The influence of growth-induced stress from the surrounding medium on the development of multicell spheroids

Journal of Mathematical Biology

Volumn 43, Issue 3, 2001, Pages 191-220

  Chen, C Y ^a   Byrne, H M ^a   King, J R ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CELL DIVISION; COMPUTER SIMULATION; HUMAN; MULTICELLULAR SPHEROID; NECROSIS; NEOPLASM; PATHOLOGY; PHYSIOLOGY;

ANIMALS; CELL DIVISION; COMPUTER SIMULATION; HUMANS; MODELS, BIOLOGICAL; NECROSIS; NEOPLASMS; SPHEROIDS, CELLULAR;

EID: 0035462048     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850100091     Document Type: Article

References (20)

1. Adam, J.A.: A mathematical model of tumour growth. II. Effects of geometry and spatial nonuniformity on stability, Math. Biosci., 86, 183-211 (1987)
2. Byrne, H.M., Chaplain, M.A.J.: Modelling the role of cell-cell adhesion in the growth and development of carcinomas, Math. Comp. Mod., 24, 1-17 (1996)
3. Chaplain, M.A.J., Sleeman, B.D.: Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory, J. Math. Biol., 3, 431-471 (1992)
4. Folkman, J., Hochberg, M.: Self-regulation of growth in three dimensions, J. Exp. Med., 138, 745-753 (1973)
5. Freyer, J.P.: Role of necrosis in regulating the growth saturation of multicellular spheroids, Canc. Res., 48, 2432-2439 (1988)
6. Greenspan, H.P.: On the self-inhibited growth of cell cultures, Growth, 38, 81-95 (1974)
7. Greenspan, H.P.: On the growth and stability of cell cultures and solid tumours, J. Theor. Biol., 56, 229-242 (1976)
8. Haji-Karim, M., Carlsson, J.: Proliferation and viability in cellular spheroids of human origin, Canc. Res., 38, 1457-1464 (1978)
9. Helmlinger, G., Netti, P.A., Lichtenbeld, H.C., Melder, R.J., Jain, R.K.: Solid stress inhibits the growth of multicellular tumour spheroids, Nature Biotech., 5, 778-783 (1997)
10. Holmes M.H.: Finite deformation of soft tissue: analysis of a mixture model in uni-axial compression, ASME J. Biomech. Eng., 108, 372-381 (1986)
11. Landman, K., Please, C.P.: Tumour dynamics and necrosis: surface tension and stability. To appear
12. Please, C.P., Pettet, G., McElwain, D.L.S.: A new approach to modelling the formation of necrotic regions in tumours, Appl. Math. Letters, 11, 89-94 (1997)
13. Please, C.P., Pettet, G., McElwain, D.L.S.: Avascular tumour dynamics and necrosis, Math. Mod. Meth. Appl. S9, 569-579 (1999)
14. Landman, K., White, L.R.: Solid/liquid separation of flocculated suspensions, Advances in Colloid and Interface Sci., 51, 175-246 (1994)
15. Perumpanani, A.J., Byrne, H.M.: Extracellular Matrix Concentration Exerts Selection Pressure on Invasive Cells, Eur. J. Cancer, 35, 1274-1280 (1999)
16. Simon, B.R., Kaufmann, M.V., McAfee, M.A., Baldwin, A.L.: Finite Element Models for Arterial Wall Mechanics, J. Biomech. Eng., 115, 489-496 (1993)
17. Spencer, A.J.M.: Continuum Mechanics, Longman Scientific & Technical (1980)
18. Ward, J.P., King, J.R.: Mathematical modelling of avascular-tumour growth, IMA J. Math. Appl. Med. Biol., 14, 39-69 (1997)
19. Ward, J.P., King, J.R.: Mathematical modelling of avascular-tumour growth II: Modelling growth saturation, IMA J. Appl. Math. Med. Biol., 16, 171-211 (1999a)
20. Ward, J.P., King, J.R.: Mathematical modelling of the effects of mitotic inhibitors on avascular tumour growth, J. Theor. Med., 1, 287-311 (1999b)