Modified Richardson's method versus the box-counting method in neuroscience

The morphology of dendrites, including apical dendrites of pyramidal neurons, is already well-known. However, the quantification of their complexity still remains open. Fractal analysis has proven to be a valuable method of analyzing the degree of complexity of dendrite morphology.

Richardson's method is a technique of measuring the fractal dimension of open and closed lines of objects. This method was modified in order to measure the fractal dimension of neuronal arborization. The focus of this experiment was on the apical dendrites of superficial and deep pyramidal neurons in the rat cerebral cortex.

Apical dendrites of superficial cortical pyramidal neurons have a higher mean value of the fractal dimension as compared to deep pyramidal neurons.

Using the modified Richardson's method we showed that the mean value of the fractal dimension of apical dendrites in superficial pyramidal neurons is highly statistically significant as compared to the value of the fractal dimension in deep pyramidal neurons. On the other hand, the mean values of the fractal dimension between the same groups of apical dendrites measured by the most popular box-counting method showed merely a statistically significant difference.

The modified Richardson's method of fractal analysis is an efficient mathematical method for calculating the fractal dimension of dendrites and could be used in order to calculate the complexity of dendrite arborization.