Radiopharmaceutical Dosimetry Calculator (MIRD)
Estimate absorbed dose to a target organ and whole-body effective dose from radiopharmaceutical administration using the MIRD method.
🏥 What is the Radiopharmaceutical Dosimetry Calculator (MIRD)?
Radiopharmaceutical dosimetry quantifies the radiation dose delivered to organs and the whole body from internally administered radioactive compounds used in nuclear medicine. Unlike external beam radiotherapy, where dose is controlled by the radiation machine, internal dosimetry depends on the biodistribution, retention, and physical decay of the radiopharmaceutical in each organ. Accurate dosimetry is essential for setting safe activity limits in diagnostic scanning and for optimizing therapeutic efficacy in targeted radionuclide therapy (TRT).
This calculator implements the MIRD (Medical Internal Radiation Dosimetry) method, the international standard developed by the MIRD Committee of the Society of Nuclear Medicine. In Organ Dose mode, the calculator uses the fundamental MIRD equation D = A_tilde x S, where A_tilde (cumulated activity) is the total number of radioactive disintegrations in the source organ over the irradiation period and S is the absorbed dose per unit cumulated activity. The simplified S-value formula D = 576.7 x A_tilde x E x phi / m expresses absorbed dose as a function of the mean energy per disintegration, the absorbed fraction, and the organ mass. Preset isotope data are provided for the seven most clinically important radionuclides: Tc-99m, F-18, I-131, I-123, Lu-177, Ga-68, and Y-90.
The Effective Dose mode uses published effective dose coefficients from ICRP Publication 128 (2013) for nine common radiopharmaceuticals. Effective dose aggregates the absorbed doses to all organs, weighted by their tissue sensitivity factors, into a single number that represents the overall stochastic health risk from the procedure. Results are expressed in millisieverts (mSv) and compared to the equivalent number of chest X-rays for context. These coefficients apply to a standard adult patient and are accepted by national regulatory bodies for dose reporting in nuclear medicine.
Typical diagnostic nuclear medicine procedures deliver 1 to 20 mSv effective dose, comparable to a few months to a few years of natural background radiation. Therapeutic administrations (I-131 thyroid ablation, Lu-177 PRRT, Y-90 radioembolization) are designed to deliver tumoricidal doses of tens to hundreds of Gy to the target tissue while keeping organ doses below accepted tolerance limits. The MIRD method and this calculator support both the educational understanding and the early-stage planning calculations for these treatments.
📐 Formula
D (mGy) = 576.7 × Ã × &Ebar; × φ ÷ m
D = absorbed dose to target organ (mGy)
à = cumulated activity = A₀ × f × Teff / ln(2) (MBq·h)
A₀ = injected activity (MBq)
f = fractional uptake in source organ (dimensionless)
Teff = effective half-life = Tphys × Tbio / (Tphys + Tbio)
&Ebar; = mean energy per disintegration for non-penetrating radiation (MeV/dis)
φ = absorbed fraction (0 to 1); = 1.0 for beta emitters
m = organ mass (g)
576.7 = conversion factor = 10⁹ Bq/MBq × 3600 s/h × 1.602×10⁻¹³ J/MeV × 1000 mGy/Gy × 1000 g/kg
Effective dose: E (mSv) = A₀ (MBq) × k (mSv/MBq), where k is the ICRP 128 dose coefficient
Example: Tc-99m renal scan: 370 MBq injected, 30% kidney uptake, T½bio = 1h, T½eff = 0.857h, m = 150g, E = 0.0215 MeV, phi = 1: Atilde = 137.3 MBq·h, D = 576.7 x 137.3 x 0.0215 x 1.0 / 150 = 11.3 mGy
📖 How to Use This Calculator
Steps
1
Select isotope and enter injected activity - Choose the radiopharmaceutical isotope from the dropdown. The physical half-life and mean non-penetrating energy per disintegration are auto-filled from published data. Enter the injected or administered activity in MBq.
2
Enter organ uptake fraction and biological half-life - Type the percent of injected activity that accumulates in the target organ (e.g. 30% for renal DTPA in both kidneys). Enter the biological half-life of the radiopharmaceutical in that organ in hours. Leave biological half-life blank if there is no biological clearance.
3
Set absorbed fraction and organ mass - Enter the absorbed fraction: use 1.0 for pure beta emitters (Y-90, Lu-177 beta component) or for self-dose when penetrating radiation is negligible. For Tc-99m or I-123 with significant gamma, consult MIRD pamphlets for the organ-specific phi. Enter the organ mass in grams (typical kidney: 150 g, liver: 1800 g, thyroid: 20 g).
