Principal component analysis: a suitable method for the 3-dimensional study of the shape, dimensions and orientation of dendritic arborizations.

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.