Marked point process analysis of epidermal nerve fibres

Epidermal nerve fibre (ENF) density and summed length of ENFs per epidermal surface area are reduced, and ENFs may appear more clustered within the epidermis in subjects suffering from diabetic neuropathy compared to healthy subjects. Therefore, it is important to understand the spatial behaviour of ENFs in healthy and neuropathy subjects. By using confocal microscopy data , we study the spatial structure of epidermal nerves by regarding the nerve tree locations as realizations of marked point processes . The termination points of the fibres of a nerve tree are used to define a reactive territory which is taken as a mark for the nerve tree location. We study the differences in the spatial pattern of ENFs between healthy subjects and subjects suffering from mild diabetic neuropathy by using Ripley's $$ function and the mark correlation function. In addition, we propose a marked sequential point process model for the nerve tree locations. Data are replicated point patterns, where we have several patterns from each subject and from each group.