On some descriptive and predictive methods for the dynamics of cancer growth

Abstract

Cancer is a widely spread disease that affects a large proportion of the human population, and many research teams are developing algorithms to help medics to understand this disease. In particular, tumor growth has been studied from different viewpoints and several mathematical models have been proposed. In this paper, we review a set of comprehensive and modern tools that are useful for prediction of cancer growth in space and time. We comment on three alternative approaches. We first consider spatio-temporal stochastic processes within a Bayesian framework to model spatial heterogeneity, temporal dependence and spatio-temporal interactions amongst the pixels, providing a general modeling framework for such dynamics. We then consider predictions based on geometric properties of plane curves and vectors, and propose two methods of geometric prediction. Finally we focus on functional data analysis to statistically compare tumor contour evolutions. We also analyze real data on brain tumor.