The study of biofluids is an active multi-disciplinary field of research involving soft matter and statistical physics, fluid mechanics and microfluidics. We are interested in hydrodynamic modeling of spermatozoa cells either at the individual or collective levels. Nevertheless, since beating cilia are generic from unicellular cells up to complex multicellular organisms, most of the developed models are relevant to a broader context. 
How active forces acting on flagella or cilia can be modeled? Combining models with observations of flagella/cilia beating kinematics, is it possible to identify and evaluate these forces? How collective interactions are driving the transition from random to organized collective motion? How the observed collective behavior depends on cell concentration and how steric interactions can influence orientational order in dense packing? 
We analyzed the individual beating of spermatozoa both using original automatic segmentation tools (Yang et al, 2014) and bead models (Delmotte et al, 2015). The interest of bead modelsBead models are articulated spheres or ellipsoids used to model flexible filaments subjected to various forces (including Brownian forcing) within a fluid.
They are widely used in polymer modeling.
resides in their ability to consider possibly complex mechanical anchoring conditions and/or assemblies of cilia. Furthermore, we have shown that measuring the beating kinematics of cilia do not permit the identification and evaluation of the underlying active forcing (even for time-periodic ones) except when two independent measurements performed within two distinct and independent external flows are performed (Plouraboué et al, 2017). Regarding collective effects, we numerically analyzed the effect of long-range hydrodynamic interactions of a large number of active swimmers (pushers or pullers) leading to orientational order (Delmotte et al, 2015, Delmotte et al., 2018).
They are widely used in polymer modeling.
We also experimentally analyzed the random motion of dense ram semen, showing similarities with 2D turbulence in confined parallel Hele-Shaw cells (Creppy et al, 2015). When confined within an annulus, such concentrated semen displays spontaneous rotation, the existence of which has been linked with steric interactions among cells as well as long-range orientational order (Creppy et al, 2016).
Publications
2019
Sulaiman, Mostafa; Climent, Éric; Delmotte, Blaise; Fede, Pascal; Plouraboué, Franck; Verhille, Gautier
Numerical modelling of long flexible fibers in homogeneous isotropic turbulence Journal Article
In: European Physical Journal E, 42 (132), 2019.
@article{oatao25639,
title = {Numerical modelling of long flexible fibers in homogeneous isotropic turbulence},
author = {Mostafa Sulaiman and {É}ric Climent and Blaise Delmotte and Pascal Fede and Franck Plouraboué and Gautier Verhille},
url = {https://oatao.univ-toulouse.fr/25639/},
doi = {10.1140/epje/i2019-11894-7},
year = {2019},
date = {2019-10-01},
journal = {European Physical Journal E},
volume = {42},
number = {132},
publisher = {EDP Sciences},
abstract = {We numerically investigated the transport, deformation and buckling events of an isolated elastic fiber in Taylor-Green vortices and studied the dynamics of long filaments in homogeneous isotropic turbulence. The fiber is modelled by an assembly of spherical beads. The contact between beads enforces the inextensibility of the filament while bending is accounted for by the Gears Bead Model (GBM) proposed by Delmotte et al. (2015). In the cellular Taylor-Green flow, the buckling probability is a function of a dimensionless number, called Sperm number, which is a balance between the compression rate of the flow and the elastic response of the filament. The shapes of the filament and its ability to buckle have been successfully validated through comparisons with experiments from the work by Quennouz et al. (2015). The deformation statistics of long flexible fibers in sustained homogeneous isotropic turbulence were analyzed for various flow and fiber material conditions. Two regimes have been identified depending on the ratio of fiber length to persistence length which is a measure of turbulent forcing to flexibility. The numerical results are in good agreement with existing experimental data (C. Brouzet et al., Phys. Rev. Lett. 112,
074501 (2014)) validating the assumptions of our model for the configurations we investigated.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We numerically investigated the transport, deformation and buckling events of an isolated elastic fiber in Taylor-Green vortices and studied the dynamics of long filaments in homogeneous isotropic turbulence. The fiber is modelled by an assembly of spherical beads. The contact between beads enforces the inextensibility of the filament while bending is accounted for by the Gears Bead Model (GBM) proposed by Delmotte et al. (2015). In the cellular Taylor-Green flow, the buckling probability is a function of a dimensionless number, called Sperm number, which is a balance between the compression rate of the flow and the elastic response of the filament. The shapes of the filament and its ability to buckle have been successfully validated through comparisons with experiments from the work by Quennouz et al. (2015). The deformation statistics of long flexible fibers in sustained homogeneous isotropic turbulence were analyzed for various flow and fiber material conditions. Two regimes have been identified depending on the ratio of fiber length to persistence length which is a measure of turbulent forcing to flexibility. The numerical results are in good agreement with existing experimental data (C. Brouzet et al., Phys. Rev. Lett. 112,
074501 (2014)) validating the assumptions of our model for the configurations we investigated.
074501 (2014)) validating the assumptions of our model for the configurations we investigated.
2018
Delmotte, Blaise; Keaveny, Eric E; Climent, Éric; Plouraboué, Franck
Simulations of Brownian tracer transport in squirmer suspensions Journal Article
In: IMA Journal of Applied Mathematics, 83 (4), pp. 680–699, 2018.
