Fractal and spectral dimension analysis of liver fibrosis in needle biopsyspecimens

OBJECTIVE: To evaluate the usefulness of a reliable and reproducible mathem atical scoring system based on fractal geometry for quantifying the irregul ar pattern in fibrosis commonly seen in liver biopsy specimens from chronic liver diseases. STUDY DESIGN: The study used 26 standard liver biopsy specimens obtained fr ont patients with chronic hepatitis C virus-related liver disease. The degr ee of fibrosis in each specimen was estimated using a quantitative scoring system based on the computer-assisted evaluation of both the fractal and sp ectral dimensions of deposited collagen. The fractal dimension was then com pared with the percent area of collagen measured using an image analysis sy stem. RESULTS: The fractional dimension of its irregular shape defines fibrosis a s a natural fractal structure. The complex distribution gf 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 prop osed method is reproducible, rapid and inexpensive; furthermore, supported by specific software, its mathematical approach excludes subjectivity and e liminates the external factors capable of influencing staging and classific ation. CONCLUSION: This study demonstrated that it is possible to quantify the irr egularity of the structures of the liver in an objective manner and that th e box-counting fractal dimension does lot depend on the amount of collagen deposited on the slide. Furthermore, as has been found in other fields of i nvestigation, study of the fractal properties of the liver is likely to rev eal more about its structure and the pathogenesis of liver diseases.