Modelling fluid deformable surfaces with an emphasis on biological interfaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 10 Jun 2019Embargo end date: 01 Jan 2018 English Publisher:Cambridge University Press (CUP)Journal:Journal of Fluid Mechanics, volume 872, pages 218-271 (issn: 0022-1120, eissn: 1469-7645,

Copyright policy )Funded by:EC | EpiMech, EC | MECHANO-CONTROL

Authors: Torres-Sánchez, Alejandro; Millán, Daniel; Arroyo, Marino;

doi: 10.1017/jfm.2019.341 , 10.48550/arxiv.1812.02837

arXiv: 1812.02837

handle: 2117/165676 , 11336/175807

Modelling fluid deformable surfaces with an emphasis on biological interfaces

- Summary
- Subjects
- Metrics

Abstract

Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number interfacial hydrodynamics, chemistry and geometry, and govern important biological processes such as cellular traffic, division, migration or tissue morphogenesis. To address the modelling challenges posed by this class of problems, in which interfacial phenomena tightly interact with the shape and dynamics of the surface, we develop a general continuum mechanics and computational framework for fluid deformable surfaces. The dual solid–fluid nature of fluid deformable surfaces challenges classical Lagrangian or Eulerian descriptions of deforming bodies. Here, we extend the notion of arbitrarily Lagrangian–Eulerian (ALE) formulations, well-established for bulk media, to deforming surfaces. To systematically develop models for fluid deformable surfaces, which consistently treat all couplings between fields and geometry, we follow a nonlinear Onsager formalism according to which the dynamics minimizes a Rayleighian functional where dissipation, power input and energy release rate compete. Finally, we propose new computational methods, which build on Onsager’s formalism and our ALE formulation, to deal with the resulting stiff system of higher-order partial differential equations. We apply our theoretical and computational methodology to classical models for lipid bilayers and the cell cortex. The methods developed here allow us to formulate/simulate these models in their full three-dimensional generality, accounting for finite curvatures and finite shape changes.

Related Organizations

Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
Institute for Bioengineering of Catalonia
Spain
National Scientific and Technical Research Council
Argentina
FUNDACIO INSTITUT DE BIOENGINYERIA DE CATALUNYA
Spain

View all View all

Keywords

:Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], MEMBRANES, Physiological flows, Fluid interfaces, 510, Classificació AMS::65 Numerical analysis::65D Numerical approximation and computational geometry, computational methods, https://purl.org/becyt/ford/1.6, :65 Numerical analysis::65D Numerical approximation and computational geometry [Classificació AMS], CAPSULE/CELL DYNAMICS, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica, :92 Biology and other natural sciences::92B Mathematical biology in general [Classificació AMS], Physics - Fluid Dynamics, Computational Physics (physics.comp-ph), Engineering, Mechanical, capsule/cell dynamics, membranes, Biological Physics (physics.bio-ph), Physics - Computational Physics, Numerical analysis, Engineering, Civil, Biomatemàtica, Engineering, Multidisciplinary, FOS: Physical sciences, Classificació AMS::92 Biology and other natural sciences::92B Mathematical biology in general, Condensed Matter - Soft Condensed Matter, :Matemàtiques i estadística::Anàlisi numèrica [Àrees temàtiques de la UPC], Actin cortex, Arbitrarily Lagrangian-Eulerian, https://purl.org/becyt/ford/2.3, Engineering, Ocean, Physics - Biological Physics, https://purl.org/becyt/ford/2, https://purl.org/becyt/ford/1, Engineering, Aerospace, Engineering, Biomedical, Biomathematics, Anàlisi numèrica, Subdivision surfaces, Fluid Dynamics (physics.flu-dyn), Lipid membranes, Computer Science, Software Engineering, Engineering, Marine, Engineering, Manufacturing, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, COMPUTATIONAL METHODS, Engineering, Industrial, Soft Condensed Matter (cond-mat.soft)

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	85
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 1%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 1%