@article{oatao20744,
title = {Simulations of Brownian tracer transport in squirmer suspensions},
author = {Blaise Delmotte and Eric E Keaveny and {É}ric Climent and Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/20744/},
doi = {10.1093/imamat/hxy012},
year = {2018},
date = {2018-02-01},
journal = {IMA Journal of Applied Mathematics},
volume = {83},
number = {4},
pages = {680--699},
publisher = {Oxford University Press},
abstract = {In addition to enabling movement towards environments with favourable living conditions, swimming by microorganisms has also been linked to enhanced mixing and improved nutrient uptake by their populations. Experimental studies have shown that Brownian tracer particles exhibit enhanced diffusion due to the swimmers, while theoretical models have linked this increase in diffusion to the flows generated by the swimming microorganisms, as well as collisions with the swimmers. In this study, we perform detailed simulations based on the force-coupling method and its recent extensions to the swimming and Brownian particles to examine tracer displacements and effective tracer diffusivity in squirmer suspensions. By isolating effects such as hydrodynamic or steric interactions, we provide physical insight into experimental measurements of the tracer displacement distribution. In addition, we extend results to the semi-dilute regime where the swimmer?swimmer interactions affect tracer transport and the effective tracer diffusivity no longer scales linearly with the swimmer volume fraction.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In addition to enabling movement towards environments with favourable living conditions, swimming by microorganisms has also been linked to enhanced mixing and improved nutrient uptake by their populations. Experimental studies have shown that Brownian tracer particles exhibit enhanced diffusion due to the swimmers, while theoretical models have linked this increase in diffusion to the flows generated by the swimming microorganisms, as well as collisions with the swimmers. In this study, we perform detailed simulations based on the force-coupling method and its recent extensions to the swimming and Brownian particles to examine tracer displacements and effective tracer diffusivity in squirmer suspensions. By isolating effects such as hydrodynamic or steric interactions, we provide physical insight into experimental measurements of the tracer displacement distribution. In addition, we extend results to the semi-dilute regime where the swimmer?swimmer interactions affect tracer transport and the effective tracer diffusivity no longer scales linearly with the swimmer volume fraction.
David, Ingrid; Kohnke, Philippa L.; Fehrenbach, Jérôme; Simoes, Ana Rita Lopes; Debreuve, Eric; Descombes, Xavier; Plouraboué, Franck; Degond, Pierre; Druart, Xavier
New objective measurements of semen wave motion are associated with fertility in sheep Journal Article
In: Reproduction Fertility and Development, 30 (6), pp. 889–896, 2018.
@article{oatao20121,
title = {New objective measurements of semen wave motion are associated with fertility in sheep},
author = {Ingrid David and Philippa L. Kohnke and Jérôme Fehrenbach and Ana Rita Lopes Simoes and Eric Debreuve and Xavier Descombes and Franck Plouraboué and Pierre Degond and Xavier Druart},
url = {http://www.publish.csiro.au/rd/RD17472
https://oatao.univ-toulouse.fr/20121/},
doi = {10.1071/RD17472},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Reproduction Fertility and Development},
volume = {30},
number = {6},
pages = {889--896},
publisher = {CSIRO Publishing},
abstract = {In sheep, wave motion in semen is currently used by AI centres to select ejaculates for insemination. Despite its low cost, convenience and established ability to predict fertility, the subjectivity of this assessment is a limiting factor for its applicability. The aims of the present study were to establish an objective method for the analysis of wave motion and to assess the associations of objective parameters with fertility after cervical insemination. Collective sperm motion in undiluted semen was observed by phase contrast microscopy at low magnification in a 100-?m deep glass chamber. Images of moving dark waves over a grey background were recorded and analysed by the optic flow method, producing several velocity-related parameters. Turbulence was assessed from the motion of fluorescent polystyrene beads. Among objective parameters, optical flow entropy and the average speed of beads were both able to discriminate ejaculates suitable for insemination. Two synthetic variables of optic flow and bead motion and a global objective variable were computed from linear combinations of individual parameters and compared with the subjective motion score for their predictive value. These were as efficient as the wave motion score for assessing fertility and can be proposed for the assessment of ram semen in routine AI procedures.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In sheep, wave motion in semen is currently used by AI centres to select ejaculates for insemination. Despite its low cost, convenience and established ability to predict fertility, the subjectivity of this assessment is a limiting factor for its applicability. The aims of the present study were to establish an objective method for the analysis of wave motion and to assess the associations of objective parameters with fertility after cervical insemination. Collective sperm motion in undiluted semen was observed by phase contrast microscopy at low magnification in a 100-?m deep glass chamber. Images of moving dark waves over a grey background were recorded and analysed by the optic flow method, producing several velocity-related parameters. Turbulence was assessed from the motion of fluorescent polystyrene beads. Among objective parameters, optical flow entropy and the average speed of beads were both able to discriminate ejaculates suitable for insemination. Two synthetic variables of optic flow and bead motion and a global objective variable were computed from linear combinations of individual parameters and compared with the subjective motion score for their predictive value. These were as efficient as the wave motion score for assessing fertility and can be proposed for the assessment of ram semen in routine AI procedures.
