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Analysis of fetal cortical complexity from MR images using 3D entropy based information fractal dimension

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Abstract

The fetal cortical complexity is a significant quantification for assessing the development of fetal brain. This study attempts to quantify the development of fetal cortical complexity using the concept of fractal dimension (FD) analysis. Thirty-two fetal MR images were selected from Taipei Veterans General Hospital at 27–37 weeks of gestational age (GA). To investigate the FD of fetal cortical complexity, the entropy based information fractal dimension method (FD EBI), which is modified from Box-Counting method, was adopted and extended from 2D to 3D. The FD results from overall whole fetal brains show that the increase of cortical complexity is highly correlated with the gestational age of the fetus. Moreover, the FD values of right hemispheric brain are larger than those of left hemispheric brain, show that the development of right hemispheric fetal cortical complexity earlier than the left. These results are in good agreement with normal fetal brain development and suggest that the FD is an effective means for the quantification of fetal cortical complexity.

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References

  1. Prayer, D., Kasprian, G., Krampl, E., Ulm, B., Witzani, L., Prayer, L., Brugger, P.C.: MRI of normal fetal brain development. Eur. J. Radiol. 57, 199–216 (2006)

    Article  Google Scholar 

  2. Mandelbrot, B.B.: The Fractal Geometry of Nature. Freeman, New York (1982)

    MATH  Google Scholar 

  3. Falconer, K.: Fractal Geometry—Mathematical Foundations and Applications, 2nd edn. Wiley, New York (2003)

    MATH  Google Scholar 

  4. Ghafari, S.H., Golnaraghi, F., Ismail, F.: Effect of localized faults on chaotic vibration of rolling element bearings. Nonlinear Dyn. 53(4), 287–301 (2008)

    Article  MATH  Google Scholar 

  5. Lin, G., Feeny, B.F., Das, T.: Fractional derivative reconstruction of forced oscillators. Nonlinear Dyn. 55(3), 239–250 (2009)

    Article  MATH  Google Scholar 

  6. Sharkovsky, A.N.: Ideal turbulence. Nonlinear Dyn. 44(1–4), 15–27 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Shan, Z.Y., Liu, J.Z., Glassa, J.O., Gajjarc, A., Lid, C.S., Reddicka, W.E.: Quantitative morphologic evaluation of white matter in survivors of childhood medulloblastoma. Magn. Reson. Imaging 24, 1015–1022 (2006)

    Article  Google Scholar 

  8. Liu, J.Z., Zhang, L.D., Yue, G.H.: Fractal dimension in human cerebellum measured by magnetic resonance imaging. Biophys. J. 85, 4041–4046 (2003)

    Article  Google Scholar 

  9. Kiselev, V.G., Hahn, K.R., Auer, D.P.: Is the brain cortex a fractal? Neuroimage 20(3), 1765–1774 (2003)

    Article  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. Lee, J.M., Yoon, U., Kim, J.J., Kim, I.Y., Lee, D.S., Kwon, J.S., Kim, S.I.: Analysis of the hemispheric asymmetry using fractal dimension of a skeletonized cerebral surface. IEEE Trans. Biomed. Eng. 51(8), 1494–1498 (2004)

    Article  Google Scholar 

  12. Esteban, F.J., Sepulcre, J., de Mendizábal, N.V., Goñi, J., Navas, J., de Miras, J.R., Bejarano, B., Masdeu, J.C., Villoslada, P.: Fractal dimension and white matter changes in multiple sclerosis. NeuroImage 36, 543–549 (2007)

    Article  Google Scholar 

  13. Sandu, A.L., Rasmussen Jr., I.A.B., Lundervold, A., Frank Kreuder, F., Neckelmann, G., Hugdahl, K., Specht, K.: Fractal dimension analysis of MR images reveals grey matter structure irregularities in schizophrenia. Comput. Med. Imaging Graph. 32, 150–158 (2008)

    Article  Google Scholar 

  14. Zook, J.M., Iftekharuddin, K.M.: Statistical analysis of fractal-based brain tumor detection algorithms. Magn. Reson. Imaging 23, 671–678 (2005)

    Article  Google Scholar 

  15. Esteban, F.J., Sepulcre, J., de Miras, J.R., Navas, J., de Mendizábal, N.V., Goñi, J., Quesada, J.M., Bejarano, B., Villoslada, P.: Fractal dimension analysis of grey matter in multiple sclerosis. J. Neurosci. 282, 67–71 (2009)

