Fractal dimension of external linear contour of human cerebellum (magnetic resonance imaging study)

  • N.I. Maryenko Kharkiv National Medical University, Kharkiv, Ukraine
  • O.Y. Stepanenko Kharkiv National Medical University, Kharkiv, Ukraine
Keywords: fractal analysis, caliper, box counting, cerebellum, magnetic resonance imaging.

Abstract

Fractal analysis is a method of mathematical analysis, which provides quantitative assessment of the spatial configuration complexity of the anatomical structures and may be used as a morphometric method. The purpose of the study was to determine the values of the fractal dimension of the outer linear contour of human cerebellum by studying the magnetic resonance images of the brain using the authors’ modification of the caliper method and compare to the values determined using the box counting method. Brain magnetic resonance images of 30 relatively healthy persons aged 18-30 years (15 men and 15 women) were used in the study. T2-weighted digital magnetic resonance images were studied. The midsagittal MR sections of the cerebellar vermis were investigated. The caliper method in the author’s modification was used for fractal analysis. The average value of the fractal dimension of the linear contour of the cerebellum, determined using the caliper method, was 1.513±0.008 (1.432÷1.600). The average value of the fractal dimension of the linear contour of the cerebellum, determined using the box counting method, was 1.530±0.010 (1.427÷1.647). The average value of the fractal dimension of the cerebellar tissue as a whole, determined using the box counting method, was 1.760±0.006 (1.674÷1.837). The values of the fractal dimension of the outer linear contour of the cerebellum, determined using the caliper method and the box counting method were not statistically significantly different. Therefore, both methods can be used for fractal analysis of the linear contour of the cerebellum. Fractal analysis of the outer linear contour of the cerebellum allows to quantify the complexity of the spatial configuration of the outer surface of the cerebellum, which is difficult to estimate using traditional morphometric methods. The data obtained from this study and the methodology of the caliper method of fractal analysis in the author’s modification can be used for morphometric investigations of the human cerebellum in morphological studies, as well as in assessment of cerebellar MR images for diagnostic purposes.