2017
Plouraboué, Franck; Thiam, E. Ibrahima; Delmotte, Blaise; Climent, Éric
Identification of internal properties of fibres and micro-swimmers Journal Article
In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 473 (2197), pp. 20160517, 2017.
@article{oatao17447,
title = {Identification of internal properties of fibres and micro-swimmers},
author = {Franck Plouraboué and E. Ibrahima Thiam and Blaise Delmotte and Éric Climent},
url = {https://oatao.univ-toulouse.fr/17447/
http://rspa.royalsocietypublishing.org/content/473/2197/20160517},
doi = {10.1098/rspa.2016.0517},
year = {2017},
date = {2017-01-01},
urldate = {2017-01-01},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science},
volume = {473},
number = {2197},
pages = {20160517},
publisher = {The Royal Society},
abstract = {In this paper, we address the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibres or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibres, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalized velocities from computing contact forces. This linear formulation then permits one to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for generalized elastic parameters in the presence of Langevin-like forcing with Gaussian noise using a Bayesian approach. These theoretical results are illustrated in various configurations showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this paper, we address the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibres or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibres, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalized velocities from computing contact forces. This linear formulation then permits one to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for generalized elastic parameters in the presence of Langevin-like forcing with Gaussian noise using a Bayesian approach. These theoretical results are illustrated in various configurations showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.
2016
Creppy, Adama Kpatagnon; Plouraboué, Franck; Praud, Olivier; Druart, Xavier; Cazin, Sébastien; Yu, Hui; Degond, Pierre
Symmetry-breaking phase transitions in highly concentrated semen Journal Article
In: Journal of The Royal Society Interface, 13 (123), pp. 1–12, 2016.
@article{oatao16244,
title = {Symmetry-breaking phase transitions in highly concentrated semen},
author = {Adama Kpatagnon Creppy and Franck Plouraboué and Olivier Praud and Xavier Druart and Sébastien Cazin and Hui Yu and Pierre Degond},
url = {https://oatao.univ-toulouse.fr/16244/},
doi = {10.1098/rsif.2016.0575},
year = {2016},
date = {2016-10-01},
urldate = {2016-10-01},
journal = {Journal of The Royal Society Interface},
volume = {13},
number = {123},
pages = {1--12},
publisher = {The Royal Society Publishing},
abstract = {New experimental evidence of self-motion of a confined active suspension is presented. Depositing fresh semen sample in an annular shaped microfluidic chip leads to a spontaneous vortex state of the fluid at sufficiently large sperm concentration. The rotation occurs unpredictably clockwise or counterclockwise and is robust and stable. Furthermore, for highly active and concentrated semen, richer dynamics can occur such as self-sustained or damped rotation oscillations. Experimental results obtained with systematic dilution provide a clear evidence of a phase transition towards collective motion associated with local alignment of spermatozoa akin to the Vicsek model. A macroscopic theory based on previously derived self-organized hydrodynamics models is adapted to this context and provides predictions consistent with the observed stationary motion.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
New experimental evidence of self-motion of a confined active suspension is presented. Depositing fresh semen sample in an annular shaped microfluidic chip leads to a spontaneous vortex state of the fluid at sufficiently large sperm concentration. The rotation occurs unpredictably clockwise or counterclockwise and is robust and stable. Furthermore, for highly active and concentrated semen, richer dynamics can occur such as self-sustained or damped rotation oscillations. Experimental results obtained with systematic dilution provide a clear evidence of a phase transition towards collective motion associated with local alignment of spermatozoa akin to the Vicsek model. A macroscopic theory based on previously derived self-organized hydrodynamics models is adapted to this context and provides predictions consistent with the observed stationary motion.
2015
Delmotte, Blaise; Keaveny, Eric; Plouraboué, Franck; Climent, Éric
Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method Journal Article
In: Journal of Computational Physics, 302 , pp. 524–547, 2015.
@article{oatao14290,
title = {Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method},
author = {Blaise Delmotte and Eric Keaveny and Franck Plouraboué and {É}ric Climent},
url = {https://oatao.univ-toulouse.fr/14290/},
doi = {10.1016/j.jcp.2015.09.020},
year = {2015},
date = {2015-12-01},
urldate = {2015-12-01},
journal = {Journal of Computational Physics},
volume = {302},
pages = {524--547},
publisher = {Elsevier},
abstract = {We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, are considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method's ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection (10^4-10^5) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, are considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method’s ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection (10^4-10^5) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models.
David, Ingrid; Kohnke, Philippa L.; Lagriffoul, Gilles; Praud, Olivier; Plouraboué, Franck; Degond, Pierre; Druart, Xavier
Mass sperm motility is associated with fertility in sheep Journal Article
In: Animal Reproduction Science, 161 , pp. 75–81, 2015.
