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On the Mathematical Model of Vascular Endothelial Growth Connected with a Tumor Proliferation

Authors: N. Khatiashvili, Ch. Pirumova, V. Akhobadze

Abstract:

In the paper the mathematical model of tumor growth is considered. New capillary network formation, which supply cancer cells with the nutrients, is taken into the account. A formula estimating a tumor growth in connection with the number of capillaries is obtained.

Keywords: Differential Equations, Mathematical Models, Vascular Endothelial, Tumor

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1061513

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References:


[1] R. K. Jain, Sci. Am., no. 271, pp.58-65, 1994.
[2] K. Groebe, P. Vanpel, "Evaluation of oxygen diffusion distances in human breast cancer". J.of Radiation Oncology, vol .15, Issue 3. pp.691-697, 1988.
[3] M.V. Denhirst , "Perivascular oxygen tensions in transplantable mammary tumor".J. Radiation Research, pp.17-182, 1992.
[4] D.Goldman, Theoretical Models of Microvascular Oxygen Transport to Tissue, J. Microvasculation, vol. 15, Issue 8, pp. 795-811, 2008.
[5] J. Clairambult, " A Step Toward Optimization of Cancer Therapeutics ". IEEE Jan./Feb., pp. 10-16 2008.
[6] M.B. Kaston, J. Bartek, "Cell-cycle check points and cancer". Nature, vol.432, no. 7015, pp.316-323, 2004.
[7] T. Inai, M. Mansuco, Hashizume . Am.J. Pathol. ,no. 165,pp. 35-52, 2004.
[8] A. Krogh, "The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue", J. Physiol.no.52,pp. 409-415.
[9] G. Mchedlishvili, M. Varazashvili, A. Mamaladze, N. Momtselidze, "Blood flow structuring and its alterations in capillaries of the cerebral cortex". Microvasc. Res.no. 53, pp.201-210,1997.
[10] M. Khizanishvili, M. Shakarashvili, "Correction of NO-inducible apoptosis with Plaferon LB in theJurcat cells culture", http://www.kheladze.ge/journal_3_folder/Correction%20of%20NOinducible% 20apoptosis%20with%20Plaferon%20LB%20in%20the.pdf
[11] Knut Smidt-Nielsen, Animal Philosiology. Cambrige University Press (5th ed), 607 p.,1997.
[12] J. T. Ottesen, M. S. Olufen, J.K. Larsen, Applied Mathematical Models in Human Physiology, SIAM, Philadelpia, 295 p. , 2004.