Fractals in Neuroimaging.

Classification Computed tomography Detrended fluctuation analysis Fractal dimension Hurst exponent Magnetic resonance imaging Neuroimaging Statistical tests

Journal

Advances in neurobiology
ISSN: 2190-5215
Titre abrégé: Adv Neurobiol
Pays: United States
ID NLM: 101571545

Informations de publication

Date de publication:
2024
Historique:
medline: 12 3 2024
pubmed: 12 3 2024
entrez: 12 3 2024
Statut: ppublish

Résumé

Several natural phenomena can be described by studying their statistical scaling patterns, hence leading to simple geometrical interpretation. In this regard, fractal geometry is a powerful tool to describe the irregular or fragmented shape of natural features, using spatial or time-domain statistical scaling laws (power-law behavior) to characterize real-world physical systems. This chapter presents some works on the usefulness of fractal features, mainly the fractal dimension and the related Hurst exponent, in the characterization and identification of pathologies and radiological features in neuroimaging, mainly, magnetic resonance imaging.

Identifiants

pubmed: 38468046
doi: 10.1007/978-3-031-47606-8_22
doi:

Types de publication

Journal Article

Langues

eng

Sous-ensembles de citation

IM

Pagination

429-444

Informations de copyright

© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.

Références

Akar E, Kara S, Akdemir H, Kiris A. Fractal dimension analysis of cerebellum in chiari malformation type I. Comput Biol Med. 2015;64:179–86.
doi: 10.1016/j.compbiomed.2015.06.024 pubmed: 26189156
Bui AV, Manasseh R, Liffman K, Sutalo ID. Development of optimized vascular fractal tree models using level set distance function. Med Eng Phys. 2010;32:790–4.
doi: 10.1016/j.medengphy.2010.04.014 pubmed: 20472487
Di Ieva A, Matula C, Grizzi F, Grabner G, Trattnig S, Tschabitscher M. 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. 2012;77(785):e11–21.
Di Ieva A, God S, Grabner G, Grizzi F, Sherif C, Matula C, et al. Three-dimensional susceptibility-weighted imaging at 7 T using fractal-based quantitative analysis to grade gliomas. Neuroradiology. 2013;55:35–40.
doi: 10.1007/s00234-012-1081-1 pubmed: 22903580
Di Ieva A, Boukadoum M, Lahmiri S, Cusimano MD. Computational analyses of arteriovenous malformations in neuroimaging. J Neuroimaging. 2014;25:354–60.
doi: 10.1111/jon.12200 pubmed: 25521662
Di Ieva A, Esteban FJ, Grizzi F, Klonowski W, Martin-Landrove M. Fractals in the neurosciences, part II: clinical applications and future perspectives. Neuroscientist. 2015;21:30–43.
doi: 10.1177/1073858413513928 pubmed: 24362814
Di Ieva A, Le Reste PJ, Carsin-Nicol B, Ferre JC, Cusimano MD. Diagnostic value of fractal analysis for the differentiation of brain tumors using 3-tesla MR susceptibility-weighted imaging. Neurosurgery. 2016;79(6):830–46.
Di Matteo T. Multi-scaling in finance. Quant Finan. 2007;7:36.
doi: 10.1080/14697680600969727
Esteban FJ, Sepulcre J, de Mendizabal NV, Goni J, Navas J, de Miras JR, et al. Fractal dimension and white matter changes in multiple sclerosis. NeuroImage. 2007;36:543–9.
doi: 10.1016/j.neuroimage.2007.03.057 pubmed: 17499522
Esteban FJ, Sepulcre J, de Miras JR, Navas J, de Mendizabal NV, Goni J, et al. Fractal dimension analysis of grey matter in multiple sclerosis. J Neurol Sci. 2009;282:67–71.
doi: 10.1016/j.jns.2008.12.023 pubmed: 19167728
