On the Fractal Design in Human Brain and Nervous Tissue

DOI: 10.4236/am.2014.512165   PDF   HTML     3,812 Downloads   5,049 Views   Citations


Digital imaging techniques have enabled to gain insight into complex structure-functional processes involved in the neo-cortex maturation and in brain development, already recognized in anatomical and histological preparations. Despite such a refined technical progress most diagnostic records sound still elusive and unreliable because of use of conventional morphometric approaches based on a unique scale of measure, inadequate for investigating irregular cellular components and structures which shape nervous and brain tissues. Instead, these could be efficiently analyzed by adopting principles and methodologies derived from the Fractal Geometry. Through his masterpiece, The Fractal Geometry of Nature [1], Benoît Mandelbrot has provided a novel epistemological framework for interpreting the real life and the natural world as they are, preventing whatever approximation or subjective sight. Founded upon a body of well-defined laws and coherent principles, the Fractal Geometry is a powerful tool for recognizing and quantitatively describing a good many kinds of complex shapes, living forms, organized patterns, and morphologic features long range correlated with a broad network of functional interactions and metabolic processes that contribute to building up adaptive responses making life sustainable. Scale free dynamics characterized biological systems which develop through the iteration of single generators on different scales thus preserving proper self-similar traits. In the last decades several studies have contributed to showing how relevant may be the recognition of fractal properties for a better understanding of brain and nervous tissues either in healthy conditions or in altered and pathological states.

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Losa, G. (2014) On the Fractal Design in Human Brain and Nervous Tissue. Applied Mathematics, 5, 1725-1732. doi: 10.4236/am.2014.512165.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Mandelbrot, B. (1983) The Fractal Geometry of Nature. Freeman, San Francisco.
[2] Piccolino, M. (2008) Neuroscienze Controverse: Da Aristotele alla moderna scienza del linguaggio. Bollati Boringhieri, Torino.
[3] Golgi, C. (1903) Sulla fine anatomia degli organi centrali del sistema nervoso. Opera Omnia, I, Hoepli Milano.
[4] Ramón and Cajal, S. (1888) Sobre las fibras nerviosa de la capa molecular del cerebelo. Rev. Trim. Histol. Normal. Patology, 2.
[5] Losa, G.A. (2012) Fractals in Biology and Medicine. In: Meyers, R., Ed., Encyclopedia of Molecular Cell Biology and Molecular Medicine, Wiley-VCH Verlag, Berlin, 1-25.
[6] Fractals, M.B. (1977) Form, Chance and Dimension. W.H. Freeman & Company, San Francisco.
[7] Mandelbrot, B. (1967) How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science, 155, 636-640.
[8] Losa, G.A. and Nonnenmacher, T.F. (1996) Self-Similarity and Fractal Irregularity in Pathologic Tissues. Modern Pathology, 9, 174-186.
[9] Döllinger, J.W., Metzler, R. and Nonnenmacher, T.F. (1998) Bi-Asymptotic Fractals: Fractals between Lower and Upper Bounds. Journal of Physics A: Mathematical and General, 31, 3839-3847.
[10] Belaubre, G. (2006) L’irruption des Géométries Fractales dans les Sciences. Editions Académie Européenne Interdisciplinaire des Sciences (AEIS), Paris.
[11] Paumgartner, D., Losa, G.A. and Weibel, E.R. (1981) Resolution Effect on the Stereological Estimation of Surface and Volume and Its Interpretation in Terms of Fractal Dimensions. Journal of Microscopy, 121, 51-63.
[12] Ristanovic, D. and Losa, G.A. (2013) A Contribution to Definitions of Some Fractal Concepts. The Fractal Laboratory Journal, 2, 2-14.
[13] De Felipe, J. (2011) The Evolution of the Brain, the Human Nature of Cortical Circuits, and Intellectual Creativity. Frontiers iNeuronatomy, 5, 1-17.
[14] Smith, T.G., Marks, W.B. and Lange, C.D. (1989) A Fractal Analysis of Cell Images. Journal of Neuroscience Methods, 7, 173-180.
