From tissue to particles: Few mathematical challenges toward molecular computational anatomy

A lot of unexpected mathematical developments around shape spaces and statistics of shapes has been fueled by the need to analyze biological shape variations in neuroimaging leading to the new field of computational anatomy. Nevertheless, current descriptions of brain diseases usually need to put together several orders of magnitude ranging from the millimeter scale for tissues in standard imaging devices to the micron or even nano scale for neural cells and molecules and to go across modalities. I will present some of the new challenges for mathematicians and our recent attempts to make a step in that direction.