ii Spatial Analysis and Modelling Motivated by Epidermal Nerve Fiber Patterns

Recent breakthroughs in imaging of skin tissue reveal new details on the distribution of nerve fibers in the epidermis. This thesis deals with analysis and modelling of such patterns. Our par-ticular interest lies in comparing between epidermal nerve fiber patterns coming from healthy subjects and patterns coming from subject suffering from diabetes. Development of diagnostic statistical tools for determining early stages of diabetic neuropathy may allow diagnosis early in the progress of the disease when neuropathy is most likely to respond to treatment. In this thesis we suggest some spatial analysis techniques to detect differences in ENF patterns coming from subjects in different states of neuropathy. Furthermore, we introduce a set of models based on bivariate point processes serving as a starting point in modelling nerve fiber patterns. Fiber-like patterns are constructed by connecting the points of the processes, according to predetermined rules, via a line segment. We also derive integral formulas for the correlation between the vol-umes of the typical Poisson-Voronoi cell and the typical Stienen sphere in arbitrary dimensions