Abstract
Physicians and scientists can use fractal analysis as a tool to objectively quantify complex patterns found in neuroscience and neurology. Fractal analysis has the potential to allow physicians to make predictions about clinical outcomes, categorize pathological states, and eventually generate diagnoses. In this review, we categorize and analyze the applications of fractal theory in neuroscience found in the literature. We discuss how fractals are applied and what evidence exists for fractal analysis in neurodegeneration, neoplasm, neurodevelopment, neurophysiology, epilepsy, neuropharmacology, and cell morphology. The goal of this review is to introduce the medical community to the utility of applying fractal theory in clinical neuroscience.
References
Al-Kadi, O.S. (2015). A multiresolution clinical decision support system based on fractal model design for classification of histological brain tumours. Comput. Med. Imaging Graph. 41, 67–79.10.1016/j.compmedimag.2014.05.013Suche in Google Scholar
Arle, J.E. and Simon, R.H. (1990). An application of fractal dimension to the detection of transients in the electroencephalogram. Electroencephalogr. Clin. Neurophysiol. 75, 296–305.10.1016/0013-4694(90)90108-VSuche in Google Scholar
Bernard, F., Bossu, J.L., and Gaillard, S. (2001). Identification of living oligodendrocyte developmental stages by fractal analysis of cell morphology. J. Neurosci. Res. 65, 439–445.10.1002/jnr.1172Suche in Google Scholar
Bourke, P. (2003). Fractal Dimension Calculator. Available at: http://paulbourke.net/fractals/fracdim/. Accessed March 10, 2015.Suche in Google Scholar
Bullmore, E.T., Brammer, M.J., Bourlon, P., Alarcon, G., Polkey, C.E., Elwes, R., and Binnie, C.D. (1994). Fractal analysis of electroencephalographic signals intracerebrally recorded during 35 epileptic seizures: evaluation of a new method for synoptic visualisation of ictal events. Electroencephalogr. Clin. Neurophysiol. 91, 337–345.10.1016/0013-4694(94)00181-2Suche in Google Scholar
Cook, M.J., Free, S.L., Manford, M.R., Fish, D.R., Shorvon, S.D., and Stevens, J.M. (1995). Fractal description of cerebral cortical patterns in frontal lobe epilepsy. Eur. Neurol. 35, 327–335.10.1159/000117155Suche in Google Scholar PubMed
Costa, A. (2013). Hausdorff Fractal Dimension. MatLab Central. Available at: http://www.mathworks.com/matlabcentral/fileexchange/30329-hausdorff--box-counting--fractal-dimension. Accessed March 10, 2015.Suche in Google Scholar
Crampton, S. (2012). A Java Applet to Compute Fractal Dimension. Available at: http://www.stevec.org/fracdim/. Accessed March 10, 2015.Suche in Google Scholar
Di Ieva, A., Grizzi, F., Ceva-Grimaldi, G., Russo, C., Gaetani, P., Aimar, E., Levi, D., Pisano, P., Tancioni, F., Nicola, G., et al. (2007). Fractal dimension as a quantitator of the microvasculature of normal and adenomatous pituitary tissue. J. Anat. 211, 673–680.10.1111/j.1469-7580.2007.00804.xSuche in Google Scholar PubMed PubMed Central
Di Ieva, A., Grizzi, F., Ceva-Grimaldi, G., Aimar, E., Serra, S., Pisano, P., Lorenzetti, M., Tancioni, F., Gaetani, P., Crotti, F., et al. (2010a). The microvascular network of the pituitary gland: a model for the application of fractal geometry to the analysis of angioarchitecture and angiogenesis of brain tumors. J. Neurosurg. Sci. 54, 49–54.Suche in Google Scholar
Di Ieva, A., Grizzi, F., Tschabitscher, M., Colombo, P., Casali, M., Simonelli, M., Widhalm, G., Muzzio, P.C., Matula, C., Chiti, A., et al. (2010b). Correlation of microvascular fractal dimension with positron emission tomography [(11)C]-methionine uptake in glioblastoma multiforme: preliminary findings. Microvasc. Res. 80, 267–273.10.1016/j.mvr.2010.04.003Suche in Google Scholar PubMed
Di Ieva, A., Bruner, E., Widhalm, G., Minchev, G., Tschabitscher, M., and Grizzi, F. (2012a). Computer-assisted and fractal-based morphometric assessment of microvascularity in histological specimens of gliomas. Sci. Rep. 2, 429.10.1038/srep00429Suche in Google Scholar PubMed PubMed Central
