Study of scaling behavior of tumor gro-wth by using of continues growth equations

Authors

Abstract

Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy (MBE). So using the same equations for tumor growth is sensible. However, tumor substrate unlike MBE is not planar that makes necessary a geometrical treatment of the growth equations. A variety of mathematical models have been proposed to describe tumor growth. The justification for these models mainly depends on how well they fit the clinical datas. We can then include the effects of different therapies as mathematical terms. The valid models are used to predict optimal sequencing of different therapies. Tumors diffuse as well as they proliferate. So considering spatial changes as well as temporal changes is necessary. These considerations are involved in reaction-diffusion equation. Here, we consider the growth equation analytically by using of small noise expansion to study the scaling behavior of tumor growth

Keywords


Barabasi, A.L. and Stanley, H.E.; Fractal Concepts in Surface Growth, Cambridge University Press (1995).
Escudero, C.; “Geometrical approach to tumor growth” Mathematical Institute: University of Oxford
(2006).
Esudero, C.; “Stochastic models for tumoral growth” Phys. Rev. E 73: (2006) 1-4.
Kapral, R., Livi R., Oppo G., and Politi A.; “Dynamics of complex interfaces” Phys. Rev. E 49: (1994)
2009-2022.
Bell D.R., Wein L.M; “Analysis and comparison of multimodal cancer treatments” IMA J. Math. Appl.
Med. Biol 18: (2001) 343-376.
Bell D.R., Wein L.M; “Sequencing surgery, radiotherapy and chemotherapy: insights from a mathematical
analysis” Breast Cancer Res. Treat 74: (2002) 279-286.
Powathil G., Kohandel M., Sivaloganathan S., Oza A., and Milosevic M.; “Mathematical modeling of
brain tumors: effects of radiotherapy and chemotherapy” Phys. Med. Biol. 52: (2007) 3291-3306.
Sachs, R.K., Hlathky, L.R., and Hahnfeldt, P.; “Simple ODE model of tumor growth and anti-angiogenic
or radiation treatment” Math. Comput. Model 33: (2001) 1297-305.
Laird, A.; “Dynamics of tumor growth” Brit. J. Cancer 18, (1964) 490-502.
Kohandel, M., Sivaloganathan, S., and Oza, A.; “Mathematical modeling of ovarian cancer treatments:
Sequencing of surgery and chemotherapy” J. Theor. Biol 242: (2006) 62-68.
Murray, J.D.; Mathematical Biology I and II Interdisciplinary Applied Mathematics, 3nd ed., Berlin:
Springer (2003).
Halphin-Healy, T. and Zhang Y.; ”Kinetic roughening phenomena. Stochastic growth” Directed polymers
and all that Phys. Rep 254: (1995) 215-414.
Kohandel, M., Kardar, M., Milosevic, M., and Sivaloganathan, S.; “Dynamics of tumor growth and
combination of anti-angiogenic and cytotoxic therapies” Phys. Med. Biol 52: (2007) 3665-3677.
Garcia-Ojalvo, J., and Sancho, J.M.; “Noise in spatially extended systems” Springer, New York (1999)