title: Fractal dimension rectified meter for quantification of liver fibrosis and other irregular microscopic objects.
abstract: OBJECTIVE
  To introduce a new mathematical method based on the principles of fractal geometry analysis that permits more realistic quantification of some of the physical (morphologic) aspects of irregular bodies appearing under microscopy.
  
  
  METHODS
  The principles of the method were tested on microscopic images of irregular collagen deposition in liver tissue. The method uses an ad hoc rectified meter implemented in a computer-assisted planar image analysis system that has been adapted to give metric measures of irregular outlines and surfaces that can be used to produce an index capable of quantifying the typical wrinkledness of biologic objects. Prototypical example measures of liver fibrosis were made on biopsy specimens showing chronic hepatitis C virus-related disease. Measurements were also made of the microscopic images of the abnormal deposition of lipid droplets in hepatocytes, a case of amyloid deposition in an osteoarthromuscular structure and a cytologic specimen of human dendritic cells.
  
  
  RESULTS
  The proposed computer-aided method permits rapid measurements of the image of a whole biopsy section digitized at high magnification. The snapshot measurement of liver fibrosis deposition offered by a biopsy pattern is a valid means of more rigorously identifying the staging of the process.
  
  
  CONCLUSIONS
  This method can measure liver fibrosis during chronic liver disease as well as any other irregular biologic structure that cannot be correctly quantified using traditional Euclidean-based metric methodologies.
authors.affiliation: Istituto Clinico Humanitas, Fondazione Michele Rodriguez per lo Studio dei Metodi Quantitativi in Medicina, Rozzano, MI, Italy. nicola.dioguardi@humanitas.it
authors.forename: Nicola
authors.initials: N
authors.lastname: Dioguardi
authors.forename: Barbara
authors.initials: B
authors.lastname: Franceschini
authors.forename: Giacomo
authors.initials: G
authors.lastname: Aletti
authors.forename: Carlo
authors.initials: C
authors.lastname: Russo
authors.forename: Fabio
authors.initials: F
authors.lastname: Grizzi
mesh_terms: D001707:Biopsy, Needle; D003094:Collagen / Q000032:analysis*; D017709:Fractals; D019698:Hepatitis C, Chronic / Q000473:pathology*; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008103:Liver Cirrhosis / Q000473:pathology*; D008962:Models, Theoretical; D013194:Staining and Labeling
chemical_list: D003094:Collagen