Toward a more reliable characterization of fractal properties of the cerebral cortex of healthy subjects during the lifespan.
Journal
Scientific reports
ISSN: 2045-2322
Titre abrégé: Sci Rep
Pays: England
ID NLM: 101563288
Informations de publication
Date de publication:
12 10 2020
12 10 2020
Historique:
received:
26
03
2020
accepted:
14
09
2020
entrez:
13
10
2020
pubmed:
14
10
2020
medline:
9
3
2021
Statut:
epublish
Résumé
The cerebral cortex manifests an inherent structural complexity of folding. The fractal geometry describes the complexity of structures which show self-similarity in a proper interval of spatial scales. In this study, we aimed at evaluating in-vivo the effect of different criteria for selecting the interval of spatial scales in the estimation of the fractal dimension (FD) of the cerebral cortex in T
Identifiants
pubmed: 33046812
doi: 10.1038/s41598-020-73961-w
pii: 10.1038/s41598-020-73961-w
pmc: PMC7550568
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
16957Références
Smith, T. G. J., Lange, G. D. & Marks, W. B. Fractal methods and results in cellular morphology—Dimensions, lacunarity and multifractals. J. Neurosci. Methods 69, 123–136 (1996).
doi: 10.1016/S0165-0270(96)00080-5
Sarkar, N. & Chaudhuri, B. B. An efficient differential box-counting approach to compute fractal dimension of image. IEEE Trans. Syst. Man Cybern. 24, 115–120 (1994).
doi: 10.1109/21.259692
Mandelbrot, B. The Fractal Geometry of Nature (Times Books, New York, 1982).
Falconer, K. J. Fractal Geometry: Mathematical Foundations and Applications (Wiley, New York, 2005).
Free, S. L., Sisodiya, S. M., Cook, M. J., Fish, D. R. & Shorvon, S. D. Three-dimensional fractal analysis of the white matter surface from magnetic resonance images of the human brain. Cereb. Cortex 6, 830–836 (1996).
doi: 10.1093/cercor/6.6.830
Foroutan-pour, K., Dutilleul, P. & Smith, D. L. Advances in the implementation of the box-counting method of fractal dimension estimation. Appl. Math. Comput. 105, 195–210 (1999).
Di Ieva, A. The Fractal Geometry of the Brain (Springer, New York, 2016).
doi: 10.1007/978-1-4939-3995-4
Di Ieva, A., Esteban, F. J., Grizzi, F., Klonowski, W. & Martin-Landrove, M. Fractals in the neurosciences, Part II: Clinical applications and future perspectives. Neuroscientist 21, 30–43. https://doi.org/10.1177/1073858413513928 (2015).
doi: 10.1177/1073858413513928
pubmed: 24362814
Di Ieva, A., Grizzi, F., Jelinek, H., Pellionisz, A. J. & Losa, G. A. Fractals in the neurosciences, Part I: General principles and basic neurosciences. Neuroscientist 20, 403–417. https://doi.org/10.1177/1073858413513927 (2014).
doi: 10.1177/1073858413513927
pubmed: 24362815
Reishofer, G. et al. Age is reflected in the fractal dimensionality of MRI diffusion based tractography. Sci. Rep. 8, 5431. https://doi.org/10.1038/s41598-018-23769-6 (2018).
doi: 10.1038/s41598-018-23769-6
pubmed: 29615717
pmcid: 5883031
Cassot, F., Lauwers, F., Fouard, C., Prohaska, S. & Lauwers-Cances, V. A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex. Microcirculation 13, 1–18. https://doi.org/10.1080/10739680500383407 (2006).
doi: 10.1080/10739680500383407
pubmed: 16393942
Panerai, R. B. Complexity of the human cerebral circulation. Philos. Trans. Ser. A math. Phys. Eng. Sci. 367, 1319–1336. https://doi.org/10.1098/rsta.2008.0264 (2009).
doi: 10.1098/rsta.2008.0264
Kiselev, V. G., Hahn, K. R. & Auer, D. P. Is the brain cortex a fractal?. Neuroimage 20, 1765–1774 (2003).
doi: 10.1016/S1053-8119(03)00380-X
Zhang, L., Liu, J. Z., Dean, D., Sahgal, V. & Yue, G. H. A three-dimensional fractal analysis method for quantifying white matter structure in human brain. J. Neurosci. Methods 150, 243–253 (2006).
