The nature of the stresses induced during tissue growth

被引:17
作者
Araujo, RP [1 ]
McElwain, DLS [1 ]
机构
[1] Queensland Univ Technol, Applicable Math & Adv Computat Program, Sch Math Sci, Brisbane, Qld 4001, Australia
关键词
tissue stresses; linear elasticity; anisotropic growth; stress relaxation;
D O I
10.1016/j.aml.2004.09.019
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This work employs the constitutive principles of linear elasticity to examine the nature of growth-induced stresses in soft tissues. An analysis of the simpler case of isotropic growth gives insight into the effect of the spatial non-uniformity of the growth process on both the nature and distribution tissue stresses. Anisotropic growth is also considered, illustrating its role in relieving growth-induced stresses. The genesis of growth-induced stresses in soft tissues has important implications for a variety of physiological phenomena, including the collapse of blood vessels in solid tumours. (c) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1081 / 1088
页数:8
相关论文
共 10 条
[1]   A linear-elastic model of anisotropic tumour growth [J].
Araujo, RP ;
McElwain, DLS .
EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2004, 15 :365-384
[2]  
ARAUJO RP, 2003, P 2 MIT C COMP FLUID
[3]  
BOUCHER Y, 1992, CANCER RES, V52, P5110
[4]   WHAT ARE THE RESIDUAL-STRESSES DOING IN OUR BLOOD-VESSELS [J].
FUNG, YC .
ANNALS OF BIOMEDICAL ENGINEERING, 1991, 19 (03) :237-249
[5]  
FUNG YC, 1995, MATH PHYS, V46, pS469
[6]   Mathematical oncology: Cancer summed up [J].
Gatenby, RA ;
Maini, PK .
NATURE, 2003, 421 (6921) :321-321
[7]   A mathematical model of the stress induced during avascular tumour growth [J].
Jones, AF ;
Byrne, HM ;
Gibson, JS ;
Dold, JW .
JOURNAL OF MATHEMATICAL BIOLOGY, 2000, 40 (06) :473-499
[8]  
Shannon M. A., 1992, ADV BIOL HEAT MASS T, V231, P35
[9]   Compatibility and the genesis of residual stress by volumetric growth [J].
Skalak, R ;
Zargaryan, S ;
Jain, RK ;
Netti, PA ;
Hoger, A .
JOURNAL OF MATHEMATICAL BIOLOGY, 1996, 34 (08) :889-914
[10]  
Timoshenko S. P., 1970, THEORY ELASTICITY