Nonlinear Dynamics

, 58:745

Using three-dimensional fractal dimension to analyze the complexity of fetal cortical surface from magnetic resonance images

  • Yu-Te Wu
  • Kuo-Kai Shyu
  • Tzong-Rong Chen
  • Wan-Yuo Guo
Original paper

DOI: 10.1007/s11071-009-9515-y

Cite this article as:
Wu, Y., Shyu, K., Chen, T. et al. Nonlinear Dyn (2009) 58: 745. doi:10.1007/s11071-009-9515-y


This study aims to investigate the complexity of the developing fetal cortical surface based on the notion of fractal dimension (FD). Forty-four fetal MR images were selected at 22–36 weeks of gestational age (GA) and distributed between two groups: 32 normal fetal brains (excluding twins) and 12 abnormal fetal brains, including twins, mild ventricular dilatation, Cornelia de Lange syndrome (small brain), and cortical dysplasia (developmental delay). We adopted the commonly used box-counting (BC) method to estimate the FD of the developing fetal cortical surface. Results from normal fetal brains show that the increase of cortical complexity is highly correlated with fetal developing weeks of GA. In addition, after 28 weeks of GA, the value of FD increases more rapidly because of the faster development of convolved folds. In comparison with results from the normal fetal group, the abnormal fetal brains were examined and the results show that: (1) mild ventricular dilatation has no significant developing difference compared with normal fetal brains; (2) twins had lower FD than that of normal fetal brains, which may be a delay of 2–3 weeks; (3) the case of cortical dysplasia also had low FD, indicating that developing delay may mean less cortical complexity. The results of the normal group are in good agreement with fetal brain development and demonstrate the effectiveness of FD as a promising means for the quantification of complexity of the fetal cortical surface.


Fetal cortical surfaceFractal dimensionBox-counting method

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Yu-Te Wu
    • 1
    • 2
    • 3
  • Kuo-Kai Shyu
    • 4
  • Tzong-Rong Chen
    • 4
    • 5
  • Wan-Yuo Guo
    • 6
  1. 1.Department of Biomedical Imaging and Radiological ScienceNational Yang-Ming UniversityTaipeiROC
  2. 2.Institute of Brain ScienceNational Yang-Ming UniversityTaipeiROC
  3. 3.Integrated Brain Research LaboratoryDepartment of Medical Research and Education, Taipei Veterans General HospitalTaipeiROC
  4. 4.Department of Electrical EngineeringNational Central UniversityChung-LiROC
  5. 5.Department of Electronic EngineeringChing Yun UniversityChung-LiROC
  6. 6.Department of RadiologyTaipei Veterans General HospitalTaipeiROC