Methods & references

Relative activity of Ac‑225 and its daughters over time after a pure Ac‑225 sample, with branching and emitted radiation for each nuclide.

Based on

• A five-state decay model; At‑217 and Po‑213 are treated as in instantaneous equilibrium with their parents.
• Half-lives and branching as summarised in the Bi‑213 review [1] and NIST Ac‑225 activity measurements [2].

Checked against

• Not separately benchmarked: an educational visualisation of ingrowth and branching.

Limits

• A closed system: no biology, chemical separation or daughter escape.
• Not a dose, detector-response or dose-calibrator tool.

Mean organ alpha absorbed dose from Ac‑225 and its four alpha-emitting daughters by local energy deposition: dose = time-integrated activity × mean alpha energy per decay ÷ organ mass. A separate RBE-weighted column.

Based on

• Mean alpha energy per decay from every listed alpha line in NNDC NuDat 3 (ENSDF) [3], including Bi‑213’s 2.14% alpha branch and the 97.86% branch to Po‑213.
• ICRP 110 adult reference organ masses [5], from the OpenDose packages [4].
• Daughter-specific imaging option after Liubchenko et al. [7]: Fr‑221 (218 keV) and Bi‑213 (440 keV) curves, with an optional separate Ac‑225 curve.
• RBE 5 for deterministic effects as suggested by MIRD Pamphlet 22 [8] (user-adjustable).

Checked against

• Reproduces the kidney dose of Tronchin et al. 2024 [6], Table 3, within 0.5% for both adult reference phantoms (229.8 and 259.1 mGy/MBq).
• Mean alpha energies agree within 0.2% with those implied by Tronchin et al. 2024, Table 4.

Limits

• Alpha self-dose only; beta, photon and cross-organ dose are not included (a few percent of the chain energy).
• Reference anatomy and uniform activity within each organ.
• Daughter redistribution before the first scan is captured only by the curve fitted to 0 h.

Mean absorbed dose to target organs from source-organ time-integrated activity using published organ S-values (MIRD formalism), with self and cross contributions shown separately and an illustrative 3D organ display.

Based on

• OpenDose S-value tables for the ICRP 110 adult male and female phantoms [4, 5], snapshot of 11 October 2026 with source URLs and SHA-256 hashes in a manifest.
• Physical half-lives from ICRP Publication 107 [9].

Checked against

• S-values are used exactly as published; a missing coefficient blocks the calculation rather than being treated as zero.
• Unit, time-integration and source-to-target arithmetic covered by automated tests.

Limits

• Reference anatomy, not patient anatomy; no voxel dosimetry.
• The 3D display anatomy (BodyParts3D [12]) is illustrative and is not the calculation phantom.

Where Ac‑225, Fr‑221 and Bi‑213 go in the body over time, and the kidney and tumour alpha dose with and without daughter migration. In Nuclear Studio, the model can be fitted to your own kidney (and optionally blood) Fr‑221 and Bi‑213 measurements to give a model-based kidney dose with uncertainty and a fit-quality check. Both carrier models are fitted and ranked automatically (AICc), and a schedule check estimates how accurately a given set of scan times would recover the kidney dose.

Based on

• The compartment model of Tronchin et al. 2024 [6]: unlabeled Ac‑225 in plasma with element-specific ICRP biokinetics for actinium, francium and bismuth.
• An extension for labelled carriers (PSMA-like small molecule, IgG antibody) with daughter release on recoil. Each parameter is marked as calibrated, chosen or illustrative.
• Francium mobility as a parameter: the ICRP model treats free francium like caesium, while mouse organ counting found little Fr‑221 transport between organs [10].

Checked against

• Reproduces the kidney doses of Tronchin et al. 2024 with daughter migration (adult male 260.8, adult female 294.0 mGy/MBq) and the increase of about 13.5% over daughters decaying at the Ac‑225 site.
• The in-browser version reproduces the research implementation to one part in a million across 12 reference cases, and the fit recovers the kidney dose of simulated patients with known parameters within a few percent.
• In 40 simulated patients per case, model comparison picked the right carrier 95–100% of the time whenever the wrong one would shift the kidney dose by more than 10%; when it could not tell them apart, both gave the same dose within a few percent.
• Compared, without retuning, with a second clinical study (Zhang et al. [15], ²²⁵Ac-PSMA-CY313, 4 patients): simulating their scan times and exponential-fit method, the model predicts the kidney dose they would report as 0.21–0.22 Gy/MBq (RBE 5) against their 0.23 ± 0.07. Their reported kidney Bi‑213/Fr‑221 residence ratio (0.78) is below what the model can produce (≥ 1), which points to a 440 keV quantification question or faster bismuth loss than ICRP assumes.
• PSMA-like kidney uptake calibrated to the kidney dose of Liubchenko et al. [7]; the antibody blood half-life chosen to match the human projection of Schwartz et al. [11], so those are fits, not validations.

Limits

• Human reference biokinetics; carrier parameters beyond the calibrated ones are illustrative.
• A weak prior keeps the Fr‑221 and Bi‑213 kidney uptakes near the ICRP reference (1 SD = ×3); a patient far outside that range would be pulled toward it.
• Fit uncertainties are statistical and do not include model-structure error beyond the candidates compared; whether francium is freed from its carrier needs blood measurements to be determined.
• For research and education, not patient dose estimation.

Simulated imaging of Fr‑221 and Bi‑213 with a Si/CdTe Compton camera, quantification of kidney activity, and a kinetic-model fit that recovers the kidney dose of a simulated patient with known parameters.

Based on

• Geant4 11.4 through OpenGATE 10.1 [13] with low-energy (Livermore) photon physics.
• A Si/CdTe camera geometry after Orita et al. [14]; a clinical SPECT baseline from the GE Discovery NM670 model shipped with OpenGATE.
• The daughter kinetics model above as the simulated truth.

Checked against

• SPECT baseline resolution close to textbook collimator estimates (within about 5% on average).
• In simulation, the model fit recovered the kidney dose within a few percent across several scenarios; robustness checks for cross-talk, wrong models and francium mobility are documented with the code.

Limits

• Simulation only, not peer-reviewed: a mouse-sized phantom in air (no tissue attenuation or scatter) with human kinetics.
• A methods study, not a prediction for any animal or patient.