### Abstract

Using maximum principles for parabolic and elliptic operators, we examine, in a general way, some models of tissue growth. These typically consist of a model mechanism for the diffusion of a mitotic inhibitor (growth inhibitory factor, GIF) throughout the tissue. Central to the modeling is the inclusion of a source function that models the production of GIF throughout the tissue. We examine the effect this term has on the resulting distribution of GIF in the tissue and comment on the appropriateness of different source functions, in particular a uniform production rate or a nonuniform production rate of inhibitor. Given that it is more appropriate to infer from the patterns of mitosis that are observed experimentally in various tissues the GIF concentration profile rather than the source function profile, it may be more appropriate to use these types of models to determine the qualitative form of the source term rather than proposing this function a priori.

Original language | English |
---|---|

Pages (from-to) | 77-89 |

Number of pages | 13 |

Journal | Mathematical Biosciences |

Volume | 113 |

Issue number | 1 |

Publication status | Published - Jan 1993 |

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### Keywords

- Animals
- Growth
- Growth Inhibitors
- Humans
- Mitosis
- Models, Biological
- Models, Theoretical

### Cite this

*Mathematical Biosciences*,

*113*(1), 77-89.

**A qualitative analysis of some models of tissue growth.** / Britton, N F; Chaplain, M A.

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 113, no. 1, pp. 77-89.

}

TY - JOUR

T1 - A qualitative analysis of some models of tissue growth

AU - Britton, N F

AU - Chaplain, M A

PY - 1993/1

Y1 - 1993/1

N2 - Using maximum principles for parabolic and elliptic operators, we examine, in a general way, some models of tissue growth. These typically consist of a model mechanism for the diffusion of a mitotic inhibitor (growth inhibitory factor, GIF) throughout the tissue. Central to the modeling is the inclusion of a source function that models the production of GIF throughout the tissue. We examine the effect this term has on the resulting distribution of GIF in the tissue and comment on the appropriateness of different source functions, in particular a uniform production rate or a nonuniform production rate of inhibitor. Given that it is more appropriate to infer from the patterns of mitosis that are observed experimentally in various tissues the GIF concentration profile rather than the source function profile, it may be more appropriate to use these types of models to determine the qualitative form of the source term rather than proposing this function a priori.

AB - Using maximum principles for parabolic and elliptic operators, we examine, in a general way, some models of tissue growth. These typically consist of a model mechanism for the diffusion of a mitotic inhibitor (growth inhibitory factor, GIF) throughout the tissue. Central to the modeling is the inclusion of a source function that models the production of GIF throughout the tissue. We examine the effect this term has on the resulting distribution of GIF in the tissue and comment on the appropriateness of different source functions, in particular a uniform production rate or a nonuniform production rate of inhibitor. Given that it is more appropriate to infer from the patterns of mitosis that are observed experimentally in various tissues the GIF concentration profile rather than the source function profile, it may be more appropriate to use these types of models to determine the qualitative form of the source term rather than proposing this function a priori.

KW - Animals

KW - Growth

KW - Growth Inhibitors

KW - Humans

KW - Mitosis

KW - Models, Biological

KW - Models, Theoretical

M3 - Article

VL - 113

SP - 77

EP - 89

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -