Radiopharmaceutical Dosimetry Calculator (MIRD)

The MIRD (Medical Internal Radiation Dosimetry) method, developed by the MIRD Committee of the Society of Nuclear Medicine (SNM), calculates the absorbed dose to target organs from internally distributed radioactivity. The key formula is D = A_tilde × S, where A_tilde is the cumulated activity (total number of disintegrations in the source organ) and S is the S-value (mean absorbed dose per unit cumulated activity in the target organ from the source organ). The simplified form for self-dose is D = 576.7 × A_tilde × E × φ / m.

Cumulated activity A_tilde (also written A-tilde) is the total number of radioactive disintegrations occurring in the source organ over the entire irradiation period, expressed in Bq·s or MBq·h. For a monoexponential clearance with effective half-life T_eff, A_tilde = A₀ × f × T_eff / ln(2), where A₀ is the injected activity, f is the fraction taken up by the organ, and T_eff is the effective half-life. The effective half-life is the harmonic mean of physical and biological half-lives: T_eff = T_phys × T_bio / (T_phys + T_bio).

The effective half-life T_eff combines the physical decay and the biological clearance from the organ: T_eff = T_phys × T_bio / (T_phys + T_bio). It is always shorter than both T_phys and T_bio. For example, I-131 in the thyroid has T_phys = 8.02 days and a typical T_bio of 80 days, giving T_eff = 8.02 × 80 / (8.02 + 80) = 7.29 days. If there is no biological clearance (T_bio = infinity), then T_eff = T_phys.

The absorbed fraction φ is the fraction of the emitted radiation energy that is absorbed within the target organ. For non-penetrating radiation (alpha, beta, Auger electrons), φ = 1 for self-dose because all energy is deposited within the source organ. For penetrating radiation (gamma, X-rays), φ depends on the organ size, geometry, and photon energy. For small soft tissue organs and 100-400 keV gamma rays, φ is typically 0.005 to 0.05. The product E × φ is the effective absorbed energy per disintegration.

The S-value S(T←S) is the mean absorbed dose delivered to the target organ T per unit cumulated activity in the source organ S. It has units of Gy/(Bq·s) or mGy/(MBq·h). The S-value encapsulates all the geometry, penetration, and energy transport information for a given source-target organ pair. Published S-values for standard organ geometries are tabulated in MIRD Pamphlets and the OLINDA/EXM software for each radionuclide.

The simplified formula D = 576.7 × A_tilde × E × φ / m gives absorbed dose estimates accurate to within a factor of 2 to 5 for simple cases. Accuracy improves when: the organ is the source and target (self-dose), the radiation is non-penetrating (beta), the organ geometry is roughly spherical, and the uptake and clearance follow monoexponential kinetics. For clinical targeted radionuclide therapy dosimetry, Monte Carlo-based calculations or OLINDA/EXM with patient-specific data are required for accuracy better than 20%.

Absorbed dose (Gy or mGy) measures energy deposited per unit mass. Effective dose (Sv or mSv) accounts for the relative biological effectiveness of the radiation type (radiation weighting factor wR) and the sensitivity of specific organs to radiation-induced cancer (tissue weighting factor wT), providing a single number representing overall radiation risk. For nuclear medicine (gamma and beta emitters), wR = 1, so equivalent dose numerically equals absorbed dose. Effective dose sums the equivalent doses to all organs weighted by wT.

A standard Tc-99m MDP bone scan with 740 MBq gives an effective dose of about 4.1 mSv (0.0055 mSv/MBq × 740 MBq), equivalent to approximately 200 chest X-rays or about 16 months of natural background radiation in the UK. The highest absorbed dose occurs in the bladder wall (due to urinary excretion) at approximately 46 mGy for 740 MBq.

In Lu-177 DOTATATE peptide receptor radionuclide therapy (PRRT) for neuroendocrine tumors, each cycle of 7,400 MBq delivers 3 to 10 Gy to the kidneys and 20 to 100+ Gy to tumor tissue, depending on the somatostatin receptor expression. Four cycles are typically administered at 8-week intervals. The kidney dose per cycle is monitored to stay below the cumulative tolerance of 23 Gy recommended by EANM guidelines.

Y-90 is a pure beta emitter (Emax = 2.28 MeV, mean 0.9337 MeV) with no significant gamma emission. In Y-90 microsphere therapy (SIR-Spheres, TheraSphere) for liver tumors, all beta energy is absorbed locally in the liver tissue. The absorbed fraction φ = 1.0 for the liver as both source and target. The absorbed dose to the liver is simply D = 576.7 × A_tilde × 0.9337 × 1.0 / m_liver. The standard dosimetry model uses a uniform liver distribution to estimate mean dose.

A typical nuclear medicine scan delivers 1 to 20 mSv effective dose. For comparison: natural background in the UK is about 2.7 mSv/year; a CT of the abdomen is 8 to 10 mSv; a chest X-ray is 0.02 mSv; transcontinental flight is 0.08 mSv. Therapeutic administrations of I-131 for thyroid cancer (3,700 to 7,400 MBq) deliver 800 to 1600 mSv effective dose but are justified by the therapeutic benefit to the patient.

The kidneys are the dose-limiting organ in most targeted radionuclide therapies because they concentrate the radiopharmaceutical during renal excretion. The EANM guideline recommends a maximum cumulative kidney absorbed dose of 23 Gy based on partial-volume irradiation models. Some centers use 28 Gy for patients with no pre-existing renal disease. Kidney dosimetry is performed by measuring kidney activity over time from SPECT-CT or serial planar images during each therapy cycle.