@article{oatao14247,
title = {Mass sperm motility is associated with fertility in sheep},
author = {Ingrid David and Philippa L. Kohnke and Gilles Lagriffoul and Olivier Praud and Franck Plouraboué and Pierre Degond and Xavier Druart},
url = {https://oatao.univ-toulouse.fr/14247/
https://www.sciencedirect.com/science/article/pii/S0378432015300014},
doi = {10.1016/j.anireprosci.2015.08.006},
year = {2015},
date = {2015-10-01},
urldate = {2015-10-01},
journal = {Animal Reproduction Science},
volume = {161},
pages = {75--81},
publisher = {Elsevier},
abstract = {The study was to focus on the relationship between wave motion (mass sperm motility, measured by a mass sperm motility score, manually assessed by artificial insemination (AI) center operators) and fertility in male sheep. A dataset of 711,562 artificial inseminations performed in seven breeds by five French AI centers during the 2001?2005 time period was used for the analysis. Factors influencing the outcome of the insemination, which is a binary response observed at lambing of either success (1) or failure (0), were studied using a joint model within each breed and AI center (eight separate analyses). The joint model is a multivariate model where all information related to the female, the male and the insemination process were included to improve the estimation of the factor effects. Results were consistent for all analyses. The male factors affecting AI results were the age of the ram and the mass motility. After correction for the other factors of variation, the lambing rate increased quasi linearly from three to more than ten points with the mass sperm motility score depending on the breed and the AI center. The consistency of the relationship for all breeds indicated that mass sperm motility is predictive of the fertility resulting when sperm are used from a specific ejaculate. Nonetheless, predictability could be improved if an objective measurement of mass sperm motility were available as a substitute for the subjective scoring currently in use in AI centers.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The study was to focus on the relationship between wave motion (mass sperm motility, measured by a mass sperm motility score, manually assessed by artificial insemination (AI) center operators) and fertility in male sheep. A dataset of 711,562 artificial inseminations performed in seven breeds by five French AI centers during the 2001?2005 time period was used for the analysis. Factors influencing the outcome of the insemination, which is a binary response observed at lambing of either success (1) or failure (0), were studied using a joint model within each breed and AI center (eight separate analyses). The joint model is a multivariate model where all information related to the female, the male and the insemination process were included to improve the estimation of the factor effects. Results were consistent for all analyses. The male factors affecting AI results were the age of the ram and the mass motility. After correction for the other factors of variation, the lambing rate increased quasi linearly from three to more than ten points with the mass sperm motility score depending on the breed and the AI center. The consistency of the relationship for all breeds indicated that mass sperm motility is predictive of the fertility resulting when sperm are used from a specific ejaculate. Nonetheless, predictability could be improved if an objective measurement of mass sperm motility were available as a substitute for the subjective scoring currently in use in AI centers.
Creppy, Adama Kpatagnon; Praud, Olivier; Druart, Xavier; Kohnke, Philippa L.; Plouraboué, Franck
Turbulence of swarming sperm Journal Article
In: Physical Review E, 92 (3), pp. n/a, 2015.
@article{oatao14317,
title = {Turbulence of swarming sperm},
author = {Adama Kpatagnon Creppy and Olivier Praud and Xavier Druart and Philippa L. Kohnke and Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/14317/
http://journals.aps.org/pre/pdf/10.1103/PhysRevE.92.032722},
doi = {10.1103/PhysRevE.92.032722},
year = {2015},
date = {2015-09-01},
urldate = {2015-09-01},
journal = {Physical Review E},
volume = {92},
number = {3},
pages = {n/a},
publisher = {American Physical Society},
abstract = {Collective motion of self-sustained swarming flows has recently provided examples of small-scale turbulence arising where viscous effects are dominant. We report the first observation of universal enstrophy cascade in concentrated swarming sperm consistent with a body of evidence built from various independent measurements. We found a well-defined k-3 power-law decay of a velocity field power spectrum and relative dispersion of small beads consistent with theoretical predictions in 2D turbulence. Concentrated living sperm displays long-range, correlated whirlpool structures of a size that provides an integral scale of turbulence. We propose a consistent explanation for this quasi-2D turbulence based on self-structured laminated flow forced by steric interactions and alignment, a state of active matter that we call "swarming liquid crystal". We develop scaling arguments consistent with this interpretation.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Collective motion of self-sustained swarming flows has recently provided examples of small-scale turbulence arising where viscous effects are dominant. We report the first observation of universal enstrophy cascade in concentrated swarming sperm consistent with a body of evidence built from various independent measurements. We found a well-defined k-3 power-law decay of a velocity field power spectrum and relative dispersion of small beads consistent with theoretical predictions in 2D turbulence. Concentrated living sperm displays long-range, correlated whirlpool structures of a size that provides an integral scale of turbulence. We propose a consistent explanation for this quasi-2D turbulence based on self-structured laminated flow forced by steric interactions and alignment, a state of active matter that we call "swarming liquid crystal". We develop scaling arguments consistent with this interpretation.
Delmotte, Blaise; Climent, Éric; Plouraboué, Franck
A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number Journal Article
In: Journal of Computational Physics, 286 , pp. 14–37, 2015.
