The MIRD Schema for Internal Dosimetry

Introduction

The MIRD schema is the standardized method nuclear medicine uses to estimate the radiation absorbed dose that an internally administered radiopharmaceutical delivers to organs and tissues. In its modern, harmonized form, the absorbed dose to a target region is simply the time-integrated activity in each source region multiplied by a dose factor—the S value—summed over all sources. ¹

That deceptively simple structure separates the problem into two halves. One half is biology: how much activity localizes in each region of the body and how long it stays there. The other half is physics: how the radionuclide's emissions deposit energy in the target tissue given the anatomy. The MIRD schema, developed and refined by the Medical Internal Radiation Dose Committee of the Society of Nuclear Medicine and Molecular Imaging (SNMMI), provides the framework that ties these halves together with consistent nomenclature. ¹

Internal dosimetry has moved from a research curiosity to a clinical necessity. The rise of theranostics—paired diagnostic and therapeutic radiopharmaceuticals such as Lu-177 DOTATATE and Lu-177 PSMA—has made patient-specific absorbed-dose estimation central to safe, effective radiopharmaceutical therapy. This guide explains the MIRD equation, its physical and biological inputs, the S value, the supporting software, and how the schema underpins modern dosimetry. DRPS supports nuclear medicine programs with PET/CT and nuclear medicine physics and medical physicist consulting across its service areas.

Topic Explanation

What the MIRD schema is—and is not

The MIRD schema is a framework for converting measured activity in the body, over time, into absorbed dose. It is not a single number, a single software package, or a fixed protocol. It is the conceptual and mathematical structure—standardized nomenclature, defined quantities, and the master dose equation—within which many different methods (organ-level, voxel-level, Monte Carlo) operate. ¹

The schema was originally published in 1968, revised in 1976, and presented in didactic form as the MIRD primer in 1988 and 1991. MIRD Pamphlet No. 21, published in 2009, restated the schema to harmonize MIRD and International Commission on Radiological Protection (ICRP) nomenclature and to formally adopt the quantities equivalent dose and effective dose for comparative risk evaluation. ¹

The two ingredients

Every MIRD calculation needs two things for each source region:

Time-integrated activity $\tilde{A} (r_{S})$ — the total number of nuclear transformations in source region $r_{S}$ over the integration period. This is biology, measured by quantitative imaging or sampling. ²
S value $S (r_{T} \leftarrow r_{S})$ — the absorbed dose to target region $r_{T}$ per unit time-integrated activity in source $r_{S}$ . This is physics, derived from radionuclide emission data and anatomical models. ¹

For background on the emission characteristics that drive S values, see our overview of common PET and radiopharmaceutical-therapy isotopes, and for the activity-quantification side, see PET SUV quantification.

Key Technical Principles

The master MIRD equation

The mean absorbed dose to a target region $r_{T}$ over a dose-integration period $T_{D}$ is: ¹

D (r_{T}, T_{D}) = r_{S} \sum \tilde{A} (r_{S}, T_{D}) S (r_{T} \leftarrow r_{S})

The sum runs over every source region that contains activity, including the target region itself (self-dose). This single equation is the heart of internal dosimetry. ¹

Time-integrated activity

The time-integrated activity is the area under the activity–time curve for a source region: ^{1, 2}

\tilde{A} (r_{S}) = \int_{0}^{\infty} A (r_{S}, t) d t

In the common case where uptake is fast and clearance follows a single exponential, the activity decays with an effective decay constant that combines physical decay and biological clearance:

λ_{eff} = λ_{phys} + λ_{bio}, T_{eff} = \frac{T _{phys} T _{bio}}{T _{phys} + T _{bio}}

and the time-integrated activity reduces to:

\tilde{A} (r_{S}) = \frac{A _{0}}{λ _{eff}} = \frac{A _{0} T _{eff}}{ln 2}

The effective half-life is always shorter than either the physical or biological half-life alone—a key reason the residence time of a radiopharmaceutical in tissue is often much shorter than its physical half-life would suggest. ²

The S value

The S value packages all of the radionuclide physics and anatomy: ¹

S (r_{T} \leftarrow r_{S}) = \frac{1}{M ( r _{T} )} i \sum E_{i} Y_{i} ϕ (r_{T} \leftarrow r_{S}, E_{i})

where $E_{i}$ and $Y_{i}$ are the energy and yield of the $i$ -th emission, $ϕ (r_{T} \leftarrow r_{S}, E_{i})$ is the absorbed fraction (the fraction of energy $E_{i}$ emitted in the source that is deposited in the target), and $M (r_{T})$ is the target mass. The emission data come from standardized decay-data compilations such as ICRP Publication 107; the absorbed fractions come from anatomical (phantom or voxel) models. ^{1, 5}

