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Related Experiment Videos

Comments on a time-dependent version of the linear-quadratic model.

S L Tucker1, E L Travis

  • 1Department of Biomathematics, University of Texas M.D. Anderson Cancer Center, Houston 77030.

Radiotherapy and Oncology : Journal of the European Society for Therapeutic Radiology and Oncology
|June 1, 1990
PubMed
Summary

The "LQ + time" model inaccurately describes lung irradiation effects over time. Reanalysis suggests a nonlinear time dependence, challenging previous high alpha/beta estimates for lung tissue.

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Area of Science:

  • Radiation Oncology
  • Radiobiology
  • Medical Physics

Background:

  • The linear-quadratic (LQ) model is standard for fractionated radiotherapy.
  • The "LQ + time" model attempts to account for overall treatment time.
  • Previous studies reported high alpha/beta ratios for lung using this model.

Purpose of the Study:

  • To evaluate the accuracy of the "LQ + time" model for lung irradiation.
  • To investigate the reasons for high alpha/beta values derived from lung data.
  • To determine the true time dependence of isoeffect doses in lung.

Main Methods:

  • Literature data reanalysis.
  • Statistical regression procedures.
  • Comparison with published isoeffect data for lung.

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Main Results:

  • The "LQ + time" model does not accurately predict isoeffect dose changes with treatment time for lung.
  • High gamma/alpha values and alpha/beta ratios derived from lung data are partly artifacts of the model's limitations.
  • Reanalysis with improved statistical methods yielded lower, more typical alpha/beta estimates for lung (around 3 Gy).
  • Lung isoeffect data suggest a nonlinear, not linear, time dependence, influenced by effect level and dose per fraction.

Conclusions:

  • The "LQ + time" model is not a suitable general isoeffect model for lung irradiation.
  • The apparent overestimation of time effects by the model is due to its formulation.
  • Accurate modeling of lung response requires accounting for nonlinear time dependencies and other factors beyond simple linear time addition.