@article{oatao13585,
title = {A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number},
author = {Blaise Delmotte and {É}ric Climent and Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/13585/
http://www.sciencedirect.com/science/article/pii/S0021999115000303},
doi = {10.1016/j.jcp.2015.01.026},
year = {2015},
date = {2015-04-01},
urldate = {2015-04-01},
journal = {Journal of Computational Physics},
volume = {286},
pages = {14--37},
publisher = {Elsevier},
abstract = {This contribution provides a general framework to use Lagrange multipliers for the simulation of low Reynolds number fiber dynamics based on Bead Models (BM). This formalism provides an efficient method to account for kinematic constraints. We illustrate, with several examples, to which extent the proposed formulation offers a flexible and versatile framework for the quantitative modeling of flexible fibers deformation and rotation in shear flow, the dynamics of actuated filaments and the propulsion of active swimmers. Furthermore, a new contact model called Gears Model is proposed and successfully tested. It avoids the use of numerical artifices such as repulsive forces between adjacent beads, a source of numerical difficulties in the temporal integration of previous Bead Models.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
This contribution provides a general framework to use Lagrange multipliers for the simulation of low Reynolds number fiber dynamics based on Bead Models (BM). This formalism provides an efficient method to account for kinematic constraints. We illustrate, with several examples, to which extent the proposed formulation offers a flexible and versatile framework for the quantitative modeling of flexible fibers deformation and rotation in shear flow, the dynamics of actuated filaments and the propulsion of active swimmers. Furthermore, a new contact model called Gears Model is proposed and successfully tested. It avoids the use of numerical artifices such as repulsive forces between adjacent beads, a source of numerical difficulties in the temporal integration of previous Bead Models.
2014
Yang, Hue-Fang; Descombes, Xavier; Prigent, Sylvain; Malandain, Grégoire; Druart, Xavier; Plouraboué, Franck
Head tracking and flagellum tracing for sperm motility analysis Unpublished
2014, (This work is supported by ANR MOTIMO Project).
@unpublished{oatao10591,
title = {Head tracking and flagellum tracing for sperm motility analysis},
author = {Hue-Fang Yang and Xavier Descombes and Sylvain Prigent and Grégoire Malandain and Xavier Druart and Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/10591/},
year = {2014},
date = {2014-01-01},
booktitle = {ISBI - IEEE International Symposium on Biomedical Imaging},
address = {Beijing, CN},
abstract = {Sperm quality assessment plays an essential role in human fertility and animal breeding. Manual analysis is time-consuming and subject to intra- and inter-observer variability. To automate the analysis process, as well as to offer a means of statistical analysis that may not be achieved by visual inspection, we present a computational framework that tracks the heads and traces the tails for analyzing sperm motility, one of the most important attributes in semen quality evaluation. Our framework consists of 3 modules: head detection, head tracking, and flagellum tracing. The head detection module detects the sperm heads from the image data, and the detected heads are the inputs to the head tracking module for obtaining the head trajectories. Finally, a flagellum tracing algorithm is proposed to obtain the flagellar beat patterns. Our framework aims at providing both the head trajectories and the flagellar beat patterns for quantitatively assessing sperm motility. This distinguishes our work from other existing methods that analyze sperm motility based merely on the head trajectories. We validate our framework using two confocal microscopy image sequences of ram semen samples that were imaged at two different conditions, at which the sperms behave differently. The results show the effectiveness of our framework.},
note = {This work is supported by ANR MOTIMO Project},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
Sperm quality assessment plays an essential role in human fertility and animal breeding. Manual analysis is time-consuming and subject to intra- and inter-observer variability. To automate the analysis process, as well as to offer a means of statistical analysis that may not be achieved by visual inspection, we present a computational framework that tracks the heads and traces the tails for analyzing sperm motility, one of the most important attributes in semen quality evaluation. Our framework consists of 3 modules: head detection, head tracking, and flagellum tracing. The head detection module detects the sperm heads from the image data, and the detected heads are the inputs to the head tracking module for obtaining the head trajectories. Finally, a flagellum tracing algorithm is proposed to obtain the flagellar beat patterns. Our framework aims at providing both the head trajectories and the flagellar beat patterns for quantitatively assessing sperm motility. This distinguishes our work from other existing methods that analyze sperm motility based merely on the head trajectories. We validate our framework using two confocal microscopy image sequences of ram semen samples that were imaged at two different conditions, at which the sperms behave differently. The results show the effectiveness of our framework.
Climent, Éric; Delmotte, Blaise; Keaveny, Eric; Plouraboué, Franck
2014.
