A fractal analysis of human cranial sutures

Jack C. Yu, Ronald L. Wright, Matthew A. Williamson, James P. Braselton, Martha L. Abell

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Objectives: Many biological structures are products of repeated iteration functions. As such, they demonstrate characteristic, scale-invariant features. Fractal analysis of these features elucidates the mechanism of their formation. The objectives of this project were to determine whether human cranial sutures demonstrate self-similarity and measure their exponents of similarity (fractal dimensions). Design: One hundred three documented human skulls from the Terry Collection of the Smithsonian Institution were used. Their sagittal sutures were digitized and the data converted to bitmap images for analysis using box-counting method of fractal software. Results: The log-log plots of the number of boxes containing the sutural pattern, Nr, and the size of the boxes, r, were all linear, indicating that human sagittal sutures possess scale-invariant features and thus are fractals. The linear portion of these log-log plots has limits because of the finite resolution used for data acquisition. The mean box dimension, Db, was 1.29289 ± 0.078457 with a 95% confidence interval of 1.27634 to 1.30944. Conclusions: Human sagittal sutures are self-similar and have a fractal dimension of 1.29 by the box-counting method. The significance of these findings includes: sutural morphogenesis can be described as a repeated iteration function, and mathematical models can be constructed to produce self-similar curves with such Db. This elucidates the mechanism of actual pattern formation. Whatever the mechanisms at the cellular and molecular levels, human sagittal suture follows the equation log Nr = 1.29 log 1/r, where Nr is the number of square boxes with sides r that are needed to contain the sutural pattern and r equals the length of the sides of the boxes.

Original languageEnglish (US)
Pages (from-to)409-415
Number of pages7
JournalCleft Palate-Craniofacial Journal
Volume40
Issue number4
DOIs
StatePublished - Jul 1 2003

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Cranial Sutures
Fractals
Sutures
Morphogenesis
Skull
Theoretical Models
Software
Confidence Intervals

Keywords

  • Fractal analysis
  • Fractal dimension
  • Human sagittal suture

ASJC Scopus subject areas

  • Oral Surgery
  • Otorhinolaryngology

Cite this

A fractal analysis of human cranial sutures. / Yu, Jack C.; Wright, Ronald L.; Williamson, Matthew A.; Braselton, James P.; Abell, Martha L.

In: Cleft Palate-Craniofacial Journal, Vol. 40, No. 4, 01.07.2003, p. 409-415.

Research output: Contribution to journalArticle

Yu, JC, Wright, RL, Williamson, MA, Braselton, JP & Abell, ML 2003, 'A fractal analysis of human cranial sutures', Cleft Palate-Craniofacial Journal, vol. 40, no. 4, pp. 409-415. https://doi.org/10.1597/1545-1569(2003)040<0409:AFAOHC>2.0.CO;2
Yu, Jack C. ; Wright, Ronald L. ; Williamson, Matthew A. ; Braselton, James P. ; Abell, Martha L. / A fractal analysis of human cranial sutures. In: Cleft Palate-Craniofacial Journal. 2003 ; Vol. 40, No. 4. pp. 409-415.
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