Modelli matematici a sostegno della ricerca contro il cancro
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 1, pp. 55-76.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
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Preziosi, L. Modelli matematici a sostegno della ricerca contro il cancro. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 1, pp. 55-76. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_1_a2/

[1] J.ADAM - N.BELLOMO EDS., Survey of Models on Tumor Immune Systems Dynamics, Birkhäuser, Boston, 1996. | Zbl

[2] D. Ambrosi - N. Bellomo - L. Preziosi, Modelling the immune response to tumor heterogeneity and progression, J. Theor. Medicine, 4, (2002), 51-66. | Zbl

[3] D. Ambrosi - F. Mollica, On the mechanics of a growing tumor, Int. J. Engng. Sci., 40 (2002), 1297-1316. | MR | Zbl

[4] D. Ambrosi - F. Mollica, Mechanical models in tumour growth, in Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, Boca Raton, 2003. | MR

[5] D. Ambrosi - F. Mollica, The role of stress in the grouth of a multicell spherad, J. Math. Biol., in press. | Zbl

[6] D. Ambrosi - L. Preziosi, On the closure of mass balance models for tumour growth, Math. Models Methods Appl. Sci., 12 (2002), 737-754. | MR | Zbl

[7] A. R. A. Anderson - M. A. J. Chaplain, Continuous and discrete mathematical models of tumour-induced angiogenesis, Bull. Math. Biol., 60 (1998), 857-899. | Zbl

[8] L. Arlotti - N. Bellomo - E. De Angelis, Generalized kinetic (Boltzmann) models: mathematical structures and applications, Math. Models Meth. Appl. Sci., 12 (2002), 567-591. | MR | Zbl

[9] N.BELLOMO Ed., Math. Comp. Modell., 23 (1996).

[10] N.BELLOMO - E.DE ANGELIS Eds., Math. Comp. Model. (2003).

[11] N. Bellomo - G. Forni, Dynamics of tumor interaction with the host immune system, Math. Comp. Modell., 20 (1994), 107-122. | Zbl

[12] N. Bellomo - M. Lo Schiavo, Lecture Notes on the Generalized Boltzmann Equation, World Scientific (2000). | MR

[13] A. Bertuzzi - A. Fasano - A. Gandolfi - D. Marangi, Cell kinetics in tumour cords studied by a model with variable cell cycle length, Math. Biosci., 177 \& 178 (2002), 103-125. | MR | Zbl

[14] A. Bertuzzi - A. D’Onofrio - A. Fasano - A. Gandolfi, Regression and regrowth of tumour cords following single-dose anticancer treatment, Bull. Math. Biol., 65 (2003), 903-931.

[15] C. J. W. Breward - H. M. Byrne - C. E. Lewis, 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 | Zbl

[16] H. M. Byrne, Modelling avascular tumor growth, in Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, Boca Raton, 2003. | MR

[17] H. M. Byrne - L. Preziosi, IMA J. Math. Appl. Med. Biol., in press.

[18] M. A. J.CHAPLAIN Ed., Special Issue, Math. Models Methods Appl. Sci., 9 (1999).

[19] M. A. J.CHAPLAIN Ed., Special Issue on Mathematical Modelling and Simulations of Aspects of Cancer Growth, J. Theor. Medicine, 4 (2002). | Zbl

[20] M. A. J. Chaplain - A. R. A. Anderson, Mathematical modelling of tissue invasion in Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, Boca Raton, 2003. | MR

[21] M. A. J. Chaplain - L. Graziano - L. Preziosi, Misperception of stress as a cause of hyperplasia and dysplasia (2004).

