From the Big Bang theory to the fractal geometry: a systemic reflection for Alzheimer’s disease

Maria Gabriela Valle Gottlieb


The continuous process of the universe expansion is triggering global cooling, energy loss and its “degeneration”. Delineating an analogy between the process of expansion or “aging” of the universe and neurodegeneration, such as occurs in Alzheimer’s disease, is a difficult and complex task. However, assuming that we are an integral part of the universe, sharing the same atoms and particles as well as the same laws that govern it, we can make use of philosophical, scientific and technological tools to help us better understand both the universal and neurodegenerative phenomena. The complexity and chaos theories and fractal geometry bring light on these issues and provide a better understanding about this inseparable, self-creative, self-organized “disorder” which involves all complex systems. In addition, fractal geometry has been described as a useful tool to improve the description of neurons’ image. However, fractal dimension alone does not completely specify the morphology of a cell, in fact it is a statistical parameter to identify and differentiate the neuronal cell types. Studies have shown that fractal dimension is correlated with cognitive impairment, and that the fractal dimension analysis can be a useful method for assessing the Alzheimer’s disease progression. Within this context, the purpose of this manuscript is to perform a systemic reflection on what may be associated with Alzheimer’s disease in the light of concepts of physics, mathematics and biological sciences.


Aging; Universe; Complexity theory; Chaos theory; Fractal geometry; Alzheimer’s disease.


Gamow G. The Evolution of the Universe. Nature. 1948;162:680-2.

Hubble E. A relation between distance and radial velocity among extra-galactic nebulae. PNAS. 1929;15:168-73.

Bugaj R. Corpus Hermeticum in history. Kwart Hist Nauki Tech. 2001;46(4):7-36.


Holm S. Does chaos theory have major implications for philosophy of medicine. Med Humanit. 2002;28(78-81):78.

Sharma V. Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier. Open Cardiovasc Med J. 2009;3:110-23

Capra F. A teia da via. Uma nova compreensão científica dos sistemas vivos. 11ed. São Paulo: Editora Cultrix; 1996.

Lorenz EN. Deterministic nonperiodic flow. J Atmos Sciences. 1662;20:130-41.

Damasceno BP. Envelhecimento cerebral. O problema dos limites entre o normal e o patológico. Arq Neuropsiquiatr. 1999;57(1):78-83.

Nordon DG, Guimarães RR, Kozonoe DY, et al. Perda cognitiva em idosos. Rev Fac Cienc Med Sorocaba. 2009;11(3):5-8.

Dorszewska J. Cell biology of normal brain aging: synaptic plasticity-cell death. Aging Clin Exp Res. 2013;25(1):25-34.

Dukart J, Schroeter ML, Mueller K, Alzheimer’s Disease Neuroimaging I. Age correction in dementia – matching to a healthy brain. PloS one. 2011;6(7):e22193.

Heilig CW, Knopmann DS, Maestri AR. Dementia without Alzheimer pathology. Neurology. 1985;35(5):762-5.

Clark CM, Sharon X, Chittams KD, et al. Cerebrospinal fluid tau and beta amyloid. How well do these biomarkers reflect autopsy-confirmed dementia diagnoses? Arch Neurol. 2003;60:1696-702.

Katzman R, Terry R, De Teresa R et al. Clinical, pathological, and neurochemical changes in dementia: a subgroup with preserved mental status and numerous neocortical plaques. Ann Neurol. 2004;23(2):138-44.

Prince M, Acosta D, Ferri CP, et al. Dementia incidence and mortality in middle-income countries, and associations with indicators of cognitive reserve: a 10/66 Dementia Research Group population-based cohort study. Lancet. 2012;380(9836):50-8.

Nithianantharajah J, Hannan AJ. The neurobiology of brain and cognitive reserve: mental and physical activity as modulators of brain disorders. Prog Neurobiol. 2009;89(4):369-82.

Machado JC, Ribeiro RCL, Cotta RMM, et al. Declínio cognitivo de idosos e sua associação com fatores epidemiológicos em Viçosa, Minas Gerais. Rev Bras Geriat Gerontol. 2011;14(1):109-21.

Santos CS. Visão termodinâmica de alguns processo biológicos. Brasília, DF: Universidade Católica de Brasília; 2010.

Fernandez E, Jelinek HF. Use of fractal theory in neuroscience: methods, advantages, and potential problems. Methods. 2001;24(4):309-21.

Mandelbrot BB. Self-Affine Fractals and Fractal Dimension. Physica Scripta. 1985;32:257-60.

Mandelbrot BB. The fractal geometry of nature. New York: W.H. Freeman and Company; 1982.

Di Ieva A, Esteban FJ, Grizzi F, et al. Fractals in the neurosciences, Part II: clinical applications and future perspectives. Neuroscientist. 2015;21(1):30-43.

Iannaccone PM, Khokha M. Fractal Geometry in Biological Systems: An Analytical Approach. New York: CRC Press; 1996. 384 p.

Karperien A, Jelinek HF, Milošević NT. Multifractals: a Review with an Application in Neuroscience. In: IAFA, editor. CSCS18-18th International Conference on Control Systems and Computer Science: Fifth Symposium on Interdisciplinary Approaches in Fractal Analysis Proceedings; Bucharest, Romania: Politehnica press; 2011. p. 888-93.

Vicsek T, Family F, Meakin P. Multifractal Geometry of Diffusion-Limited Aggregates. Europhys Lett. 1990; 12(3):217-22.

Zhang L, Dean D, Liu JZ, et al. Quantifying degeneration of white matter in normal aging using fractal dimension. Neurobiol Aging. 2007;28(10):1543-55.

King RD, Brown B, Hwang M, et al, Alzheimer’s Disease Neuroimaging I. Fractal dimension analysis of the cortical ribbon in mild Alzheimer’s disease. Neuroimage. 2010;53(2):471-9.

Nagao M, Sugawara Y, Ikeda M, et al. Heterogeneity of cerebral blood flow in frontotemporal lobar degeneration and Alzheimer’s disease. Eur J Nucl Med Mol Imaging. 2004;31(2):162-8.

Nagao M, Sugawara Y, Ikeda M, et al. Heterogeneity of posterior limbic perfusion in very early Alzheimer’s disease. Neurosci Res. 2006;55(3):285-91.

Nagao M, Murase K, Kikuchi T, et al. Fractal analysis of cerebral blood flow distribution in Alzheimer’s disease. J Nucl Med. 2001;42(10):1446-50.

Driver SP, Wright AH, Andrews SK, et al. Galaxy And Mass Assembly (GAMA) project. International Astronomical Union XXIX General Assembly in Honolulu, Hawaii, 10 August 2015.

Goldberger JP, Rigney DR, West BJ. Chaos and fractals in human physiology. Scientific American. 1990;262(2): 42-9.

Sussillo D, Abbott LF. Generating coherent patterns of activity from chaotic neural networks. Neuron. 2009;63: 544-57.

Buonomano DV, Maass W. State-dependent computations: spatiotemporal processing in cortical networks. Nat Rev Neurosci. 2009;10(2):113-25.

Laje R, Buonomano DV. Robust timing and motor patterns by taming chaos in recurrent neural networks. Nat Neurosci. 2013;16(7):925-33.

Borges-Osório MR, Robinson WM. Genética Humana. Porto Alegre-RS: Artmed.; 2013.


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