Free boundary value problems associated with the growth and development of multicellular spheroids

被引:145
作者
Byrne, HM
Chaplain, MAJ
机构
[1] Univ Manchester, Inst Sci & Technol, Dept Math, Manchester M60 1QD, Lancs, England
[2] Univ Dundee, Dept Math & Comp Sci, Dundee DD1 4HN, Scotland
关键词
D O I
10.1017/S0956792597003264
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper a generalized model for the growth of avascular tumours is presented. The formulation leads naturally to the incorporation of free boundaries which define the outer tumour surface explicitly and various inner surfaces implicitly. A combination of numerical simulations, asymptotic analysis and perturbation techniques is used to study the model and yields results, which agree well with experimentally-observed phenomena.
引用
收藏
页码:639 / 658
页数:20
相关论文
共 47 条
[2]   A MATHEMATICAL-MODEL OF TUMOR-GROWTH .3. COMPARISON WITH EXPERIMENT [J].
ADAM, JA .
MATHEMATICAL BIOSCIENCES, 1987, 86 (02) :213-227
[3]   DIFFUSION REGULATED GROWTH-CHARACTERISTICS OF A SPHERICAL PREVASCULAR CARCINOMA [J].
ADAM, JA ;
MAGGELAKIS, SA .
BULLETIN OF MATHEMATICAL BIOLOGY, 1990, 52 (04) :549-582
[4]  
[Anonymous], 1982, RES NOTES MATH
[5]   A MATHEMATICAL-MODEL OF TUMOR-INDUCED CAPILLARY GROWTH [J].
BALDING, D ;
MCELWAIN, DLS .
JOURNAL OF THEORETICAL BIOLOGY, 1985, 114 (01) :53-73
[6]   GROWTH OF NONNECROTIC TUMORS IN THE PRESENCE AND ABSENCE OF INHIBITORS [J].
BYRNE, HM ;
CHAPLAIN, MAJ .
MATHEMATICAL BIOSCIENCES, 1995, 130 (02) :151-181
[7]   Growth of necrotic tumors in the presence and absence of inhibitors [J].
Byrne, HM ;
Chaplain, MAJ .
MATHEMATICAL BIOSCIENCES, 1996, 135 (02) :187-216
[8]   Modelling the role of cell-cell adhesion in the growth and development of carcinoma [J].
Byrne, HM ;
Chaplain, MAJ .
MATHEMATICAL AND COMPUTER MODELLING, 1996, 24 (12) :1-17
[9]   MATHEMATICAL-MODELS FOR TUMOR ANGIOGENESIS - NUMERICAL SIMULATIONS AND NONLINEAR-WAVE SOLUTIONS [J].
BYRNE, HM ;
CHAPLAIN, MAJ .
BULLETIN OF MATHEMATICAL BIOLOGY, 1995, 57 (03) :461-486
[10]   EXISTENCE AND STABILITY FOR SPHERICAL CRYSTALS GROWING IN A SUPERSATURATED SOLUTION [J].
CHADAM, J ;
HOWISON, SD ;
ORTOLEVA, P .
IMA JOURNAL OF APPLIED MATHEMATICS, 1987, 39 (01) :1-15