Nuova Frontiera della Ricerca Matematica nelle Scienze Mediche e Biologiche Immunologia e Oncologia Matematica
Bellomo, Nicola
Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 415-448 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

Questo lavoro propone una analisi critica sulle applicazioni della matematica allo studio di sistemi biologici complessi con particolare attenzione ai fenomeni della crescita tumorale in competizione con il sistema immunitario. Il lavoro delinea, a seguito di una descrizione fenomenologica, il problema matematico della modellizzazione multiscala e pone in evidenza come l'applicazione dei modelli allo studio di fenomeni di interesse nelle scienze biologiche generino problemi analitici e computazionali di notevole interesse e complessità. L'ultima parte del lavoro tratta alcune questioni relative alla formazione di matematici nel contesto nazionale ed europeo sempre con riferimento al tema trattato.

This paper deals with a critical analysis on the application of mathematics to the study of complex biological systems with particular attention to tumor growth phenomena in competition with immune system. The paper, after a phenomenological description, outlines the mathematical problem of multiscales modelling and shows how the application of models to he study of phenomena of interest in biological science s may generate analytic and computational problems of great interest and complexity. The last part of the paper deals with some aspects of the education in mathematical sciences in the national and European framework.

Publié le : 2006-12-01
@article{BUMI_2006_8_9A_3-1_415_0,
     author = {Nicola Bellomo},
     title = { Nuova Frontiera della Ricerca Matematica nelle Scienze Mediche e Biologiche Immunologia e Oncologia Matematica},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {9-A},
     year = {2006},
     pages = {415-448},
     zbl = {1195.00011},
     mrnumber = {2309898},
     language = {it},
     url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9A_3-1_415_0}
}

Bellomo, Nicola.  Nuova Frontiera della Ricerca Matematica nelle Scienze Mediche e Biologiche Immunologia e Oncologia Matematica. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 415-448. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9A_3-1_415_0/

[1] May, R.M., Uses and abuses of mathematics in biology, Science, 303 (2004), 790-793.

[2] Hartwell, H.L., Hopfield, J.J., Leibner, S. e Murray, A.W., From molecular to modular cell biology, Nature, 402 (1999), c47-c52.

[3] Reed, R., Why is mathematical biology so hard?, Notices of the American Mathematical Society, 51 (2004), 338-342. | Zbl 1168.92303

[4] Vicsek, T., A question of scale, Nature, 418 (2004), 131.

[5] Gatenby, R.A., Vincent, T.L. e Gillies, R.J., Evolutionary dynamics in carcinogenesis, Mathematical Models and Methods in Applied Sciences, 15 (2005), 1619-1638. | Zbl 1077.92031

[6] Novak, M.A. e Sigmund, K., Evolutionary dynamics of biological games, Science, 303 (2004), 793-799.

[7] Bellomo, N. e Forni, G., Dynamics of tumor interaction with the host immune system, Mathematical Computer Modelling, 20 (1994), 107-122. | Zbl 0811.92014

[8] Greller, L., Tobin, F. e Poste, G., Tumor Heterogeneity and progression: conceptual foundation for modeling, Invasion and Metastasis, 16 (1996), 177-208.

[9] Adam J. e Bellomo N., Eds., A Survey of Models on Tumor Immune Systems Dynamics, Birkhäuser, Boston, (1997).

[10] Preziosi L., Ed., Modeling Cancer Growth, CRC-Press - Chapman Hall, Boca Raton, (2003). | Zbl 1039.92022

[11] Chaplain M.A.J., Ed., Special Issue on Mathematical Modelling and Simulation of Aspects of Cancer Growth, Journal of Theoretical Medicine, 1 (2002), 1-93.

[12] Bellomo, N. e Maini, P.K., Preface and Special issue on Multiscale Cancer Modelling - A New Frontier in Applied Mathematics, Mathematical Models and Methods in Applied Sciences, 15 (2005), iii-viii.