Di Ieva, A., Matula, C., Grizzi, F., Grabner, G., Trattnig, S., and Tschabitscher, M. (2012b). Fractal analysis of the susceptibility weighted imaging patterns in malignant brain tumors during antiangiogenic treatment: technical report on four cases serially imaged by 7 T magnetic resonance during a period of four weeks. World Neurosurg. 77, 785 e711–721.10.1016/j.wneu.2011.09.006Suche in Google Scholar PubMed
Di Ieva, A., God, S., Grabner, G., Grizzi, F., Sherif, C., Matula, C., Tschabitscher, M., and Trattnig, S. (2013a). Three-dimensional susceptibility-weighted imaging at 7 T using fractal-based quantitative analysis to grade gliomas. Neuroradiology 55, 35–40.10.1007/s00234-012-1081-1Suche in Google Scholar PubMed
Di Ieva, A., Grizzi, F., Jelinek, H., Pellionisz, A.J., and Losa, G.A. (2013b). Fractals in the neurosciences, Part I: general principles and basic neurosciences. Neuroscientist 20, 403–417.10.1177/1073858413513927Suche in Google Scholar PubMed
Di Ieva, A., Esteban, F.J., Grizzi, F., Klonowski, W., and Martin-Landrove, M. (2015). Fractals in the neurosciences, Part II: clinical applications and future perspectives. Neuroscientist 21, 30–43.10.1177/1073858413513928Suche in Google Scholar PubMed
Fernandez, E. and Jelinek, H.F. (2001). Use of fractal theory in neuroscience: methods, advantages, and potential problems. Methods 24, 309–321.10.1006/meth.2001.1201Suche in Google Scholar PubMed
Free, S.L., Sisodiya, S.M., Cook, M.J., Fish, D.R., and Shorvon, S.D. (1996). Three-dimensional fractal analysis of the white matter surface from magnetic resonance images of the human brain. Cereb. Cortex 6, 830–836.10.1093/cercor/6.6.830Suche in Google Scholar PubMed
Gazit, Y., Baish, J.W., Safabakhsh, N., Leunig, M., Baxter, L.T., and Jain, R.K. (1997). Fractal characteristics of tumor vascular architecture during tumor growth and regression. Microcirculation 4, 395–402.10.3109/10739689709146803Suche in Google Scholar PubMed
Gomez, C., Mediavilla, A., Hornero, R., Abasolo, D., and Fernandez, A. (2009). Use of the Higuchi’s fractal dimension for the analysis of MEG recordings from Alzheimer’s disease patients. Med. Eng. Phys. 31, 306–313.10.1016/j.medengphy.2008.06.010Suche in Google Scholar PubMed
Grizzi, F., Weber, C., and Di Ieva, A. (2008). Antiangiogenic strategies in medulloblastoma: reality or mystery. Pediatr. Res. 63, 584–590.10.1203/01.pdr.0000305884.29279.6bSuche in Google Scholar PubMed
Hadjidimitriou, S., Zacharakis, A., Doulgeris, P., Panoulas, K., Hadjileontiadis, L., and Panas, S. (2010). Sensorimotor cortical response during motion reflecting audiovisual stimulation: evidence from fractal EEG analysis. Med. Biol. Eng. Comput. 48, 561–572.10.1007/s11517-010-0606-1Suche in Google Scholar PubMed
Hadjidimitriou, S.K., Zacharakis, A.I., Doulgeris, P.C., Panoulas, K.J., Hadjileontiadis, L.J., and Panas, S.M. (2011). Revealing action representation processes in audio perception using fractal EEG analysis. IEEE Trans. Biomed. Eng. 58, 1120–1129.10.1109/TBME.2010.2047016Suche in Google Scholar PubMed
Hofman, M.A. (1991). The fractal geometry of convoluted brains. J. Hirnforsch. 32, 103–111.Suche in Google Scholar
Im, K., Lee, J.M., Yoon, U., Shin, Y.W., Hong, S.B., Kim, I.Y., Kwon, J.S., and Kim, S.I. (2006). Fractal dimension in human cortical surface: multiple regression analysis with cortical thickness, sulcal depth, and folding area. Hum. Brain Mapp. 27, 994–1003.10.1002/hbm.20238Suche in Google Scholar PubMed PubMed Central
Kalmanti, E. and Maris, T.G. (2007). Fractal dimension as an index of brain cortical changes throughout life. In Vivo 21, 641–646.Suche in Google Scholar
Karperien, A., Ahammer, H., and Jelinek, H.F. (2013). Quantitating the subtleties of microglial morphology with fractal analysis. Front. Cell. Neurosci. 7, 3.10.3389/fncel.2013.00003Suche in Google Scholar PubMed PubMed Central
Kedzia, A., Rybaczuk, M., and Andrzejak, R. (2002). Fractal dimensions of human brain cortex vessels during the fetal period. Med. Sci. Monit. 8, MT46–51.Suche in Google Scholar
