Fractal and spectral dimension analysis of liver fibrosis in needle biopsy specimens

Nicola Dioguardi, Fabio Grizzi, Paola Bossi, Massimo Roncalli

Research output: Contribution to journalArticlepeer-review


OBJECTIVE: To evaluate the usefulness of a reliable and reproducible mathematical scoring system based on fractal geometry for quantifying the irregular pattern in fibrosis commonly seen in liver biopsy specimens from chronic liver diseases. STUDY DESIGN: The study used 26 standard liver biopsy specimens obtained from patients with chronic hepatitis C virus-related liver disease. The degree of fibrosis in each specimen was estimated using a quantitative scoring system based on the computer-assisted evaluation of both the fractal and spectral dimensions of deposited collagen. The fractal dimension was then compared with the percent area of collagen measured using an image analysis system. RESULTS: The fractional dimension of its irregular shape defines fibrosis as a natural fractal structure. The complex distribution of its collagenous components (unmeasurable by means of the usual morphometric parameters) can be optimally quantified using a single numerical score that seems to be a better alternative to the semiquantitative methods adopted so far. The proposed method is reproducible, rapid and inexpensive; furthermore, supported by specific software, its mathematical approach excludes subjectivity and eliminates the external factors capable of influencing staging and classification. CONCLUSION: This study demonstrated that it is possible to quantify the irregularity of the structures of the liver in an objective manner and that the box-counting fractal dimension does not depend on the amount of collagen deposited on the slide. Furthermore, as has been found in other fields of investigation, study of the fractal properties of the liver is likely to reveal more about its structure and the pathogenesis of liver diseases.

Original languageEnglish
Pages (from-to)262-266
Number of pages5
JournalAnalytical and Quantitative Cytology and Histology
Issue number3
Publication statusPublished - Jun 1999


  • Biopsy
  • Fractals
  • Liver fibrosis
  • Needle
  • Spectral dimensions

ASJC Scopus subject areas

  • Anatomy
  • Histology
  • Cell Biology


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