A qualitative analysis of some models of tissue growth

N F Britton, M A Chaplain

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)77-89
Number of pages13
JournalMathematical Biosciences
Volume113
Issue number1
Publication statusPublished - Jan 1993

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Qualitative Analysis
qualitative analysis
Tissue
Growth
Inhibitor
Parabolic Operator
Maximum principle
Model
Source Terms
Maximum Principle
Elliptic Operator
Mitosis
mitosis
Inclusion
tissues
growth inhibitory factor
Intercellular Signaling Peptides and Proteins
Term
Modeling
Profile

Keywords

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

Cite this

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

In: Mathematical Biosciences, Vol. 113, No. 1, 01.1993, p. 77-89.

Research output: Contribution to journalArticle

Britton, N F ; Chaplain, M A. / A qualitative analysis of some models of tissue growth. In: Mathematical Biosciences. 1993 ; Vol. 113, No. 1. pp. 77-89.
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