Liu, J. Z., Zhang, L. D. & Yue, G. H. Fractal dimension in human cerebellum measured by magnetic resonance imaging. Biophys. J. 85, 4041–4046. https://doi.org/10.1016/S0006-3495(03)74817-6 (2003).
doi: 10.1016/S0006-3495(03)74817-6
pubmed: 14645092
pmcid: 1303704
Hofman, M. A. The fractal geometry of convoluted brains. J. Hirnforsch. 32, 103–111 (1991).
pubmed: 1811015
Majumdar, S. & Prasad, R. R. The fractal dimension of cerebral surfaces using magnetic resonance images. Comput. Phys. 2, 69–73. https://doi.org/10.1063/1.168314 (1988).
doi: 10.1063/1.168314
Bullmore, E. et al. Wavelets and functional magnetic resonance imaging of the human brain. Neuroimage 23(Suppl 1), S234-249. https://doi.org/10.1016/j.neuroimage.2004.07.012 (2004).
doi: 10.1016/j.neuroimage.2004.07.012
pubmed: 15501094
Li, Y. C. & Huang, Y. A. Fractal analysis of spontaneous fluctuations of the BOLD signal in the human brain networks. J. Magn. Reson. Imaging 39, 1118–1125. https://doi.org/10.1002/jmri.24274 (2014).
doi: 10.1002/jmri.24274
pubmed: 24027126
Rubin, D., Fekete, T. & Mujica-Parodi, L. R. Optimizing complexity measures for FMRI data: Algorithm, artifact, and sensitivity. PLoS ONE 8, e63448. https://doi.org/10.1371/journal.pone.0063448 (2013).
doi: 10.1371/journal.pone.0063448
pubmed: 23700424
pmcid: 3660309
Cutting, J. E. & Garvin, J. J. Fractal curves and complexity. Percept. Psychophys. 42, 365–370 (1987).
doi: 10.3758/BF03203093
Fernandez, E. & Jelinek, H. F. Use of fractal theory in neuroscience: Methods, advantages, and potential problems. Methods 24, 309–321. https://doi.org/10.1006/meth.2001.1201 (2001).
doi: 10.1006/meth.2001.1201
pubmed: 11465996
Tolle, C. R., McJunkin, T. R., Rohrbaugh, D. T. & LaViolette, R. A. Lacunarity definition for ramified data sets based on optimal cover. Physica D 179, 129–152 (2003).
doi: 10.1016/S0167-2789(03)00029-0
Im, K. et al. Fractal dimension in human cortical surface: Multiple regression analysis with cortical thickness, sulcal depth, and folding area. Hum. Brain Mapp. 27, 994–1003. https://doi.org/10.1002/hbm.20238 (2006).
doi: 10.1002/hbm.20238
pubmed: 16671080
pmcid: 6871396
King, R. D., Brown, B., Hwang, M., Jeon, T. & George, A. T. Fractal dimension analysis of the cortical ribbon in mild Alzheimer’s disease. Neuroimage 53, 471–479. https://doi.org/10.1016/j.neuroimage.2010.06.050 (2010).
doi: 10.1016/j.neuroimage.2010.06.050
pubmed: 20600974
pmcid: 2942777
King, R. D. et al. Characterization of atrophic changes in the cerebral cortex using fractal dimension analysis. Brain Imaging Behav 3, 154–166 (2009).
doi: 10.1007/s11682-008-9057-9
Madan, C. R. & Kensinger, E. A. Cortical complexity as a measure of age-related brain atrophy. Neuroimage 134, 617–629. https://doi.org/10.1016/j.neuroimage.2016.04.029 (2016).
doi: 10.1016/j.neuroimage.2016.04.029
pubmed: 27103141
pmcid: 4945358
Madan, C. R. & Kensinger, E. A. Predicting age from cortical structure across the lifespan. Eur. J. Neurosci. 47, 399–416. https://doi.org/10.1111/ejn.13835 (2018).
doi: 10.1111/ejn.13835
pubmed: 29359873
pmcid: 5835209
Marzi, C. et al. Structural complexity of the cerebellum and cerebral cortex is reduced in spinocerebellar ataxia type 2. J. Neuroimaging 28, 688–693. https://doi.org/10.1111/jon.12534 (2018).
