title: Application of different methods for nuclear shape analysis with special reference to the differentiation of brain tumors.
abstract: OBJECTIVE
  To study the discriminatory power of different methods designed for nuclear shape analysis with reference to the differentiation and grading of brain tumors and the differentiation between proliferating and nonproliferating nuclei.
  
  
  METHODS
  At least 300 tumor cell nuclei per case were measured by means of a digital image analysis system. Fourier amplitudes no. 1 to 15, moments no. 1 to 7 according to Hu, roundness factor, ellipse shape factor, concavity factor, Feret ratio, fractal dimension and bending energy were determined for each nucleus. The discriminatory power of these parameters was tested in three pairwise comparisons: (1) oligodendrogliomas WHO grade II (n = 13) vs. grade III (n = 11), (2) medulloblastomas WHO grade IV (n = 14) vs. anaplastic ependymomas WHO grade III (n = 12), (3) Ki-67-positive vs. Ki-67-negative tumor cell nuclei in the 14 medulloblastomas.
  
  
  RESULTS
  When data from Fourier analysis were included in statistical analysis, cross-validated discriminant analysis led to a 100% correct reclassification for the first and for the second pairwise comparison and to a 75% correct reclassification when comparing Ki-67-positive and Ki-67-negative nucleifrom medulloblastomas. Different combinations of the other shape parameters led to a lower percentage of correctly reclassified cases for all three pairwise comparisons, especially when Fourier analysis was not included in the analysis.
  
  
  CONCLUSIONS
  Fourier analysis provided an optimal statistical discrimination between different brain tumor entities and between data sets from proliferating and nonproliferating tumor cell nuclei. Since nuclear shape is an important criterion for the investigation of tumors, the application of Fourier analysis is therefore recommended for quantitative histologic investigations in neuro-oncology.
authors.affiliation: Department of Neuroradiology, Clinics of JW Goethe-University, Hannover, Germany. r.nafe@em.uni-frankfurt.de
authors.forename: Reinhold
authors.initials: R
authors.lastname: Nafe
authors.forename: Bernard
authors.initials: B
authors.lastname: Yan
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Schlote
authors.forename: Berthold
authors.initials: B
authors.lastname: Schneider
mesh_terms: D001932:Brain Neoplasms / Q000175:diagnosis* / Q000473:pathology; D002454:Cell Differentiation; D002467:Cell Nucleus / Q000473:pathology*; D003937:Diagnosis, Differential; D016002:Discriminant Analysis; D004806:Ependymoma / Q000473:pathology*; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008527:Medulloblastoma / Q000175:diagnosis* / Q000473:pathology*; D009837:Oligodendroglioma / Q000473:pathology*