Fractal analysis of dendrite morphology using modified box-counting method

Abstract

The box-counting dimension of a non-stellate neuron changes continuously with its rotation. During preprocessing for box-counting, non-stellate neurons should be arranged so that the major diameters of their dendrite fields are parallel. A non-stellate neuronal picture should have the smallest fractal dimension when the angle between the horizontal axis and its major diameter is about 45°. The box-counting method does not consider the position of a picture on the computer screen. Therefore a dispersion of the box dimension values of a neuronal sample is rather large and their mean value is with larger variance. Modified box-counting method partly diminishes these findings. To improve a dependence of neuronal rotation on the box-counting dimension of non-stellate neurons, prior to applying box-counting method, non-stellate neurons should be arranged so that the major diameters of their dendrite fields are parallel.