title: Lymphoma and leukemia cells possess fractal dimensions that correlate with their biological features.
abstract: BACKGROUND
  Living cells can be viewed as complex adaptive systems that exhibit non-linear dynamics and fractal features. We investigated the fractal qualities of normal and malignant hematological cells and their potential as a tool for characterizing cell phenotype and clinical behavior.
  
  
  METHODS
  A mathematical algorithm and an optic tool for fractal analysis of nuclei were developed. A total of 4,713 lymphoid cells derived from 66 patients of five distinct diagnostic groups (normal and reactive lymphocytes, low-grade lymphomas and an aggressive lymphoma) were assessed for their fractal dimension. In addition, in 19 patients fractal analysis of leukemia cells was compared to clinical endpoints.
  
  
  RESULTS
  After validating our method, hematological cells possessed fractal dimensions corresponding to their clinical entity. There was a highly significant overall difference in fractal dimensions between various types of hematological malignancies. A preliminary correlation was found between the fractal dimension and the clinical outcome of leukemia patients.
  
  
  CONCLUSIONS
  Hematological cells possess fractal dimensions that correlate with their biological properties. Measurement of fractal dimension seems to be a sensitive method to assess the hematological cell phenotype and to define a clinical group. This tool may be potentially useful for the evaluation of clinical behavior of hematological diseases.
authors.affiliation: Department of Internal Medicine A, Rabin Medical Center-Beilinson Hospital, Petah Tikva, Israel.
authors.forename: Adi
authors.initials: A
authors.lastname: Mashiah
authors.forename: Ofir
authors.initials: O
authors.lastname: Wolach
authors.forename: Judith
authors.initials: J
authors.lastname: Sandbank
authors.forename: Orit
authors.initials: O
authors.lastname: Uziel
authors.forename: Pia
authors.initials: P
authors.lastname: Raanani
authors.forename: Meir
authors.initials: M
authors.lastname: Lahav
mesh_terms: D000465:Algorithms; D001853:Bone Marrow / Q000473:pathology; D016000:Cluster Analysis; D015331:Cohort Studies; D017709:Fractals; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D015451:Leukemia, Lymphocytic, Chronic, B-Cell / Q000473:pathology*; D015470:Leukemia, Myeloid, Acute / Q000401:mortality / Q000473:pathology; D008198:Lymph Nodes / Q000473:pathology*; D008214:Lymphocytes / Q000648:ultrastructure*; D008224:Lymphoma, Follicular / Q000473:pathology*; D016403:Lymphoma, Large B-Cell, Diffuse / Q000473:pathology*; D010784:Photomicrography / Q000295:instrumentation / Q000379:methods*; D011379:Prognosis; D019310:Pseudolymphoma / Q000473:pathology; D012680:Sensitivity and Specificity; D016896:Treatment Outcome