### Abstract

Original language | English |
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Title of host publication | Integral Methods in Science and Engineering |

Subtitle of host publication | Analytic treatment and Numerical Approximations |

Editors | Christian Constanda, Paul Harris |

Publisher | Birkhäuser |

Chapter | 13 |

Pages | 163-172 |

Number of pages | 10 |

ISBN (Electronic) | 9783030160777 |

ISBN (Print) | 9783030160760 |

DOIs | |

Publication status | Published - 19 Jul 2019 |

Event | 15th International Conference On Integral Methods In Science And Engineering - Brighton, United Kingdom Duration: 16 Jul 2018 → 20 Jul 2018 |

### Conference

Conference | 15th International Conference On Integral Methods In Science And Engineering |
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Country | United Kingdom |

City | Brighton |

Period | 16/07/18 → 20/07/18 |

### Fingerprint

### Cite this

*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

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*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.

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Chapter › Research › peer-review

TY - CHAP

T1 - A Combined Boundary Element And Finite Element Model Of Cell Motion Due To Chemotaxis

AU - Harris, Paul

PY - 2019/7/19

Y1 - 2019/7/19

N2 - 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.

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.

U2 - 10.1007/978-3-030-16077-7_13

DO - 10.1007/978-3-030-16077-7_13

M3 - Chapter

SN - 9783030160760

SP - 163

EP - 172

BT - Integral Methods in Science and Engineering

A2 - Constanda, Christian

A2 - Harris, Paul

PB - Birkhäuser

ER -