Mathematical modeling of the tumor growth
Keywords:
mathematical growth, malignant tumor growth, oxygenation, proliferation rate, normoxia and hypoxiaAbstract
Hypothesis, allowing quantitatively to describe connection between tumor cells fission rate and degree of
their oxygenation, has been formulated. Mathematical model of the tumors growth has been made on the
basis of this hypothesis and well-known methods of oxygen distribution in malignant simple shape
tumors (spherical and plane). Analitical expressions, describing dependence on time of such parameters
as tumor size, coordinates of surfaces, being boundary between normoxic and hypoxic areas, between
proliferating and non-proliferating areas, between hypoxic and necrosis zone, have been received.
Calculation results of indicated dependences in case of normoxic and hypoxic environment have been
produced.
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