Worked example: time-integrated activity for a Lu-177 therapy

Suppose quantitative SPECT/CT shows an initial kidney activity of $A_{0} = 2.0$ GBq after a Lu-177 therapy administration, with a measured effective half-life in the kidneys of $T_{eff} = 50$ h. The effective decay constant is:

λ_{eff} = \frac{ln 2}{T _{eff}} = \frac{0.693}{50 \times 3600 s} = 3.85 \times 1 0^{- 6} s^{- 1}

Converting the activity to transformations per second ( $2.0 GBq = 2.0 \times 1 0^{9} s^{- 1}$ ), the time-integrated activity is:

\tilde{A} = \frac{A _{0}}{λ _{eff}} = \frac{2.0 \times 1 0 ^{9} s ^{- 1}}{3.85 \times 1 0 ^{- 6} s ^{- 1}} \approx 5.2 \times 1 0^{14} transformations

The kidney absorbed dose then follows directly from $D = \tilde{A} S_{kidney \leftarrow kidney}$ (plus cross-dose terms from other source organs), using a kidney self-dose S value taken from MIRD or OLINDA/EXM tabulations for Lu-177. The point of the example is the structure: the imaging gives $\tilde{A}$ , and the standardized S value converts it to dose. Realistic multi-cycle Lu-177 kidney dosimetry sums these contributions across treatment cycles. ^{3, 4, 5}

Harmonized MIRD and ICRP nomenclature

MIRD Pamphlet 21 explicitly aligned MIRD and ICRP terminology so the two communities could communicate. The correspondence is summarized below. ¹

Quantity	MIRD term / symbol	ICRP analog
Total nuclear transformations in a source	Time-integrated activity, $\tilde{A}$	Time-integrated activity coefficient
Dose per unit time-integrated activity	S value, $S (r_{T} \leftarrow r_{S})$	Specific effective energy / dose coefficient
Fraction of emitted energy absorbed in target	Absorbed fraction, $ϕ$	Absorbed fraction (AF)
Absorbed fraction per unit target mass	Specific absorbed fraction, $Φ$	Specific absorbed fraction (SAF)

Clinical Impact

The MIRD schema is what makes patient-specific radiopharmaceutical therapy dosimetry possible. In theranostics, the same molecular target is imaged with a diagnostic radionuclide and treated with a therapeutic one, and the MIRD schema converts quantitative images into absorbed dose to tumors and to organs at risk. ^{1, 5}

For Lu-177–based therapies, MIRD Pamphlet No. 26 provides joint EANM/MIRD guidance specifically for quantitative Lu-177 SPECT applied to dosimetry of radiopharmaceutical therapy, recognizing that the accuracy of any absorbed-dose estimate depends directly on the accuracy of the activity quantification at each imaging time point. ⁵ This is why dose estimation is inseparable from rigorous quantitative imaging—see our guides to Lu-177 theranostics dosimetry and Y-90 radioembolization dosimetry.

The clinical stakes are concrete:

Organs at risk. Kidney and bone-marrow absorbed dose can be dose-limiting in Lu-177 and Y-90 therapy; MIRD dosimetry supports cumulative-dose tracking across cycles.
Tumor dose–response. Absorbed dose to lesions correlates with response in several therapies, motivating dosimetry-guided rather than fixed-activity prescribing.
Diagnostic dose estimates. For diagnostic radiopharmaceuticals, ICRP Publication 128 provides standardized biokinetic models and dose coefficients (organ doses and effective dose) compiled within the same conceptual framework. ⁶

For pediatric patients, where organ masses and biokinetics differ substantially from adults, dose estimation must use age-appropriate models—an issue we address in pediatric nuclear medicine dosing.

Practical Optimization Tips

A defensible MIRD calculation follows a consistent workflow.

1. Quantify activity correctly

The dose is only as good as the time-integrated activity. This requires calibrated, attenuation- and scatter-corrected SPECT or PET, a known camera calibration factor, and accurate volume-of-interest definition. MIRD Pamphlet No. 16 details acceptable biodistribution data-acquisition methods. ²

2. Sample enough time points

The activity–time curve must be sampled well enough to characterize uptake and clearance. Too few time points—or a poorly chosen final point—can bias the integral substantially. Match the sampling to the effective half-life of the agent in each region. ²

3. Choose the right S value source

Organ-level dosimetry: standardized phantom S values, as in OLINDA/EXM, are appropriate for many applications. ^{3, 4}
Patient-specific therapy: voxel-level or Monte Carlo methods better capture individual anatomy and heterogeneous uptake. ⁵

4. Document anatomical and biokinetic assumptions

Record the phantom or patient model, the masses used, the decay data source, the fitting method for the time–activity curve, and any corrections applied. This documentation is what makes the result reproducible and defensible.