@unpublished{oatao11043,
title = {Numerical simulation of large populations of motile cells with the Force Coupling Method: effect of shape and concentration.},
author = {Éric Climent and Blaise Delmotte and Eric Keaveny and Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/11043/},
year = {2014},
date = {2014-01-01},
booktitle = {17th U.S. National Congress on Theoretical & Applied Mechanics},
address = {Lansing, US},
abstract = {The statistics of the collective motions in an active suspension depend highly on the length scale of observation. Obtaining representative and reliable statistics requires simulating large numbers of individual interacting swimmers beyond what most simulation methods can hardly afford. As coupling between individuals are mainly mediated through fluid flow perturbations, efficient solvers for many-body hydrodynamic interactions are required. In the context of HPC (high performance computing), a highly parallelized code has been developed on an extension of the Force Coupling Method (FCM) to active suspensions. This efficient tool uses the latest FFT libraries (P3DFFT) for the Stokes flow solver and can handle the many-body hydrodynamic interactions between O(105) swimmers while accounting also for finite size effects. Since its original development by Maxey & Patel (Int. J. Mult. Flows, 2001), the FCM has been improved further and extensively validated for particulate, non-motile suspensions. Each particle is modelled via a 3D Gaussian envelope related to the actual size of the particle. Using the FCM framework, we show that additional flow perturbations induced by motile particles (pushers, pullers, and squirmers) can be included through an appropriate regularized multipole expansion of the forcing terms in the Stokes equations. Preliminary FCM simulations with spherical swimmers show very good agreement with Stokesian Dynamics results (Ishikawa et al., J. Fluid Mech. 2008, Mehandia & Nott, J. Fluid Mech. 2008) whilst the number of swimmers in the FCM simulations is two orders of magnitude larger. Our approach also captures the influence of shape (spheroidal and ellipsoidal swimmers), swimming gait (pusher, puller and squirmer) and suspension concentration on the collective dynamics and bulk properties of the suspension. The resulting statistics reveal non-trivial unsteady spatial arrangements of swimmers. Preferential orientation of the swimmers and the contribution of particle stresses to non-Newtonian effects are also currently being investigated.},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
The statistics of the collective motions in an active suspension depend highly on the length scale of observation. Obtaining representative and reliable statistics requires simulating large numbers of individual interacting swimmers beyond what most simulation methods can hardly afford. As coupling between individuals are mainly mediated through fluid flow perturbations, efficient solvers for many-body hydrodynamic interactions are required. In the context of HPC (high performance computing), a highly parallelized code has been developed on an extension of the Force Coupling Method (FCM) to active suspensions. This efficient tool uses the latest FFT libraries (P3DFFT) for the Stokes flow solver and can handle the many-body hydrodynamic interactions between O(105) swimmers while accounting also for finite size effects. Since its original development by Maxey & Patel (Int. J. Mult. Flows, 2001), the FCM has been improved further and extensively validated for particulate, non-motile suspensions. Each particle is modelled via a 3D Gaussian envelope related to the actual size of the particle. Using the FCM framework, we show that additional flow perturbations induced by motile particles (pushers, pullers, and squirmers) can be included through an appropriate regularized multipole expansion of the forcing terms in the Stokes equations. Preliminary FCM simulations with spherical swimmers show very good agreement with Stokesian Dynamics results (Ishikawa et al., J. Fluid Mech. 2008, Mehandia & Nott, J. Fluid Mech. 2008) whilst the number of swimmers in the FCM simulations is two orders of magnitude larger. Our approach also captures the influence of shape (spheroidal and ellipsoidal swimmers), swimming gait (pusher, puller and squirmer) and suspension concentration on the collective dynamics and bulk properties of the suspension. The resulting statistics reveal non-trivial unsteady spatial arrangements of swimmers. Preferential orientation of the swimmers and the contribution of particle stresses to non-Newtonian effects are also currently being investigated.
2013
Degond, Pierre; Praud, Olivier; Creppy, Adama Kpatagnon; Plouraboué, Franck
Dispositif de traitement d’un échantillon d’un fluide biologique actif Patent
2013.
@patent{oatao11460,
title = {Dispositif de traitement d'un échantillon d'un fluide biologique actif},
author = {Pierre Degond and Olivier Praud and Adama Kpatagnon Creppy and Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/11460/},
year = {2013},
date = {2013-11-01},
urldate = {2013-11-01},
keywords = {},
pubstate = {published},
tppubtype = {patent}
}
Creppy, Adama Kpatagnon; Plouraboué, Franck; Praud, Olivier; Viel, Alexis
Collective motility of sperm in confined cells Journal Article
In: Computer Methods in Biomechanics and Biomedical Engineering, 16 (supp. 1), pp. 11–12, 2013.
@article{oatao9314,
title = {Collective motility of sperm in confined cells},
author = {Adama Kpatagnon Creppy and Franck Plouraboué and Olivier Praud and Alexis Viel},
url = {https://oatao.univ-toulouse.fr/9314/
http://www.tandfonline.com/doi/abs/10.1080/10255842.2013.815899},
doi = {10.1080/10255842.2013.815899},
year = {2013},
date = {2013-08-01},
urldate = {2013-08-01},
journal = {Computer Methods in Biomechanics and Biomedical Engineering},
volume = {16},
number = {supp. 1},
pages = {11--12},
publisher = {Taylor & Francis},
abstract = {Mammalian fertility analysis is an important industrial issue because of the selection for breeding. This is one reason, beside fundamental interest, for which many studies analyse the individual motion of the spermatozoon (Gaffney et al. 2011). On the other hand, more recent reviews suggest that neither individual motion indicators or molecular markers can be clearly correlated to fertility (Kastelic and Thundathil 2008; Nathali and Turek 2011). This is why the industry still uses the scoring of sperm motility from the observation of semen sessile drop with a phase-contrast microscope. This observation of pure semen displays wave motion associated with millions of sperm moving together in circular waves and whirlpools. The moving speed, deformation and size of whirlpools were ranked and scored. Similar collective movements have also been observed in different biological suspensions above a certain concentration (Sokolov et al. 2007). But until today, there has been no clear analysis of the origin of the observed whirlpools dynamics in semen. In this article, we provide new insights on the origin of whirlpools. As the sessile drops do not permit a careful control of the micro-hydrodynamic boundary conditions associated with surface tension variations, we investigate collective effects in controlled rectangular cells confined span wise with 20 and 100mm depth. We mainly analyse the influence of the confinement and the concentration on the appearance of whirlpools.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Mammalian fertility analysis is an important industrial issue because of the selection for breeding. This is one reason, beside fundamental interest, for which many studies analyse the individual motion of the spermatozoon (Gaffney et al. 2011). On the other hand, more recent reviews suggest that neither individual motion indicators or molecular markers can be clearly correlated to fertility (Kastelic and Thundathil 2008; Nathali and Turek 2011). This is why the industry still uses the scoring of sperm motility from the observation of semen sessile drop with a phase-contrast microscope. This observation of pure semen displays wave motion associated with millions of sperm moving together in circular waves and whirlpools. The moving speed, deformation and size of whirlpools were ranked and scored. Similar collective movements have also been observed in different biological suspensions above a certain concentration (Sokolov et al. 2007). But until today, there has been no clear analysis of the origin of the observed whirlpools dynamics in semen. In this article, we provide new insights on the origin of whirlpools. As the sessile drops do not permit a careful control of the micro-hydrodynamic boundary conditions associated with surface tension variations, we investigate collective effects in controlled rectangular cells confined span wise with 20 and 100mm depth. We mainly analyse the influence of the confinement and the concentration on the appearance of whirlpools.
