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research article

Biomembrane modeling with isogeometric analysis

Bartezzaghi, Andrea  
•
Dede, Luca  
•
Quarteroni, Alfio  
April 15, 2019
Computer Methods In Applied Mechanics And Engineering

We consider the numerical approximation of lipid biomembranes at equilibrium described by the Canham-Helfrich model, according to which the bending energy is minimized under area and volume constraints. Energy minimization is performed via L-2-gradient flow of the Canham-Helfrich energy using two Lagrange multipliers to weakly enforce the constraints. This yields a highly nonlinear, high order, time dependent geometric Partial Differential Equation (PDE). We represent the biomembranes as single-patch NURBS closed surfaces. We discretize the geometric PDEs in space with NURBS-based Isogeometric Analysis and in time with Backward Differentiation Formulas. We tackle the nonlinearity in our formulation through a semi-implicit approach by extrapolating, at each time level, the geometric quantities of interest from previous time steps. We report the numerical results of the approximation of the Canham-Helfrich problem on ellipsoids of different aspect ratio, which leads to the classical biconcave shape of lipid vesicles at equilibrium. We show that this framework permits an accurate approximation of the Canham-Helfrich problem, while being computationally efficient. (C) 2019 Elsevier B.Y. All rights reserved.

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Type
research article
DOI
10.1016/j.cma.2018.12.025
Web of Science ID

WOS:000460284800005

Author(s)
Bartezzaghi, Andrea  
•
Dede, Luca  
•
Quarteroni, Alfio  
Date Issued

2019-04-15

Publisher

ELSEVIER SCIENCE SA

Published in
Computer Methods In Applied Mechanics And Engineering
Volume

347

Start page

103

End page

119

Subjects

Engineering, Multidisciplinary

•

Mathematics, Interdisciplinary Applications

•

Mechanics

•

Engineering

•

Mathematics

•

lipid biomembrane

•

canham-helfrich energy

•

geometric partial differential equation

•

isogeometric analysis

•

backward differentiation formulas

•

lagrange multiplier

•

partial-differential-equations

•

finite-element-method

•

erythrocyte cytoskeleton

•

large-deformation

•

bending energy

•

shape

•

simulations

•

membranes

•

bilayers

•

flow

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
CIB  
CMCS  
RelationURL/DOI

IsNewVersionOf

https://infoscience.epfl.ch/record/267616
Available on Infoscience
June 18, 2019
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/157212
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