Finite element modeling of avascular tumor growth focusing on the constitutive model

Mathematical modeling of tumor growth as modeling of other biological tissues is important since these models enable us to predict and evaluate the parameters that could not be measured easily. The accuracy of a derived model depends upon considering more involved factors and mechanisms and will lead us toward a realistic modelling. In this study, a finite element model of avascular tumor growth is represented. This model concentrates on the constitutive behavior of tissues and the resulting stresses. The tumor and its host are assumed to behave as a hyperelastic material. The tumor model is supplied with a growth term which is a function of nutrient concentration, solid content of the tumor and rate of cell proliferation and death. The evolved stresses during growth and interactions between tumor and the surrounding host could be evaluated using the presented model. The results show that the exerted stresses on tumor increase as time passes which lead to reduction of tumor growth rate until it gradually reaches an asymptotic radius. The effects of variation of the bulk modulus which is a determinant of compressibility are investigated. Since biological tissues consist mainly of water so we should impose the condition of incompressibility. It is found that the increase of bulk modulus which leads to more incompressibility causes stress elevation.