The impact of inter-fraction dose variations on biological equivalent dose (BED): the concept of equivalent constant dose
Bibliographic record
Abstract
Inter-fraction dose fluctuations, which appear as a result of setup errors, organ motion and treatment machine output variations, may influence the radiobiological effect of the treatment even when the total delivered physical dose remains constant. The effect of these inter-fraction dose fluctuations on the biological effective dose (BED) has been investigated. Analytical expressions for the BED accounting for the dose fluctuations have been derived. The concept of biological effective constant dose (BECD) has been introduced. The equivalent constant dose (ECD), representing the constant physical dose that provides the same cell survival fraction as the fluctuating dose, has also been introduced. The dose fluctuations with Gaussian as well as exponential probability density functions were investigated. The values of BECD and ECD calculated analytically were compared with those derived from Monte Carlo modelling. The agreement between Monte Carlo modelled and analytical values was excellent (within 1%) for a range of dose standard deviations (0-100% of the dose) and the number of fractions (2 to 37) used in the comparison. The ECDs have also been calculated for conventional radiotherapy fields. The analytical expression for the BECD shows that BECD increases linearly with the variance of the dose. The effect is relatively small, and in the flat regions of the field it results in less than 1% increase of ECD. In the penumbra region of the 6 MV single radiotherapy beam the ECD exceeded the physical dose by up to 35%, when the standard deviation of combined patient setup/organ motion uncertainty was 5 mm. Equivalently, the ECD field was approximately 2 mm wider than the physical dose field. The difference between ECD and the physical dose is greater for normal tissues than for tumours.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".