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The correlation between a drug's dosage and its impact on a biological system is a cornerstone of pharmacology and toxicology. Conventional dose–response curves, which include graded and quantal relationships, are key to this understanding. Graded dose–response curves depict the spectrum of a biological reaction to different doses within an individual, indicating that as the drug dosage increases, so does the intensity of the response. On the other hand, quantal dose–response relationships...
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Dose-Dependent LET Constraints and Constraint Resolution for Interpreting Proton Therapy Toxicity.

Hong Qi Tan1, Calvin Wei Yang Koh2, Kah Seng Lew3

  • 1Division of Radiation Oncology, National Cancer Centre Singapore, Singapore; Division of Physics and Applied Physics, School of Physical and Mathematical Science, Nanyang Technological University, Singapore; Oncology Academic Clinical Programme, Duke-NUS Medical School, Singapore.

International Journal of Radiation Oncology, Biology, Physics
|July 8, 2026
PubMed
Summary

Probabilistic dose-averaged linear energy transfer (LETD) constraints offer a biologically consistent approach to proton therapy, improving upon single-value thresholds by accounting for dose and LET dependencies in normal tissue toxicity.

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Area of Science:

  • Radiation Oncology
  • Medical Physics
  • Radiobiology

Background:

  • Dose-averaged linear energy transfer (LETD) is crucial for predicting normal tissue toxicity in proton therapy.
  • Current LETD constraints often use single-value thresholds, neglecting the coupled dose-LET relationship vital for biological effects.

Purpose of the Study:

  • Develop and evaluate a probabilistic framework for dose-dependent LETD constraints.
  • Assess the consistency of these probabilistic constraints with existing clinical toxicity data.

Main Methods:

  • Derived dose-LETD constraint curves using linear quadratic-based variable relative biological effectiveness (RBE) models.
  • Incorporated uncertainty from RBE models, tissue radiosensitivity, and fractionation into probabilistic envelopes.
  • Compared derived constraints with clinical toxicity data for brainstem necrosis, brain necrosis, RIBI, rib fracture, and osteoradionecrosis.

Main Results:

  • Probabilistic constraints aligned well with clinical data for brainstem necrosis, RIBI, and osteoradionecrosis.
  • Toxicity-associated dose-LETD values in patients exceeded constraint envelope upper bounds.
  • Limited empirical support for higher LET constraints was found, especially with the newest RBE model.

Conclusions:

  • Dose-dependent probabilistic LETD constraints offer a biologically sound alternative to single-value thresholds in proton therapy.
  • This framework better reflects the interplay of dose and LET in predicting normal tissue complications.