Questo articolo, a prevalente carattere di rassegna, ha lo scopo di presentare gli ambiti matematici e gli approcci metodologici utilizzati nello sviluppo di modelli matematici a sostegno della ricerca contro il cancro. La necessità di un approccio interdisciplinare e multiscala è messo in evidenza. Infine, alcuni modelli operanti alla scala macroscopica e mesoscopica sono presentati a titolo di esempio.
The aim of this review paper is to discuss the mathematical frameworks and the methodological approaches used in developing mathematical models in the field of cancer research. The need for an interdisciplinary and multiscale approach is put in evidence. Some examples of models operating at the macroscopic and the mesoscopic scale are presented.
@article{BUMI_2005_8_8B_1_55_0,
author = {L. Preziosi},
title = {Modelli matematici a sostegno della ricerca contro il cancro},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {8-A},
year = {2005},
pages = {55-76},
zbl = {1182.92041},
mrnumber = {2122975},
language = {it},
url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_1_55_0}
}
Preziosi, L. Modelli matematici a sostegno della ricerca contro il cancro. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 55-76. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_1_55_0/
[1] - EDS., Survey of Models on Tumor Immune Systems Dynamics, Birkhäuser, Boston, 1996. | Zbl 0874.92020
[2] - - , Modelling the immune response to tumor heterogeneity and progression, J. Theor. Medicine, 4, (2002), 51-66. | Zbl 1050.92026
[3] - , On the mechanics of a growing tumor, Int. J. Engng. Sci., 40 (2002), 1297-1316. | MR 1914120 | Zbl 1211.74161
[4] - , Mechanical models in tumour growth, in Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, Boca Raton, 2003. | MR 2005056
[5] - , The role of stress in the grouth of a multicell spherad, J. Math. Biol., in press. | Zbl 1058.92005
[6] - , On the closure of mass balance models for tumour growth, Math. Models Methods Appl. Sci., 12 (2002), 737-754. | MR 1909425 | Zbl 1016.92016
[7] - , Continuous and discrete mathematical models of tumour-induced angiogenesis, Bull. Math. Biol., 60 (1998), 857-899. | Zbl 0923.92011
[8] - - , Generalized kinetic (Boltzmann) models: mathematical structures and applications, Math. Models Meth. Appl. Sci., 12 (2002), 567-591. | MR 1899842 | Zbl 1174.82325
[9] Ed., Math. Comp. Modell., 23 (1996).
[10] - Eds., Math. Comp. Model. (2003).
[11] - , Dynamics of tumor interaction with the host immune system, Math. Comp. Modell., 20 (1994), 107-122. | Zbl 0811.92014
[12] - , Lecture Notes on the Generalized Boltzmann Equation, World Scientific (2000). | MR 1823800
[13] - - - , Cell kinetics in tumour cords studied by a model with variable cell cycle length, Math. Biosci., 177 \& 178 (2002), 103-125. | MR 1923805 | Zbl 0999.92021
[14] - - - , Regression and regrowth of tumour cords following single-dose anticancer treatment, Bull. Math. Biol., 65 (2003), 903-931.
[15] - - , Modeling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour, Eur. J. Appl. Math., 12 (2001), 529-556. | MR 1870857 | Zbl 0987.92019
[16] , Modelling avascular tumor growth, in Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, Boca Raton, 2003. | MR 2005055
[17] - , IMA J. Math. Appl. Med. Biol., in press.
[18] Ed., Special Issue, Math. Models Methods Appl. Sci., 9 (1999).
[19] Ed., Special Issue on Mathematical Modelling and Simulations of Aspects of Cancer Growth, J. Theor. Medicine, 4 (2002). | Zbl 1111.65300
[20] - , Mathematical modelling of tissue invasion in Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, Boca Raton, 2003. | MR 2005061
[21] - - , Misperception of stress as a cause of hyperplasia and dysplasia (2004).
[22] - , Qualitative analysis of a mean field model of tumorimmune system competition, Math. Models Meth. Appl. Sci., 13 (2003), 197-220. | Zbl 1043.92012
[23] - , Mathematical frameworks and applications on tumors and immune system interactions, Math. Models Methods Appl. Sci., 11 (2001), 1609-1630. | MR 1872685 | Zbl 1013.92016
[24] - , Advection-diffusion models for solid tumour evolution in vivo and related free boundary problem, Math. Models Methods Appl. Sci., 10 (2000), 379-407. | MR 1753118 | Zbl 1008.92017
[25] , Cellular Automata and Biological Pattern Formation, Birkhäuser, Boston, 2003.
[26] , A new mechanism of aggregation in a lattice-gas cellular automaton model, Math. Comp. Model., 31 (2002), 35-40. | MR 1756745 | Zbl 1042.82583
[27] - , On Darcys law for growing porous media, Int. J. Nonlinear Mech., 37 (2001), 485-491. | Zbl pre05138050
[28] - , On the existence of spatially patterned dormant malignancies in a model for the growth of non-necrotic vascular tumours, Math. Models Methods Appl. Sci., 11 (2001), 601-625. | MR 1832995 | Zbl 1013.92024
[29] - - - - - - - - , Percolation, self-organization and Burgers dynamics in blood vessel formation, Phys. Rev. Lett., 90 (2003), 118101.
[30] - , Multiphase models of tumour growth: General framework and particular cases, in Mathematical Modelling and Computing in Biology and Medicine, Ed., Esculapio, Milano, 518-525 (2003). | MR 2093306
[31] - - , Tumor heterogeneity and progression: Conceptual foundation for modeling, Invasion and Metastasis, 16 (1006), 177-208.
[32] - , A constrained mixture model and remodeling of soft tissues, Math. Models Meth. Appl. Sci., 12 (2002), 407-430. | MR 1894260 | Zbl 1021.74026
[33] - - , On the stability of homogeneous solutions to some aggregation models, Discrete and Continuous Dynamical Systems B, 4 (2004), 203-220. | MR 2028822 | Zbl 1040.92006
[34] , From microscopic to macroscopic description for general kinetic models, Math. Models Meth. Appl. Sci., 12 (2002), 993-1011. | MR 1918170 | Zbl 1174.82328
[35] - - - -, Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma, Bull. Math. Biol., 63 (2001), 801-863. | Zbl 0977.92013
[36] - , Modelling tumour induced angiogenesis, in Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, Boca Raton, 2003. | MR 2005057
[37] - , Multiphase mechanics of capsule formation in tumours, J. Biomech. Engng., 124 (2002), 237-243.
[38] - - - - , Mathematical modelling of flow in 2D and 3D vascular networks application, Math. Comp. Model. (2004). | Zbl 1080.92050
[39] , Qualitative analysis of a mathematical model for capillary formation in tumor angiogenesis, Math. Models Meth. Appl. Sci., 13 (2003), 19-34. | MR 1956956 | Zbl 1043.92014
[40] , Ed., Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, (2003). | MR 2005054 | Zbl 1039.92022
[41] - - - - - , Modelling the early stages of vascular network assembly, EMBO J. Biol., 22 (2003), 1771-1779.
[42] , Stability of some mechanisms of chemotactic aggregation, SIAM J. Appl. Math., 62 (2002), 1581-1633. | MR 1918569 | Zbl 1013.35004
[43] - , Mathematical modelling of the effects of mitotic inhibitors on avascular tumour growth, J. Theor. Med., 1 (1999), 171-211. | Zbl 0981.92012