Measuring contour functions deformation by Principal Differential Analysis:a distance based approach for the analysis of Gioblastoma Multiform

This paper introduces an explorative functional data analysis approach for the analysis of brain tumor contour functions deformation. A dataset of 15 patients affected by Gioblastoma multiform related to two different stages is analyzed. The purpose is to study the dynamic of a sequence of two sets of tumor contour functions related to the two stages, thus Principal Differential Analysis has been performed into the two steps. The estimated proposed operator approximates efficiently the observed functions not only taking into account the observed functions, but also their derivatives. A distance among the coefficients of the differential equation is proposed to define the degree of the contour functions changes.