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 behaviour as neuropathy advances.

翻译：糖尿病神经病变是一种以神经功能受损和表皮每单位面积神经纤维数量减少为特征的疾病。此外，随着神经病变相关的神经纤维丢失和再生随时间进展，神经的二维空间排列变得更加聚集。这些观察结果表明，随着神经病变的发展，皮肤神经支配减少的空间模式由一种尚未完全阐明的稀疏化过程所定义。我们将健康对照者和糖尿病神经病变患者的样本视为由神经入口点和神经末梢组成的平面点过程的实现，并提出基于空间稀疏化的点过程模型来描述神经病变进展中的变化。首先，通过健康模式的独立随机稀疏化测试了神经移除完全随机发生的假设。然后，提出了一种有利于移除孤立神经树的依赖参数稀疏化模型。采用近似贝叶斯计算来推断模型参数的分布，并使用非空间和空间汇总统计量评估模型的拟合优度。我们的研究结果表明，神经死亡过程的行为随着神经病变的进展而发生变化。