[22] E. De Angelis - P. E. Jabin, Qualitative analysis of a mean field model of tumorimmune system competition, Math. Models Meth. Appl. Sci., 13 (2003), 197-220. | Zbl

[23] E. De Angelis - L. Mesin, Mathematical frameworks and applications on tumors and immune system interactions, Math. Models Methods Appl. Sci., 11 (2001), 1609-1630. | MR | Zbl

[24] E. De Angelis - L. Preziosi, Advection-diffusion models for solid tumour evolution in vivo and related free boundary problem, Math. Models Methods Appl. Sci., 10 (2000), 379-407. | MR | Zbl

[25] A. Deutsch, Cellular Automata and Biological Pattern Formation, Birkhäuser, Boston, 2003.

[26] A. Deutsch, A new mechanism of aggregation in a lattice-gas cellular automaton model, Math. Comp. Model., 31 (2002), 35-40. | MR | Zbl

[27] A. Farina - L. Preziosi, On Darcy’s law for growing porous media, Int. J. Nonlinear Mech., 37 (2001), 485-491. | Zbl

[28] A. Friedman - F. Reitich, 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 | Zbl

[29] A. Gamba - D. Ambrosi - F. Bussolino - A. Coniglio - A. De Candia - S. Di Talia - E. Giraudo - G. Serini - L. Preziosi, Percolation, self-organization and Burgers dynamics in blood vessel formation, Phys. Rev. Lett., 90 (2003), 118101.

[30] L. Graziano - L. Preziosi, Multiphase models of tumour growth: General framework and particular cases, in Mathematical Modelling and Computing in Biology and Medicine, V.Capasso Ed., Esculapio, Milano, 518-525 (2003). | MR

[31] L. Greller - F. Tobin - G. Poste, Tumor heterogeneity and progression: Conceptual foundation for modeling, Invasion and Metastasis, 16 (1006), 177-208.

[32] J. D. Humphrey - K. R. Rajagopal, A constrained mixture model and remodeling of soft tissues, Math. Models Meth. Appl. Sci., 12 (2002), 407-430. | MR | Zbl

[33] R. Kowalczyk - A. Gamba - L. Preziosi, On the stability of homogeneous solutions to some aggregation models, Discrete and Continuous Dynamical Systems B, 4 (2004), 203-220. | MR | Zbl

[34] M. Lachowicz, From microscopic to macroscopic description for general kinetic models, Math. Models Meth. Appl. Sci., 12 (2002), 993-1011. | MR | Zbl

[35] H. Levine - S. Pamuk - B. Sleeman - M. Nilsen-Hamilton, Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma, Bull. Math. Biol., 63 (2001), 801-863. | Zbl

[36] H. A. Levine - B. D. Sleeman, Modelling tumour induced angiogenesis, in Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, Boca Raton, 2003. | MR

[37] S. R. Lubkin - T. Jackson, Multiphase mechanics of capsule formation in tumours, J. Biomech. Engng., 124 (2002), 237-243.

[38] A. Stefanon - S. R. Mcdougall - A. R. A. Anderson - M. A. J. Chaplain - J. A. Sherratt, Mathematical modelling of flow in 2D and 3D vascular networks application, Math. Comp. Model. (2004). | Zbl

[39] S. Pamuk, Qualitative analysis of a mathematical model for capillary formation in tumor angiogenesis, Math. Models Meth. Appl. Sci., 13 (2003), 19-34. | MR | Zbl

[40] L.PREZIOSI, Ed., Cancer Modelling and Simulation, Chapman \& Hall/CRC Press, (2003). | MR | Zbl

[41] G. Serini - D. Ambrosi - A. Gamba - E. Giraudo - L. Preziosi - F. Bussolino, Modelling the early stages of vascular network assembly, EMBO J. Biol., 22 (2003), 1771-1779.

[42] J. J. L. Velázquez, Stability of some mechanisms of chemotactic aggregation, SIAM J. Appl. Math., 62 (2002), 1581-1633. | MR | Zbl

[43] J. Ward - J. King, Mathematical modelling of the effects of mitotic inhibitors on avascular tumour growth, J. Theor. Med., 1 (1999), 171-211. | Zbl