A Spatial Cluster Process Model for the Regeneration of Epidermal Nerve Fiber Patterns

Abstract

Epidermal nerve fibers (ENFs) play a key role in sensory function and are valuable indicators to detect different stages of diabetic neuropathy. Previous studies developed spatial point process models to describe the spatial structure of ENFs and the distribution of their end points. However, modeling how ENFs regrow after damage is still an open problem. In this thesis, we develop a branching cluster (BC) model to describe ENF regeneration by modeling multi-level branching points and end points based on entry points. The model aims to reconstruct nerve patterns in damaged areas, following hypotheses proposed by neurologists. According to these hypotheses, ENF regrowth involves two steps: existing nerve fibers grow into the damaged region, and new ENFs emerge within it. To evaluate the model, we apply a global envelope test using Ripley’s K-function to examine the spatial pattern of end points in the damaged region. The results suggest that the BC model captures the observed structure well within small distances. Coverage analysis also shows that the model can regenerate ENF patterns that reflect the healing process. Overall, the BC model offers a statistical framework that incorporates full branching structures to describe and simulate ENF regrowth in damaged skin areas.