Abstract.
Macroscopic modeling is used to describe various aspects of cancer growth. A recently proposed “dysnamical exponent” hypothesis is critically examined in the context of the angiogenic development. It is also shown that the emergence of necroses facilitates the growth of avascular tumors; the model yields an excellent fit to available experimental data, allowing for the determination of growth parameters. Finally, the global effects of an applied antitumoral immunotherapy are investigated. It is shown that, in the long run, the application of a therapeutical course leads to bigger tumors by weakening the intraspecific competition between surviving viable cancer cells. The strength of this model lies in its simplicity and in the amount of information that can be gleaned using only very general ideas.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
For a lucid introduction see N.F. Britton, Essential Mathematical Biology (Springer, London, 2003)
M. Scalerandi, A. Romano, G.P. Pescarmona, P.P. Delsanto, C.A. Condat, Phys. Rev. E 59, 2206 (1999)
M. Scalerandi, B. Capogrosso Sansone, C. Benati, C.A. Condat, Phys. Rev. E 65, 051908 (2002)
S.C. Ferreira Jr., M.L. Martins, M.J. Vilela, Phys. Rev. E 67, 051914 (2003)
Yi Jiang, J. Pjesivac-Grbovic, Ch. Cantrell, J.P. Freyer, Biophs. J. 89, 3884 (2005)
C. Guiot, P.G. Degiorgis, P.P. Delsanto, P. Gabriele, T.S. Deisboeck, J. Theor. Biol. 225, 147 (2003)
G.B. West, J.H. Brown, B.J. Enquist, Nature 413, 628 (2001)
P.P. Delsanto, C. Guiot, P.G. Degiorgis, C.A. Condat, Y. Mansury, T.S. Deisboeck, Appl. Phys. Lett. 85, 4225 (2004)
C.A. Condat, S.A. Menchón, Physica A 371, 76 (2006)
C. Guiot et al., J. Theor. Biol. 240, 459 (2006)
M.J. Holmes, B.D. Sleeman, J. Theor. Biol. 202, 95 (2000)
B. Capogrosso Sansone, M. Scalerandi, C.A. Condat, Phys. Rev. Lett. 87, 128102 (2001)
R.S. Kerbel, Science 312, 1171 (2006)
W. Mueller-Klieser, Crit. Rev. Oncol./Hematol. 36, 123 (2000)
A.C. Burton, Growth 30, 159 (1966)
G.G. Steel, Growth Kinetics of Tumours (Oxford, Clarendon Press, Oxford, 1977)
R. Ramos, C.A. Condat, unpublished; G. Rivera, M.S. thesis. Univ. of Puerto Rico, Mayagüez, PR (2005)
D. Kirschner, J.C. Panetta, J. Math. Biol. 37, 235 (1998)
O. Sotolongo-Costa, L. Morales Molina, D. Rodríguez Pérez, J.C. Antoranz, M. Chacón Reyes, Physica D 178, 242 (2003)
See, for example, A.M. Hicks et al., Proc. Nat. Acad. Sci. (USA) 103, 7753 (2006)
P.P. Delsanto, M. Griffa, C.A. Condat, S. Delsanto, L. Morra, Phys. Rev. Lett. 94, 148105 (2005)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Menchón, S., Condat, C. Macroscopic dynamics of cancer growth. Eur. Phys. J. Spec. Top. 143, 89–94 (2007). https://doi.org/10.1140/epjst/e2007-00075-1
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2007-00075-1