doi: 10.1111/jon.12534
pubmed: 29975004
Pantoni, L. et al. Fractal dimension of cerebral white matter: A consistent feature for prediction of the cognitive performance in patients with small vessel disease and mild cognitive impairment. NeuroImage Clin. 24, 101990 (2019).
doi: 10.1016/j.nicl.2019.101990
Krohn, S. et al. Evaluation of the 3D fractal dimension as a marker of structural brain complexity in multiple-acquisition MRI. Hum. Brain Mapp. 40, 3299–3320. https://doi.org/10.1002/hbm.24599 (2019).
doi: 10.1002/hbm.24599
pubmed: 31090254
pmcid: 6865657
Esteban, F. J. et al. Fractal dimension analysis of grey matter in multiple sclerosis. J. Neurol. Sci. 282, 67–71. https://doi.org/10.1016/j.jns.2008.12.023 (2009).
doi: 10.1016/j.jns.2008.12.023
pubmed: 19167728
Wu, Y. T., Shyu, K. K., Chen, T. R. & Guo, W. Y. Using three-dimensional fractal dimension to analyze the complexity of fetal cortical surface from magnetic resonance images. Nonlinear Dyn. 58(4), 745 (2009).
doi: 10.1007/s11071-009-9515-y
Ha, T. H. et al. Fractal dimension of cerebral cortical surface in schizophrenia and obsessive-compulsive disorder. Neurosci. Lett. 384, 172–176 (2005).
doi: 10.1016/j.neulet.2005.04.078
Nenadic, I., Yotter, R. A., Sauer, H. & Gaser, C. Cortical surface comlexity in frontal and temporal areas varies across subgroups of schizophrenia. Hum. Brain Mapp. 35, 1691–1699 (2014).
doi: 10.1002/hbm.22283
Sandu, A.-L. et al. Fractal dimension analysis of MR images reveals grey matter structure irregularities in schizophrenia. Comput. Med. Imaging Graph. 32, 150–158 (2008).
doi: 10.1016/j.compmedimag.2007.10.005
Sheelakumari, R. et al. Quantitative analysis of grey matter degeneration in FTD patients using fractal dimension analysis. Brain Imaging Behav. https://doi.org/10.1007/s11682-017-9784-x (2017).
doi: 10.1007/s11682-017-9784-x
Losa, G. A. The fractal geometry of life. Riv. Biol. 102, 29–59 (2009).
pubmed: 19718622
Goñi, J. et al. Robust estimation of fractal measures for characterizing the structural complexity of the human brain: Optimization and reproducibility. Neuroimage 83, 646–657. https://doi.org/10.1016/j.neuroimage.2013.06.072 (2013).
doi: 10.1016/j.neuroimage.2013.06.072
pubmed: 23831414
pmcid: 3897251
40Jelinek, H., Elston, N. & Zietsch, B. In Fractals in Biology and Medicine Mathematics and Biosciences in Interaction (eds G. A. Losa, D Merlini, T. F Nonnenmacher, & E. R. Weibel) 85–94 (Birkhauser, 2005).
Caserta, F. et al. Determination of fractal dimension of physiologically characterized neurons in two and three dimensions. J. Neurosci. Methods 56, 133–144 (1995).
doi: 10.1016/0165-0270(94)00115-W
Nooner, K. B. et al. The NKI-rockland sample: A model for accelerating the pace of discovery science in psychiatry. Front. Neurosci. 6, 152. https://doi.org/10.3389/fnins.2012.00152 (2012).
doi: 10.3389/fnins.2012.00152
pubmed: 23087608
pmcid: 3472598
Zuo, X. N. et al. An open science resource for establishing reliability and reproducibility in functional connectomics. Sci. Data 1, 140049. https://doi.org/10.1038/sdata.2014.49 (2014).
doi: 10.1038/sdata.2014.49
pubmed: 25977800
pmcid: 4421932
Jelinek, H. F. & Fernandez, E. Neurons and fractals: How reliable and useful are calculations of fractal dimensions?. J. Neurosci. Methods 81, 9–18 (1998).
doi: 10.1016/S0165-0270(98)00021-1
Mandelbrot, B. How long is the coast of Britain? Statistical self-similarity and fractal dimension. Science 156, 636–638 (1967).
doi: 10.1126/science.156.3775.636
Avnir, D., Biham, O., Lidar, D. & Malcai, O. Is the geometry of nature fractal?. Science 279, 39. https://doi.org/10.1126/science.279.5347.39 (1998).