    Google Scholar 

  16. Ha, T.H., Yoon, U., Lee, K.J., Shin, Y.W., Lee, J.M., Kim, I.Y., Ha, K.S., Kim, S.I., Kwon, J.S.: Fractal dimension of cerebral cortical surface in schizophrenia and obsessive–compulsive disorder. Neurosci. Lett. 384, 172–176 (2005)

    Article  Google Scholar 

  17. Zhang, L., Dean, D., Liu, J.Z., Sahgal, V., Wang, X., Yue, G.H.: Quantifying degeneration of white matter in normal aging using fractal dimension. Neurobiol. Aging 28, 1543–1555 (2007)

    Article  Google Scholar 

  18. 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), 745–752 (2009)

    Article  MATH  Google Scholar 

  19. Garel, C.: MRI of the Fetal Brain. Springer, New York (2004)

    Google Scholar 

  20. Garel, C., Chantrel, E., Brisse, H., Elmaleh, M., Luton, D., Oury, J.F., Sebag, G., Hassan, M.: Fetal cerebral cortex: Normal gestational landmarks identified using prenatal MR imaging. AJNR 22(1), 184–189 (2001)

    Google Scholar 

  21. Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Addison-Wesley, Reading (1993)

    Google Scholar 

  22. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. Int. J. Comput. Vis. 1(4), 321–331 (1987)

    Article  Google Scholar 

  23. Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3D surface construction algorithm. Proc. SIGGRAPH Comput. Graph. 21(4), 163–169 (1987)

    Article  Google Scholar 

  24. Peitgen, H.O., Jurgens, H., Saupe, D.: Chaos and Fractals New Frontiers of Science. Springer, New York (1992)

    MATH  Google Scholar 

  25. Vicsek, T.: Fractal Growth Phenomena. World Scientific, Singapore (1990)

    Google Scholar 

  26. Liu, S.: Fractals and Their Applications in Condensed Matter Physics. Academic Press, San Diego (1986)

    Google Scholar 

  27. Theiler, J.: Estimating fractal dimension. J. Opt. Soc. Am. 7(6), 1055–1073 (1990)

    Article  MathSciNet  Google Scholar 

  28. Thomas, M.C., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley, New York (2006)

    MATH  Google Scholar 

  29. Herbert, F.J., Fernandez, E.: Neurons and fractals: how reliable and useful are calculations of fractal dimensions? J. Neurosci. Methods 81(1–2), 9–18 (1998)

    Google Scholar 

  30. Smith, T.G., Behar, T.N., Lange, G.D., Sheriff, W.H., Neale, E.A.: A fractal analysis of cell images. J. Neurosci. Methods 27, 173–180 (1989)

    Article  Google Scholar 

  31. Chi, J.G., Dooling, E.C., Gilles, F.H.: Gyral development of the human brain. Ann. Neurol. 1, 86–93 (1977)

    Article  Google Scholar 

  32. Guo, W.Y., Wong, T.T.: Screening of fetal CNS anomalies by MR imaging. Child’s Nerv. Syst. 19, 410–414 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, National Central University, Chung-Li, Taiwan, ROC

    Kuo-Kai Shyu & Tzong-Rong Chen

  2. Department of Biomedical Imaging and Radiological Science, National Yang-Ming University, Taipei, Taiwan, ROC

    Yu-Te Wu, Hui-Yun Chen & Hui-Hsin Hu

  3. Institute of Brain Science, National Yang-Ming University, Taipei, Taiwan, ROC

    Yu-Te Wu

  4. Integrated Brain Research Laboratory, Department of Medical Research and Education, Taipei Veterans General Hospital, Taipei, Taiwan, ROC

    Yu-Te Wu

  5. Department of Electronic Engineering, Ching Yun University, Chung-Li, Taiwan, ROC

    Tzong-Rong Chen

  6. Department of Radiology, Taipei Veterans General Hospital, Taipei, Taiwan, ROC

    Wan-Yuo Guo

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  1. Kuo-Kai Shyu
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  2. Yu-Te Wu
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  3. Tzong-Rong Chen
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  4. Hui-Yun Chen
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  6. Wan-Yuo Guo
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Correspondence to Tzong-Rong Chen.

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Shyu, KK., Wu, YT., Chen, TR. et al. Analysis of fetal cortical complexity from MR images using 3D entropy based information fractal dimension. Nonlinear Dyn 61, 363–372 (2010). https://doi.org/10.1007/s11071-010-9654-1

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  • DOI: https://doi.org/10.1007/s11071-010-9654-1

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