No abstract

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.

In this paper, the spatial arrangement and possible interactions between epidermal nerve fibre endings are investigated and modelled by using confocal microscopy data. We are especially interested in possible differences between patterns from healthy volunteers and patients suffering from mild diabetic neuropathy. The locations of the points, where nerves enter the epidermis, the first branching points and the points where the nerve fibres terminate, are regarded as realizations of spatial point processes. We propose an anisotropic point process model for the locations of the nerve fibre endings in three dimensions, where the points interact in cylindrical regions. First, the locations of end points in ℝ 2 are modelled as clusters around the branching points and then, the model is extended to three dimensions using a pairwise interaction Markov field model with cylindrical neighbourhood for the 𝑧-coordinates conditioned on the planar locations of the points. We fit the model to samples taken from healthy subjects and subjects suffering from diabetic neuropathy. In both groups, after a hardcore radius, there is some attraction between the end points. However, the range and strength of attraction are not the same in the two groups. Performance of the model is evaluated by using a cylindrical version of Ripley's 𝐾 function due to the anisotropic nature of the data. Our findings suggest that the proposed model is able to capture the 3D spatial structure of the end points.

Diabetic neuropathy is a disorder characterized by impaired nerve function and reduction of the number of epidermal nerve fibers per epidermal surface. Additionally, as neuropathy related nerve fiber loss and regrowth progresses over time, the two‐dimensional spatial arrangement of the nerves becomes more clustered. These observations suggest that with development of neuropathy, the spatial pattern of diminished skin innervation is defined by a thinning process which remains incompletely characterized. We regard samples obtained from healthy controls and subjects suffering from diabetic neuropathy as realisations of planar point processes consisting of nerve entry points and nerve endings, and propose point process models based on spatial thinning to describe the change as neuropathy advances. Initially, the hypothesis that the nerve removal occurs completely at random is tested using independent random thinning of healthy patterns. Then, a dependent parametric thinning model that favors the removal of isolated nerve trees is proposed. Approximate Bayesian computation is used to infer the distribution of the model parameters, and the goodness‐of‐fit of the models is evaluated using both non‐spatial and spatial summary statistics. Our findings suggest that the nerve mortality process changes as neuropathy advances.