Resumen de Mathematical methods to predict the dynamic shape evolution of cancer growth based on spatio-temporal bayesian and geometrical models

Iulian Teodor Vlad

• The aim of this research is to observe the dynamics of cancer tumors and to develop and implement new methods and algorithms for prediction of tumor growth. I offer some tools to help physicians for a better understanding this disease and to check if the prescribed treatment have the desired results.

  The plan of the thesis is the following. In Chapter 1 I briefly recall some properties and classification of points processes with some examples of spatio-temporal point processes. Chapter 2 presents a short overview of the theory of Levy bases and integration with respect to such basis is given, I recall standard results about spatial Cox processes, and finally I propose different types of growth models and a new algorithm, the Cobweb, which is presented and developed based on the proposed methodology. Chapters 3, 4 and 5 are dedicated to present new prediction methods. The implementation in Matlab software comes in Chapter 6. The thesis ends with some conclusion and future research.