σ-LEM – Analytical Local Effect Model for AuNP Radiosensitisation

Reference implementation & reproducibility notebooks for
“An analytical model for gold nanoparticle radiosensitisation”
P. Teles, arXiv : 2506.06671 (2025)

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Overview

σ-LEM provides a closed-form, variance-driven Local-Effect Model that eliminates Monte-Carlo voxel scoring.
Key equations (Eqs. 9–37 of the paper) are implemented exactly as printed — including

• variance-only,
• variance + mixed term, and
• full 2nd-order σ² models —
  plus the truncated-Gaussian correction for negative-dose tails (Eq. 27).

All figures, tables and numerical values in the manuscript can be re-generated with the notebooks below.

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Repository layout

sigma_lem/                      # core Python functions (model, fitting, utils)
notebooks/
 ├─ K_c.ipynb                   # Fig. 2 & Tables 2-3 (K_c vs energy)
 ├─ Survival_curves-truncated.ipynb   # Fig. 3-4, survival curves w/ truncation
 ├─ DEF80-truncated.ipynb       # DEF_80 calculations (Tab. C.6-C.8)
 └─ FIT_results-truncated.ipynb # α′, β′ fits (Tab. 4-5)
LICENSE                         # GPL v3
CITATION.cff                    # citation metadata
requirements.txt                # tested package versions
README.md                       # you are here


### Tested versions

| Package    | Version |
|------------|---------|
| numpy      | 1.26 |
| scipy      | 1.12 |
| matplotlib | 3.9 |
| jupyter    | 1.0 |
| tqdm       | 4.66 |

*(Python ≥ 3.9; other 3.x versions should work but are untested.)*

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## Quick start

```bash
# interactive notebook
jupyter notebook notebooks/K_c.ipynb

# or, non-interactive full reproduction
python -m sigma_lem.demo   # recreates all manuscript numbers in <60 s

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Reproducibility checklist

Manuscript item	Notebook / script	✓ SHA-256 check
Fig. 2 – (K_\mathrm{c}(E)) curve	K_c.ipynb	✓
Tables 2–3 – (K_\mathrm{c}) values & DER	K_c.ipynb	✓
Figs. 3–4 – σ, σ + mixed, σ² models	Survival_curves-truncated.ipynb	✓
DEF_80 hierarchy (Tab. C.6–C.8)	DEF80-truncated.ipynb	✓
α′ / β′ fits (Tab. 4–5)	FIT_results-truncated.ipynb	✓

All notebooks were last executed against commit <hash>

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Citing this work

If you use the code or model, please cite both the software release and the pre-print:

@software{teles_sigmaLEM,
  author       = {Pedro Teles},
  title        = {{σ-LEM}: Log-normal Analytical Local Effect Model},
  version      = {v1.0.2},
  date         = {2025},
  doi          = {10.5281/zenodo.15734277},  
  url          = {[https://github.com/PedroTelesFCUP/sigma-LEM]}
}

@article{teles_2025,
  author  = {Pedro Teles},
  title   = {An analytical model for gold nanoparticle radiosensitisation},
  journal = {arXiv e-prints},
  year    = {2025},
  eprint  = {2506.06671},
  url     = {https://arxiv.org/abs/2506.06671}
}

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License

Distributed under the GPL v3 licence.
See LICENSE for the full text.

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Contributing

Pull requests with bug fixes, additional test cases, or new beam-quality data are welcome.
Please open an issue first to discuss major changes.

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Contact

Pedro Teles – ppteles@fc.up.pt