On the Mathematical Model of Vascular Endothelial Growth Connected with a Tumor Proliferation
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.
[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
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(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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54780", author = "N. Khatiashvili and Ch. Pirumova and V. Akhobadze", title = "On the Mathematical Model of Vascular Endothelial Growth Connected with a Tumor Proliferation", 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", volume = "5", number = "7", pages = "967-3", }
