Fractal analysis of the laminar organization of spinal cord neurons

Images of Golgi impregnated neurons from different laminae of the human and rat dorsal horns were subjected to a quantitative analysis to support the Rexed's laminar scheme in mammals. Four methods of fractal analysis were performed in the proceedings: box-counting, mass-radius, cumulative intersection, and vectorized intersection. The results show that the box-counting method is more precise than the other fractal methods performed, and offers support for the conclusion that fractal analysis can successfully discriminate the neuron populations among different laminae. The analysis supports the concept of Rexed's cytoarchitectonic lamination of the dorsal horn.

[1]  J. Beal,et al.  Neurons with asymmetrical dendritic arbors in the substantia gelatinosa of the rat spinal cord , 2004, Experimental Brain Research.

[2]  Joseph J. Capowski,et al.  Computer Techniques in Neuroanatomy , 1989, Springer US.

[3]  G. E. Goldsmith,et al.  Hypothalamic control of nocireceptive and other neurones in the marginal layer of the dorsal horn of the medulla (trigeminal nucleus caudalis) in the rat , 2004, Experimental Brain Research.

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

[5]  Herbert F. Jelinek,et al.  Categorization of physiologically and morphologically characterized non-?/non-? cat retinal ganglion cells using fractal geometry , 1997 .

[6]  Herbert F. Jelinek,et al.  Dendritic Branching of Pyramidal Cells in the Visual Cortex of the Nocturnal Owl Monkey: A Fractal Analysis , 2003 .

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

[8]  J. Schoenen.  The dendritic organization of the human spinal cord: The dorsal horn , 1982, Neuroscience.

[9]  D. Lima,et al.  A Golgi study of the neuronal population of the marginal zone (lamina I) of the rat spinal cord , 1986, The Journal of comparative neurology.

[10]  E. Ramón-Moliner,et al.  An attempt at classifying nerve cells on the basis of their dendritic patterns , 1962, The Journal of comparative neurology.

[11]  A. Craig.  Distribution of brainstem projections from spinal lamina I neurons in the cat and the monkey , 1995, The Journal of comparative neurology.

[12]  Edward B. Roessler,et al.  Introduction to Probability and Statistics , 1961, The Mathematical Gazette.

[13]  Toshiaki Takeda,et al.  Fractal dimension of dendritic tree of cerebellar Purkinje cell during onto- and phylogenetic development , 1992, Neuroscience Research.

[14]  William Mendenhall,et al.  Introduction to Probability and Statistics , 1961, The Mathematical Gazette.

[15]  G. Elston,et al.  Dendritic branching patterns of pyramidal cells in the visual cortex of the new world marmoset monkey, with comparative notes on the old world macaque monkey , 2001 .

[16]  B. Rexed,et al.  A cytoarchitectonic atlas of the spinal coed in the cat , 1954, The Journal of comparative neurology.

[17]  H. Uylings,et al.  Topological Analysis of Individual Neurons , 1989 .

[18]  H. Kolb,et al.  Complexity and scaling properties of amacrine, ganglion, horizontal, and bipolar cells in the turtle retina , 1994, The Journal of comparative neurology.

[19]  R. Porter,et al.  A fractal analysis of pyramidal neurons in mammalian motor cortex , 1991, Neuroscience Letters.

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

[21]  M. J. Friedlander,et al.  Morphogenesis and territorial coverage by isolated mammalian retinal ganglion cells , 1991, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[22]  Sholl Da.  Dendritic organization in the neurons of the visual and motor cortices of the cat. , 1953 .

[23]  T. G. Smith,et al.  Surface complexity of human neocortical astrocytic cells: changes with development, aging, and dementia. , 1995, Journal fur Hirnforschung.

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

[25]  B. Rexed.  The cytoarchitectonic organization of the spinal cord in the cat , 1952, The Journal of comparative neurology.

[26]  V. Galhardo,et al.  Structural characterization of marginal (lamina I) spinal cord neurons in the cat: A golgi study , 1999, The Journal of comparative neurology.

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

[28]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

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

[30]  A. Craig,et al.  Morphology and Distribution of Spinothalamic Lamina I Neurons in the Monkey , 1997, The Journal of Neuroscience.

[31]  Y. Fukuda,et al.  Fractal analysis of ganglion cell dendritic branching patterns of the rat and cat retinae. , 1989, Neuroscience research. Supplement : the official journal of the Japan Neuroscience Society.

[32]  Herbert Jelinek,et al.  Application of artificial neural networks to cat retinal ganglion cell categorization , 1994 .

[33]  J. Schoenen.  [Cytoarchitectonic organization of the spinal cord in different mammals including man (author's transl)]. , 1973, Acta neurologica Belgica.

[34]  David Cornforth,et al.  Fractop: a tool for automated biological image clas sification , 2002 .