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

• We define two spatial point process models for epidermal nerve fibers (ENFs).
• The two stage Poisson model provides baseline results and reference values.
• The non-orphan cluster model better mimics the generation of end points of fibers.
• We provide inference regarding physiological properties of epidermal nerve fibers.
• Our hierarchical models offer a rich framework for study of spatial ENF structure.

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, ΦbΦb and ΦeΦe, describing the locations of the base and end   points of the fibers. Each point of ΦeΦe (the end point process) is connected to a unique point in ΦbΦb (the base point process). In the first model, both ΦeΦe and ΦbΦb 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 ΦeΦe as a cluster process conditioned on the realization of ΦbΦb 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.