Fractal analysis of dendrite morphology using modified box-counting method

Fractal Analysis of Skeletal Muscle Tissue of Rats Subjected to Stretch Injury

“…FD is already used as a diagnostic tool in many fields of research, including studies of; neurons (Ristanovic´ et al, 2014); retinal vasculature (Mendonca et al); bronchial tree (Gupta et al, 2014); tissue blood perfusion (Michallek & Dewey 2014); diagnosis of hepatocellular carcinoma (Lee et al); degree of differentiation of osteoblasts (Park et al, 2014) and degree of myocardial cellular rejection after heart transplantation (Moreira et al), among others. However; despite being a technique with good applicability for histological analysis, no research was found in the scientific literature assessing injured skeletal muscle tissue using fractal dimension.…”

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

“…In order to process the images to an adequate skeletonized format and calculate the fractal dimensions, ImageJ software (National Institute of Health, Bethesda, USA; http://rsbweb.nih.gov/ij; version 1.48v) was used. A detailed description of the applied experimental procedure as well as the information on tissue and data processing, can be found in Ristanović et al (2013).…”

“…But in neuroscience, where cell morphology is investigated, the problem of measuring the fractal dimension of profuse dendrite arborization applying Richardson's method has not been completely solved (Ristanović et al, 2013). To apply the Richardson's method to apical dendrites of neocortical pyramidal neurons, Richardson's approach was modified as follows: the picture of every apical dendrite was broken down into three to five different pictures (depending on the complexity of the arbors), so that none of them contained any branching parts of the dendrite.…”

“…1A) a primary stem was chosen as the starting line (it corresponds to 1 in Fig. 1B), and the lateral branches were numbered (Ristanović et al, 2013). For each chosen opening of the divider, r, the number of steps, N(r), along all numbered segments was counted, and the fractal dimension calculated.…”

“…The main difference between Richardson's and box-counting method is that the fractal dimension obtained by Richardson's method measures the waviness or ruggedness of the objects border, whereas the fractal dimension D b obtained by the box-counting method includes the space-filling value in addition. Hence, the Richardson's fractal dimension should be somewhat smaller than the corresponding box-counting dimension of the same geometrical object or pattern (Ristanović et al, 2013). However, precise comparison of these methods has not been done so far.…”