Delmotte, Blaise; Climent, Éric; Plouraboué, Franck
Hydrodynamic interactions among large populations of swimming micro-organisms Journal Article
In: Computer Methods in Biomechanics and Biomedical Engineering, 16 (supp. 1), pp. 6–8, 2013.
@article{oatao9315,
title = {Hydrodynamic interactions among large populations of swimming micro-organisms},
author = {Blaise Delmotte and {É}ric Climent and Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/9315/
http://www.tandfonline.com/doi/abs/10.1080/10255842.2013.815881},
doi = {10.1080/10255842.2013.815881},
year = {2013},
date = {2013-08-01},
urldate = {2013-08-01},
journal = {Computer Methods in Biomechanics and Biomedical Engineering},
volume = {16},
number = {supp. 1},
pages = {6--8},
publisher = {Taylor & Francis},
abstract = {Bio-convection, biofilm forming or mechanics of reproduction are connected to the motility and collective behaviour of micro-organisms. For instance, spermatozoa suspensions exhibit coherent motion whose frequency and lifespan are strongly correlated to semen fertility (Moore et al. 2002). As interplays in many-bodied systems result in intricate patterns, the understanding of these requires an in-depth knowledge of the suspension microstructure and statistics. Representative and reliable statistics require a large number Np of interactive swimmers that many simulation methods can hardly afford [e.g. Np ? 40 in Mehandia and Nott (2008) or Np # 216 in Ishikawa et al. (2008)]. In the following, a spherical swimmer model is derived from the classical low Reynolds number framework and implemented in the force-coupling method (FCM) for large populations. Resulting statistics reveals non-trivial spatial arrangements of swimmers depending on their swimming gait.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Bio-convection, biofilm forming or mechanics of reproduction are connected to the motility and collective behaviour of micro-organisms. For instance, spermatozoa suspensions exhibit coherent motion whose frequency and lifespan are strongly correlated to semen fertility (Moore et al. 2002). As interplays in many-bodied systems result in intricate patterns, the understanding of these requires an in-depth knowledge of the suspension microstructure and statistics. Representative and reliable statistics require a large number Np of interactive swimmers that many simulation methods can hardly afford [e.g. Np ? 40 in Mehandia and Nott (2008) or Np # 216 in Ishikawa et al. (2008)]. In the following, a spherical swimmer model is derived from the classical low Reynolds number framework and implemented in the force-coupling method (FCM) for large populations. Resulting statistics reveals non-trivial spatial arrangements of swimmers depending on their swimming gait.
2012
Bardan, Gérald; Plouraboué, Franck; Zagzoule, Mokhtar; Balédent, Olivier
Pressure drop reconstruction in the aqueduct of sylvius from MRI acquisitions Journal Article
In: Computer Methods in Biomechanics and Biomedical Engineering, 15 , pp. 79–80, 2012, (Published in a special issue (Supplement 1 : 37th Congress of the Societe de Biomecanique). Open access is not allowed for this article.).
@article{oatao6856,
title = {Pressure drop reconstruction in the aqueduct of sylvius from MRI acquisitions},
author = {Gérald Bardan and Franck Plouraboué and Mokhtar Zagzoule and Olivier Balédent},
url = {https://oatao.univ-toulouse.fr/6856/},
doi = {10.1080/10255842.2012.713735},
year = {2012},
date = {2012-09-01},
journal = {Computer Methods in Biomechanics and Biomedical Engineering},
volume = {15},
pages = {79--80},
publisher = {Taylor & Francis},
abstract = {Pressure drop reconstruction in the aqueduct of sylvius
from MRI acquisitions},
note = {Published in a special issue (Supplement 1 : 37th Congress of the Societe de Biomecanique). Open access is not allowed for this article.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Pressure drop reconstruction in the aqueduct of sylvius
from MRI acquisitions
from MRI acquisitions
1996
Silva, Adriana S.; Bond, Robert; Plouraboué, Franck; Wirtz, Denis
Fluctuation dynamics of a single magnetic chain Journal Article
In: Physical Review E, 54 (5), pp. 5502–5510, 1996.
