Spatial analysis and modeling of nerve fiber patterns

Sammanfattning: Diabetic neuropathy is a condition associated with diabetes affecting the epidermal nerve fibers (ENFs). This thesis presents analysis methods and models for ENF data, with two main puroposes: to find early signs of diabetic neuropathy and to characterize how this condition changes the nerve fiber structure. Early detection is of interest to be able to take measures to slow down the progression of the condition, and a more detailed description of the changes in the nerve fiber structure could improve the understanding of its underlying mechanisms. The ENF samples are mainly analyzed as point patterns, where the points are the locations where nerve fibers enter the epidermis or terminate. The analysis is partly based on existing summary statistics for point patterns, but we also propose a new summary statistic to quantify the proportion of the skin covered by the nerve fibers. Two cluster processes are introduced as models for the patterns consisting only of the locations where the nerve fibers enter the epidermis. For one of the models, a Bayesian hierarchical method for parameter estimation is proposed. A model for the end points is also presented, and non-spatial models for individual nerve fibers, which are used to perform unsupervised classification of the subjects. From the results we find that while all patterns are aggregated, the level of aggregation tends to increase with increased severity of the neuropathy. The results from the modeling indicate that the increased aggregation is caused by a decrease in the number of clusters, while the structure within clusters appears to be similar in all disease groups. The results from the non-spatial analysis indicate that the nerve fibers from healthy subjects tend to extend further than those from subjects with diabetic neuropathy. The use of methods and models developed in this thesis is not limited to ENF data, but can be applied to point pattern data in general. In particular, the models for the base point patterns and the methods for estimating the parameters of these models are contributions to the point process literature.