Yelnik J, Percheron G, François C, Burnod Y
J Neurosci Methods. 1983 Oct;9(2):115-25. doi: 10.1016/0165-0270(83)90125-5.
Our study proposes an objective method of describing 3-dimensional dendritic arborizations of neurons in the best possible conditions. The method is based upon a particular exploitation of statistical "principal component analysis". For each arborization, 3 principal axes are calculated which are its axes of inertia. The first two axes define the "principal plane" of the arborization. The shape of the arborization is determined from the statistical distribution of its dendritic points along each of these axes. Shapes are quantified by using an "index of axialization" (a) and an "index of flatness" (p) both of which may vary from zero to 1. The dimensions of the arborization, "length" (1), "width" (w) and "thickness" (t) are also measured along the principal axes. Orientation of arborizations is quantified by considering the orientation of the first principal axis for axialized arborization (a close to 1) and/or the orientation of the principal plane for flattened arborizations (p close to 1). In both cases 2 angles (azimuth and polar angle) are calculated. For spherical arborizations (a and p close to 1), no orientation is significant. The significance level of the defined orientations is evaluated from the values of the shape indices. Several examples are illustrated and other existing methods are discussed.
我们的研究提出了一种在尽可能理想的条件下描述神经元三维树突分支的客观方法。该方法基于对统计“主成分分析”的一种特殊应用。对于每个分支，计算出3个主轴，即其惯性轴。前两个轴定义了分支的“主平面”。分支的形状由其树突点沿这些轴各自的统计分布确定。通过使用“轴化指数”（a）和“扁平指数”（p）对形状进行量化，这两个指数的值均可在0到1之间变化。分支的尺寸，即“长度”（l）、“宽度”（w）和“厚度”（t）也沿着主轴进行测量。对于轴化的分支（a接近1），通过考虑第一主轴的方向和/或对于扁平分支（p接近1）通过考虑主平面的方向来量化分支的方向。在这两种情况下，都计算两个角度（方位角和极角）。对于球形分支（a和p接近1），不存在显著的方向。根据形状指数的值评估所定义方向的显著性水平。文中给出了几个示例，并讨论了其他现有的方法。
