Abstract
The box-counting method for calculating the fractal dimension (D) with the ImageJ 1.20s software is used as a tool for quantitative analysis of the neuronal morphology in the fish brain. The fractal dimension was determined for several types of neurons in the brain of two teleost species, Pholidapus dybowskii and Oncorhynchus keta. These results were compared with those obtained for some neurons of the human brain. The fractal (fractional) dimension (D), as a quantitative index of filling of two-dimensional space by the black and white image of a cell, is shown to vary from 1.22 to 1.72 depending on the type of neuron. The fractal dimension reaches its maximum in less specialized neurons that carry out a number of different functions. On the other hand, highly specialized neurons display a relatively low fractal dimension. Thus, the fractal dimension serves as a numerical measure of the spatial complexity of the neuron and correlates with the morphofunctional organization of the cell.
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REFERENCES
Andreeva, N.G. and Obukhov, D.K., Evolyutsionnaya morfologiya nervnoi sistemy pozvonochnykh (Evolutionary Morphology of the Nervous System of Vertebrates), St. Petersburg: Lan', 1999.
Isaeva, V.V., Sinergetica dlya biologov. Vvodnyi kurs (Synergetics for Biologists. An Introductory Course), Vladivostok: Izd. DVGU, 2003.
Isaeva, V.V., Chernyshev, A.V., and Shkuratov, D.Yu., Fractals and Chaos in Organism Morphology, Vestn. DVO RAN, 2001, no. 2, pp. 71–79.
Leontovich, T.A., Neironnaya organizatsiya podkorkovykh obrazovanii perednego mozga (Neuronal Organization of the Subcortical Structures of the Forebrain, Moscow: Meditsina, 1978.
Pushchina, E.V. and Varaksin, A.A., Argirophilic and Nitroxidergic Bipolar Neurons (Lugaro Cells) in the Cerebellum of Pholidapus dybowskii, Zh. Evol. Biokhim. i Fiziol., 2001, vol. 37,no. 5, pp. 437–441.
Savel'ev, S.V., Sravnitel'naya anatomiya nervnoi sistemy pozvonochnykh (Comparative Anatomy of the Nervous System of Vertebrates), Moscow: GEOTARMED, 2001.
Sepp, E.K., Istoriya razvitiya nervnoi sistemy pozvonochnykh (History of the Development of the Nervous System in Vertebrates), Moscow: Medgiz, 1959.
Feder, J., Fractals, New York: Plenum Press, 1988. Translated under the title Fraktaly, Moscow: Mir, 1991.
Shul'govskii, V.V., Fiziologiya tsentral'noi nervnoi sistemy (Physiology of the Central Nervous System), Moscow: MGU, 1997.
Barinaga, M., New Clues to How Neurons Strengthen Their Connections, Science, 1999, vol. 284,no. 5421, pp. 1755–1757.
Barinaga, M., Synapses Call the Shots, Science, 2000, vol. 290,no. 5492, pp. 735–738.
Caserta, F., Stanley, H.E., Eldred, W.D., et al., Physical Mechanisms Underlying Neurite Outgrowth; a Quantitative Analysis of Neuronal Shape, Phys. Rev. Lett., 1990, vol. 64, pp. 95–98.
Costa, L.C., Manoel, E.T.M., Faucereau, F., et al., A Shape Analysis Framework for Neuromorphometry, Network: Comput. Neural. Syst., 2002, vol. 13, pp. 283–310.
Dickson, B.J., Molecular Mechanisms of Axon Guidance, Science, 2002, vol. 298,no. 5600, pp. 1959–1964.
Fernandez, E., Bolea, J.A., Ortega, G., and Louis, E., Are Neurons Multifractals? J. Neurosci. Meth., 1999, vol. 89, pp. 151–157.
Goldberger, A.L., Fractal Variability versus Pathological Periodicity: Complexity and Stereotypy in Disease, Perspect. Biol. Med., 1997, vol. 40,no. 4, pp. 543–561.
Goldberger, A.L., Rigley, D.R., and West, B.J., Chaos and Fractals in Human Physiology, Sci. Amer., 1990, vol. 162,no. 2, pp. 43–49.
Häusser, M., Spruston, N., and Stuart, G.J., Diversity and Dynamics of Dendritic Signalling, Science, 2000, vol. 290,no. 5492, pp. 739–744.
Jelinek H.F. and Fernandez, E., Neurons and Fractals: How Reliable and Useful Are Calculations of Fractal Dimensions? J. Neurosc. Meth., 1998, vol. 81, pp. 9–18.