Feder J. Fractals. New York: Plenum Press; 1988.
doi: 10.1007/978-1-4899-2124-6
Gonzalez RC, Woods RE. Digital image processing. 3rd ed. Prentice Hall: Pearson; 2009.
Haykin S. Neural networks and learning machines. 3rd ed. Prentice Hall: Pearson; 2008.
Huang NE, Shen Z, Long SR. A new view of water waves – the Hilbert spectrum. Annu Rev Fluid Mech. 1999;31:417–57.
doi: 10.1146/annurev.fluid.31.1.417
Hurst HE. Long-term storage capacity of reservoirs. Trans Am Soc Civ Eng. 1951;116:770–808.
doi: 10.1061/TACEAT.0006518
Iftekharuddin KM, Zheng J, Islam MA, Ogg RJ. Fractal-based brain tumor detection in multimodal MRI. Appl Math Comput. 2009;207:23–41.
Jang K, Russo C, Di Ieva A. Radiomics in gliomas: clinical implications of computational modeling and fractal-based analysis. Neuroradiology. 2020;62(7):771–90. https://doi.org/10.1007/s00234-020-02403-1 .
doi: 10.1007/s00234-020-02403-1 pubmed: 32249351
Jayasuriya SA, Liew AW, Law NF. Brain symmetry plane detection based on fractal analysis. Comput Med Imaging Graph. 2013;37:568–80.
doi: 10.1016/j.compmedimag.2013.06.001 pubmed: 23820390
Jian B, Vemuri BC, Ozarslan E, Carney PR, Mareci TH. A novel tensor distribution model for the diffusion-weighted MR signal. NeuroImage. 2007;37:164–76.
doi: 10.1016/j.neuroimage.2007.03.074 pubmed: 17570683
Jian A, Jang K, Russo C, Liu S, Di Ieva A. Foundations of multiparametric brain tumour imaging characterisation using machine learning. Acta Neurochir Suppl. 2022;134:183–93. https://doi.org/10.1007/978-3-030-85292-4_22 .
doi: 10.1007/978-3-030-85292-4_22 pubmed: 34862542
Jolliffe IT. Principal component analysis. 2nd ed. New York: Springer-Verlag; 2002.
King RD, et al. Characterization of atrophic changes in the cerebral cortex using fractal dimensional analysis. Brain Imaging Behav. 2009;3(2):154–66.
doi: 10.1007/s11682-008-9057-9 pubmed: 20740072 pmcid: 2927230
King RD, Brown B, Hwang M, Jeon T, George AT. Alzheimer’s disease neuroimaging initiative. Fractal dimension analysis of the cortical ribbon in mild alzheimer’s disease. NeuroImage. 2010;53:471–9.
doi: 10.1016/j.neuroimage.2010.06.050 pubmed: 20600974
Lahmiri S, Boukadoum M. Automatic brain MR images diagnosis based on edge fractal dimension and spectral signature. IEEE EMBC. 2012a;2012:6243–6.
pubmed: 23367356
Lahmiri S, Boukadoum M. Automatic brain MR images diagnosis based on edge fractal dimension and spectral energy signature. Conf Proc IEEE Eng Med Biol Soc. 2012b;2012:6243–6.
Lahmiri S, Boukadoum M. Automatic detection of alzheimer disease in brain magnetic resonance images using fractal features. IEEE EMBC Neural Eng. 2013a;1508:1508.
Lahmiri S, Boukadoum M. Alzheimer’s disease detection in brain magnetic resonance images using multiscale fractal analysis. ISRN Radiol. 2013b;2013:627303.
doi: 10.5402/2013/627303 pubmed: 24967286 pmcid: 4045563
Lahmiri S, Boukadoum M. New approach for automatic classification of alzheimer’s disease, mild cognitive impairment and healthy brain magnetic resonance images. IET Healthc Technol Lett. 2014;1:32–6.
doi: 10.1049/htl.2013.0022
Lahmiri S, Boukadoum M, Di Ieva A. Detrended fluctuation analysis of brain hemisphere magnetic resonance imaging to detect cerebral arteriovenous malformations. In: Circuits and systems (ISCAS), IEEE international symposium; 2014. p. 2409–12.
doi: 10.1109/ISCAS.2014.6865658
