Mathematical modeling of the growth of malignant neoplasms under a synergistic effect spatially inhomogeneous external physical factor and chemotherapy drug
Main Article Content
Abstract
This article presents mathematic model for kinetic of tumor grows under the synergetic treatment of cytotoxic drug and under the influence of a spatial nonuniform electromagnetic field. It is demonstrated that a spatial nonuniform electromagnetic field is capable to essentially improve the therapy tumors effectiveness.
Article Details

This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
References
D. L. Dexter and J. T. Leith, “Tumor heterogeneity and drug resistance”., Journal of Clinical Oncology, vol. 4, no. 2, pp. 244–257, Feb. 1986. DOI:10.1200/JCO.1986.4.2.244
J. L. Yu, J. W. Rak, P. Carmeliet, A. Nagy, R. S. Kerbel, and B. L. Coomber, “Heterogeneous Vascular Dependence of Tumor Cell Populations”, The American Journal of Pathology, vol. 158, no. 4, pp. 1325–1334, Apr. 2001. DOI:10.1016/S0002-9440(10)64083-7
G. Haken, Synergetics, Moscow: Mir, 1980, p. 406.
J. Marie, Nonlinear differential equations in biology. Lectures on models, Moscow: Mir, 1983, p. 398.
L. V. Beloussov and V. I. Grabovsky, “Information about a form (on the dynamic laws of morphogenesis)”, Biosystems, vol. 87, no. 2-3, pp. 204–214, Feb. 2007. DOI:10.1016/j.biosystems.2006.09.015
A.V. Makrushin, “Evolutionary precursors of oncogenesis and senile involution”, Uspekhi gerontol, no. 13, pp. 32–43, 2004.
V. I. Karpenko, O. S. Korostinska, P. Loshitsky, and M. Nikolov, “Inflow of electromagneticfields of non-thermal intensity on activitybiological objects”, Scientific notes. Biology and ecology, vol. 18, pp. 51–55, 2000.
V.E. Orel, N.A. Nikolov, and A.V. Romanov, “The influence of electromagnetic field heterogeneity on the enhancement of doxorubicin antitumor activity”, Electronics and Communications, no. 3-4, pp. 173–177, 2008.
V.E. Orel, M.O. Nikolov, and N.M. Dzyatkovska, “The influence of changes in the spatial heterogeneity of the electromagnetic field on the transformation of radio waves and thermal characteristics of Lewis phantoms and lung carcinomas”, Physics of the living, vol. 16, no. 2, pp. 92–98, 2008.
V. E. Orel, I. I. Dzyatkovska, and M. O. Nikolov, “The influence of spatially inhomogeneous electromagnetic field on the antitumor activity of cisplatin when acting on the resistant to it strain of lung carcinoma ‘Lewis’”, URZh, vol. 17, pp. 72–77, 2009.
A.D. Bazykin, Mathematical biophysics of interacting populations, Moscow: Nauka, 1985, p. 182.
S. Linn, “Prognostic relevance of P-glycoprotein expression in breast cancer”, Annals of Oncology, vol. 6, no. 7, pp. 679–685, Sep. 1995. DOI:10.1093/oxfordjournals.annonc.a059284



