Proton loss model for therapeutic beam dose calculations
Bibliographic record
Abstract
A transport algorithm called the proton loss (PL) model is developed for proton pencil beams of therapeutic energies. The PL model takes into account inelastic nuclear reactions, pathlength straggling, and energy-loss straggling and predicts the 3D dose distribution from a proton pencil beam. In proton beams, the multiple scattering and ionizational energy loss processes approach their diffusional limit where scattering and energy loss probability densities become Gaussian. Therefore we chose to derive the PL model from the Fermi-Eyges diffusional multiple scattering theory and the Gaussian theory of energy straggling. We first introduce a generalization of the Fermi-Eyges equation for proton pencil beams, labeled the proton loss (PL) transport equation. This new equation includes terms that model inelastic nuclear reactions as a depth-dependent absorption and pathlength straggling as a quasi-absorption. Then energy straggling is taken into account by using a weighted superposition of a discrete number of elementary pencil beams. These elementary pencil beams have different initial energies and lose energy according to the CSDA, thus they have different ranges of penetration. A final solution for the proton beam transport is obtained as a linear combination of elementary pencil beam solutions with weights defined by the Gaussian evolution of the proton energy spectrum with depth. A numerical comparison of the dose distribution predictions of the PL model with measurements and PTRAN Monte Carlo simulations indicates the model is both computational fast and accurate.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".