Kekovic, G., Culic, M., Martac, L., Stojadinovic, G., Capo, I., Lalosevic, D., and Sekulic, S. (2010a). Fractal dimension values of cerebral and cerebellar activity in rats loaded with aluminium. Med. Biol. Eng. Comput. 48, 671–679.10.1007/s11517-010-0620-3Suche in Google Scholar PubMed
Kekovic, G., Stojadinovic, G., Martac, L., Podgorac, J., Sekulic, S., and Culic, M. (2010b). Spectral and fractal measures of cerebellar and cerebral activity in various types of anesthesia. Acta Neurobiol. Exp. (Wars) 70, 67–75.Suche in Google Scholar
King, R.D., George, A.T., Jeon, T., Hynan, L.S., Youn, T.S., Kennedy, D.N., and Dickerson, B. (2009). Characterization of atrophic changes in the cerebral cortex using fractal dimensional analysis. Brain Imaging Behav. 3, 154–166.10.1007/s11682-008-9057-9Suche in Google Scholar PubMed PubMed Central
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, 471–479.10.1016/j.neuroimage.2010.06.050Suche in Google Scholar PubMed PubMed Central
Kuikka, J.T., Tiihonen, J., Karhu, J., Bergstrom, K.A., and Rasanen, P. (1997). Fractal analysis of striatal dopamine re-uptake sites. Eur. J. Nucl. Med. 24, 1085–1090.Suche in Google Scholar
Lee, J.S., Lee, D.S., Park, K.S., Chung, J.K., and Lee, M.C. (2004). Changes in the heterogeneity of cerebral glucose metabolism with healthy aging: quantitative assessment by fractal analysis. J. Neuroimaging. 14, 350–356.10.1111/j.1552-6569.2004.tb00262.xSuche in Google Scholar
Li, X., Polygiannakis, J., Kapiris, P., Peratzakis, A., Eftaxias, K., and Yao, X. (2005). Fractal spectral analysis of pre-epileptic seizures in terms of criticality. J. Neural. Eng. 2, 11–16.10.1088/1741-2560/2/2/002Suche in Google Scholar PubMed
Losa, G. (2009). The fractal geometry of life. Riv. Biol. 1, 29–59.Suche in Google Scholar
Manabe, Y., Honda, E., Shiro, Y., Sakai, K., Kohira, I., Kashihara, K., Shohmori, T., and Abe, K. (2001). Fractal dimension analysis of static stabilometry in Parkinson’s disease and spinocerebellar ataxia. Neurol. Res. 23, 397–404.10.1179/016164101101198613Suche in Google Scholar PubMed
Mandelbrot, B. (1994). A Fractal’s Lacunarity, and How It Can Be Tuned and Measured. Fractals in Biology and Medicine. T. F. Nonnenmacher, G. A. Losa, and E. R. Weibel, eds. (Basel: Birkhauser), pp. 8–21.10.1007/978-3-0348-8501-0_2Suche in Google Scholar
Martin-Landrove, M., Pereira, D., Caldeira, M.E., Itriago, S., and Juliac, M. (2007). Fractal analysis of tumoral lesions in brain. Conf. Proc. IEEE Eng. Med. Biol. Soc., 2007, 1306–1309.Suche in Google Scholar
Milosevic, N.T., Ristanovic, D., Gudovic, R., Rajkovic, K., and Maric, D. (2007). Application of fractal analysis to neuronal dendritic arborisation patterns of the monkey dentate nucleus. Neurosci. Lett. 425, 23–27.10.1016/j.neulet.2007.08.009Suche in Google Scholar PubMed
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. J. Nucl. Med. 42, 1446–1450.Suche in Google Scholar
Paramanathan, P. and Uthayakumar, R. (2008). Application of fractal theory in analysis of human electroencephalographic signals. Comput. Biol. Med. 38, 372–378.10.1016/j.compbiomed.2007.12.004Suche in Google Scholar PubMed
Parker, D. and Srivastava, V. (2013). Dynamic systems approaches and levels of analysis in the nervous system. Front. Physiol. 4, 15.10.3389/fphys.2013.00015Suche in Google Scholar
Pirici, D., Mogoanta, L., Margaritescu, O., Pirici, I., Tudorica, V., and Coconu, M. (2009). Fractal analysis of astrocytes in stroke and dementia. Rom. J. Morphol. Embryol. 50, 381–390.Suche in Google Scholar
Pirici, D., Van Cauwenberghe, C., Van Broeckhoven, C., and Kumar-Singh, S. (2011). Fractal analysis of amyloid plaques in Alzheimer’s disease patients and mouse models. Neurobiol. Aging 32, 1579–1587.10.1016/j.neurobiolaging.2009.10.010Suche in Google Scholar
Porter, R., Ghosh, S., Lange, G.D., and Smith, T.G., Jr. (1991). A fractal analysis of pyramidal neurons in mammalian motor cortex. Neurosci. Lett. 130, 112–116.10.1016/0304-3940(91)90240-TSuche in Google Scholar