Liu S, Meng T, Russo C, Di Ieva A, Berkovsky S, Peng L, Dou W, Qian L. Brain volumetric and fractal analysis of synthetic MRI: a comparative study with conventional 3D T1-weighted images. Eur J Radiol. 2021;141:109782. https://doi.org/10.1016/j.ejrad.2021.109782 .
doi: 10.1016/j.ejrad.2021.109782 pubmed: 34049059
Mandelbrot BB, Wallis JR. Noah, Joseph, and operational hydrology. Water Resour Res. 1968;4:909–18.
doi: 10.1029/WR004i005p00909
Michallek F, Dewey M. Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review. Eur Radiol. 2014;24:60–9.
doi: 10.1007/s00330-013-2977-9 pubmed: 23974703
Møller MF. A scaled conjugate gradient algorithm for fast supervised learning. Neural Netw. 1993;6:525–33.
doi: 10.1016/S0893-6080(05)80056-5
Peng CK, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL. Mosaic organization of DNA nucleotides. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994;49:1685–9.
pubmed: 9961383
Petrujkić K, Milošević N, Rajković N, Stanisavljević D, Gavrilović S, Dželebdžić D, Ilić R, Di Ieva A, Maksimović R. Computational quantitative MR image features – a potential useful tool in differentiating glioblastoma from solitary brain metastasis. Eur J Radiol. 2019;119:108634. https://doi.org/10.1016/j.ejrad.2019.08.003 .
doi: 10.1016/j.ejrad.2019.08.003 pubmed: 31473463
Rajagopalan V, Liu Z, Allexandre D, Zhang L, Wang XF, Pioro EP, et al. Brain white matter shape changes in amyotrophic lateral sclerosis (ALS): a fractal dimension study. PLoS One. 2013;8:e73614.
doi: 10.1371/journal.pone.0073614 pubmed: 24040000 pmcid: 3767806
Sandu AL, Rasmussen IA Jr, Lundervold A, Kreuder F, Neckelmann G, Hugdahl K, et al. Fractal dimension analysis of MR images reveals grey matter structure irregularities in schizophrenia. Comput Med Imaging Graph. 2008;32:150–8.
doi: 10.1016/j.compmedimag.2007.10.005 pubmed: 18068333
Sonka M. Image processing analysis and computing vision. London: Brooks/Cole; 2001.
Stanley HE, Amaral LAN, Goldberger AL, Havlin S, Ivanov PC, Peng CK. Statistical physics and physiology: monofractal and multifractal approaches. Physica A. 1999;270:309–24.
doi: 10.1016/S0378-4371(99)00230-7 pubmed: 11543220
Tanaka KW, Russo C, Liu S, Stoodley MA, Di Ieva A. Use of deep learning in the MRI diagnosis of Chiari malformation type I. Neuroradiology. 2022;64(8):1585–92. https://doi.org/10.1007/s00234-022-02921-0 .
doi: 10.1007/s00234-022-02921-0 pubmed: 35199210 pmcid: 9271110
Wardlaw G, Wong R, Noseworthy MD. Identification of intratumour low frequency microvascular components via BOLD signal fractal dimension mapping. Phys Med. 2008;24:87–91.
doi: 10.1016/j.ejmp.2008.01.006 pubmed: 18294894
Zook JM, Iftekharuddin KM. Statistical analysis of fractal-based brain tumor detection algorithms. Magn Reson Imaging. 2005;23:671–8.
doi: 10.1016/j.mri.2005.04.002 pubmed: 16051042

Auteurs

Salim Lahmiri (S)

Department of Supply Chain & Business Technology Management, John Molson School of Business, Concordia University, Montreal, Canada.

Mounir Boukadoum (M)

RESMIQ, Labo microPro, Université du Québec à Montréal (UQAM), Montreal, Canada.

Antonio Di Ieva (A)

Computational NeuroSurgery (CNS) Lab & Macquarie Neurosurgery, Macquarie Medical School, Faculty of Medicine, Human and Health Sciences, Macquarie University, Sydney, NSW, Australia. antonio.diieva@mq.edu.au.

Classifications MeSH