title: CD30 cell graphs of Hodgkin lymphoma are not scale-free--an image analysis approach.
abstract: BACKGROUND
  Hodgkin lymphoma (HL) is a type of B-cell lymphoma. To diagnose the subtypes, biopsies are taken and immunostained. The slides are scanned to produce high-resolution digital whole slide images (WSI). Pathologists manually inspect the spatial distribution of cells, but little is known on the statistical properties of cell distributions in WSIs. Such properties would give valuable information for the construction of theoretical models that describe the invasion of malignant cells in the lymph node and the intercellular interactions.
  
  
  RESULTS
  In this work, we define and discuss HL cell graphs. We identify CD30(+) cells in HL WSIs, bringing together the fields of digital imaging and network analysis. We define special graphs based on the positions of the immunostained cells. We present an automatic analysis of complete WSIs to determine significant morphological and immunohistochemical features of HL cells and their spatial distribution in the lymph node tissue under three different medical conditions: lymphadenitis (LA) and two types of HL. We analyze the vertex degree distributions of CD30 cell graphs and compare them to a null model. CD30 cell graphs show higher vertex degrees than expected by a random unit disk graph, suggesting clustering of the cells. We found that a gamma distribution is suitable to model the vertex degree distributions of CD30 cell graphs, meaning that they are not scale-free. Moreover, we compare the graphs for LA and two subtypes of HL. LA and classical HL showed different vertex degree distributions. The vertex degree distributions of the two HL subtypes NScHL and mixed cellularity HL (MXcHL) were similar.
  
  
  METHODS
  The CellProfiler pipeline used for cell detection is available at https://sourceforge.net/projects/cellgraphs/.
  
  
  BACKGROUND
  ina.koch@bioinformatik.uni-frankfurt.de
  
  
  BACKGROUND
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Department of Molecular Bioinformatics, Institute of Computer Science, Cluster of Excellence Macromolecular Complexes, Johann Wolfgang Goethe-University Frankfurt am Main, Robert-Mayer-Str. 11-15, 60325 Frankfurt am Main and.
authors.forename: Hendrik
authors.initials: H
authors.lastname: Schäfer
authors.affiliation: Department of Molecular Bioinformatics, Institute of Computer Science, Cluster of Excellence Macromolecular Complexes, Johann Wolfgang Goethe-University Frankfurt am Main, Robert-Mayer-Str. 11-15, 60325 Frankfurt am Main and.
authors.forename: Tim
authors.initials: T
authors.lastname: Schäfer
authors.affiliation: Department of Molecular Bioinformatics, Institute of Computer Science, Cluster of Excellence Macromolecular Complexes, Johann Wolfgang Goethe-University Frankfurt am Main, Robert-Mayer-Str. 11-15, 60325 Frankfurt am Main and.
authors.forename: Jörg
authors.initials: J
authors.lastname: Ackermann
authors.affiliation: Department of Molecular Bioinformatics, Institute of Computer Science, Cluster of Excellence Macromolecular Complexes, Johann Wolfgang Goethe-University Frankfurt am Main, Robert-Mayer-Str. 11-15, 60325 Frankfurt am Main and.
authors.forename: Norbert
authors.initials: N
authors.lastname: Dichter
authors.affiliation: Dr. Senckenbergisches Institut für Pathologie, Universitätsklinikum Frankfurt, Theodor-Stern-Kai 7, 60590 Frankfurt am Main, Germany.
authors.forename: Claudia
authors.initials: C
authors.lastname: Döring
authors.affiliation: Dr. Senckenbergisches Institut für Pathologie, Universitätsklinikum Frankfurt, Theodor-Stern-Kai 7, 60590 Frankfurt am Main, Germany.
authors.forename: Sylvia
authors.initials: S
authors.lastname: Hartmann
authors.affiliation: Dr. Senckenbergisches Institut für Pathologie, Universitätsklinikum Frankfurt, Theodor-Stern-Kai 7, 60590 Frankfurt am Main, Germany.
authors.forename: Martin-Leo
authors.initials: ML
authors.lastname: Hansmann
authors.affiliation: Department of Molecular Bioinformatics, Institute of Computer Science, Cluster of Excellence Macromolecular Complexes, Johann Wolfgang Goethe-University Frankfurt am Main, Robert-Mayer-Str. 11-15, 60325 Frankfurt am Main and.
authors.forename: Ina
authors.initials: I
authors.lastname: Koch
mesh_terms: D002449:Cell Aggregation; D002452:Cell Count; D006689:Hodgkin Disease / Q000378:metabolism* / Q000473:pathology*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D017730:Ki-1 Antigen / Q000378:metabolism*; D015203:Reproducibility of Results
chemical_list: D017730:Ki-1 Antigen