@article{oatao5502,
title = {Fluctuation dynamics of a single magnetic chain},
author = {Adriana S. Silva and Robert Bond and Franck Plouraboué and Denis Wirtz},
url = {https://oatao.univ-toulouse.fr/5502/},
doi = {10.1103/PhysRevE.54.5502},
year = {1996},
date = {1996-01-01},
urldate = {1996-01-01},
journal = {Physical Review E},
volume = {54},
number = {5},
pages = {5502--5510},
publisher = {American Physical Society},
abstract = {"Tunable" fluids such as magnetorheological "MR" and electrorheological "ER" fluids are comprised of paramagnetic or dielectric particles suspended in a low-viscosity liquid. Upon the application of a magnetic or electric field, these fluids display a dramatic, reversible, and rapid increase of the viscosity. This change in viscosity can, in fact, be tuned by varying the applied field, hence the name "tunable fluids". This effect is due to longitudinal aggregation of the particles into chains in the direction of the applied field and the subsequent lateral aggregation into larger semisolid domains. A recent theoretical model by Halsey and Toor "HT" explains chain aggregation in dipolar fluids by a fluctuation-mediated long-range interaction between chains and predicts that this interaction will be equally efficient at all applied fields. This paper describes video-microscopy observations of long, isolated magnetic chains that test HT theory. The measurements show that, in contrast to the HT theory, chain aggregation occurs more efficiently at higher magnetic field strength (H0) and that this efficiency scales as H0?. Our experiments also yield the steady-state and time-dependent ?uctuation spectra C(x,x')? [h(x)-h(x')]?ensuremath>? and C(x,x',t,t')? ensuremath<[h(x,t)-h(x',t')]? ensuremath>? for the instantaneous deviation h(x,t) from an axis parallel to the ?eld direction to a point x on the chain. Results show that the steady-state ?uctuation growth is similar to a biased random walk with respect to the interspacing ? ensuremath|x-x'ensuremath| along the chain, C(x,x')$approx$ensuremath|x-x'ensuremath| ensuremathalpha, with a roughness exponent ensuremathalpha =0.53$pm$0.02. This result is partially confirmed by Monte Carlo simulations. Time-dependent results also show that chain relaxation is slowed down with respect to classical Brownian diffusion due to the magnetic chain connectivity, C(x,x',t,t')$approx$ensuremath|t-t'ensuremath|ensuremathbeta, with a growth exponent ensuremathbeta=0.35$pm$0.05ensuremath
keywords = {},
pubstate = {published},
tppubtype = {article}
}
"Tunable" fluids such as magnetorheological "MR" and electrorheological "ER" fluids are comprised of paramagnetic or dielectric particles suspended in a low-viscosity liquid. Upon the application of a magnetic or electric field, these fluids display a dramatic, reversible, and rapid increase of the viscosity. This change in viscosity can, in fact, be tuned by varying the applied field, hence the name "tunable fluids". This effect is due to longitudinal aggregation of the particles into chains in the direction of the applied field and the subsequent lateral aggregation into larger semisolid domains. A recent theoretical model by Halsey and Toor "HT" explains chain aggregation in dipolar fluids by a fluctuation-mediated long-range interaction between chains and predicts that this interaction will be equally efficient at all applied fields. This paper describes video-microscopy observations of long, isolated magnetic chains that test HT theory. The measurements show that, in contrast to the HT theory, chain aggregation occurs more efficiently at higher magnetic field strength (H0) and that this efficiency scales as H0?. Our experiments also yield the steady-state and time-dependent ?uctuation spectra C(x,x’)? [h(x)-h(x’)]?ensuremath>? and C(x,x’,t,t’)? ensuremath<[h(x,t)-h(x’,t’)]? ensuremath>? for the instantaneous deviation h(x,t) from an axis parallel to the ?eld direction to a point x on the chain. Results show that the steady-state ?uctuation growth is similar to a biased random walk with respect to the interspacing ? ensuremath|x-x’ensuremath| along the chain, C(x,x’)$approx$ensuremath|x-x’ensuremath| ensuremathalpha, with a roughness exponent ensuremathalpha =0.53$pm$0.02. This result is partially confirmed by Monte Carlo simulations. Time-dependent results also show that chain relaxation is slowed down with respect to classical Brownian diffusion due to the magnetic chain connectivity, C(x,x’,t,t’)$approx$ensuremath|t-t’ensuremath|ensuremathbeta, with a growth exponent ensuremathbeta=0.35$pm$0.05ensuremath<?. All data can be collapsed onto a single curve according to C(x,x’,t,t’)$approx$ensuremath|x-x’ensuremath| ensuremathalpha ensuremathpsi (ensuremath|t-t’ensuremath| / ensuremath|x-x’ensuremath| z ), with a dynamic exponent z= ensuremathalpha /ensuremathbeta? 1.42.