doi: 10.1126/science.279.5347.39
Pakkenberg, B. et al. Aging and the human neocortex. Exp. Gerontol. 38, 95–99 (2003).
doi: 10.1016/S0531-5565(02)00151-1
Peters, A., Morrison, J. H., Rosene, D. L. & Hyman, B. T. Feature article: Are neurons lost from the primate cerebral cortex during normal aging?. Cereb. Cortex 8, 295–300 (1998).
doi: 10.1093/cercor/8.4.295
Jacobs, B., Driscoll, L. & Schall, M. Life-span dendritic and spine changes in areas 10 and 18 of human cortex: A quantitative Golgi study. J. Comp. Neurol. 386, 661–680 (1997).
doi: 10.1002/(SICI)1096-9861(19971006)386:4<661::AID-CNE11>3.0.CO;2-N
Armstrong, E., Schleicher, A., Omran, H., Curtis, M. & Zilles, K. The ontogeny of human gyrification. Cereb. Cortex 5, 56–63. https://doi.org/10.1093/cercor/5.1.56 (1995).
doi: 10.1093/cercor/5.1.56
pubmed: 7719130
Li, G. et al. Mapping longitudinal development of local cortical gyrification in infants from birth to 2 years of age. J. Neurosci. 34, 4228–4238. https://doi.org/10.1523/JNEUROSCI.3976-13.2014 (2014).
doi: 10.1523/JNEUROSCI.3976-13.2014
pubmed: 24647943
pmcid: 3960466
Cao, B. et al. Lifespan gyrification trajectories of human brain in healthy individuals and patients with major psychiatric disorders. Sci. Rep. 7, 511. https://doi.org/10.1038/s41598-017-00582-1 (2017).
doi: 10.1038/s41598-017-00582-1
pubmed: 28360420
pmcid: 5428697
Hogstrom, L. J., Westlye, L. T., Walhovd, K. B. & Fjell, A. M. The structure of the cerebral cortex across adult life: Age-related patterns of surface area, thickness, and gyrification. Cereb. Cortex 23, 2521–2530. https://doi.org/10.1093/cercor/bhs231 (2013).
doi: 10.1093/cercor/bhs231
pubmed: 22892423
Raznahan, A. et al. How does your cortex grow?. J. Neurosci. 31, 7174–7177. https://doi.org/10.1523/JNEUROSCI.0054-11.2011 (2011).
doi: 10.1523/JNEUROSCI.0054-11.2011
pubmed: 21562281
pmcid: 3157294
White, T., Su, S., Schmidt, M., Kao, C. Y. & Sapiro, G. The development of gyrification in childhood and adolescence. Brain Cogn. 72, 36–45. https://doi.org/10.1016/j.bandc.2009.10.009 (2010).
doi: 10.1016/j.bandc.2009.10.009
pubmed: 19942335
Zilles, K., Palomero-Gallagher, N. & Amunts, K. Development of cortical folding during evolution and ontogeny. Trends Neurosci. 36, 275–284. https://doi.org/10.1016/j.tins.2013.01.006 (2013).
doi: 10.1016/j.tins.2013.01.006
pubmed: 23415112
Haydar, T. F., Kuan, C. Y., Flavell, R. A. & Rakic, P. The role of cell death in regulating the size and shape of the mammalian forebrain. Cereb. Cortex 9, 621–626. https://doi.org/10.1093/cercor/9.6.621 (1999).
doi: 10.1093/cercor/9.6.621
pubmed: 10498280
Kochunov, P. et al. Age-related morphology trends of cortical sulci. Hum. Brain Mapp. 26, 210–220. https://doi.org/10.1002/hbm.20198 (2005).
doi: 10.1002/hbm.20198
pubmed: 16161162
pmcid: 6871665
Magnotta, V. A. et al. Quantitative in vivo measurement of gyrification in the human brain: Changes associated with aging. Cereb. Cortex 9, 151–160. https://doi.org/10.1093/cercor/9.2.151 (1999).
doi: 10.1093/cercor/9.2.151
pubmed: 10220227
Blanton Rebecca, E. et al. Mapping cortical asymmetry and complexity patterns in normal children. Psychiatry Res. Neuroimaging 107(1), 29–43 (2001).
