The Steady State of Multicellular Tumour Spheroids: A Modelling Challenge - Mathematical Methods and Models in Biomedicine - page 191

Acknowledgments The present work was partially supported by the PRIN (2008): “Modelli
matematici per sistemi a molte componenti nelle scienze mediche ed ambientali” (MIUR).
References
1. Adam, J.A.: A mathematical model of tumour growth. iii. Comparison with experiment. Math.
Biosci. 86 , 213-227 (1987)
2. Adam, J.A., Maggelakis, S.A.: Mathematical models of tumour growth. iv. Effects of a necrotic
core. Math. Biosci. 97 , 121-136 (1989)
3. Adam, J.A., Maggelakis, S.A.: Diffusion regulated growth characteristics of a spherical
prevascular carcinoma. Bull. Math. Biol. 52 , 549-582 (1990)
4. Ambrosi, D., Preziosi, L.: On the closure of mass balance for tumour growth. Math. Mod.
Meth.Appl.Sci. 12 , 737-754 (2002)
5. Ambrosi, D., Preziosi, L.: Cell adhesion mechanisms and stress relaxation in the mechanics of
tumours. Biomech. Model. MechanoBiol. 8 , 397-413 (2009)
6. Araujo, R.P., McElwain, D.L.S.: A history of the study of solid tumour growth: The contribu-
tion of mathematical modelling, Bull. Math. Biol. 66 , 1039-1091 (2004)
7. Astanin, S., Preziosi, L.: Mathematical modelling of the Warburg effect in tumour cords,
J. Theor. Biol. 258 , 578-590 (2009).
8. Astanin, S., Tosin, A.: Mathematical model of tumour cord growth along the source of nutrient,
Math. Model. Nat. Phenom. 2 , 153-177 (2007)
9. Bertuzzi, A., Fasano, A., Gandolfi, A.: A free boundary problem with unilateral constraints
describing the evolution of a tumour cord under the influence of cell killing agents. SIAM J.
Math. Analysis 36 , 882-915 (2004).
10. Bertuzzi, A., Fasano, A., Gandolfi, A., Sinisgalli, C.: ATP production and necrosis formation
in a tumour spheroid model. Math. Model. Nat. Phenom. 2 , 30-46 (2007)
11. Bertuzzi, A., Fasano, A., Gandolfi, A., Sinisgalli, C.: Necrotic core in EMT6/Ro tumor
spheroids: Is it caused by an ATP deficit?. J. Theor. Biol. 262 , 142-150 (2010)
12. Bertuzzi, A., Bruni, C., Fasano, A., Gandolfi, A., Papa, F., Sinisgalli, C.: Response of tumor
spheroids to radiation: Modeling and parameter identification. Bull. Math. Biol. 72 , 1069-1091
(2010)
13. Bianchini, L., Fasano, A.: A model combining acid-mediated tumour invasion and nutrient
dynamics. Nonlin. Anal. Real World Appl. 10 , 1955-1975 (2009)
14. Bredel-Geissler, A., Karbach, U., Walenta, S., Vollrath, L., Mueller-Klieser, W.: Proliferation-
associated oxygen consumption and morphology of tumour cells in monolayer and spheroid
culture. J. Cell. Physiol. 153 , 44-52 (1992)
15. Breward, C.J., Byrne, H.M., Lewis, C.E.: The role of cell-cell interactions in a two-phase model
for avascular tumour growth. J. Math. Biol. 45 , 125-152 (2002)
16. Burton, A.C.: Rate of growth of solid tumours as a problem of diffusion. Growth 30 , 157-176
(1966)
17. Byrne, H.M., Chaplain, M.A.J.: Growth of necrotic tumors in the presence and absence of
inhibitors. Math. Biosci. 135 , 187-216 (1996)
18. Byrne, H., Preziosi, L.: Modeling solid tumor growth using the theory of mixtures. Math. Med.
Biol. 20 , 341-366 (2003)
19. Byrne, H.M., King, J.R., McElwain, D.L.S., Preziosi, L.: A two-phase model of solid tumour
growth. Appl. Math. Lett. 16 567-573 (2003)
20. Casciari, J.J., Sotirchos, S.V., Sutherland, R.M.: Variation in tumor cell growth rates and
metabolism with oxygen concentration, glucose concentration, and extracellular pH. J. Cell.
Physiol. 151 , 386-394 (1992)
21. Casciari, J.J., Sotirchos, S.V., Sutherland, R.M.: Mathematical modelling of microenvironment
and growth in EMT6/Ro multicellular tumour spheroids. Cell Prolif. 25 , 1-22 (1992)