title: Steepness of the dose-response curve as a function of volume in an experimental tumor irradiated under ambient or hypoxic conditions.
abstract: OBJECTIVE
  Radiation dose-response curves play a fundamental role in the attempts to optimize radiotherapy, and it is a major task in clinical and experimental radiation research to characterize and quantify the factors that determine the position and shape of dose-response curves. A convenient measure of the steepness of radiation dose-response curves is the normalized dose-response gradient, gamma, which represents the increase in response, in percentage points, for a 1% increase in dose. Theoretically, the normalized dose-response gradient should increase with increasing clonogenic cell number or, assuming a constant clonogen density, with increasing tumor volume. The aim of this study was to test this hypothesis over a range of tumor volumes and to study how this relationship is affected by heterogeneity in tumor oxygenation.
  
  
  METHODS
  A C3H mouse mammary carcinoma implanted in the feet of female CDF1 mice was used. Groups of tumors with various volumes were irradiated with single graded radiation doses in air or after making them artificially hypoxic by clamping. The end point used was tumor control defined as complete absence of a macroscopic relapse within 90 days after irradiation. A Poisson dose-response model was assumed to describe tumor control probability in each volume group. The dose needed to control 37% of the tumors (D37) and the normalized dose-response gradient at this dose (gamma37) were estimated by the maximum likelihood method. In another group of animals with tumors in the same volume range, oxygenation status was assessed by a polarographic needle electrode. The percentage of pO2 values <3 mmHg was selected to represent the relative volume of the tumor with radiobiological hypoxia.
  
  
  RESULTS
  The D37 values increased as a function of tumor volume under both clamped and ambient conditions. For tumors irradiated under clamped conditions, gamma37 increased with increasing tumor volume throughout the range of volumes studied. However, for tumors irradiated under ambient conditions, there was an initial increase in gamma37 with tumor volume up to 100 mm3 with no further increase beyond that volume. As the tumor volume increased, both the level of hypoxia and the tumor-to-tumor heterogeneity in that level increased.
  
  
  CONCLUSIONS
  This study has confirmed the hypothesis that gamma37 increases with increasing tumor volume when tumors are irradiated under clamped condition. The increased heterogeneity of the hypoxic volume fraction with increasing tumor volume could explain why the steepness of the dose-response curve did not increase with increasing tumor volume when irradiation was done under ambient condition.
authors.affiliation: Danish Cancer Society, Department of Experimental Clinical Oncology, Aarhus University Hospital, Denmark.
authors.forename: A A
authors.initials: AA
authors.lastname: Khalil
authors.forename: S M
authors.initials: SM
authors.lastname: Bentzen
authors.forename: J
authors.initials: J
authors.lastname: Overgaard
mesh_terms: D000818:Animals; D015687:Cell Hypoxia; D004307:Dose-Response Relationship, Radiation; D005260:Female; D008325:Mammary Neoplasms, Experimental / Q000473:pathology / Q000532:radiotherapy*; D051379:Mice; D009368:Neoplasm Transplantation; D016012:Poisson Distribution