Box-Counting Method of 2D Neuronal Image: Method Modification and Quantitative Analysis Demonstrated on Images from the Monkey and Human Brain

This study calls attention to the difference between traditional box-counting method and its modification. The appropriate scaling factor, influence on image size and resolution, and image rotation, as well as different image presentation, are showed on the sample of asymmetrical neurons from the monkey dentate nucleus. The standard BC method and its modification were evaluated on the sample of 2D neuronal images from the human neostriatum. In addition, three box dimensions (which estimate the space-filling property, the shape, complexity, and the irregularity of dendritic tree) were used to evaluate differences in the morphology of type III aspiny neurons between two parts of the neostriatum.

[1]  K. Doi,et al.  Fractal analysis of senile plaque observed in various animal species , 2001, Neuroscience Letters.

[2]  A. Giuliani,et al.  Fractal analysis in a systems biology approach to cancer. , 2011, Seminars in cancer biology.

[3]  Dušan Ristanović,et al.  Fractal dimension of apical dendritic arborization differs in the superficial and the deep pyramidal neurons of the rat cerebral neocortex , 2015, Neuroscience Letters.

[4]  N. Milosevic.  The Morphology of the Brain Neurons: Box-Counting Method in Quantitative Analysis of 2D Image , 2016 .

[5]  T. G. Smith,et al.  Early dendrite development in spinal cord cell cultures: A quantitative study , 1993, Journal of neuroscience research.

[6]  Ching Y. Suen,et al.  A fast parallel algorithm for thinning digital patterns , 1984, CACM.

[7]  Dušan Ristanović,et al.  Fractality of dendritic arborization of spinal cord neurons , 2006, Neuroscience Letters.

[8]  Antonio Di Ieva,et al.  On the Fractal Nature of Nervous Cell System , 2011, Front. Neuroanat..

[9]  Dušan Ristanović,et al.  Application of fractal analysis to neuronal dendritic arborisation patterns of the monkey dentate nucleus , 2007, Neuroscience Letters.

[10]  Herbert F. Jelinek,et al.  Monofractal and multifractal analysis for interpretation of function-structure relationships in finite size biological material , 2011 .

[11]  W. B. Marks,et al.  A fractal analysis of cell images , 1989, Journal of Neuroscience Methods.

[12]  Wlodzimierz Klonowski,et al.  Fractals in the Neurosciences, Part II , 2015, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[13]  H F Jelinek,et al.  Use of fractal theory in neuroscience: methods, advantages, and potential problems. , 2001, Methods.

[14]  H. Jelinek,et al.  Box-Counting and Multifractal Analysis in Neuronal and Glial Classification , 2013 .

[15]  R. Haaxma.  548 pp., 293 figs., US $ 105.20 Chan-Palay Cerebellar dentate nucleus , 1978, Clinical Neurology and Neurosurgery.

[16]  H. E. Stanley,et al.  Determination of fractal dimension of physiologically characterized neurons in two and three dimensions , 1995, Journal of Neuroscience Methods.

[17]  Dušan Ristanović,et al.  Fractal analysis of dendrite morphology of rotated neuronal pictures: the modified box counting method. , 2014, Theoretical biology forum.

[18]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[19]  G. Losa.  The fractal geometry of life. , 2009, Rivista di biologia.

[20]  Herbert F Jelinek,et al.  Neurons and fractals: how reliable and useful are calculations of fractal dimensions? , 1998, Journal of Neuroscience Methods.

[21]  Neboja T. Miloevic.  Fractal Analysis of Two Dimensional Images: Parameters of the Space-Filling and Shape , 2015, 2015 20th International Conference on Control Systems and Computer Science.

[22]  W. B. Marks,et al.  Fractal methods and results in cellular morphology — dimensions, lacunarity and multifractals , 1996, Journal of Neuroscience Methods.

[23]  H. F. Jelinek,et al.  Fractal Analysis: Pitfalls and Revelations in Neuroscience , 2005 .

[24]  Fabio Grizzi,et al.  Fractals in the Neurosciences, Part I , 2014, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.