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Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes

Research output: Contribution to journalArticle

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Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes. / Chaplain, Mark Andrew Joseph; Giverso, Chiara; Lorenzi, Tommaso; Preziosi, Luigi.

In: SIAM Journal of of Applied Mathematics, 30.07.2019.

Research output: Contribution to journalArticle

Harvard

Chaplain, MAJ, Giverso, C, Lorenzi, T & Preziosi, L 2019, 'Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes', SIAM Journal of of Applied Mathematics.

APA

Chaplain, M. A. J., Giverso, C., Lorenzi, T., & Preziosi, L. (Accepted/In press). Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes. SIAM Journal of of Applied Mathematics.

Vancouver

Chaplain MAJ, Giverso C, Lorenzi T, Preziosi L. Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes. SIAM Journal of of Applied Mathematics. 2019 Jul 30.

Author

Chaplain, Mark Andrew Joseph ; Giverso, Chiara ; Lorenzi, Tommaso ; Preziosi, Luigi. / Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes. In: SIAM Journal of of Applied Mathematics. 2019.

Bibtex - Download

@article{3fc2d092d39b43c09ff15de0195bf863,
title = "Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes",
abstract = "We consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the membranes. We reduce the original problem to a limiting transmission problem whereby each thin membrane is replaced by an effective interface, and we develop a formal asymptotic method that enables the derivation of a set of biophysically consistent transmission conditions to close the limiting problem. The formal results obtained are validated via numerical simulations showing that the relative error between the solutions to the original transmission problem and the solutions to the limiting problem vanishes when the thickness of the membranes tends to zero. In order to show potential applications of our effective interface conditions, we employ the limiting transmission problem to model cancer cell invasion through the basement membrane and the metastatic spread of ovarian carcinoma.",
author = "Chaplain, {Mark Andrew Joseph} and Chiara Giverso and Tommaso Lorenzi and Luigi Preziosi",
note = "Funding: UK EPSRC grant no. EP/N014642/1.",
year = "2019",
month = "7",
day = "30",
language = "English",
journal = "SIAM Journal of of Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes

AU - Chaplain, Mark Andrew Joseph

AU - Giverso, Chiara

AU - Lorenzi, Tommaso

AU - Preziosi, Luigi

N1 - Funding: UK EPSRC grant no. EP/N014642/1.

PY - 2019/7/30

Y1 - 2019/7/30

N2 - We consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the membranes. We reduce the original problem to a limiting transmission problem whereby each thin membrane is replaced by an effective interface, and we develop a formal asymptotic method that enables the derivation of a set of biophysically consistent transmission conditions to close the limiting problem. The formal results obtained are validated via numerical simulations showing that the relative error between the solutions to the original transmission problem and the solutions to the limiting problem vanishes when the thickness of the membranes tends to zero. In order to show potential applications of our effective interface conditions, we employ the limiting transmission problem to model cancer cell invasion through the basement membrane and the metastatic spread of ovarian carcinoma.

AB - We consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the membranes. We reduce the original problem to a limiting transmission problem whereby each thin membrane is replaced by an effective interface, and we develop a formal asymptotic method that enables the derivation of a set of biophysically consistent transmission conditions to close the limiting problem. The formal results obtained are validated via numerical simulations showing that the relative error between the solutions to the original transmission problem and the solutions to the limiting problem vanishes when the thickness of the membranes tends to zero. In order to show potential applications of our effective interface conditions, we employ the limiting transmission problem to model cancer cell invasion through the basement membrane and the metastatic spread of ovarian carcinoma.

M3 - Article

JO - SIAM Journal of of Applied Mathematics

JF - SIAM Journal of of Applied Mathematics

SN - 0036-1399

ER -

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ID: 260335515

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