UC Santa Barbara

Studying spatial arrangement and relationships in full tissue samples can improve our understanding of the various developmental/pathological processes that underlie proper organ or organism function. In particular, it has been found that neuronal or vascular structures are pervasive in many tissues, and oftentimes are spatially correlated with other cells. This work aims to discover those relationships, by extracting biological knowledge from cellular and sub-

cellular imaging using spatial point process methods.

In this dissertation, we present discoveries on spatial distributions and attributes of dendritic spines and retinal astrocytes, two crucial elements in the mammalian nervous system. Although little is known about the spatial distributions of either respective to their surroundings and attributes, this thesis attempts to pose some possible biological hypotheses based on strong statistical evidence, as well as further extend the tools used for spatial analysis. In particular, we develop a multitype version of the linear network K-function, a summary function used for measuring clustering or repulsion of point features existing on a linear network.