Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems

Mathematical Models and Methods in Applied Sciences

Volumn 16, Issue 7, 2006, Pages 1001-1029

  Bellomo, Nicola ^a   Forni, Guido ^b  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF TURIN   (Italy)

Author keywords

Complex systems in biology; Kinetic theory; Nonlinearity; Statistical mechanics

Indexed keywords

EID: 33746069282     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202506001443     Document Type: Article

References (40)

1. Eds. J. Adam and N. Bellomo, A Survey of Models on Tumor Immune Systems Dynamics (Birkhäuser, 1997).
2. T. Alarcön, H. M. Byrne and P. K. Maini, A mathematical model of the effects of hypoxia on the cell-cycle of normal cancer cells, J. Theor. Biol. 229 (2004) 395-411.
3. T. Alarcón, H. M. Byrne and P. K. Maini, A multiple scale model for tumor growth, SIAM J. Multiscale Simul. 3 (2005) 440-475.
4. + T-cell memory, Nature Rev. - Immunology 5 (2005) 1001-111.
5. N. Bellomo and G. Forni, Dynamics of tumor interaction with the host immune system, Math. Comput. Model. 20 (1994) 107-122.
6. N. Bellomo, E. De Angelis and L. Preziosi, Multiscale modeling and mathematical problems related to tumor evolution and medical therapy, J. Theor. Med. 5 (2003) 111-136.
7. N. Bellomo, A. Bellouquid and M. Delitala, Mathematical topics on the modelling of multicellular systems in the competition between tumor and immune cells, Math. Mod. Meth. Appl. Sci. 14 (2004) 1683-1733.
8. N. Bellomo and A. Bellouquid, From a class of kinetic models to macroscopic equations for multicellular systems in biology, Discr. Cont. Dynam. Syst. B 4 (2004) 59-80.
9. Eds. N. Bellomo and E. De Angelis, Modeling complex systems in molecular biology and tumor dynamics and control, Math. Comput. Model. 41 (2005) xiii-xv; 1055-1203.
10. N. Bellomo and P. K. Maini, Preface, Math. Mod. Meth. Appl. Sci. 15 (2005) iii-viii.
11. Eds. N. Bellomo and P. K. Maini, Special Issue on Cancer Modelling, Math. Mod. Meth. Appl. Sci. 15 (2005) 1619-1794.
12. A. Bellouquid and M. Delitala, Mathematical methods and tools of kinetic theory towards modelling complex biological systems, Math. Mod. Meth. Appl. Sci. 15 (2005) 1639-1666.
13. M. L. Bertotti and M. Delitala, From discrete kinetic and stochastic game theory to modeling complex systems in applied sciences, Math. Mod. Meth. Appl. Sci. 14 (2004) 1061-1084.
14. A. Bertuzzi, A. Fasano and A. Gandolfi, A mathematical model for tumor cords incorporating the flow of interstitial fluids, Math. Mod. Meth. Appl. Sci. 15 (2005) 1735-1777.
15. T. Blankenstein, The role of tumor stroma in the interaction between tumor and immune system, Current Opinion Immunology 17 (2005) 180-186.
16. P. Blume-Jensen and T. Hunter, Oncogenic kinase signalling, Nature 411 (2001) 355-365.
17. A. Bru, J. M. Pastor, I. Fernaud, I. Bru, S. Melle and C. Berenguer, Super-rough dynamics on tumor growth, Phys. Rev. Lett. 81 (1998) 4008-4011.
18. M. A. J. Chaplain and G. Lolas, Spatio-temporal heterogeneity arising in a mathematical model of cancer invasion of tissue, Math. Mod. Meth. Appl. Sci. 15 (2005) 1685-1734.
19. L. Derbel, Analysis of a new model for tumor-immune system competition including long time scale effects, Math. Mod. Meth. Appl. Sci. 14 (2004) 1657-1681.
20. U. Dieckmann and M. Doebeli, On the origin of species by simpatric speciation, Nature 400 (1999) 364-367.
21. G. P. Dunn, A. T. Bruce, H. Ikeda, L. J. Old and R. D. Schreiber, Cancer immunoediting: From immunosurveillance to tumor escape, Nature Immunology 3 (2002) 991-998.
22. P. Friendl, A. T. den Boer and M. Gunzer, Tuning immune responses: Diversity and adaptation of the immunological synapse, Nature Rev. Immunology 5 (2005) 532-545.
23. J. Folkman, Role of angiogenesis in tumor growth and methastasis, Semi. Oncology 29 (2002) 15-18.
24. R. A. Gatenby and P. K. Maini, Mathematical oncology: Cancer summed up, Nature 421 (2003) 321-323.
25. R. A. Gatenby, T. L. Vincent and R. J. Gillies, Evolutionary dynamics in carcinogenesis, Math. Mod. Meth. Appl. Sci. 15 (2005) 1619-1638.
26. L. Greller, F. Tobin and G. Poste, Tumor Heterogeneity and progression: Conceptual foundation for modeling, Invasion Metastasis 16 (1996) 177-208.
27. H. L. Hartwell, J. J. Hopfield, S. Leibner and A. W. Murray, From molecular to modular cell biology, Nature 402 (1999) c47-c52.
28. H. Hatzikirou, A. Deutsch, C. Schaller, M. Simon and K. Swanson, Mathematical modelling of glioblastoma tumor development, Math. Mod. Meth. Appl. Sci. 15 (2005) 1779-1794.
29. M. Kolev, Mathematical modeling of the competition between acquired immunity and cancer, Appl. Math. Comp. Sci. 13 (2003) 289-297.
30. M. Kolev, A mathematical model of cellular immune response to leukemia, Math. Comput. Model. 41 (2005) 1071-1082.
31. M. Kolev, E. Kozlowska and M. Lachowicz, Mathematical model of tumor invasion along linear or tubular structures, Math. Comput. Model. 41 (2005) 1083-1096.
32. M. Lachowicz, Micro and meso scales of description corresponding to a model of tissue invasion by solid tumors, Math. Mod. Meth. Appl. Sci. 15 (2005) 1667-1683.
33. R. M. May, Uses and abuses of mathematics in biology, Science 303 (2004) 790-793.
34. M. A. Novak and K. Sigmund, Evolutionary dynamics of biological games, Science 303 (2004) 793-799.
35. G. Pawelec, S. Heinzel, S. Kiessling, L. Muller, Q. Ouyang and J. Zeuthen, Escape mechanism in tumor immunity: A year 2000 update, Critical Rev. Oncology 11 (2000) 97-133.
36. L. Preziosi, Modeling Cancer Growth (CRC Press & Chapman Hall, 2003).
37. R. Reed, Why is mathematical biology so hard?, Not. Amer. Math. Soc. 51 (2004) 338-342.
38. T. Vicsek, A question of scale, Nature 418 (2004) 131.
39. T. Vicsek, The bigger picture, Nature 411 (2004) 421.
40. E. Wigner, The unreasonable effectiveness of mathematics in the natural sciences, Comm. Pure Appl. Math. 13 (1960) 1-14.