Mathematical models of tumor growth

Abstract

Cancer is one of the deadliest diseases, therefore it is necessary to develop tools that will be useful in the decision-making process. One of those are mathematical models that are used to predict the growth of tumors and the changes that occur as a result of radiation. The determination of the most suitable model is based on the type of tumor. The models presented in this paper are based on ordinary differential equations. Gompertz model is presented as a model that originated from the generalized two-parameter model. Although the Gompertz model is used for determining tumor volume, in this paper it is shown how it can be used to determine the maximum volume of a tumor. The second model presented in this paper is the kinetic model. Kinetic model is used for showing changes in cancer volume before, during and after the active radiation effect. In addition, it can be used for comparing the affect of different radiation doses. The Gompertz model is applied to a benign tumor (meningioma), while the kinetic model is applied to a malignant tumor (hepatocellular carcinoma). As observing the volume at a certain time span implies solving a system of ordinary differential equations, proposed models are written in the form of codes in MATLAB.