Modeling of Tumor Occurrence and Growth – II

Abstract

This paper considers the mathematical model of tumor growth along a blood vessel. The model employs the mixture theory approach to describe a tissue that consists of cells, extracellular matrix, and liquid. The growing tumor tissue is supposed to be surrounded by the host tissue. Tumors, where complete oxidation of glucose prevails, are considered. Special attention is paid to consistent descriptions of oxygen consumption and growth processes based on the energy balance. The level set method is used to track an interface between the tissues. The simulations show localization of the tumor within a limited distance from the vessels and constant expansion speed along the vessels. Cancer disease manifests itself as abnormally excessive cell proliferation. This is the result of dysregulation of normal constraints on cellular proliferation. This fact has serious implications on the morphology of the growth. The intensive proliferation of tumor cells creates cell populations distant from blood vessels and deprived of nutrient and oxygen supply while most of the cells in the human body are within few cell diameters from a blood vessel. This leads to the formation of cylindrical structures around blood vessels.