Observer-based techniques for the identification and analysis of avascular tumor growth

Cancer represents one of the most challenging issues for the biomedical research, due its large impact on the public health state. For this reason, many mathematical methods have been proposed to forecast the time evolution of cancer size and invasion. In this paper, we study how to apply the Gompertz's model to describe the growth of an avascular tumor in a realistic setting. To this aim, we introduce mathematical techniques to discretize the model, an important requirement when discrete-time measurements are available. Additionally, we describe observed-based techniques, borrowed from the field of automation theory, as a tool to estimate the model unknown parameters. This identification approach is a promising alternative to traditional statistical methods, and it can be easily extended to other models of cancer growth as well as to the evaluation of not measurable variables, on the basis of the available measurements. We show an application of this method to the analysis of solid tumor growth and parameters estimation in presence of a chemotherapy agent.