Bjaalie J G, Diggle P J, Nikundiwe A, Karagülle T, Brodal P
Department of Anatomy, Institute of Basic Medical Sciences, Oslo, Norway.
Anat Rec. 1991 Dec;231(4):510-23. doi: 10.1002/ar.1092310413.
This study applies terms and methods for describing spatial interactions between multivariate spatial point patterns, which are, to our knowledge, new in neurobiology. We consider two categories of points, type 1 and 2, distributed within a certain reference volume (such as a nucleus of the brainstem or a cortical area). The points may, for example, represent different categories of labelled cells or axonal fields of termination. We say that there is spatial neutrality between points of type 1 and 2 if the types are signed by random labelling. If a mechanism drives the two point categories together, we say that the point patterns are positively associated. Conversely, if a mechanism drives type 1 and 2 points apart, we say that they are segregated. By comparing two cumulative distribution functions of distances between points, we can distinguish neutrality, positive association, and segregation. One function, H12(t), is the cumulative distribution function of the distance t between a pair of randomly selected points of type 1 and 2. The other, H00(t), is the corresponding function for a pair of points randomly selected without reference to type. Plots of the estimated difference between these two functions give an indication of positive association, neutrality, or segregation. A statistical test, based on simulations of random (neutral) distributions, can be used to see whether deviations from neutrality are significant. We apply the analysis described above to a major pathway of the brain, namely the ponto-cerebellar projection. Different types of cells in the pontine nuclei are retrogradely labelled with the fluorescent tracers Rhodamine-B-isothiocyanate, Fluoro-Gold, and Fast Blue. The tracers are injected in adjacent or more distant folia of the cerebellar paraflocculus. The location of the somata of labelled cells are recorded and the total distribution reconstructed in three dimensions and displayed on a dynamic graphics workstation. We ask whether different units (folia) in the paraflocculus receive information from the same population, from two different positively associated populations, or from segregated cell populations. We find a statistically significant tendency for cell populations projecting to adjacent folia to be positively associated, although there are few cells containing multiple labels. Populations of neurons projecting to folia wider apart are significantly segregated. From inspections of the reconstructions, using real-time rotations, we find that the swarms of labelled neurons tend to accumulate in shells or lamellae in the pons. Within the lamellae, the cells are aggregated in clusters and bands with empty holes (containing unlabelled ponto-cerebellar cell bodies, presumably projecting to other cerebellar targets) in between.(ABSTRACT TRUNCATED AT 400 WORDS)
本研究应用了描述多变量空间点模式之间空间相互作用的术语和方法，据我们所知，这些术语和方法在神经生物学领域尚属新颖。我们考虑两类点，即1型和2型，分布在特定的参考体积内（如脑干的一个核团或一个皮质区域）。例如，这些点可能代表不同类别的标记细胞或终末轴突场。如果通过随机标记对类型进行标记，我们就说1型和2型点之间存在空间中性。如果有一种机制促使这两类点聚集在一起，我们就说点模式呈正相关。相反，如果有一种机制促使1型和2型点分开，我们就说它们是分离的。通过比较点之间距离的两个累积分布函数，我们可以区分中性、正相关和分离。一个函数H12(t)是一对随机选择的1型和2型点之间距离t的累积分布函数。另一个函数H00(t)是一对不考虑类型随机选择的点的相应函数。这两个函数估计差值的图表明了正相关、中性或分离。基于随机（中性）分布模拟的统计检验可用于查看与中性的偏差是否显著。我们将上述分析应用于大脑的一条主要通路，即脑桥-小脑投射。脑桥核中的不同类型细胞用荧光示踪剂异硫氰酸罗丹明、氟金和快蓝进行逆行标记。示踪剂注射到小脑旁绒球相邻或更远的小叶中。记录标记细胞胞体的位置，并在三维空间中重建其总体分布，并显示在动态图形工作站上。我们要问的是，旁绒球中的不同单元（小叶）是从同一群体、两个不同的正相关群体还是从分离的细胞群体接收信息。我们发现，投射到相邻小叶的细胞群体有统计学上显著的正相关趋势，尽管含有多个标记的细胞很少。投射到距离更远小叶的神经元群体明显分离。通过对重建图像进行实时旋转观察，我们发现成群的标记神经元倾向于在脑桥的壳层或薄片中聚集。在薄片内，细胞聚集成簇和带，其间有空洞（包含未标记的脑桥-小脑细胞体，推测投射到其他小脑靶点）。
