A new method for the topological analysis of neuronal tree structures

Statistical analysis of the frequencies of observed branching patterns of neuronal arborescences is an important means of studying neuronal growth and of characterizing axonal or dendritic populations. We recently derived simple formulae for the exact probabilities of occurrence of types of neuronal trees for both segmental and terminal growth. Additionally, the existence of a natural ordering of the neuronal tree types enables the application of the Kolmogorov goodness-of-fit test. In the present report it is illustrated how these facilities can be incorporated in the analysis of neuronal arborizations. Interesting features are that very large neuronal arborizations can be analyzed completely and that only small sample sizes are required for the estimation of the critical level corresponding to the growth hypothesis. Further, it is indicated how populations of neuronal tree structures may be compared with each other without reference to a particular growth theory.