Using Topological Data Analysis to Understand Microglia Shape Variability in Space and Time

The aim of the project is to advance the state of the art in the morphological analysis of microglia, and we propose three different ways in which this can be achieved. The understanding of microglia behaviour is of pivotal importance to unveil the systems that regulate the evolution and adaptation mechanisms of the brain. This, in turn, has deep consequences for the diagnosis and treatment of neurodegenerative diseases like Alzheimer's and Parkinson's and age-related cognitive decline. To this end, we wish to improve the state of the art in the analysis of microglia 1) obtaining improved shapedescriptors of microglia morphology, containing more information about the spatial structure of microglia cells 2) improving the exploration of the shape-space of microglia cells by employing advanced tools taken from non-Euclidean statistics and topological machine learning 3) analysing the dynamics of microglia adaptations on short time-scales, using Optimal Transport to describe the adaptations of the cells.