<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 <italic>nm</italic>) is much smaller than the overall size (≃ 8000 <italic>nm</italic>). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.</p></abstract>

This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 nm) is much smaller than the overall size (≃ 8000 nm). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.

A new two-component approach in modeling red blood cells

Instituto de Ciências Matemáticas e de Computação

Istituto per le Applicazioni del Calcolo “M. Picone”

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"A new two-component approach in modeling red blood cells"}

This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient...

A new two-component approach in modeling red blood cells

Publié en ligne: 31 oct. 2020

Pages: 55 - 71

DOI: https://doi.org/10.2478/caim-2020-0004

Mots clés
Red blood cell, Mathematical modeling, Biological fluid mechanics, Lipid membrane, cytoskeleton, Fluid-solid interactions, Cell biology

© 2020 Luca Meacci et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A new two-component approach in modeling red blood cells

Publié en ligne: 31 oct. 2020

Pages: 55 - 71

DOI: https://doi.org/10.2478/caim-2020-0004

Mots clésRed blood cell, Mathematical modeling, Biological fluid mechanics, Lipid membrane, cytoskeleton, Fluid-solid interactions, Cell biology

© 2020 Luca Meacci et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Red blood cell, Mathematical modeling, Biological fluid mechanics, Lipid membrane, cytoskeleton, Fluid-solid interactions, Cell biology