Spatial modeling of epidermal nerve fiber patterns

• Published in: Statistics in medicine Vol. 40; no. 29; pp. 6479 - 6500
• Main Authors: Konstantinou, Konstantinos, Särkkä, Aila
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 20.12.2021
• Subjects: 2nd-order analysis; branching point; competition; Diabetic Neuropathies; Diabetic neuropathy; end point; Environmental; epidermal active territory; Epidermis - innervation; Humans; Matematik; Mathematical & Computational Biology; Mathematical sciences; Mathematics; Medical Informatics; Medicine; Nerve Fibers; Occupational Health; point patterns; point process; Public; Research & Experimental; two-step model; branching point; end point; competition; epidermal active territory; point process; two-step model
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.9194

Peripheral neuropathy is a condition associated with poor nerve functionality. Epidermal nerve fiber (ENF) counts per epidermal surface are dramatically reduced and the two‐dimensional (2D) spatial structure of ENFs tends to become more clustered as neuropathy progresses. Therefore, studying the spatial structure of ENFs is essential to fully understand the mechanisms that guide those morphological changes. In this article, we compare ENF patterns of healthy controls and subjects suffering from mild diabetic neuropathy by using suction skin blister specimens obtained from the right foot. Previous analysis of these data has focused on the analysis and modeling of the spatial ENF patterns consisting of the points where the nerves enter the epidermis, base points, and the points where the nerve fibers terminate, end points, projected on a 2D plane, regarding the patterns as realizations of spatial point processes. Here, we include the first branching points, the points where the nerve trees branch for the first time, and model the three‐dimensional (3D) patterns consisting of these three types of points. To analyze the patterns, spatial summary statistics are used and a new epidermal active territory that measures the volume in the epidermis that is covered by the individual nerve fibers is constructed. We developed a model for both the 2D and the 3D patterns including the branching points. Also, possible competitive behavior between individual nerves is examined. Our results indicate that changes in the ENFs spatial structure can more easily be detected in the later parts of the ENFs.