Residual stress generation and necrosis formation in multi-cell tumour spheroids

Journal of Mathematical Biology

Volumn 49, Issue 6, 2004, Pages 537-552

  MacArthur, Ben D ^a   Please, Colin P ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Continuum mechanics; Growth induced stress; Multi cell tumour spheroid; Necrosis

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; CELL GROWTH; ELASTICITY; HUMAN; MULTICELLULAR SPHEROID; NECROSIS; NEOPLASM; NONLINEAR SYSTEM; PATHOLOGY; PHYSIOLOGY; VISCOSITY;

CELL GROWTH PROCESSES; ELASTICITY; HUMANS; MODELS, BIOLOGICAL; NECROSIS; NEOPLASMS; NONLINEAR DYNAMICS; SPHEROIDS, CELLULAR; VISCOSITY;

JONES;

EID: 11144221005     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00285-004-0265-7     Document Type: Article

References (25)

1. Ambrosi, D., Mollica, F.: On the mechanics of a growing tumour. Int. J. Eng. Sci. 40 (12), 1297-1316 (2002)
2. Byrne, H. M., Chaplain, M. A. J., Pettet, G. J., McElwain, D. L. S.: A mathematical model of trophoblast invasion. J. Theor. Med. 1, 275-286 (1999)
3. Chen, C. Y., Byrne, H. M., King, J. R.: The influence of growth-induced stress from the surrounding medium on the development of multicell spheroids. J. Math. Biol. 43 (3), 191-220 (2001)
4. Drozdov, A. D., Khanina, H.: A model for the volumetric growth of a soft tissue. Math. Comput. Modelling 25 (2), 11-29 (1997)
5. Greenspan, H. P.: On the growth and stability of cell cultures and solid tumors. J. Theor. Biol. 56, 229-242 (1976)
6. Helmlinger, G., Netti, P. A., Lichtenbeld, H. C., Melder, R. J., Jain, R. K.: Solid stress inhibits the growth of multicellular tumour spheroids. Nat. Biotechnol. 15, 778-783 (1997)
7. Holzapfel, G. A.: Handbook of material behaviour. Academic Press, 2000
8. Jones, A. F., Byrne, H. M., Gibson, J. S., Dold, J. W.: A mathematical model of the stress induced during avascular tumour growth. J. Math. Biol. 40 (6), 473-499 (2000)
9. Knapp, D. M., Barocas, V. H., Moon, A. G.: Rheology of reconstituted type I collagen gel in confined compression. J. Rheol. 41 (5), 971-993 (1997)
10. Kunz-Schghart, L. A., Kreutz, M., Knuechel, R.: Multicellular Spheroids: A three-dimensional in vitro culture system to study tumour biology. Int. J. Exp. Path. 79, 1-23 (1998)
11. Kunz-Schughart, L. A.: Multicellular tumour spheroids: Intermediates between monolayer culture and in vivo tumour. Cell. Biol. Int. 23 (3), 157-161 (1999)
12. Eubarda, V. A., Hoger, A.: On the mechanics of solids with a growing mass. Int. J. solids and struct. 39, 4627-4664 (2002)
13. Mueller-Klieser, W.: Tumour biology and experimental therapeutics. Crit. Rev. Oncol./Haematol. 36, 123-139 (2000)
14. Murray, J. D.: Mathematical Biology, volume 19 of Biomathematics. Springer-Verlag 2nd edition, 1993
15. Pettet, G. J., Please, C. P., Tindall, M. J., McElwain, D. E. S.: The migration of cells in multicell tumour spheroids. B. Math. Biol. 63 (2), 231-257 (2001)
16. Please, C. P., Pettet, G., McElwain, D. L. S.: A new approach to modelling the formation of necrotic regions in tumours. Appl. Math. Lett. 11 (3), 89-94 (1997)
17. Please, C. P., Pettet, G., McElwain, D. E. S.: Avascular tumour dynamics and necrosis. Math. Models Methods Appl. Sci. 9 (4), 569-579 (1999)
18. Please, C. P., Eandman, K. A.: Tumour dynamics and necrosis: Surface tension and stability. IMA. J. Math. Appl. Med. Biol. 18 (2), 131-158 (2001)
19. Rodriguez, E. K., Hoger, A., McCulloch, A.: Stress-dependant finite growth in soft elastic tissues. J. Biomech. 27 (4), 455-467 (1994)
20. Santini, M. T., Rainaldi, G.: Three-dimensional spheroid model in tumour biology. Pathobiology 67, 148-157 (1999)
21. Skalak, R.: Growth as a finite displacement field. Proceedings of the IUTAM symposium on finite elasticity. D. E. Carlson and R. T. Shield Aug. (1980)
22. Skalak, R., Dasgupta, G., Moss, M.: Analytical description of growth. J. Theor. Biol. 94, 555-577 (1982)
23. Skalak, R., Zargaryan, S., Jain, R. K., Netti, P. A., Hoger, A.: Compatibility and the genesis of residual stress by volumetric growth. J. Math. Biol. 34, 889-914 (1996)
24. Ward, J. P., King, J. R.: Mathematical modelling of avascular tumour growth. IMA J. Math. Appl. Med. 14 (1), 39-69 (1997)
25. Ward, J. P., King, J. R.: Mathematical modelling of avascular tumour growth II: modelling growth saturation. IMA J. Math. Appl. Med. Biol. 16 (2), 171-211 (1999)