[13] Bellomo, N., De Angelis, E. e Preziosi, L., Multiscale modeling and mathematical problems related to tumor evolution and medical therapy, Journal of Theoretical Medicine, 5 (2003), 111-136. | Zbl 1107.92020

[14] Kirschner, D. e Panetta, J.C., Modeling immunotherapy of the tumor-immune interaction, J. Mathematical Biology, 37 (1998), 235-252. | Zbl 0902.92012

[15] Nani, F. e Freedman, H.I., A mathematical model of cancer treatment by immunotherapy, Mathematical Biosciences, 163 (2000), 159-199. | Zbl 0997.92024

[16] D'Onofrio, A., Tumor-immune system interaction and immunotherapy: Modelling the tumor-stimulated proliferation of effectors, Mathematical Models and Methods in Applied Sciences, 16 (2006).

[17] Gyllenberg, M. e Webb, G., A nonlinear structured population model of tumour growth with quiescence, J. Mathematical Biology, 28 (1990), 671-684. | Zbl 0744.92026

[18] Kheifetz, Y., Kogan, Y. e Agur, Z., Long-range predicability in midels of cell populations subjected to phase-specific drugs: Growth-rate approximation using properties of positive compact operators, Mathematical Models and Methods in Applied Sciences, 16 (2006). | Zbl 1094.92022

[19] Michel, P., Existence of solution of the cell division eigenproblem, Mathematical Models and Methods in Applied Sciences, 16 (2006). | Zbl 1094.92023

[20] Bellouquid, A. e Delitala, M., Kinetic (cellular) models of cell progression and competition with the immune system, Z. Agnewande Mathematical Physics, 55 (2004), 295-317. | Zbl 1047.92022

[21] Derbel, L., Analysis of a new model for tumor-immune system competition including long time scale effects, Mathematical Models and Methods in Applied Sciences, 14 (2004), 1657-1682. | Zbl 1057.92036

[22] Kolev, M., Kozlowska, E., e Lachowicz, M., Mathematical model of tumor invasion along linear or tubular structures, Mathematical Computer Modelling, 41 (2005), 1083-1096. | Zbl 1085.92019

[23] Bellomo, N., Bellouquid, A. e Delitala, M., Mathematical topics on the modelling of multicellular systems in the competition between tumor and immune cells, Mathematical Models and Methods in Applied Sciences, 14 (2004), 1683-1733. | Zbl 1060.92029

[24] Bellouquid, A. e Delitala, M., Mathematical methods and tools of kinetic theory towards modelling complex biological systems, Mathematical Models and Methods in Applied Sciences, 15 (2005), 1639-1666. | Zbl 1093.82016

[25] Bellomo, N. e Forni, G., Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems, Mathematical Models and Methods in Applied Sciences, 16 (2006). | Zbl 1093.92002

[26] Greenspan, H.P., Models for the growth of a solid tumour by diffusion, J. Theoretical Biology, 52 (1972), 317-340. | Zbl 0257.92001

[27] Adam, J. e Noren, R., Equilibrium model of a vascularized spherical carcinoma with central necrosis, J. Mathematical Biology, 31 (1993), 735-745. | Zbl 0777.92007

[28] Chaplain, M.A.J., From mutation to metastasis: The mathematical modelling of the stages of tumor development, in J. Adam and N. Bellomo, Eds., A Survey of Models on Tumor Immune Systems Dynamics (Birkhäuser, Boston, 1997), 187-236.

[29] Chaplain, M.A.J. e Lolas, G., Spatio-temporal heterogeneity arising in a mathematical model of cancer invasion of tissue, Mathematical Models and Methods in Applied Sciences, 15 (2005), 1735-1734.

