Mathematical modelling of avascular-tumour growth II: Modelling growth saturation

IMA Journal of Mathemathics Applied in Medicine and Biology

Volumn 16, Issue 2, 1999, Pages 171-211

  Ward, J P ^a   King, J R ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Asymptotic analysis; Mathematical modelling; Numerical solution; Tumour growth

Indexed keywords

CELL GROWTH; GROWTH RATE; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; REVIEW; SOLID TUMOR; TUMOR GROWTH;

NUMERICAL MODELS; TUMORS;

CELLULAR MATERIAL; DEPLETION MECHANISM; LIVE CELL; LOCAL VOLUME CHANGE; MATHEMATICAL MODELING; NUMERICAL SOLUTION; STEADY STATE; TUMOR GROWTH; TUMOR HETEROGENEITY; VELOCITY FIELD;

ASYMPTOTIC ANALYSIS;

EID: 0033028947     PISSN: 02650746     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb16.2.171     Document Type: Review

References (34)

1. ACKER, H., CARLSSON, J., HOLTERMANN, G., NEDERMAN, T., & NYLEN, T. 1987 Influence of glucose and buffer capacity in the culture medium on growth and pH in spheroids of human thyroid carcinoma and human glioma origin. Cancer Res. 47, 3504-3508.
2. ADAM, J. A. 1986 A simplified mathematical model of tumour growth. Math. Biosci. 81, 224-229.
3. BOURRAT-FLOECK, B., GROEBE, K., & MUELLER-KLIESER, W. 1991 Biological response of multicellular EMT6 spheroids to exogenous lactate. Int. J. Cancer 47, 792-799.
4. BYRNE, H. M. & CHAPLAIN, M. A. J. 1995 Growth of non-necrotic tumours in the presence and absence of inhibitors. Math. Biosci. 130, 151-181.
5. BYRNE, H. M. & CHAPLAIN, M. A. J. 1996 Growth of necrotic tumours in the presence and absence of inhibitors. Math. Biosci. 135, 187-216.
6. CARLSSON, J. 1977 A proliferation gradient in three-dimensional colonies of cultured human glioma cells. Int. J. Cancer 20, 129-136.
7. CASCIARI, J. J., SOTIRCHOS, S. V., & SUTHERLAND, R. M. 1988 Glucose diffusivity in multicellular tumour spheroids. Cancer Res. 48, 3905-3909.
8. CASCIARI, J. J., SOTIRCHOS, S. V., & SUTHERLAND, R. M. 1992 Mathematical modelling of micro-environment and growth in EMT6/RO multicellular tumour spheroids. Cell Prolif. 25, 1-22.
9. CONGAR, A. D. & ZISKIN, M. C. 1983 Growth of mammalian multicellular tumour spheroids. Cancer Res. 43, 558-560.
10. FOLKMAN, J. & HOCHBERG, M. 1973 Self-regulation of growth in three dimensions J. Exp. Med. 138, 745-753.
11. FRANKO, A. J. & SUTHERLAND, R. M. 1978 Oxygen diffusion distance and the development of necrosis in multicell spheroids. Radiat. Res. 79, 439-453.
12. FREYER, J. P. 1988 Role of necrosis in regulating the growth saturation of multicell spheroids. Cancer Res. 48, 2432-2439.
13. FREYER, J. P. & SCHOR, P. L. 1989 Regrowth kinetics of cells from different regions of multicellular spheroids of 4 cell-lines. J. Cell. Physiol. 138, 384-392.
14. FREYER, J. P. & SUTHERLAND, R. M. 1980 Selective dissociation and characterization of cells from different regions of multicell tumour spheroids. Cancer Res. 40, 3956-3965.
15. FREYER, J. P. & SUTHERLAND, R. M. 1986 Regulation of growth saturation and development of necrosis in EMT6/RO multicellular spheroids glucose and oxygen supply. Cancer Res. 46, 3504-3512.
16. GREENSPAN, H. P. 1972 Models for the growth of a solid tumour by diffusion. Stud. Appl. Math. 51, 317-340.
17. GROEBE, K. & MUELLER-KLIESER, W. 1996 On the relation between size of necrosis and diameter of tumor spheroids. Int. J. Radiat. Onc. Biol. Phys. 34, 395-401.
18. HLATKY, L., SUCHS, R. K., & ALPEN, E. L. 1988 Joint oxygen-glucose deprivation as the cause of necrosis in a tumour analogue. J. Cell Phys. 134, 167-178.
19. INCH, W. R., MCCREDIE, J. A., & SUTHERLAND, R. M. 1970 Growth of nodular carcinomas in rodents compared with multicell spheroids in tissue culture. Growth 34, 271-282.
20. KERR, J. F. R., SEARLE, J., HARMON, B. V., & BISHOP, C. J. 1987 Apoptosis. In: Perspectives in Mammalian Cell Death (C.S. Potten, ed.). Oxford University Press.
21. LANDRY, J., FREYER, J. P., & SUTHERLAND, R. M. 1981 Shedding of mitotic cells from the surface of multicell spheroids during growth. J. Cell Physiol. 106, 23-32.
22. LANDRY, J., FREYER, J. P., & SUTHERLAND, R. M. 1982 A model for the growth of multicellular spheroids. Cell Tiss. Kinet. 15, 585-594.
23. LEVINE, A. E., HAMILTON, D. A., YEOMAN, L. C., BUSCH, H., & BRATTAIN, M. G. 1984 Identification of a tumour inhibitory factor in rat ascites fluid. Biochem. Biophys. Res. Comm. 119, 76-82.
24. MAGGELAKIS, S. A. & ADAM, J. A. 1990 Mathematical model of prevascular growth of a spheroid carcinoma. Math. Comput. Mod. 13, 23-38.
25. MCELWAIN, D. L. S. & MORRIS, L. E. 1978 Apoptosis as a volume loss mechanism in mathematical models of solid tumour growth. Math. Biosci. 39, 147-157.
26. MUELLER-KLIESER, W. F., FREYER, J. P., & SUTHERLAND, R. M. 1983 Evidence for a major role of glucose in controlling development of necrosis in EMT6/RO multicell tumour spheroids. Adv. Exp. Med. Biol. 159, 487-495.
27. MUELLER-KLIESER, W. F., FREYER, J. P., & SUTHERLAND, R. M. 1985 Influence of glucose and oxygen supply conditions on the oxygenation of multicellular tumour spheroids. Br. J. Cancer 53, 345-353.
28. NUGENT, L. & JAIN, R. K. 1984 Extravascular diffusion in normal and neoplastic tissues. Cancer Res. 44, 238-244.
29. SHYMKO, R. M. & GLASS, L. 1976 Cellular and geometric control of tissue growth and mitotic instability. J. Theor. Biol. 63, 355-374.
30. TANNOCK, I. F. & KOPELYAN, I. 1986a Influence of glucose-concentration on growth and formation of necrosis in spheroids derived from a human bladder cancer cell-line. Cancer Res. 46, 3105-3110.
31. o2 in the growth and formation of spheroids-interaction with glucose to influence spherical growth and necrosis. Br. J. Cancer 53, 823-827.
32. WARD, J. P. 1997 Mathematical modelling of avascular tumour growth. PhD Thesis, Nottingham University.
33. WARD, J. P. & KING, J. R. 1997 Mathematical modelling of avascular-tumour growth. IMA J. Math. Appl. Med. Biol. 14, 39-69.
34. WEISS, L. 1978 Some mechanisms involved in cancer cell detachment by necrotic material. Int. J. Cancer 22, 196-203.