Application of growth models to the topology of neuronal branching patterns

The variation in topological structure of branching patterns may contain essential information with respect to the way these branching patterns have grown. For the understanding of how growth modes finally result in a particular variety in topological patterns, model studies may provide indispensible tools. These studies imply the mathematical formulation of growth models and the development of statistical procedures to compare model predictions with observed data. Recent literature shows two main approached in these model studies, viz. subtree partition analysis (SPA) and vertex analysis. This paper will briefly review the current status with respect to SPA and will apply the model approach to sets of dendritic trees taken from pyramidal, multipolar non-pyramidal and from Purkinje cells. The results show that the topological properties of many dendrites are not in agreement with the hypothesis of random terminal growth and that substantial branching of intermediate segments and/or branching dependent of the position of segments in the tree (topological distance from the cell body) must be assumed. Only two parameters are required to incorporate these assumptions in the model. In all cases up to now it is possible to find parameter values such that the model predictions of topological properties are in agreement with the observations.