Residency · Residency · Nuclear Medicine

Radiation Dosimetry and Internal Dose Calculation

Fundamental Dosimetric Quantities

Absorbed Dose

Absorbed dose (D) is the most fundamental dosimetric quantity, representing the energy deposited per unit mass of tissue. It is measured in Gray (Gy), where 1 Gy equals 1 joule per kilogram. The older unit, the rad, relates as 1 Gy = 100 rad. Absorbed dose applies to any type of radiation and any tissue, but it does not account for the varying biological effectiveness of different radiation types.

Equivalent Dose

Equivalent dose (H) builds on absorbed dose by incorporating a radiation weighting factor (w_R) that accounts for the different biological impacts of different radiation types. The relationship is simply H = D x w_R. For gamma rays and beta particles, the weighting factor is 1, meaning equivalent dose equals absorbed dose. For alpha particles, the factor is 20, reflecting their far greater biological damage per unit absorbed dose. Neutrons have energy-dependent weighting factors ranging from 5 to 20. Equivalent dose is measured in Sieverts (Sv), with the older unit being the rem (1 Sv = 100 rem).

Effective Dose

Effective dose (E) extends the concept further by weighting the equivalent dose to each organ by a tissue weighting factor (w_T) that reflects that organ's relative radiosensitivity to stochastic effects. The effective dose is the sum of (w_T x H_T) across all irradiated organs. Tissue weighting factors from ICRP 103 assign red bone marrow, colon, lung, breast, and remainder tissues each a weight of 0.12, while gonads receive 0.08, with other organs ranging from 0.01 to 0.04. Effective dose, measured in Sieverts, is the standard quantity for comparing radiation risk across different procedures and imaging modalities. It is designed for radiation protection and risk communication purposes, not for therapy planning.

Committed Dose

The committed effective dose represents the total effective dose that will accumulate over 50 years for adults (or to age 70 for children) following the intake of a radioactive material. This concept is relevant for both accidental internal contamination and intentional radiopharmaceutical administration, as it accounts for the ongoing irradiation that occurs while retained radionuclides continue to decay within the body.

The MIRD Schema

Overview

The Medical Internal Radiation Dose (MIRD) Committee of the Society of Nuclear Medicine developed the standard framework used worldwide for calculating internal radiation doses from administered radiopharmaceuticals. The MIRD schema calculates the absorbed dose to any target organ from radioactivity distributed across one or more source organs. The fundamental equation is: D(target) = sum over all sources of [A_tilde(source) x S(target <- source)].

Cumulated Activity (A-tilde)

Cumulated activity represents the total number of radioactive disintegrations that occur in a source organ over time. Mathematically, it is the integral of the time-activity curve from zero to infinity: A_tilde = integral of A(t) dt, expressed in units of Bq-seconds or MBq-hours. The cumulated activity in any organ depends on the administered activity, the fraction taken up by that organ, the biological half-life of clearance from the organ, and the physical half-life of the radionuclide. The effective half-life, which combines physical and biological clearance through the reciprocal relationship 1/T_eff = 1/T_phys + 1/T_biol, determines how quickly activity disappears from the organ.

Residence Time

Residence time (tau) normalizes the cumulated activity to the administered activity: tau = A_tilde / A_0, measured in hours. It can be understood as the total time that the administered activity would need to reside in an organ to produce the same total number of disintegrations. Residence times are determined from serial imaging studies (planar, SPECT, or PET) acquired at multiple time points after radiopharmaceutical administration.

S-Values

The S-value represents the absorbed dose delivered to a target organ per unit cumulated activity in a source organ, expressed in units such as Gy/(Bq-s) or mGy/(MBq-s). S-values depend on the types and energies of the radionuclide's emissions, the sizes, shapes, and separations of the source and target organs, and the tissue composition and density between them. These values are pre-calculated and tabulated for standard reference phantoms in MIRD pamphlets and in software tools like OLINDA.

OLINDA/EXM Software

OLINDA (Organ Level Internal Dose Assessment) is the standard software for internal dose calculations in nuclear medicine. It contains pre-computed S-values for adult male, adult female, pediatric (multiple ages), and pregnant female phantoms. The user inputs residence times for each source organ, and the software outputs absorbed dose (mGy/MBq) and effective dose (mSv/MBq) for all target organs. The updated version, OLINDA 2.0, employs more anatomically realistic voxel-based phantoms.

Determining Time-Activity Curves

Serial Imaging

Constructing the time-activity curve requires measuring organ activity at multiple time points after injection. This can be accomplished through quantitative planar imaging using the conjugate view method, quantitative SPECT or SPECT/CT at multiple time points, or quantitative PET/CT for positron-emitting theranostic pairs. Blood and urine sampling can complement imaging data to account for circulating and excreted activity.

Conjugate View Method

The conjugate view method uses simultaneously acquired anterior and posterior planar images. Taking the geometric mean of anterior and posterior counts corrects for depth-dependent attenuation, since a deeper source will be closer to one detector while farther from the other. An attenuation correction based on measured or estimated body thickness, along with a calibration factor from a known activity standard, converts the geometric mean counts to absolute organ activity.

Curve Fitting

Once activity is measured at several time points, the data are fitted with mono-exponential or bi-exponential curves. Integration of the fitted curve yields the cumulated activity. At least 3 to 4 time points are needed for reliable curve fitting, and it is important to capture both the uptake phase and the washout phase to avoid underestimating or overestimating the total number of disintegrations.

Clinical Applications

Diagnostic Radiopharmaceutical Dosimetry

Typical effective doses for common diagnostic nuclear medicine procedures include approximately 4 to 5 mSv for a Tc-99m MDP bone scan (740 MBq), 7 mSv for an F-18 FDG PET (370 MBq), 9 to 12 mSv for a Tc-99m sestamibi cardiac study (1110 MBq), 15 to 20 mSv for a Tl-201 cardiac study (111 MBq), and 3 to 4 mSv for a Ga-68 DOTATATE PET (150 MBq). The critical organ -- the organ receiving the highest absorbed dose -- is often the bladder, colon, or kidneys, depending on the tracer's excretion route. For renally excreted tracers, hydration and frequent voiding significantly reduce bladder dose.

Therapeutic Dosimetry

Two approaches to therapeutic dosimetry are used in practice. The empiric or fixed-dose approach administers a standard activity to all patients regardless of individual biodistribution, such as the common practice of giving 150 mCi of I-131 for thyroid cancer remnant ablation. The dosimetry-guided approach tailors the administered activity based on pre-therapy imaging to deliver a specified absorbed dose to the tumor while keeping normal organ doses within safe limits. Dose-limiting organs in radionuclide therapy include the kidneys (threshold approximately 23 to 27 Gy for Lu-177 DOTATATE), red bone marrow (approximately 2 Gy for I-131 therapy), and salivary glands (no established formal limit, though toxicity is clearly dose-related).

Voxel-Based Dosimetry

Voxel-based dosimetry is an emerging approach that uses three-dimensional activity distributions from quantitative SPECT/CT or PET/CT to calculate absorbed dose at the individual voxel level rather than averaging over entire organs. This method accounts for heterogeneous tracer distribution within both organs and tumors, making it particularly valuable for radioembolization with Y-90 and peptide receptor radionuclide therapy with Lu-177 DOTATATE. Dedicated software platforms for voxel dosimetry include PLANET Dose, Voximetry, and MIM SurePlan.

Pediatric Dosimetry Considerations

Children receive higher absorbed doses per unit administered activity than adults simply because of their smaller body size -- the same amount of energy is deposited in less tissue mass. Pediatric phantoms spanning newborn to 15-year-old body habitus are used for dose estimation. Weight-based dosing guidelines, such as the EANM dosage card, reduce the administered activity appropriately. The effective dose per MBq can be 2 to 5 times higher in neonates compared to adults, underscoring the importance of dose optimization in pediatric nuclear medicine.

<image>A flowchart illustrating the MIRD internal dosimetry schema. Start with administered activity, show its distribution to multiple source organs based on biodistribution data. For each source organ, show the time-activity curve integration yielding cumulated activity (A-tilde). Then show the S-value lookup table connecting each source organ to each target organ. Finally, show the summation of all source contributions to calculate total absorbed dose in each target organ. Include the fundamental equation D(target) = sum of A-tilde(source) x S(target from source).</image>

<image>A series of time-activity curves demonstrating the concept of cumulated activity and effective half-life. Show a typical organ uptake-washout curve with data points from serial imaging at 1, 4, 24, and 48 hours post-injection. Illustrate the bi-exponential curve fit, with the area under the curve shaded and labeled as cumulated activity (A-tilde). Include an inset showing the relationship between physical half-life, biological half-life, and effective half-life with the formula 1/T_eff = 1/T_phys + 1/T_biol.</image>

<image>A comparison diagram showing empiric versus dosimetry-guided radionuclide therapy planning. On the left, show the fixed-dose approach where all patients receive the same standard activity. On the right, show the personalized dosimetry approach with pre-therapy imaging, time-activity curves, dose calculation, and activity adjustment to achieve a target tumor dose while respecting organ dose limits. Highlight the potential advantage of personalized dosimetry in optimizing the therapeutic window.</image>

Clinical Pearls

The effective half-life is always shorter than both the physical and biological half-lives individually. This is a commonly tested concept on board examinations and follows directly from the reciprocal relationship.

For diagnostic studies, effective dose is the most appropriate quantity for comparing radiation risk across different procedures and imaging modalities. For therapeutic planning, however, absorbed dose in Gray to specific target and dose-limiting organs is the relevant quantity, and effective dose is not useful.

Hydration and frequent voiding should always be encouraged to reduce bladder dose for renally excreted tracers such as FDG, DOTATATE, and PSMA agents. This is one of the simplest and most effective dose reduction strategies available.

Tl-201 delivers one of the highest effective doses among common diagnostic radiopharmaceuticals at approximately 15 to 20 mSv per study. This unfavorable dosimetry is a primary reason Tl-201 has been largely replaced by Tc-99m agents for myocardial perfusion imaging.

Voxel-based dosimetry is increasingly important for personalized theranostic therapy, particularly for Y-90 radioembolization and Lu-177 DOTATATE, but it is not yet universally implemented or standardized across institutions.

In pediatric nuclear medicine, weight-based dose adjustment is essential. Children are more radiosensitive than adults and receive higher absorbed doses per MBq due to their smaller body mass, making dose optimization a priority.

References

• Bolch WE, et al. MIRD Pamphlet No. 21: A generalized schema for radiopharmaceutical dosimetry. J Nucl Med. 2009;50(3):477-484.
• Stabin MG. Fundamentals of Nuclear Medicine Dosimetry. Springer; 2008.
• Sgouros G, et al. ICRU Report 96: Dosimetry-guided radiopharmaceutical therapy. J ICRU. 2021;21(1).
• Lassmann M, et al. EANM Dosimetry Committee guidance on internal dosimetry. Eur J Nucl Med Mol Imaging. 2021;48(2):267-281.

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