References

[1] Akar, E., Kara, S., Akdemir, H., & Kırış, A. (2015). Fractal dimension analysis of cerebellum in Chiari Malformation type I. Computers in Biology and Medicine, 64, 179-186. https://doi.org/10.1016/j.compbiomed.2015.06.024
[2] Akar, E., Kara, S., Akdemir, H., & Kırış, A. (2017). 3D structural complexity analysis of cerebellum in Chiari malformation type I. Medical & Biological Engineering & Computing, 55(12), 2169-2182. https://doi.org/10.1007/s11517-017-1661-7
[3] Di Ieva, A., Esteban, F.J., Grizzi, F., Klonowski, W., & Martín-Landrove, M. (2015). Fractals in the neurosciences, Part II: clinical applications and future perspectives. The Neuroscientist: a Review Journal Bringing Neurobiology, Neurology and Psychiatry, 21(1), 30-43. https://doi.org/10.1177/1073858413513928
[4] Di Ieva, A., Grizzi, F., Jelinek, H., Pellionisz, A.J., & Losa, G.A. (2014). Fractals in the Neurosciences, Part I: General Principles and Basic Neurosciences. The Neuroscientist: a review Journal Bringing Neurobiology, Neurology and Psychiatry, 20(4), 403-417. https://doi.org/10.1177/1073858413513927
[5] Demaerel, P. (2002). Abnormalities of cerebellar foliation and fissuration: classification, neurogenetics and clinicoradiological correlations. Neuroradiology, 44(8), 639-646. https://doi.org/10.1007/s00234-002-0783-1
[6] Gellersen, H.M., Guo, C.C., O’Callaghan, C., Tan, R.H., Sami, S., & Hornberger, M. (2017). Cerebellar atrophy in neurodegeneration – a meta-analysis. Journal of Neurology, Neurosurgery, and Psychiatry, 88(9), 780-788. https://doi.org/10.1136/jnnp-2017-315607
[7] Grizzi, F., Castello, A., Qehajaj, D., Russo, C., & Lopci, E. (2019). The Complexity and Fractal Geometry of Nuclear Medicine Images. Molecular Imaging and Biology, 21(3), 401-409. https://doi.org/10.1007/s11307-018-1236-5
[8] Jelinek, H.F., & Fernandez, E. (1998). Neurons and fractals: how reliable and useful are calculations of fractal dimensions? Journal of Neuroscience Methods, 81(1-2), 9-18. https://doi.org/10.1016/s0165-0270(98)00021-1
[9] John, A.M., Elfanagely, O., Ayala, C.A., Cohen, M., & Prestigiacomo, C.J. (2015). The utility of fractal analysis in clinical neuroscience. Reviews in the neurosciences, 26(6), 633-645. https://doi.org/10.1515/revneuro-2015-0011
[10] King, R.D., Brown, B., Hwang, M., Jeon, T., George, A.T., & Alzheimer’s Disease Neuroimaging Initiative (2010). Fractal dimension analysis of the cortical ribbon in mild Alzheimer’s disease. NeuroImage, 53(2), 471-479. https://doi.org/10.1016/j.neuroimage.2010.06.050
[11] King, R.D., George, A.T., Jeon, T., Hynan, L.S., Youn, T.S., Kennedy, D.N., & Dickerson, B. (2009). Characterization of Atrophic Changes in the Cerebral Cortex Using Fractal Dimensional Analysis. Brain Imaging and Behavior, 3(2), 154-166. https://doi.org/10.1007/s11682-008-9057-9
[12] Kiselev, V.G., Hahn, K.R., & Auer, D.P. (2003). Is the brain cortex a fractal? NeuroImage, 20(3), 1765-1774. https://doi.org/10.1016/s1053-8119(03)00380-x
[13] Lee, K.I., Choi, S.C., Park, T.W., & You, D.S. (1999). Fractal dimension calculated from two types of region of interest. Dentomaxillofac. Radiology, 28(5), 284-289. doi: 10.1038/sj/dmfr/4600458
[14] Liu, J.Z., Zhang, L.D., & Yue, G.H. (2003). Fractal dimension in human cerebellum measured by magnetic resonance imaging. Biophysical Journal, 85(6), 4041-4046. https://doi.org/10.1016/S0006-3495(03)74817-6
[15] Liu, S., Fan, X., Zhang, C., Wang, Z., Li, S., Wang, Y. … Jiang, T. (2019). MR imaging based fractal analysis for differentiating primary CNS lymphoma and glioblastoma. European Radiology, 29(3), 1348-1354. https://doi.org/10.1007/s00330-018-5658-x
[16] Mandelbrot, B.B. (1983). The fractal geometry of nature. N.Y.: W.H. Freeman & Co.
[17] Maryenko, N., & Stepanenko, O. (2020). Fractal dimension of phylogenetically different parts of the human cerebellum (magnetic resonance imaging study). Reports of Morphology, 26(2), 67-73. https://doi.org/10.31393/morphology-journal-2020-26(2)-10
[18] Patel, S., & Barkovich, A.J. (2002). Analysis and classification of cerebellar malformations. AJNR. American Journal of Neuroradiology, 23(7), 1074-1087.
[19] Ristanović, D., & Milosević, N.T. (2012). Fractal analysis: methodologies for biomedical researchers. Theoretical Biology Forum, 105(2), 99-118.
[20] Shrout, M.K., Potter, B.J., & Hildebolt, C.F. (1997). The effect of image variations on fractal dimension calculations. Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontics, 84(1), 96-100. https://doi.org/10.1016/s1079-2104(97)90303-6
[21] Soto-Ares, G., Delmaire, C., Deries, B., Vallee, L., & Pruvo, J.P. (2000). Cerebellar cortical dysplasia: MR findings in a complex entity. AJNR. American Journal of Neuroradiology, 21(8), 1511-1519.
[22] Welker, W.I. (1990). The significance of foliation and fissuration of cerebellar cortex. The cerebellar folium as a fundamental unit of sensorimotor integration. Arch. Ital. Biol., 128(2-4), 87-109.
[23] Wu, Y.T., Shyu, K.K., Jao, C.W., Wang, Z.Y., Soong, B.W., Wu, H.M., & Wang, P.S. (2010). Fractal dimension analysis for quantifying cerebellar morphological change of multiple system atrophy of the cerebellar type (MSA-C). NeuroImage, 49(1), 539-551. https://doi.org/10.1016/j.neuroimage.2009.07.042
[24] Zaletel, I., Ristanović, D., Stefanović, B. D., & Puškaš, N. (2015). Modified Richardson’s method versus the box-counting method in neuroscience. Journal of Neuroscience Methods, 242, 93-96. https://doi.org/10.1016/j.jneumeth.2015.01.013
Published
2021-06-25
How to Cite
Maryenko, N., & Stepanenko, O. (2021). Fractal dimension of external linear contour of human cerebellum (magnetic resonance imaging study). Reports of Morphology, 27(2), 16-22. https://doi.org/10.31393/morphology-journal-2021-27(2)-03