Development and evaluation of spatial point process models for epidermal nerve fibers.

We propose two spatial point process models for the spatial structure of epidermal nerve fibers (ENFs) across human skin. The models derive from two point processes, Φb and Φe, describing the locations of the base and end points of the fibers. Each point of Φe (the end point process) is connected to a unique point in Φb (the base point process). In the first model, both Φe and Φb are Poisson processes, yielding a null model of uniform coverage of the skin by end points and general baseline results and reference values for moments of key physiologic indicators. The second model provides a mechanistic model to generate end points for each base, and we model the branching structure more directly by defining Φe as a cluster process conditioned on the realization of Φb as its parent points. In both cases, we derive distributional properties for observable quantities of direct interest to neurologists such as the number of fibers per base, and the direction and range of fibers on the skin. We contrast both models by fitting them to data from skin blister biopsy images of ENFs and provide inference regarding physiological properties of ENFs.

Second-order spatial analysis of epidermal nerve fibers.

Breakthroughs in imaging of skin tissue reveal new details on the distribution of nerve fibers in the epidermis. Preliminary neurologic studies indicate qualitative differences in the spatial patterns of nerve fibers based on pathophysiologic conditions in the subjects. Of particular interest is the evolution of spatial patterns observed in the progression of diabetic neuropathy. It appears that the spatial distribution of nerve fibers becomes more 'clustered' as neuropathy advances, suggesting the possibility of diagnostic prediction based on patterns observed in skin biopsies. We consider two approaches to establish statistical inference relating to this observation. First, we view the set of locations where the nerves enter the epidermis from the dermis as a realization of a spatial point process. Secondly, we treat the set of fibers as a realization of a planar fiber process. In both cases, we use estimated second-order properties of the observed data patterns to describe the degree and scale of clustering observed in the microscope images of blister biopsies. We illustrate the methods using confocal microscopy blister images taken from the thigh of one normal (disease-free) individual and two images each taken from the thighs of subjects with mild, moderate, and severe diabetes and report measurable differences in the spatial patterns of nerve entry points/fibers associated with disease status.