Duyckaerts C, Godefroy G, Hauw J J
Laboratoire de Neuropathologie R. Escourolle, Hôpital de La Salpêtrière, Paris, France.
J Neurosci Methods. 1994 Jan;51(1):47-69. doi: 10.1016/0165-0270(94)90025-6.
The technique that we describe aims at evaluating the numerical density of cells in highly heterogeneous regions, e.g., nuclei, layers or columns of neurones. Rather than counting the number of neuronal sections ('profiles') in a reference frame, we evaluated the 'free area' which lies around each profile. The X and Y coordinates of the neuronal profiles within a microscopical section were measured by 2 linear transducers fastened to the moving stage of the microscope. These coordinates were used by a computer programme that we developed to calculate the 'free area' around each neuronal profile. These areas are polygons that cover the plane of the section without interstice or overlap, i.e., realize a tessellation of the section plane ('Dirichlet tessellation'). Each polygon contains one neuronal profile and the area of the section closest to that profile than to any other. When that area is large, the density is low. An individual value of cellular density = 1/(area of Dirichlet polygon) could thus be assigned to each neuronal profile. Coloured density maps were obtained by attributing a colour to each polygon according to its area. Those maps were useful to demonstrate the presence of neuronal clusters (columns, layers, nuclei, etc.). A confidence interval (CI) of mean polygon areas (standard deviation (SD) of polygon areas/square root of n, n being the number of cells) could be calculated and used to determine the CI of the density of neuronal profiles. This value helped to predict the number of profiles which had to be counted in a particular area to obtain a given precision. The coefficient of variation (CV) of the polygon areas is a dimensionless value, which is not affected by atrophy, shrinkage or stretching of the section, but is sensitive to restricted cell loss. When profiles are regularly spaced, the CV is low; it is high when they are clustered. With computer simulation (Monte-Carlo testing) we established that the CVs ranged from 33% to 64% (P < 0.05) when the profiles were randomly distributed according to a Poisson point process. A value lower than 33% suggested a regular distribution, and a value higher than 64% a clustered distribution. Automatic isolation of cell clusters was made possible with Dirichlet tessellation; a cluster was defined as a group of contiguous cells, exhibiting similar numerical density, i.e., whose polygons had similar surface area.(ABSTRACT TRUNCATED AT 400 WORDS)
我们所描述的这项技术旨在评估高度异质区域（例如神经元的细胞核、层或柱）中的细胞数密度。我们不是在一个参考框架中计算神经元切片（“轮廓”）的数量，而是评估每个轮廓周围的“自由区域”。通过固定在显微镜移动载物台上的两个线性传感器测量显微镜切片内神经元轮廓的X和Y坐标。我们开发的一个计算机程序利用这些坐标来计算每个神经元轮廓周围的“自由区域”。这些区域是多边形，它们覆盖切片平面且无间隙或重叠，即实现了切片平面的镶嵌（“狄利克雷镶嵌”）。每个多边形包含一个神经元轮廓以及切片中比任何其他轮廓更靠近该轮廓的区域。当该区域较大时，密度较低。因此，可以为每个神经元轮廓赋予一个细胞密度的个体值 = 1/（狄利克雷多边形的面积）。通过根据每个多边形的面积赋予一种颜色来获得彩色密度图。这些图有助于展示神经元簇（柱、层、核等）的存在。可以计算平均多边形面积的置信区间（CI）（多边形面积的标准差（SD）/细胞数量n的平方根），并用于确定神经元轮廓密度的CI。该值有助于预测在特定区域中为获得给定精度必须计数的轮廓数量。多边形面积的变异系数（CV）是一个无量纲值，它不受切片萎缩、收缩或拉伸的影响，但对局限性细胞丢失敏感。当轮廓规则分布时，CV较低；当它们聚集时，CV较高。通过计算机模拟（蒙特卡罗测试）我们确定，当轮廓根据泊松点过程随机分布时，CV范围为33%至64%（P < 0.05）。低于33%的值表明分布规则，高于64%的值表明分布聚集。狄利克雷镶嵌使得细胞簇的自动分离成为可能；一个簇被定义为一组相邻的细胞，它们表现出相似的数密度，即其多边形具有相似的表面积。（摘要截取自400字）