[30] Byrne, H., A weakly nonlinear analysis of a model of avascular solid tumour growth, J. Mathematical Biology, 33 (1999), 59-89. | Zbl 0981.92011

[31] De Angelis, E. e Preziosi, L., Advection diffusion models for solid tumours in vivo and related free-boundary problems, Mathematical Models and Methods in Applied Sciences, 10 (2000), 379-408. | Zbl 1008.92017

[32] Folkman, J., Role of angiogenesis in tumor growth and methastasis, Seminars in Oncology, 29 (2002), 15-18.

[33] Bru, A., Pastor, J.M., Fernaud, I., Bru, I., Melle, S. e Berenguer, C., Super-rough dynamics on tumor growth, Physical Review Letters, 81 (1998), 4008-4011.

[34] Ambrosi, D. e Preziosi, L., On the closure of mass balance models for tumour growth, Mathematical Models and Methods in Applied Sciences, 12 (2002), 737-754. | Zbl 1016.92016

[35] Bertuzzi, A., Fasano, A. e Gandolfi, A., A mathematical model for tumor cords incorporating the flow of interstitial fluids, Mathematical Models and Methods in Applied Sciences, 15 (2005), 1735-1778. | Zbl 1094.92036

[36] Othmer, H.G. e Hillen, T., The diffusion limit of transport equations II: chemotaxis equations, SIAM J. Applied Mathematics, 62 (2002), 1222-1250. | Zbl 1103.35098

[37] Chalub, F., Dolak-Struss, Y., Markowich, P., Oeltz, D., Schmeiser, C. e Soref, A., Model hierarchies for cell aggregation by chemotaxis, Mathematical Models and Methods in Applied Sciences, 16 (2006). | Zbl 1094.92009

[38] Stevens, A., The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particles systems, SIAM J. Applied Mathematics, 61 (2002), 183-212. | Zbl 0963.60093

[39] Lachowicz, M., Micro and meso scales of description corresponding to a model of tissue invasion by solid tumors, Mathematical Models and Methods in Applied Sciences, 15 (2005), 1667-1684. | Zbl 1078.92036

[40] Bellomo, N. e Bellouquid, A., On the onset of nonlinearity for diffusion models of binary mixtures of biological materials by asymptotic analysis, International J. Nonlinear Mechanics, 41 (2006), 281-293. | Zbl 1160.76403

[41] Bertotti, M.L. e Delitala, M., From discrete kinetic and stochastic game theory to modeling complex systems in applied sciences, Mathematical Models and Methods in Applied Sciences, 14 (2004), 1061-1084. | Zbl 1083.92032

[42] Bellouquid, A. e Delitala, M., Modelling Complex Biological Systems - A Kinetic Theory Approach (Birkhäuser, Boston, 2006). | Zbl 1178.92002

[43] Mantzaris, N.V., Webb, S. e Othmer, H.G., Mathematical modeling of tumor-induced angiogenesis, J. Mathematical Biology, 47 (2004), 111-187. | Zbl 1109.92020

[44] Byrne, H., Alarcon, T.A., Murphy, J. e Maini, P.K., Modelling the response of vascular tumours to chemotherapy: a multiscale approach, Mathematical Models and Methods in Applied Sciences, 16 (2006). | Zbl 1094.92038

[45] Aderem, A. e Smith, K.D., A system approach to dissecting immunity and inflammation, Seminars in Immunology, 16 (2004), 55-67.

[46] Friedman, A. e Reitich, F., Analysis of a mathematical model of tumor growth, J. Mathematical Biology, 47 (1999), 391-423. | Zbl 0944.92018

[47] Friedman, A. e Lolas, G., Analysis of a mathematical model of tumor lymphangiogenesis, Mathematical Models and Methods in Applied Sciences, 15 (2005), 95-107. | Zbl 1060.92036

[48] Gillet, É.À chaque cancer son scénario aléatoire, La Récherche, 390 (2005), 73.

[49] Woese, C.R., A new biology for a new century, Microbiology and Molecular Biology Reviews, 68 (2004), 173-186.

[50] Gatenby, R.A. e Maini, P.K., Mathematical oncology: Cancer summed up, Nature, 421 (2003), 321-323.