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

BACKGROUND: 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. NEW METHOD: 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. RESULTS: Apical dendrites of superficial cortical pyramidal neurons have a higher mean value of the fractal dimension as compared to deep pyramidal neurons. COMPARISON WITH EXISTING METHOD: 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. CONCLUSION: 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.

Fractal dimension of apical dendritic arborization differs in the superficial and the deep pyramidal neurons of the rat cerebral neocortex.

Pyramidal neurons of the mammalian cerebral cortex have specific structure and pattern of organization that involves the presence of apical dendrite. Morphology of the apical dendrite is well-known, but quantification of its complexity still remains open. Fractal analysis has proved to be a valuable method for analyzing the complexity of dendrite morphology. The aim of this study was to establish the fractal dimension of apical dendrite arborization of pyramidal neurons in distinct neocortical laminae by using the modified box-counting method. A total of thirty, Golgi impregnated neurons from the rat brain were analyzed: 15 superficial (cell bodies located within lamina II-III), and 15 deep pyramidal neurons (cell bodies situated within lamina V-VI). Analysis of topological parameters of apical dendrite arborization showed no statistical differences except in total dendritic length (p=0.02), indicating considerable homogeneity between the two groups of neurons. On the other hand, average fractal dimension of apical dendrite was 1.33±0.06 for the superficial and 1.24±0.04 for the deep cortical neurons, showing statistically significant difference between these two groups (p<0.001). In conclusion, according to the fractal dimension values, apical dendrites of the superficial pyramidal neurons tend to show higher structural complexity compared to the deep ones.

Fractal analysis of dendrite morphology using modified box-counting method.

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.

Fractal analysis of dendrite morphology of rotated neuronal pictures: the modified box counting method.

The fractal dimension of a non-stellate neuron changes continuously with rotation of the neuronal picture. For a stellate neuron such changes cannot be noticed. During preprocessing for the box counting, non-stellate neurons should be arranged so that the major diameters of their dendrite fields are parallel. It was shown that a non-stellate neuronal picture had the smallest box dimension when the angle between the horizontal or vertical axis and its major diameter was about 45 degrees. The box counting method which uses ImageJ software does not consider the position of a picture on the computer's screen. A dispersion of the box dimension values of a sample is generally rather large so that their mean value is with larger standard deviation. Modified box counting method partly diminishes these findings. To improve a dependence on neuronal rotation for the box counting dimension of nonstellate neurons, prior to applying the box counting, the non-stellate neurons should be arranged so that the major diameters of their dendrite fields are parallel.

Fractal analysis of dendrites morphology using modified Richardson's and box counting method.

Fractal analysis has proven to be a useful tool in analysis of various phenomena in numerous naturel sciences including biology and medicine. It has been widely used in quantitative morphologic studies mainly in calculating the fractal dimension of objects. The fractal dimension describes an object's complexity: it is higher if the object is more complex, that is, its border more rugged, its linear structure more winding, or its space more filled. We use a manual version of Richardson's (ruler-based) method and a most popular computer-based box-counting method applying to the problem of measuring the fractal dimension of dendritic arborization in neurons. We also compare how these methods work with skeletonized vs. unskeletonized binary images. We show that for dendrite arborization, the mean box dimension of unskeletonized images is significantly larger than that of skeletonized images. We also show that the box-counting method is sensitive to an object's orientation, whereas the ruler-based dimension is unaffected by skeletonizing and orientation. We show that the mean fractal dimension measured using the ruler-based method is significantly smaller than that measured using the box-counting method. Whereas the box-counting method requires defined usage that limits its utility for analyzing dendritic arborization, the ruler-based method based on Richardson's model presented here can be used more liberally. Although this method is rather tedious to use manually, an accessible computer-based implementation for the neuroscientist has not yet been made available.

Morphology and classification of large neurons in the adult human dentate nucleus: a qualitative and quantitative analysis of 2D images.

The dentate nucleus represents the most lateral of the four cerebellar nuclei that serve as major relay centres for fibres coming from the cerebellar cortex. Although many relevant findings regarding to the structure, neuronal morphology and cytoarchitectural development of the dentate nucleus have been presented so far, very little quantitative information has been collected on the types of large neurons in the human dentate nucleus. In the present study we qualitatively analyze our sample of large neurons according to their morphology and topology, and classify these cells into four types. Then, we quantify the morphology of such cell types taking into account seven morphometric parameters which describe the main properties of the cell soma, dendritic field and dendrite arborization. By performing appropriate statistics we prove out our classification of the large dentate neurons in the adult human. To the best of our knowledge, this study represents the first attempt of quantitative analysis of morphology and classification of the large neurons in the adult human dentate nucleus.

Extraneural arterial blood vessels of human fetal sciatic nerve.

Nerves get segmental blood supply either from the neighboring muscular and cutaneous branches or from the regional main arterial trunks. The aim of our research was to detect, in the gluteal and posterior femoral region, the blood vessels which are involved in the blood supply of the human fetal sciatic nerve, as well as to establish their origin. Micro-dissection was performed on 48 fetal lower extremities which were previously fixed in 10% formalin. Micropaque solution (barium sulfate) was injected into their blood vessels. The fetal gestational age was established by measuring the crump-crown length and it ranged from the third to the ninth lunar month. The observed nutritional arteries of the human sciatic nerve originated from the inferior gluteal artery, medial circumflex femoral artery, perforating branches, and popliteal artery. The anastomotic arterial chain of the human sciatic nerve was observed in all cases. In 75% of the cases it was composed of the branches of the inferior gluteal artery, the medial circumflex femoral artery and the first two perforating arteries. The nutrient branch of the third perforating branch was less frequently (in 14.5% of the cases) part of this anastomotic arterial chain.