[15] Smith, T.G. (1994) A Fractal Analysis of Morphological Differentiation of Spinal Cord Neurons in Cell Culture. In: Losa, et al., Eds., Fractals in Biology and Medicine, Birkhäuser Press, Basel, 20-25.
[16] Milosevic, N.T. and Ristanovich, D. (2006) Fractality of Dendritic Arborization of Spinal Cord Neurons. Neuroscience Letters, 396, 172-176.
[17] Bernard, F., Bossu, J.L. and Gaillard, S. (2001) Identification of Living Oligodendrocyte Developmental Stages by Fractal Analysis of Cell Morphology. Journal of Neuroscience Research, 65, 439-445.
[18] Losa, G.A. (2012) Fractals and Their Contribution to Biology and Medicine. Medicographia, 34, 365-374.
[19] Markram, H. (2006) The Blue Brain Project. Nature Reviews Neuroscience, 7, 153-160.
[20] De Felipe, J. (2011) The Neocortical Column. Frontiers in Neuroanatomy, 5, 1-16.
[21] Romand, S., Wang, Y., Toledo-Rodriguez, M. and Markram, H. (2011) Morphological Development of Thick-Tufted Layer V Pyramidal Cells in the Rat Somatosensory Cortex. Frontiers in Neuroanatomy, 45, 1-25.
[22] Halavi, M., Hamilton, K.A., Ruchi, P. and Ascoli, G.A. (2012) Digital Reconstructions of Neuronal Morphology: Three Decades of Research Trends. Frontiers in Neuroscience, 6, 1-11.
[23] Bizzarri, M., Pasqualato, A., Cucina, A. and Pasta, V. (2013) Physical Forces and Non-Linear Dynamics Mould Fractal Cell Shape. Quantitative Morphological Parameters and Cell Phenotype. Histology and Histopathology, 28, 155-174.
[24] He, J.H. and Zhang, J. (2004) Fifth Dimension of Life and the 4/5 Allometric Scaling Law for Human Brain. Cell Biology International, 28, 809-815.
[25] Werner, G. (2010) Fractals in the Nervous System: Conceptual Implications for Theoretical Neuroscience. Frontiers in Physiology, 1, 15-30.
[26] Wyllie, A.H., Kerr, J.F.R. and Currie, A.R. (1980) Cell Death: The Significance of Apoptosis. International Review of Cytology, 68, 251-306.
[27] Edinger, A.L. and Thompson, C.B. (2004) Death by Design: Apoptosis, Necrosis and Autophagy. Current Opinion in Cell Biology, 16, 663-669.
[28] Losa, G.A. and Graber, R. (1998) Apoptotic Cell Death and the Proliferative Capacity of Human Breast Cancer. Analytical Cellular Pathology, 16, 1-10.
[29] Castelli, C., Nonnenmacher, T.F. and Losa, G.A. (2002) Morphofractal Reorganization of Plasma Membrane and Nuclear Components during the Apoptosis of Breast Cancer Cells. In: Losa, G.A., Ed., Fractals in Biology and Medicine, Mathematics and Biosciences in Interaction, Birkhäuser, Basel, 67-76.
[30] Losa, G.A. and Castelli, C. (2005) Nuclear Patterns of Human Breast Cancer Cells during Apoptosis: Characterization by Fractal Dimension and Co-Occurrence Matrix Statistics. Cell and Tissue Research, 322, 257-267.
[31] Pantic, I., Harhaji-Trajkovic, L., Pantovic, A., Milosevic, N.T. and Trajkovic, V. (2012) Changes in Fractal Dimension and Lacunarity as Early Markers of UV-Induced Apoptosis. Journal of Theoretical Biology, 303, 87-92.
[32] Yuan, J. and Yankner, B.A. (2000) Apoptosis in the Nervous System. Nature, 407, 802-809.
[33] Jakubowicz-Gil1, J., Rzeski, W., Zdzisinska, B., Dobrowolski, L. and Gawron, P.A. (2008) Cell Death and Neuronal Arborization upon Quercetin Treatment in Rat Neurons. Acta Neurobiologiae Experimentalis, 68, 139-146.
[34] Gianinazzi, C., Grandgirard, D., Simon, F., Imboden, H., Joss, P., Täuber, M. and Leib, S.L. (2004) Apoptosis of Hippocampal Neurons in Organotypic Slice Culture Models: Direct Effect of Bacteria Revisited. Journal of Neuropathology & Experimental Neurology, 63, 610-617.