4
Switch to Effective Dose mode for whole-body dose - Click the Effective Dose tab. Select the radiopharmaceutical from the list and enter the administered activity. The result shows effective dose in mSv using ICRP 128 coefficients and the equivalent number of chest X-rays for context.
💡 Example Calculations
Example 1 - Tc-99m Renal DTPA Scan
Absorbed dose to kidneys: 370 MBq Tc-99m DTPA, 30% uptake, 1h biological T1/2
1
T_eff = 6.01 x 1.0 / (6.01 + 1.0) = 6.01 / 7.01 = 0.857 h. Cumulated activity: Atilde = 370 x 0.30 x 0.857 / 0.693 = 137.3 MBq·h.
2
Using E = 0.0215 MeV/dis, phi = 1.0, m = 150 g (single kidney): D = 576.7 x 137.3 x 0.0215 x 1.0 / 150 = 11.3 mGy per kidney.
3
ICRP 128 publishes kidney absorbed dose of 9 to 14 mGy for 370 MBq Tc-99m DTPA, confirming the estimate is in the correct range for a simple first-order biokinetic model.
Kidney dose = 11.3 mGy per kidney
Try this example →Example 2 - I-131 Thyroid Ablation Dose
Absorbed dose to thyroid remnant: 3700 MBq I-131, 20% uptake, T1/2 bio = 7 days
1
T_phys = 192.5 h (8.02 d), T_bio = 168 h (7 d). T_eff = 192.5 x 168 / (192.5 + 168) = 32376 / 360.5 = 89.8 h.
2
Atilde = 3700 x 0.20 x 89.8 / 0.693 = 95,924 MBq·h. Using E = 0.182 MeV/dis (beta only, phi = 1), m = 1 g (small thyroid remnant after surgery): D = 576.7 x 95924 x 0.182 x 1.0 / 1 = 10,073,000 mGy = 10,073 Gy.
3
Very high dose to a very small remnant is expected in ablative I-131 therapy. Published thyroid remnant doses range from 1,000 to 20,000+ Gy depending on remnant mass and I-131 uptake, confirming the order of magnitude.
Thyroid remnant dose = ~10,000 Gy (confirms ablative intent)
Try this example →Example 3 - F-18 FDG PET Effective Dose
Effective dose from a standard F-18 FDG PET whole-body scan: 370 MBq
1
Using ICRP 128 effective dose coefficient for F-18 FDG = 0.019 mSv/MBq for adult patients.
2
Effective dose = 370 MBq x 0.019 mSv/MBq = 7.03 mSv.
3
Comparison: 7.03 mSv / 0.02 mSv = 352 chest X-rays equivalent, or about 2.6 years of UK natural background radiation (2.7 mSv/year).
Effective dose = 7.03 mSv (352 chest X-rays equivalent)
Try this example →❓ Frequently Asked Questions
What is the MIRD method for radiopharmaceutical dosimetry?
The MIRD (Medical Internal Radiation Dosimetry) method calculates the absorbed dose to target organs from internally distributed radioactivity using the formula D = A_tilde × S, where A_tilde is the cumulated activity (total disintegrations in the source organ in Bq·s or MBq·h) and S is the mean absorbed dose per unit cumulated activity (Gy/Bq·s). The simplified self-dose form is D = 576.7 × A_tilde × E × phi / m, where E is the mean energy per disintegration and m is the organ mass in grams.
What is cumulated activity in nuclear medicine dosimetry?
Cumulated activity A_tilde is the total number of radioactive disintegrations in the source organ integrated over the entire irradiation period. For monoexponential clearance: A_tilde = A₀ × f × T_eff / ln(2), where A₀ is the injected activity, f is the uptake fraction, and T_eff is the effective half-life. A_tilde represents the total dose delivery potential; a longer T_eff or higher uptake gives a larger A_tilde and higher absorbed dose.
How is the effective half-life calculated for a radiopharmaceutical?
T_eff = T_phys × T_bio / (T_phys + T_bio). It combines the physical decay half-life and the biological clearance half-life. T_eff is always shorter than both components. For Tc-99m DTPA in the kidney: T_phys = 6.01 h, T_bio ≈ 1 h, giving T_eff = 6.01 × 1 / 7.01 = 0.857 h. This means the dose delivery is brief, limiting kidney dose. If there is no biological clearance, T_eff = T_phys.
What is the absorbed fraction (phi) and when is it equal to 1?
The absorbed fraction phi is the fraction of emitted radiation energy that is deposited within the target organ. For non-penetrating radiation (alpha, beta, Auger electrons), phi = 1.0 because all energy is stopped within the source organ. For penetrating radiation (gamma, X-rays), phi depends on organ size, geometry, and photon energy, and is typically 0.005 to 0.05 for small organs. For therapeutic use (Y-90, Lu-177 beta), phi = 1 is a valid approximation for large organs like the liver.
