3D modelling of epidermal nerve fiber patterns

Sammanfattning: Neuropathical disorders, such as diabetic neuropathy, damage the nerve structure in the epidermis. This thesis presents statistical analyses and models for the epidermal nerve fibers (ENFs). The main objective is to improve our understanding regarding the three dimensional ENF structure and for this purpose, stochastic models are constructed. The ENF data are treated as point process configurations in three dimensional boxes, and samples from mild diabetic subjects and healthy volunteers are considered. In Paper I, the structure of the nerve trees is analyzed by comparing distributional properties of the first and later nerve tree segments. Using tools from spatial point process theory, second order properties of the underlying processes are examined and compared. We also defined a new measure, called epidermal active territory, to measure the volume of the epidermis covered by the nerves. Further, a three dimensional point process model for the nerve structure, is developed and evaluated using spatial summary statistics. The two dimensional version of the model captured the planar spatial structure, however, the complete model was unable to capture the attraction between the nerve fiber endings in the data. Therefore, a pairwise interaction Markov model allowing neighboring end points to interact was proposed in Paper II. Due to the anisotropic nature of the data, directional summary statistics were used to assess the goodness of fit of the models. The model was able to capture the attraction between the nerve fiber endings in the data.