5. Common pitfalls

Confusing physical and effective half-life. Time-integrated activity depends on the effective half-life, not the physical half-life alone.
Ignoring cross-dose. Penetrating emissions deposit dose in neighboring organs; self-dose alone underestimates the total.
Mismatched masses. Using a standard-phantom organ mass for a patient whose organ differs greatly in size biases the S value.
Over-interpreting a single time point. Robust dosimetry needs the full time–activity curve, not a snapshot.

Regulatory Considerations

Internal dosimetry intersects with the regulations that govern the medical use of byproduct material, even though the MIRD schema itself is a scientific framework rather than a regulation. ⁷

Key frameworks to reference:

10 CFR Part 35 — Medical Use of Byproduct Material. Governs authorized use, written directives, and the dose-related requirements for therapeutic administrations; dosimetry supports written directives and patient management for radiopharmaceutical therapy. ⁷
10 CFR Part 20 — Standards for Protection Against Radiation. Sets the dose limits and ALARA framework that contextualize occupational and public dose around therapy patients. ⁸
MIRD Pamphlet No. 21 and No. 26. The authoritative scientific basis for the schema and for Lu-177 quantitative dosimetry, respectively. ^{1, 5}
ICRP Publication 128. Standardized diagnostic radiopharmaceutical dose coefficients used for patient dose estimates. ⁶

Agreement States administer their own equivalent medical-use programs. Of the states DRPS serves, Florida, Maryland, Virginia, California, Nevada, Pennsylvania, New York, and New Jersey are NRC Agreement States that license medical use under their own radiation-control rules, while Washington, DC and Delaware are regulated directly by the NRC for radioactive material. A facility must verify which authority issues its license and which requirements apply. For the radiation-safety side of therapy programs, see our guide to patient release after radiopharmaceutical therapy and RPT shielding for Lu-177, Ra-223, and Ac-225.

Frequently Asked Questions (FAQs)

What is the MIRD schema?

The MIRD (Medical Internal Radiation Dose) schema is the standardized framework, developed by the MIRD Committee of the Society of Nuclear Medicine and Molecular Imaging, for calculating the radiation absorbed dose to organs and tissues from radionuclides taken into the body. In its modern form it expresses absorbed dose to a target region as the sum, over all source regions, of the time-integrated activity in each source multiplied by a dose factor called the S value.

What is the basic MIRD equation?

The absorbed dose to a target region equals the sum over all source regions of the time-integrated activity in the source region times the S value from that source to the target. The S value carries the radionuclide's emission data and the anatomical geometry, while the time-integrated activity carries the biology—how much activity was present in each source region and for how long.

What is time-integrated activity (cumulated activity)?

Time-integrated activity, historically called cumulated activity, is the total number of nuclear transformations that occur in a source region over the dose-integration period. It is the area under the activity-versus-time curve for that region and is obtained from quantitative imaging or sampling at multiple time points. It captures both how much activity localized in the tissue and how long it stayed there.

What is an S value?

An S value is the mean absorbed dose to a target region per unit time-integrated activity in a source region for a specific radionuclide. It combines the energies and yields of the radionuclide's emissions with the absorbed fractions that describe how much of that emitted energy is deposited in the target, divided by the target mass. S values are tabulated in MIRD publications and computed in software such as OLINDA/EXM.

How is the MIRD schema used in theranostics?

In radiopharmaceutical therapy with agents such as Lu-177, Y-90, or I-131, the MIRD schema converts quantitative SPECT or PET measurements of activity over time into absorbed dose to tumors and to organs at risk such as the kidneys and bone marrow. This supports treatment planning, response assessment, and the management of cumulative dose across multiple cycles.

What software implements the MIRD schema?

OLINDA/EXM is a widely used, FDA-cleared personal-computer code that implements MIRD-style internal dose calculations using standardized anatomical models and decay data; version 2.0 updated the models and decay data. Other tools include voxel-based and Monte Carlo dosimetry packages used for patient-specific therapy planning. The appropriate tool depends on whether organ-level or voxel-level dosimetry is required.

Who should perform internal dosimetry calculations?