Pressman, A. (2000). Synchronization analysis of multichannel EEG of schizophrenic during working-memory task. 21st IEEE Convention of the Electrical and Electronic Engineers in Israel, Tel-Aviv, 11 April 2000–12 April 2000, pp. 337–341.Suche in Google Scholar
Risser, L., Plouraboue, F., Steyer, A., Cloetens, P., Le Duc, G., and Fonta, C. (2007). From homogeneous to fractal normal and tumorous microvascular networks in the brain. J. Cereb. Blood Flow Metab. 27, 293–303.10.1038/sj.jcbfm.9600332Suche in Google Scholar
Russel, D., Hanson, J., and Ott, E. (1980). Dimension of strange attractors. Phys. Rev. Lett. 45, 1175–1178.10.1103/PhysRevLett.45.1175Suche in Google Scholar
Soltys, Z., Ziaja, M., Pawlinski, R., Setkowicz, Z., and Janeczko, K. (2001). Morphology of reactive microglia in the injured cerebral cortex. Fractal analysis and complementary quantitative methods. J. Neurosci. Res. 63, 90–97.10.1002/1097-4547(20010101)63:1<90::AID-JNR11>3.0.CO;2-9Suche in Google Scholar
Spasic, S., Kalauzi, A., Culic, M., Grbic, G., and Martac, L. (2005a). Estimation of parameter kmax in fractal analysis of rat brain activity. Ann. N. Y. Acad. Sci. 1048, 427–429.Suche in Google Scholar
Spasic, S., Kalauzi, A., Grbic, G., Martac, L., and Culic, M. (2005b). Fractal analysis of rat brain activity after injury. Med. Biol. Eng. Comput. 43, 345–348.10.1007/BF02345811Suche in Google Scholar
Spasic, S., Culic, M., Grbic, G., Martac, L., Sekulic, S., and Mutavdzic, D. (2008). Spectral and fractal analysis of cerebellar activity after single and repeated brain injury. Bull. Math. Biol. 70, 1235–1249.10.1007/s11538-008-9306-5Suche in Google Scholar
Takeda, T., Ishikawa, A., Ohtomo, K., Kobayashi, Y., and Matsuoka, T. (1992). Fractal dimension of dendritic tree of cerebellar Purkinje cell during onto- and phylogenetic development. Neurosci. Res. 13, 19–31.10.1016/0168-0102(92)90031-7Suche in Google Scholar
Warsi, M.A., Molloy, W., and Noseworthy, M.D. (2012). Correlating brain blood oxygenation level dependent (BOLD) fractal dimension mapping with magnetic resonance spectroscopy (MRS) in Alzheimer’s disease. MAGMA 25, 335–344.10.1007/s10334-012-0312-0Suche in Google Scholar
Wu, Y.T., Shyu, K.K., Jao, C.W., Wang, Z.Y., Soong, B.W., Wu, H.M., and Wang, P.S. (2010). Fractal dimension analysis for quantifying cerebellar morphological change of multiple system atrophy of the cerebellar type (MSA-C). Neuroimage 49, 539–551.10.1016/j.neuroimage.2009.07.042Suche in Google Scholar PubMed
Zhang, L., Dean, D., Liu, J.Z., Sahgal, V., Wang, X., and Yue, G.H. (2007). Quantifying degeneration of white matter in normal aging using fractal dimension. Neurobiol. Aging 28, 1543–1555.10.1016/j.neurobiolaging.2006.06.020Suche in Google Scholar PubMed
©2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Magnetic resonance spectroscopy of the brain: a review of physical principles and technical methods
- The utility of fractal analysis in clinical neuroscience
- The importance of the negative blood-oxygenation-level-dependent (BOLD) response in the somatosensory cortex
- Electric foot shock stress: a useful tool in neuropsychiatric studies
- Tryptophan hydroxylase 2 in seasonal affective disorder: underestimated perspectives?
- Receptor for advanced glycation end-products in neurodegenerative diseases
- Phytochemical constituents as future antidepressants: a comprehensive review
- Spotting psychopaths using technology
Artikel in diesem Heft
- Frontmatter
- Magnetic resonance spectroscopy of the brain: a review of physical principles and technical methods
- The utility of fractal analysis in clinical neuroscience
- The importance of the negative blood-oxygenation-level-dependent (BOLD) response in the somatosensory cortex
- Electric foot shock stress: a useful tool in neuropsychiatric studies
- Tryptophan hydroxylase 2 in seasonal affective disorder: underestimated perspectives?
- Receptor for advanced glycation end-products in neurodegenerative diseases
- Phytochemical constituents as future antidepressants: a comprehensive review
- Spotting psychopaths using technology