Abstract
One of the major goals in cellular neurobiology is the meaningful cell classification. However, in cell classification there are many unresolved issues that need to be addressed. Neuronal classification usually starts with grouping cells into classes according to their main morphological features. If one tries to test quantitatively such a qualitative classification, a considerable overlap in cell types often appears. There is little published information on it. In order to remove the above-mentioned shortcoming, we undertook the present study with the aim to offer a novel method for solving the class overlapping problem. To illustrate our method, we analyzed a sample of 124 neurons from adult human dentate nucleus. Among them we qualitatively selected 55 neurons with small dendritic fields (the small neurons), and 69 asymmetrical neurons with large dendritic fields (the large neurons). We showed that these two samples are normally and independently distributed. By measuring the neuronal soma areas of both samples, we observed that the corresponding normal curves cut each other. We proved that the abscissa of the point of intersection of the curves could represent the boundary between the two adjacent overlapping neuronal classes, since the error done by such division is minimal. Statistical evaluation of the division was also performed.
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References
Afifi AA, Azen SP (1979) Statistical analysis. A computer oriented approach. Academic Press, San Francisco
Alder H, Roessler EB (1972) Introduction to probability and statistics. WH Freeman and Co, San Francisco
Braak H, Braak E (1983) Morphological studies of local circuit neurons in the cerebellar dentate nucleus in man. Hum Neurobiol 2: 49–57
Chan-Palay V (1977) Cerebellar dentate nucleus: organization, cytology and transmitters. Springer, Berlin
Fiala JC, Harris KM (2001) Dendrite structure. In: Stuart G, Spruston N, Häusser M (eds) Dendrites. Oxford University Press, New York, pp 1–34
Hald A (1952) Statistical theory with engineering applications. Wiley, New York
Hayaran A, Wadhwa S, Bijlani V (1992) Cytoarchitectural development of the human dentate nucleus: a Golgi study. Dev Neurosci 14: 181–194
Hoel PG (1962) Introduction to mathematical statistics, 3rd edn. Wiley, New York
Huxlin KR, Goodchild AK (1997) Retinal ganglion cells in the Albino rat: revised morphological classification. J Comp Neurol 385: 309–313
Jelinek HF, Spence I (1997) Categorization of physiologically and morphologically characterized non-α/non-β cat retinal ganglion cells using fractal geometry. Fractals 5: 673–684
Larsell O, Jansen J (1972) The comparative anatomy and histology of the cerebellum. The human cerebellum, cerebellar connections and cerebellar cortex. University Minnesota Press, Minneapolis
Liu X, Zhao GA (2005) Fractal wormhole model for cold heavy oil production. J Can Pet Technol 44: 31–36
Lugaro E (1895) Sulla struttura del nucleo dentate del cervelletto nell’uomo. Monit Zool Ital 6: 5–12
Mihajlovic P, Zecevic N (1986) Development of the human dentate nucleus. Hum Neurobiol 5: 189–197
Milošević NT, Ristanović D, Gudović R, Rajković K, Marić D (2007) Application of fractal analysis to neuronal dendritic arborisation patterns of the monkey dentate nucleus. Neurosci Lett 425: 23–27
Milošević NT, Ristanović D, Jelinek HF, Rajković K (2009) Quantitative analysis of dendritic morphology of the alpha and delta retinal ganglion cells in the rat: a cell classification study. J Theor Biol 259: 142–150
Milošević NT, Ristanović D, Marić D, Rajković K (2010) Morphology and classification of large neurons in the adult human dentate nucleus: a quantitative study. Neurosci Lett 468: 59–63
Origin. Area version of Gaussian functions (2010) In: Curve fitting functions, Origin User’s Manual, Origin Ver. 4.0, p 13. www.originlab.com/pdfs/curvefittingfunctions.pdf
Panico J, Sterling P (1995) Retinal neurons and vessels are not fractal but space-filling. J Comp Neurol 361: 479–490
Peichl L (1989) Alpha and delta ganglion cells in the rat retina. J Comp Neurol 286: 120–139
Perry VH (1979) The ganglion cell layer of the retina of the rat: a Golgi study. Proc R Soc Lond B 204: 363–375
Rexed B (1952) The cytoarchictenotic organization of the spinal cord in the cat. J Comp Neurol 96: 414–495
Ristanović D, Milošević NT (2007) A confirmation of Rexed’s laminar hypothesis using the Sholl linear method complemented by nonparametric statistics. Neurosci Lett 414: 286–290
Ristanović D, Milošević NT, Stefanović IB, Marić D, Popov I (2009) Cell image area as a tool for neuronal classification. J Neurosci Methods 182: 272–278
Ristanović D, Milošević NT, Stefanović BD, Marić D, Rajković K (2010) Morphology and classification of large neurons in the adult human dentate nucleus: a qualitative and quantitative analysis of 2D images. Neurosci Res 67: 1–7
Saccozzi A (1887) Sul nucleo dentato del cervelletto. Riv Sperimentale di Freniatria Med Legale 13: 93–99
Schierhorn VH, Doedenes K, Nagel I (1977) Quantitative studies on the comparability of neurohistological results in rat cortical pyramids produced by different Golgi methods. J Hirnforesch 18: 423–429
Spiegel MR (1975) Probability and statistics. Schaum’s outline series in mathematics. McGraw-Hill Book Co., New York
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Ristanović, D., Milošević, N.T. & Marić, D.L. On the classification of normally distributed neurons: an application to human dentate nucleus. Biol Cybern 104, 175–183 (2011). https://doi.org/10.1007/s00422-011-0426-x
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DOI: https://doi.org/10.1007/s00422-011-0426-x