Jelinek, H.F. and Spence, I., Catergorization of Physiologically Characterized Non-α/Non-β Cat Retinal Ganglion Cells Using Fractal Geometry, Fractals, 1997, vol. 5,no. 4, pp. 673–684.
Kniffki, K.-D., Pawlak, M., and Vahle-Hinz, C., Fractal Dimensions and Dendritic Branching of Neurons in the Somatosensory Thalamus, in Fractals in Biology and Medicine, Basel: Birkhäuser, 1994, pp. 221–229.
Malevic-Savatic, M., Malinow, R., and Svoboda, K., Rapid Dendritic Morphogenesis in CA1 Hippocampal Dendrites Induced by Synaptic Activity, Science, 1999, vol. 283, pp. 1923–1926.
Mandelbrot, B.B., The Fractal Geometry of Nature, New York: Freeman, 1983.
Manso, M.J. and Anadon, R., Golgi Study of the Telecephalon of the Small-Spotted Dogfish Scyliorhinus canicula, J. Comp. Neurol., 1993, vol. 333, pp. 485–502.
Murray, J.D., Use and Abuse of Fractal Theory in Neuroscience, J. Comp. Neurol., 1995, vol. 361,no. 3, pp. 369–371.
Panico, J. and Sterling, P., Retinal Neurons and Vessels Are not Fractal but Space-Filling, J. Comp. Neurol., 1995, vol. 361, pp. 479–490.
Puschina, E.V. and Varaksin, A.A., Morphological Organization of Large Golgi Neurons in the Cerebellum of the Opisthocentrid Pholidapus dybowskii, Neurosci. Behav. Physiol., 2002, vol. 32,no. 4, pp. 341–345.
Rakic, P, Bourgeous, J.-P., Eckenhoff, M.F., et al., Concurrent Overproduction of Synapse in Diverse Regions of the Primate Cerebral Cortex, Science, 1986, vol. 232, pp. 232–235.
Schiff, S.J., Jerger, K., Duong, D.H., et al., Controlling Chaos in the Brain, Nature, 1994, vol. 370, pp. 615–620.
Smith, T.G. and Lange, G.D., Fractal Studies of Neuronal and Glial Cellular Morphology, in Fractal Geometry in Biological Systems: An Analytical Approach, Boca Raton: CRC Press, 1996, pp. 173–186.
Smith, T.G., Lange, G.D., and Marks, W.B., Fractal Methods and Results in Cellular Biology—Dimensions, Lacunarity, and Multifractals, J. Neurosci. Meth., 1996, pp. 123–136.
Smith, T.G. and Neale, E.A., A Fractal Analysis of Morphological Differentiation of Spinal Cord Neurons in Cell Culture, in Fractals in Biology and Medicine, Basel: Birkhäuser, 1994, pp. 210–220.
Stanley, H.E., Learning Concepts of Fractals and Probability by “Doing Science,” Physica D, 1989, vol. 38,nos. 1–3, pp. 330–340.
Stern, P. and Marx, J., Beautiful, Complex, and Diverse Specialists, Science, 2000, vol. 290,no. 5492, p. 735.
Waliszewski, P. and Konarski, J., Neuronal Differentiation and Synapse Formation Occur in Space and Time with Fractal Dimension, Synapse, 2002, vol. 43, pp. 252–258.
Weibel, E.R., Fractal Geometry: A Design Principle for Living Organisms, Amer. J. Physiol, 1991, vol. 261, pp. L361-L369.
Weibel, E.R., Design of Biological Organisms and Fractal Geometry, in Fractals in Biology and Medicine, Basel: Birkhäuser, 1994, pp. 68–85.
Wingate, R.J.T., Fitzgibbon, T., and Thompson, I.D., Lucifer Yellow, Retrograde Tracers, and Fractal Analysis Characterize Adult Ferret Retinal Ganglion Cells, J. Comp. Neurol., 1992, vol. 323, pp. 449–474.
Wullimann, M.F., The Central Nervous System, in The Physiology of Fishes, Boca Raton, New York: CRS Press, 1997, pp. 245–282.
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Isaeva, V.V., Pushchina, E.V. & Karetin, Y.A. The Quasi-Fractal Structure of Fish Brain Neurons. Russian Journal of Marine Biology 30, 127–134 (2004). https://doi.org/10.1023/B:RUMB.0000025989.29570.9d
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DOI: https://doi.org/10.1023/B:RUMB.0000025989.29570.9d