Universal Survival Curve and Single Fraction Equivalent Dose: Useful Tools in Understanding Potency of Ablative Radiotherapy

Clint Park, Lech Papiez, Shichuan Zhang, Michael Story, Robert D. Timmerman

Research output: Contribution to journalArticlepeer-review

481 Scopus citations


Purpose: Overprediction of the potency and toxicity of high-dose ablative radiotherapy such as stereotactic body radiotherapy (SBRT) by the linear quadratic (LQ) model led to many clinicians' hesitating to adopt this efficacious and well-tolerated therapeutic option. The aim of this study was to offer an alternative method of analyzing the effect of SBRT by constructing a universal survival curve (USC) that provides superior approximation of the experimentally measured survival curves in the ablative, high-dose range without losing the strengths of the LQ model around the shoulder. Methods and Materials: The USC was constructed by hybridizing two classic radiobiologic models: the LQ model and the multitarget model. We have assumed that the LQ model gives a good description for conventionally fractionated radiotherapy (CFRT) for the dose to the shoulder. For ablative doses beyond the shoulder, the survival curve is better described as a straight line as predicted by the multitarget model. The USC smoothly interpolates from a parabola predicted by the LQ model to the terminal asymptote of the multitarget model in the high-dose region. From the USC, we derived two equivalence functions, the biologically effective dose and the single fraction equivalent dose for both CFRT and SBRT. Results: The validity of the USC was tested by using previously published parameters of the LQ and multitarget models for non-small-cell lung cancer cell lines. A comparison of the goodness-of-fit of the LQ and USC models was made to a high-dose survival curve of the H460 non-small-cell lung cancer cell line. Conclusion: The USC can be used to compare the dose fractionation schemes of both CFRT and SBRT. The USC provides an empirically and a clinically well-justified rationale for SBRT while preserving the strengths of the LQ model for CFRT.

Original languageEnglish (US)
Pages (from-to)847-852
Number of pages6
JournalInternational Journal of Radiation Oncology Biology Physics
Issue number3
StatePublished - Mar 1 2008


  • Biologically effective dose
  • Linear quadratic model
  • Single fraction equivalent dose
  • Stereotactic body radiotherapy
  • Universal survival curve

ASJC Scopus subject areas

  • Radiation
  • Oncology
  • Radiology Nuclear Medicine and imaging
  • Cancer Research


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