Note on a diffusion model of tissue growth
type: Item
instance of: scholarly article
title: Note on a diffusion model of tissue growth
zbMATH Open document ID: 0706.92017
DOI: 10.1016/0893-9659(90)90060-O
author: Sophia A. Maggelakis
author: John A. Adam
published in: Applied Mathematics Letters
publication date: 1990-01-01T00:00:00Z
review text: The growth of cell population is governed by a conservation law of mass or cell volume. The assumptions and analytical details on how to derive the conservation law have been discussed e.g. by \textit{H. Greenspan} [Studies Appl. Math. 51, 317-340 (1972; Zbl 0257.92001), and Growth 38, 81 ff (1974)] and only a summary of results is given here. Following Greenspan, we consider the growth of a cell culture in a small tube with a small constant cross sectional area, \(\alpha\), and the three interfacial heights \(z_ 0(t)\), \(z_ g(t)\), \(z_ i(t)\) to separate the cell culture from the ambient medium, dividing from nondividing cells, and living from dead cells, respectively.
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4160543
zbMATH Keywords: growth of cell population
zbMATH Keywords: conservation law of mass
zbMATH Keywords: cell culture
zbMATH Keywords: small tube
zbMATH Keywords: constant cross sectional area
MaRDI profile type: Publication
cites work: Models for the Growth of a Solid Tumor by Diffusion
full work available at URL: 0893-9659(90)90060-o
OpenAlex ID: W2006700520
Wikidata QID: Q127121094
description: scientific article; zbMATH DE number 4160543