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A POROUS VISCOELASTIC MODEL FOR THE CELL CYTOSKELETON

Part of: Two-phase and multiphase flows Incompressible viscous fluids Numerical methods Mathematical biology in general Coupling of solid mechanics with other effects

Published online by Cambridge University Press:  25 May 2018

CALINA A. COPOS Open the ORCID record for CALINA A. COPOS [Opens in a new window]  and
ROBERT D. GUY Open the ORCID record for ROBERT D. GUY [Opens in a new window]
CALINA A. COPOS*
Affiliation:
Department of Mathematics, University of California Davis, Davis, CA 95616, USA email copos@cims.nyu.edu, guy@math.ucdavis.edu
ROBERT D. GUY
Affiliation:
Department of Mathematics, University of California Davis, Davis, CA 95616, USA email copos@cims.nyu.edu, guy@math.ucdavis.edu
*
✉copos@cims.nyu.edu
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Abstract

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The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In this work, we consider a poroelastic immersed boundary method in which a fluid permeates a porous, elastic structure of negligible volume fraction, and extend this method to include stress relaxation of the material. The porous viscoelastic method presented here is validated for a prescribed oscillatory shear and for an expansion driven by the motion at the boundary of a circular material by comparing numerical solutions to an analytical solution of the Maxwell model for viscoelasticity. Finally, an application of the modelling framework to cell biology is provided: passage of a cell through a microfluidic channel. We demonstrate that the rheology of the cell cytoplasm is important for capturing the transit time through a narrow channel in the presence of a pressure drop in the extracellular fluid.

Keywords

viscoelasticitystress relaxationcytoskeleton rheologycell mechanicsimmersed boundary method

MSC classification

Primary: 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Secondary: 74S05: Finite element methods 76T99: None of the above, but in this section 76D07: Stokes and related (Oseen, etc.) flows 92B05: General biology and biomathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 4 , April 2018 , pp. 472 - 498
Copyright
© 2018 Australian Mathematical Society 

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