title: Three dimensional staging of breast cancer.
abstract: OBJECTIVE
  Breast cancers are three dimensional solids but very few are spherical. We hypothesized that calculations based on the greatest diameter would not accurately reflect tumor volume and that three dimensional measurements would affect tumor staging.
  
  
  METHODS
  165 invasive carcinomas measuring 2.5 cm or less and having three measured diameters (a > or = b > or = c) noted were evaluated. Tumor volume was calculated using four geometric models: the spherical 4/3 pi (a/2)3, prolate spheroid 4/3 pi (a/2) (c/2)2, oblate spheroid 4/3 pi (a/2)2 (b/2), and ellipsoid 4/3 pi (a/2 x b/2 x c/2). The ellipsoid correctly determined the volume for any tumor shape. All cases were stratified according to the TNM staging system. Differences in mean volume calculated as a sphere and ellipsoid for each tumor subclass were analyzed using Student's T test. The reclassification of tumors by the ellipsoid formula was determined.
  
  
  RESULTS
  Seventy-six (46.1%) had tumors with three different diameters while only six (3.6%) were true spheres having three identical diameters. Mean tumor volume analysis of T1a, T1b, T1c, and T2 tumors demonstrated a statistically significant overestimation of volume when utilizing the sphere formula instead of the ellipsoid formula (p < 0.05). The differences in volume were more dramatic as the diameters increased. A total of 41 tumors were moved into smaller T subclasses including 10 node positive patients.
  
  
  CONCLUSIONS
  Tumor volume analysis demonstrates that use of only the greatest diameter poorly reflects the true volume of a lesion and consistently overestimates volume. The ellipsoid formula accurately calculates volume for these three dimensional tumors and when utilized has significant relevance to staging small invasive breast cancers.
authors.affiliation: Department of Surgery, University of Medicine and Dentistry of New Jersey, Robert Wood Johnson Medical School, New Brunswick 08903, USA.
authors.forename: I L
authors.initials: IL
authors.lastname: Wapnir
authors.forename: D E
authors.initials: DE
authors.lastname: Wartenberg
authors.forename: R S
authors.initials: RS
authors.lastname: Greco
mesh_terms: D001943:Breast Neoplasms / Q000473:pathology*; D005260:Female; D006801:Humans; D008962:Models, Theoretical; D009367:Neoplasm Staging