Probabilistic analysis of dendritic branching patterns of cortical neurons

Summary

It is argued that the usual method of characterizing dendritic fields of nerve cells by enumerating the number of bifurcations and end points at various distances from the perikaryon, and the number of intersections of dendrites by virtual spheres around the centre is of limited value for an adequate description. Although these parameters give a reliable indication as to the spatial density of the dendritic material, one shortcoming is that the structural content of the plexus remains rather obscure because the topological and metrical aspects are represented in an intermingled way. A statistical theory is put forward that separates the two factors. As to the first factor, many experimental data can be described by assuming that the probability of bifurcation of a segment decreases geometrically with the order of that segment. As to the second factor, it is deduced that in most instances the terminal segments are, on the average, several times longer than the intermediary situated segments.

Upon elaboration of the theory, in comparison with experimental findings reported in the literature, it seems profitable to evaluate these factors separately by measuring the distribution of the number of segments per order or generation, and the distribution of the lengths of the segments for each order. Emphasis is laid on the dynamic aspects of dendritic growth by analyzing data on changes in dendritic ramification patterns of cells in brains of animals of various ages, and reared under either normal or experimental conditions.