New dimensions in Gompertzian growth.
Bajzer, Željko, Vuk-Pavlović, Stanimir (2000)
Journal of Theoretical Medicine
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Bajzer, Željko, Vuk-Pavlović, Stanimir (2000)
Journal of Theoretical Medicine
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Matveenko, V.D. (2004)
Journal of Mathematical Sciences (New York)
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A.V. Kolobov, V.V. Gubernov, A.A. Polezhaev (2011)
Mathematical Modelling of Natural Phenomena
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A mathematical model of infiltrative tumour growth is investigated taking into account transitions between two possible states of malignant cells: proliferation and migration. These transitions are considered to depend on oxygen level in a threshold manner where high oxygen concentration allows cell proliferation, while concentration below a certain critical value induces cell migration. The infiltrative tumour spreading rate dependence on model parameters is obtained. It is shown that...
S. Astanin, A. Tosin (2010)
Mathematical Modelling of Natural Phenomena
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A mathematical model of the tumour growth along a blood vessel is proposed. The model employs the mixture theory approach to describe a tissue which consists of cells, extracellular matrix and liquid. The growing tumour tissue is supposed to be surrounded by the host tissue. Tumours where complete oxydation of glucose prevails are considered. Special attention is paid to consistent description of oxygen consumption and growth processes based on the energy balance. A finite difference...
Lomond, Jonny (2012)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 05C30, 20E08, 20F65. In this paper we consider an open problem from [1], regarding the description of the growth functions of the free group acts. Using the language of graphs, we solve this problem by providing the necessary and sufficient conditions for a function to be a growth function for a free group act.
Polatoglu, Yasar, Aydogan, Melike, Yemisci, Arzu (2012)
Mathematica Balkanica New Series
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AMS Subj. Classification: 30C45
Nan Wu, Jian Hua Zheng (2015)
Annales Polonici Mathematici
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We investigate how the growth of an algebroid function could be affected by the distribution of the arguments of its a-points in the complex plane. We give estimates of the growth order of an algebroid function with radially distributed values, which are counterparts of results for meromorphic functions with radially distributed values.
Cameron, D.A. (1997)
Journal of Theoretical Medicine
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M. Pons-Salort, B. van der Sanden, A. Juhem, A. Popov, A. Stéphanou (2012)
Mathematical Modelling of Natural Phenomena
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A computational framework for testing the effects of cytotoxic molecules, specific to a given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The model is based on a cellular automaton to describe tumour cell states transitions from proliferation to death. It is coupled with a model describing the tumour vasculature and its adaptation to the blood rheological constraints when alterations are induced by VDAs ...