Dosimetry simulator
The steps of post-therapy dosimetry on example cases: time–activity curve, cumulated activity (Ã), absorbed dose, single-time-point method, cycle totals and kidney BED. Values are representative; change the numbers in the table and watch the result.
7.4 GBq single cycle; quantitative SPECT/CT at 4, 24, 72 and 168 h (representative).
1. Time–activity data
| Time (h) | Percent of injected activity (%) | MBq |
|---|---|---|
| 296 | ||
| 192 | ||
| 104 | ||
| 31 |
Edit a cell; the calculation updates when you leave it.
2. Area under the curve (Ã)
A log-linear mono-exponential is fitted to the points after the peak; uptake up to the peak is taken as linear (triangle); Ã = triangle + integral of A·e^(−λt).
fitted curve physical decay only Ã
3. Kinetics
- Effective half-life
- 51.9 h · R² 0.994
- Cumulated activity Ã
- 20802 MBq·h
- Residence time τ = Ã / A₀
- 2.81 h
In the anterior human figure the case's organs glow over time following the tool's fitted time-activity curves; the panel accumulates each organ's cumulated activity and absorbed dose, the last step sums the cycles and shows kidney BED. Tap an organ or its row to select it.
3 If each cycle repeats the same distribution, the total dose of 4 cycles is {n} times the cycle dose; in the kidneys the dose-rate effect is assessed with BED.
Total of 4 cycles
4. Absorbed dose (self-dose)
D = Ã × E / m = 20802 MBq·h × 0.1479 MeV × 1.602×10⁻¹³ J/MeV × 3600 × 10⁶ / 310 g
- Absorbed dose (this cycle)
- 5.72 Gy
- Dose per unit activity
- 0.77 Gy/GBq
For Lu-177 the mean local energy per decay is 0.1479 MeV (β + conversion/Auger electrons); photons and organ-to-organ cross-dose are ignored. Mass from the ICRP 89 adult reference. Real dosimetry uses S values (OLINDA/IDAC) and the patient's own organ volume.
5. Single-time-point method
à ≈ A(t) × 2t / ln2 = 104 × 2 × 72 / 0.693 = 21523 MBq·h
Difference from the multi-point result: +3.5%. The Hänscheid approximation (Ã ≈ A(t)·2t/ln2) is most accurate when the measurement time is close to ~1.5 × the effective half-life.
6. Cycle total and BED
- One cycle
- 5.72 Gy
- Total of 4 cycles
- 22.9 Gy
- BED (one cycle)
- 6.37 Gy
- BED (total)
- 33.2 Gy
Total kidney BED 28–40 Gy: above the threshold if risk factors are present (hypertension, diabetes, prior chemotherapy, older age).
BED = D·[1 + (D/(α/β))·Trep/(Trep + Teff)], kidney α/β 2.6 Gy, repair half-time 2.8 h (sources use 1.5–2.8 h; editable). Total BED is approximated from the total physical dose.
Organ summary
| Organ | Gy/GBq | One cycle | Total of 4 cycles |
|---|---|---|---|
| Kidneys | 0.77 | 5.72 Gy | 22.9 Gy |
| Spleen | 0.93 | 6.91 Gy | 27.7 Gy |
| Liver (normal parenchyma) | 0.25 | 1.86 Gy | 7.4 Gy |
| Tumour (20 mL liver metastasis) | 8.04 | 59.53 Gy | 238.1 Gy |
Source: MIRD self-dose approach; Lu-177 data ENSDF; organ masses ICRP 89; single time point Hänscheid et al. J Nucl Med 2018; kidney BED Bodei et al. EJNMMI 2008 and Wessels et al. J Nucl Med 2008; Marinelli formula EANM benign thyroid RAI guideline 2023. The example time–activity values are representative of published typical ranges (Lu-177: 1 MBq·h → 8.53×10⁻⁵ J)
For education only; not for treatment decisions in real patients, and no patient data should be entered.