doi: 10.1016/S0925-4927(01)00091-9
Sandu, A. L. et al. Structural brain complexity and cognitive decline in late life—a longitudinal study in the Aberdeen 1936 Birth Cohort. Neuroimage 100, 558–563. https://doi.org/10.1016/j.neuroimage.2014.06.054 (2014).
doi: 10.1016/j.neuroimage.2014.06.054
pubmed: 24993896
Thompson, P. M., Schwartz, C., Lin, R. T., Khan, A. A. & Toga, A. W. Three-dimensional statistical analysis of sulcal variability in the human brain. J. Neurosci. 16, 4261–4274 (1996).
doi: 10.1523/JNEUROSCI.16-13-04261.1996
Mandelbrot, B. B. Is nature fractal?. Science 279, 783–784 (1998).
doi: 10.1126/science.279.5352.783c
Landini, G. & Rigaut, J. P. A method for estimating the dimension of asymptotic fractal sets. Bioimaging 5, 65–70. https://doi.org/10.1002/1361-6374(199706)5:2%3c65::aid-bio3%3e3.0.co;2-e (1997).
doi: 10.1002/1361-6374(199706)5:2<65::aid-bio3>3.0.co;2-e
Milosevic, N. T. & Ristanovic, D. Fractality of dendritic arborization of spinal cord neurons. Neurosci. Lett. 396, 172–176. https://doi.org/10.1016/j.neulet.2005.11.031 (2006).
doi: 10.1016/j.neulet.2005.11.031
pubmed: 16364544
Takeda, T., Ishikawa, A., Ohtomo, K., Kobayashi, Y. & Matsuoka, T. Fractal dimension of dendritic tree of cerebellar Purkinje cell during onto- and phylogenetic development. Neurosci. Res. 13, 19–31. https://doi.org/10.1016/0168-0102(92)90031-7 (1992).
doi: 10.1016/0168-0102(92)90031-7
pubmed: 1314350
Mazziotta, J. et al. A probabilistic atlas and reference system for the human brain: International Consortium for Brain Mapping (ICBM). Philos. Trans. R. Soc. Lond. B Biol. Sci. 356, 1293–1322. https://doi.org/10.1098/rstb.2001.0915 (2001).
doi: 10.1098/rstb.2001.0915
pubmed: 11545704
pmcid: 1088516
Fischl, B. FreeSurfer. Neuroimage 62, 774–781. https://doi.org/10.1016/j.neuroimage.2012.01.021 (2012).
doi: 10.1016/j.neuroimage.2012.01.021
pubmed: 22248573
pmcid: 3685476
Russell, D. A., Hanson, J. D. & Ott, E. Dimension of strange attractors. Phys. Rev. Lett. 45, 1175–1178 (1980).
doi: 10.1103/PhysRevLett.45.1175
Feder, J. Fractals. Vol. XXVI 284 (Springer US, 1988).
Barnsley, M. F. Fractals Everywhere (Dover Publications, Mineola, 1988).
Panico, J. & Sterling, P. Retinal neurons and vessels are not fractal but space-filling. J. Comp. Neurol. 361, 479–490. https://doi.org/10.1002/cne.903610311 (1995).
doi: 10.1002/cne.903610311
pubmed: 8550894
Cole, T. J. Too many digits: The presentation of numerical data. Arch. Dis. Child. 100, 608–609. https://doi.org/10.1136/archdischild-2014-307149 (2015).
doi: 10.1136/archdischild-2014-307149
pubmed: 25877157
pmcid: 4483789
Diciotti, S., Ciulli, S., Mascalchi, M., Giannelli, M. & Toschi, N. The, “peeking” effect in supervised feature selection on diffusion tensor imaging data. AJNR Am. J. Neuroradiol. 34, E107. https://doi.org/10.3174/ajnr.A3685 (2013).
doi: 10.3174/ajnr.A3685
pubmed: 23868167
Noirhomme, Q. et al. Biased binomial assessment of cross-validated estimation of classification accuracies illustrated in diagnosis predictions. NeuroImage. Clin. 4, 687–694. https://doi.org/10.1016/j.nicl.2014.04.004 (2014).
doi: 10.1016/j.nicl.2014.04.004
pubmed: 24936420
pmcid: 4053638
Nichols, T. E. & Holmes, A. P. Nonparametric permutation tests for functional neuroimaging: A primer with examples. Hum. Brain Mapp. 15, 1–25 (2002).
doi: 10.1002/hbm.1058