Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, S-41296 Gothenburg, Sweden.
Math Biosci. 2013 Jun;243(2):178-89. doi: 10.1016/j.mbs.2013.03.001. Epub 2013 Mar 18.
We propose two spatial point process models for the spatial structure of epidermal nerve fibers (ENFs) across human skin. The models derive from two point processes, Φb and Φe, describing the locations of the base and end points of the fibers. Each point of Φe (the end point process) is connected to a unique point in Φb (the base point process). In the first model, both Φe and Φb are Poisson processes, yielding a null model of uniform coverage of the skin by end points and general baseline results and reference values for moments of key physiologic indicators. The second model provides a mechanistic model to generate end points for each base, and we model the branching structure more directly by defining Φe as a cluster process conditioned on the realization of Φb as its parent points. In both cases, we derive distributional properties for observable quantities of direct interest to neurologists such as the number of fibers per base, and the direction and range of fibers on the skin. We contrast both models by fitting them to data from skin blister biopsy images of ENFs and provide inference regarding physiological properties of ENFs.
我们提出了两种用于描述人体皮肤表皮神经纤维（ENF）空间结构的空间点过程模型。这两个模型源自描述纤维的基点和端点位置的两个点过程Φb 和 Φe。Φe（端点过程）中的每一个点都与 Φb（基点过程）中的唯一一点相连。在第一个模型中，Φe 和 Φb 都是泊松过程，产生了一个端点在皮肤表面均匀覆盖的零模型，以及生理指标的矩的基本结果和参考值。第二个模型为每个基点生成端点提供了一个机械模型，我们通过将 Φe 定义为条件聚类过程，将其作为父点的实现，更直接地对分支结构进行建模。在这两种情况下，我们都推导出了可直接用于神经学家的观察量的分布性质，例如每个基点的纤维数量，以及纤维在皮肤上的方向和范围。我们通过将这两个模型拟合到 ENF 的皮肤水疱活检图像数据中来对比它们，并提供有关 ENF 生理特性的推断。