Internal dosimetry should be performed or overseen by a board-certified medical physicist working with the authorized user and the nuclear medicine team. The calculations depend on correct image quantification, time-activity modeling, radionuclide data, and anatomical assumptions, all of which require physics expertise to apply and document defensibly.

Key Takeaways

Dose = time-integrated activity × S value, summed over sources. This single equation is the core of the MIRD schema. ¹
The schema splits biology from physics. Time-integrated activity comes from imaging; the S value comes from standardized emission data and anatomical models. ^{1, 2}
Effective half-life, not physical half-life, drives residence time. Time-integrated activity uses the effective decay constant combining physical and biological clearance. ²
S values package emissions, absorbed fractions, and target mass. They are tabulated in MIRD publications and computed in OLINDA/EXM. ^{1, 3, 4}
Theranostics depends on the schema. Accurate Lu-177 and Y-90 therapy dosimetry requires rigorous quantitative imaging fed into the MIRD framework. ⁵
Document everything. Decay data, models, masses, sampling, and fitting assumptions make a dose estimate defensible. ²

Conclusion

The MIRD schema gives nuclear medicine a common, rigorous language for internal dosimetry. Its strength is structural clarity: absorbed dose is the time-integrated activity in each source region multiplied by an S value that encodes the radionuclide physics and the anatomy. Everything else—quantitative imaging, biokinetic modeling, anatomical phantoms, Monte Carlo transport—feeds into one of those two terms.

As radiopharmaceutical therapy expands, the schema is no longer just a tool for estimating diagnostic doses; it is the basis for patient-specific treatment planning, organ-at-risk protection, and dose–response analysis. Applied carefully by a qualified medical physicist, with documented assumptions and accurate activity quantification, the MIRD schema turns images into the absorbed-dose information that makes modern theranostics both safer and more effective.

How DRPS Can Help

Diagnostic Radiation Physics Services helps nuclear medicine and theranostics programs build defensible internal-dosimetry workflows. This may include PET/CT and nuclear medicine physics support, quantitative SPECT/PET calibration, time–activity modeling, organ- and voxel-level dose estimation, documentation review, and medical physicist consulting prepared by board-certified medical physicists.

DRPS supports facilities across our service locations, including Florida, Maryland, Virginia, Washington DC, California, Nevada, New York, Pennsylvania, New Jersey, and Delaware.

A strong dosimetry program is not just about producing a number. It is about making that number traceable, reproducible, and clinically actionable for the patient in front of you.

Related Resources

References

Bolch WE, Eckerman KF, Sgouros G, Thomas SR. MIRD pamphlet No. 21: a generalized schema for radiopharmaceutical dosimetry—standardization of nomenclature. Journal of Nuclear Medicine. 2009;50(3):477-484. doi:10.2967/jnumed.108.056036. PubMed
Siegel JA, Thomas SR, Stubbs JB, et al. MIRD pamphlet no. 16: Techniques for quantitative radiopharmaceutical biodistribution data acquisition and analysis for use in human radiation dose estimates. Journal of Nuclear Medicine. 1999;40(2):37S-61S. PubMed
Stabin MG, Sparks RB, Crowe E. OLINDA/EXM: the second-generation personal computer software for internal dose assessment in nuclear medicine. Journal of Nuclear Medicine. 2005;46(6):1023-1027. PubMed
Stabin MG. OLINDA/EXM 2—the next-generation personal computer software for internal dose assessment in nuclear medicine. Health Physics. 2023;124(5):397-406. doi:10.1097/HP.0000000000001682. PubMed
Ljungberg M, Celler A, Konijnenberg MW, et al. MIRD pamphlet No. 26: Joint EANM/MIRD guidelines for quantitative 177Lu SPECT applied for dosimetry of radiopharmaceutical therapy. Journal of Nuclear Medicine. 2016;57(1):151-162. doi:10.2967/jnumed.115.159012. PubMed
International Commission on Radiological Protection. ICRP Publication 128: Radiation Dose to Patients from Radiopharmaceuticals — A Compendium of Current Information Related to Frequently Used Substances. Annals of the ICRP. 2015;44(2S). icrp.org
U.S. Nuclear Regulatory Commission. 10 CFR Part 35: Medical Use of Byproduct Material. nrc.gov
U.S. Nuclear Regulatory Commission. 10 CFR Part 20: Standards for Protection Against Radiation. nrc.gov
International Commission on Radiological Protection. ICRP Publication 107: Nuclear Decay Data for Dosimetric Calculations. Annals of the ICRP. 2008;38(3). icrp.org
Society of Nuclear Medicine and Molecular Imaging. MIRD Committee resources and publications. snmmi.org