What is the difference between absorbed dose (Gy) and effective dose (Sv) in nuclear medicine?
Absorbed dose (Gy or mGy) measures energy deposited per unit mass in a specific organ. Effective dose (Sv or mSv) is a radiation protection quantity that sums the equivalent doses to all organs weighted by their tissue sensitivity factors, producing a single number representing the overall stochastic cancer risk. For diagnostic nuclear medicine with gamma and beta emitters, the radiation weighting factor wR = 1, so equivalent dose equals absorbed dose numerically. Effective dose allows comparison of risk between different types of radiation exposures.
What are typical absorbed doses from common nuclear medicine procedures?
Typical organ absorbed doses: Tc-99m bone scan - bladder wall 30-50 mGy per 740 MBq; F-18 FDG PET - bladder wall 50-80 mGy per 370 MBq; I-131 thyroid scan - thyroid 10,000-50,000 mGy per 400 MBq; Lu-177 DOTATATE therapy - kidneys 3-10 Gy per 7.4 GBq cycle, tumor 20-100+ Gy per cycle; Y-90 glass microsphere liver therapy - liver 80-150 Gy per treatment depending on activity and volume.
How does Y-90 differ from other therapeutic radionuclides in dosimetry?
Y-90 is a pure beta emitter (no gamma) with a mean beta energy of 0.9337 MeV and physical T½ of 64.1 h. Because there is no gamma emission, all energy is deposited locally with phi = 1 for large target volumes. Dosimetry is simplified compared to gamma emitters. However, Y-90 imaging for verification is difficult (only bremsstrahlung X-rays and a rare positron emission at 32 ppm). PET-CT with the 511 keV annihilation signal is increasingly used for Y-90 post-therapy dosimetry verification.
What are the organ dose constraints in Lu-177 PRRT?
In Lu-177 DOTATATE peptide receptor radionuclide therapy, the EANM guideline recommends a maximum cumulative kidney absorbed dose of 23 Gy (per BED model with alpha/beta = 2.5 Gy). The bone marrow dose should remain below 2 Gy to prevent severe myelosuppression. The standard protocol of four cycles at 7.4 GBq (200 mCi) each delivers approximately 3-8 Gy to the kidneys per cycle. Renal dosimetry is performed by serial SPECT-CT imaging of each cycle.
Can this calculator be used for clinical patient dosimetry?
This calculator is educational and provides first-order estimates using the simplified MIRD formula. For clinical use in therapeutic nuclear medicine, patient-specific dosimetry requires: quantitative serial SPECT-CT or PET-CT imaging at multiple time points, individualized biokinetic modeling, Monte Carlo or voxel-based dose calculation (e.g., OLINDA/EXM 2.0 or Voxel-Dose), and organ contouring from cross-sectional imaging. The simplified formula can be within a factor of 2-5 of detailed calculations when the biokinetic model is accurate.
What is the typical effective dose from a Tc-99m bone scan?
A standard Tc-99m MDP bone scan with 740 MBq delivers approximately 4.1 mSv effective dose (0.0055 mSv/MBq from ICRP 128), equivalent to about 200 chest X-rays or about 18 months of UK natural background radiation. The highest absorbed dose organ is the bladder wall, which receives about 46 mGy due to urinary excretion of the unbound Tc-99m pertechnetate fraction.
What ICRP publications govern radiopharmaceutical dosimetry?
The main ICRP publications for nuclear medicine dosimetry are: ICRP 53 (1987) - radiation dose to patients from radiopharmaceuticals; ICRP 80 (1998) - paediatric dosimetry; ICRP 106 (2008) - update on diagnostic agents; ICRP 128 (2013) - comprehensive update with dose coefficients for 125 radiopharmaceuticals in adults, covering all major modern agents including Ga-68 and Lu-177 compounds. The MIRD committee published MIRD Pamphlet 21 (2009) on patient dosimetry using the new MIRD framework with S-values for the ICRP 89 phantom family.
How is radiopharmaceutical dosimetry different from external beam radiation therapy dosimetry?
External beam radiotherapy delivers a precisely defined, spatially controlled dose from outside the patient, measured in real time with dosimeters. Radiopharmaceutical internal dosimetry relies on measuring the distribution and clearance of the radioactive drug in each patient using nuclear medicine imaging (SPECT-CT, PET-CT), then converting to dose using mathematical models. Dose gradients within organs depend on the biodistribution pattern, which varies between patients. Internal dosimetry is inherently more uncertain than external beam dosimetry, typically to within 20-50% compared to 2-5% in modern external beam treatments.