimmers is a robust phenomenon for smaller beat amplitude of the tail and smaller fluid resistance. Wall attraction is also observed, with a longer time scale of wall attraction with a larger resistance parameter.

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Hydrodynamic interactions of actuated elastic filaments near a planar wall with applications to sperm motility

Cited by 11 publications

References 0 publications

A Computational Study of Hydrodynamic Interactions Between Pairs of Sperm With Planar and Quasi-Planar Beat Forms

A Computational Study of Hydrodynamic Interactions Between Pairs of Sperm With Planar and Quasi-Planar Beat Forms

Modelling Motility: The Mathematics of Spermatozoa

Dynamics of Swimmers in Fluids with Resistance

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