A Combined Boundary Element And Finite Element Model Of Cell Motion Due To Chemotaxis

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNChapter

Abstract

Chemotaxis is the biological process whereby a cell moves in the direction in which the concentration of a chemical in the fluid medium surrounding the cell is increasing. In some cases of chemotaxis, cells secrete the chemical in order to create a concentration gradient that will attract other nearby cells to form clusters. When the cell secreting the chemical is stationary the linear diffusion equation can be used to model the concentration of the chemical as it spreads out into the surrounding fluid medium. However, if the cell is moving then its motion, and the resulting motion of the surrounding fluid, need to be taken into account in any model of how the chemical spreads out. In the case of a single, circular cell it is possible to express the fluid velocity which results from the motion of the cell in terms of a dipole located at the centre of the cell. However if the cell is not circular and/or there is more than one cell in the fluid, a more sophisticated method of determining the fluid velocity is needed. \\ This paper presents a mathematical model for simulating the concentrations of chemical secreted into the surrounding fluid medium from a moving cell. The boundary integral method is used to determine the velocity of the fluid due to the motion of the cell. The concentration of the chemical in the fluid is modelled by the convection-diffusion equation where the fluid velocity term is that given by the boundary integral equation. The resulting differential equation is then solved using the finite element method. \\ The method is illustrated with a number of typical examples.
Original languageEnglish
Title of host publicationIntegral Methods in Science and Engineering
Subtitle of host publicationAnalytic treatment and Numerical Approximations
EditorsChristian Constanda, Paul Harris
PublisherBirkhäuser
Chapter13
Pages163-172
Number of pages10
ISBN (Electronic)9783030160777
ISBN (Print)9783030160760
DOIs
Publication statusPublished - 19 Jul 2019
Event15th International Conference On Integral Methods In Science And Engineering - Brighton, United Kingdom
Duration: 16 Jul 201820 Jul 2018

Conference

Conference15th International Conference On Integral Methods In Science And Engineering
CountryUnited Kingdom
CityBrighton
Period16/07/1820/07/18

Fingerprint

Chemotaxis
Finite Element Model
Boundary Elements
Fluids
Motion
Cell
Fluid
Boundary integral equations
Boundary Integral Method
Linear Diffusion
Convection-diffusion Equation
Boundary Integral Equations
Differential equations
Diffusion equation
Dipole
Mathematical models
Finite element method
Linear equation
Express
Finite Element Method

Cite this

Harris, P. (2019). A Combined Boundary Element And Finite Element Model Of Cell Motion Due To Chemotaxis. In C. Constanda, & P. Harris (Eds.), Integral Methods in Science and Engineering: Analytic treatment and Numerical Approximations (pp. 163-172). Birkhäuser. https://doi.org/10.1007/978-3-030-16077-7_13
Harris, Paul. / A Combined Boundary Element And Finite Element Model Of Cell Motion Due To Chemotaxis. Integral Methods in Science and Engineering: Analytic treatment and Numerical Approximations. editor / Christian Constanda ; Paul Harris. Birkhäuser, 2019. pp. 163-172
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Harris, P 2019, A Combined Boundary Element And Finite Element Model Of Cell Motion Due To Chemotaxis. in C Constanda & P Harris (eds), Integral Methods in Science and Engineering: Analytic treatment and Numerical Approximations. Birkhäuser, pp. 163-172, 15th International Conference On Integral Methods In Science And Engineering, Brighton, United Kingdom, 16/07/18. https://doi.org/10.1007/978-3-030-16077-7_13

A Combined Boundary Element And Finite Element Model Of Cell Motion Due To Chemotaxis. / Harris, Paul.

Integral Methods in Science and Engineering: Analytic treatment and Numerical Approximations. ed. / Christian Constanda; Paul Harris. Birkhäuser, 2019. p. 163-172.

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNChapter

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AB - Chemotaxis is the biological process whereby a cell moves in the direction in which the concentration of a chemical in the fluid medium surrounding the cell is increasing. In some cases of chemotaxis, cells secrete the chemical in order to create a concentration gradient that will attract other nearby cells to form clusters. When the cell secreting the chemical is stationary the linear diffusion equation can be used to model the concentration of the chemical as it spreads out into the surrounding fluid medium. However, if the cell is moving then its motion, and the resulting motion of the surrounding fluid, need to be taken into account in any model of how the chemical spreads out. In the case of a single, circular cell it is possible to express the fluid velocity which results from the motion of the cell in terms of a dipole located at the centre of the cell. However if the cell is not circular and/or there is more than one cell in the fluid, a more sophisticated method of determining the fluid velocity is needed. \\ This paper presents a mathematical model for simulating the concentrations of chemical secreted into the surrounding fluid medium from a moving cell. The boundary integral method is used to determine the velocity of the fluid due to the motion of the cell. The concentration of the chemical in the fluid is modelled by the convection-diffusion equation where the fluid velocity term is that given by the boundary integral equation. The resulting differential equation is then solved using the finite element method. \\ The method is illustrated with a number of typical examples.

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Harris P. A Combined Boundary Element And Finite Element Model Of Cell Motion Due To Chemotaxis. In Constanda C, Harris P, editors, Integral Methods in Science and Engineering: Analytic treatment and Numerical Approximations. Birkhäuser. 2019. p. 163-172 https://doi.org/10.1007/978-3-030-16077-7_13