在本文中,使用共聚焦显微镜数据研究和模拟了表皮神经纤维末端之间的空间排列和可能的相互作用。我们对健康志愿者和患有轻度糖尿病神经病变的患者的模式之间的可能差异特别感兴趣。点的位置,神经进入表皮,第一个分支点和神经纤维终止的点,被视为空间点过程的实现。我们提出了一个各向异性点过程模型,用于三维神经纤维末端的位置,点在圆柱形区域中相互作用。首先,R2$\\mathbb{R}^2$中的端点位置被建模为分支点周围的簇,然后,使用具有圆柱邻域的成对相互作用的马尔可夫场模型将模型扩展到三维,以z坐标为点的平面位置。我们将模型拟合到取自健康受试者和患有糖尿病神经病变的受试者的样品。在这两组中,在硬核半径之后,终点之间有一些吸引力。然而,两组的吸引力范围和强度并不相同。由于数据的各向异性性质,通过使用Ripley的K函数的圆柱形版本来评估模型的性能。我们的发现表明,所提出的模型能够捕获终点的3D空间结构。
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 $\\mathbb {R}^2$ 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.