[35] Rajagoplan, V., Liu, Z., Allexandre, D., et al. (2013) Brain White Matter Shape Changes in Amyotrophic Lateral Sclerosis (ALS): A Fractal Dimension Study. PLoS ONE, 8, Article ID: e73614.
[36] King, R.D., Brown, B., Hwang, M., Jeon, T. and George, A.T. (2010) Fractal Dimension Analysis of the Cortical Ribbon in Mild Alzheimer’s Disease. NeuroImage, 53, 471-479.
[37] Kim, J., Kwon, N., Chang, S., Kim, K.T., Lee, D., Kim, S., Yun, S.J., Hwang, D., Kim, J.W., Hwu, Y., Margaritondo, G., Je, J.H. and Rhyu, I.J. (2011) Altered Branching Patterns of Purkinje Cells in Mouse Model for Cortical Development Disorder. Scientific Reports, 1, 122-128.
[38] Pirici, D., Mogoanta, L., Margaritescu, O., et al. (2009) Fractal Analysis of Astrocytes in Stroke and Dementia. Romanian Journal of Morphology and Embryology, 50, 381-390.
[39] Esteban, J., Sepulcre, J., de Miras, J.R., Navas, J., de Mendizábal, N.V., Goñi, J., Ma Quesada, J., Bejarano, B. and Villoslada, P. (2009) Fractal Dimension Analysis of Grey Matter in Multiple Sclerosis. Journal of the Neurological Sciences, 282, 67-71.
[40] Masters, B.R. (2004) Fractal Analysis of the Vascular Tree in the Human Retina. Annual Review of Biomedical Engineering, 6, 427-452.
[41] Milosevic, N.T., Ristanovic, D., Jelinek, H.F. and Rajkovic, K. (2010) Morphology and Cell Classification of Large Neurons in the Adult Human Dentate Nucleus: A Quantitative Study. Neuroscience Letters, 468, 59-63.
[42] Di Ieva, A. (2010) Angioarchitectural Morphometrics of Brain Tumors: Are There Any Potential Histopathological Biomarkers. Microvascolar Research, 80, 522-533.
[43] Reishofer, G., Koschutnig, K., Enzinger, C., Ebner, C. and Ahammer, H. (2012) Fractal Dimension and Vessel Complexity in Patients with Cerebral Arteriovenous Malformations. PLoS ONE, 7, Article ID: e41148.
[44] Nagao, M., Murase, K., Kikuchi, T., Ikeda, M., Nebu, A., Fukuhara, R., Sugawara, Y., Miki, H. and Ikezoe, J. (2001) Fractal Analysis of Cerebral Blood Flow Distribution in Alzheimer’s Disease. Journal of Nuclear Medicine, 42, 1446-1450.
[45] Weibel, E.R. (1991) Fractal Geometry: A Design Principle for Living Organisms. American Journal of Physiology, 261, 361-369.
[46] Honda, H. (1999) Genes Do Not Determine Biological Shape Directly. Forma, 14, 287-293.
[47] Pellionisz, A.J. (2012) The Decade of FractoGene: From Discovery to Utility-Proofs of Concept Open Genome-Based Clinical Applications. International Journal of Systemics, Cybernetics and Informatics, 17-28.
[48] Pellionisz, A. (1989) Neural Geometry: Towards a Fractal Model of Neurons. Cambridge University Press, Cambridge.
[49] Pellionisz, A. (2008) The Principle of Recursive Genome Function. Cerebellum, 7, 348-359.
[50] Agnati, L.F., Guidolin, D., Carone, C., Dam, M., Genedani, S. and Fuxe, K. (2008) Understanding Neuronal Molecular Networks Builds on Neuronal Cellular Network Architecture. Brain Research Reviews, 58, 379-399.
[51] Di Ieva, A., Grizzi, F., Jelinek, H., Pellionisz, A.J. and Losa, G.A. (2013) Fractals in the Neurosciences, Part I: General Principles and Basic Neurosciences. The Neuroscientist. [Epub ahead of print]

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