title: [Fractal geometry in the objective grading of prostate carcinoma].
abstract: BACKGROUND
  A possible approach to objectively classify complex patterns in tumor tissue is a mathematical and statistical investigation of the distribution of cell nuclei as a geometric representation of cancer cells by fractal dimensions. Both the existence and changes in the fractal structure of tumor tissue have important consequences for the objective system of tumor grading. In addition, the complexity of growth in different carcinomas or their intercellular interactions can be compared to each other.
  
  
  RESULTS
  We present a theoretical introduction into fractal geometry as well as in the computer algorithms based upon the Rényi family of fractal dimensions. Finally, a geometric model of prostate cancer is introduced and the relationship between geometric patterns of prostate tumor and the fractal dimensions of the Rényi family are explained.
authors.affiliation: Klinik für Urologie, Andrologie und Kinderurologie, Justus-Liebig-Universität, Rudolf-Buchheim-Straße 7, 35392, Gießen, Deutschland, complexityresearch@yahoo.com.
authors.forename: P
authors.initials: P
authors.lastname: Waliszewski
authors.forename: F
authors.initials: F
authors.lastname: Wagenlehner
authors.forename: S
authors.initials: S
authors.lastname: Gattenlöhner
authors.forename: W
authors.initials: W
authors.lastname: Weidner
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D002467:Cell Nucleus / Q000473:pathology*; D003627:Data Interpretation, Statistical; D017709:Fractals; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008297:Male; D008853:Microscopy / Q000379:methods*; D060787:Neoplasm Grading; D010363:Pattern Recognition, Automated / Q000379:methods; D011471:Prostatic Neoplasms / Q000473:pathology*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity