Mathematical modeling and computational analysis of neuronal cell images: Application to dendritic arborization of Golgi-impregnated neurons in dorsal horns of the rat spinal cord

Neurons of the rat spinal cord have been stained using the Golgi impregnation method. Successfully impregnated neurons from laminae I to VI were subjected to a computational analysis for complexity of dendritic tree structure. The analysis was performed using ruler-counting and circle-counting techniques. Our analysis aimed to support quantitatively the general concept of Rexed's laminar scheme of the dorsal horn of mammals. For that purpose, we have developed two mathematical models of neuronal arborization patterns, whose solutions yielded the inverse power-law and generalized power-law scaling. The latter comprises two main parameters: (i) the anfractuosity, characterizing the degree of dendritic complexity and (ii) an estimate of the total length of arbor dendrites. The anfractuosity can distinguish among the sets of drawings over all six laminae.