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Physics · Dosimetry

Internal Dosimetry: MIRD and Therapy Dosimetry

Snapshot

Internal dosimetry turns where activity goes, and for how long, into absorbed dose. The MIRD schema multiplies the number of decays in each source region (time-integrated activity, Ã) by an S value, the dose to a target per decay. Diagnostic studies are summarised by effective dose in reference phantoms; therapy needs patient-specific absorbed doses from quantitative SPECT/CT at several time points.

Absorbed dose (Gy = J/kg) predicts tissue reactions such as renal or marrow toxicity and tumour response. Effective dose (Sv) is a protection quantity for a reference person: it compares procedures but does not describe an individual patient.

D = Ã × SMIRD schema
GyAbsorbed dose — therapy
mSvEffective dose — comparison
Reference values
  • à = ∫A(t)dt (Bq·s); for mono-exponential clearance à = f·A₀/λ_eff = 1.443·f·A₀·T_eff.
  • Time-integrated activity coefficient ã = Ã/A₀ — the MIRD 21 name for residence time.
  • S(T←S) = (1/M_T)·Σ Eᵢ·Yᵢ·φᵢ(T←S), in Gy per Bq·s; independent of activity.
  • ICRP 103 w_T: 0.12 red marrow, colon, lung, stomach, breast, remainder; 0.08 gonads; 0.04 bladder, oesophagus, liver, thyroid; 0.01 bone surface, brain, salivary glands, skin.
  • ¹⁸F-FDG adult dose coefficient 0.019 mSv/MBq (ICRP 128): about 7 mSv for 370 MBq.
  • ⁹⁰Y: D (Gy) ≈ 50 × A (GBq) / M (kg) with complete local absorption.
  • ¹⁷⁷Lu-PRRT kidneys 23 Gy, or BED 28 Gy (risk factors) / 40 Gy (none); marrow 2 Gy.
  • ¹³¹I: blood ≤2 Gy; Graves' disease 150 Gy (euthyroid aim) to 200–300 Gy (ablative); toxic nodule 300–400 Gy.
Worked example

Kidney dose from mono-exponential clearance

Given. ¹⁷⁷Lu-DOTATATE 7.4 GBq. Kidneys (300 g) take up f = 3% promptly and clear with T_eff = 50 h. Electron energy ≈ 0.147 MeV per decay, fully absorbed; photon cross-dose neglected.

  1. Ã = f·A₀·T_eff/ln2 = 2.22×10⁸ Bq × (50 × 3600 s)/0.693 = 5.77×10¹³ Bq·s.
  2. S = 0.147 × 1.602×10⁻¹³ J / 0.30 kg = 7.85×10⁻¹⁴ Gy per Bq·s.
  3. D = Ã × S = 4.5 Gy per cycle (0.61 Gy/GBq); four cycles ≈ 18 Gy.
  4. Single-time-point check: A(96 h) = 0.0587 GBq; A(t)·2t/ln2 = 5.85×10¹³ Bq·s (+1.5%).

Answer. About 4.5 Gy per cycle and 18 Gy after four — below the 23-Gy constraint if the kinetics stay the same.

Two-panel graph of kidney activity against time after a lutetium-177 therapy: measured points at 4, 24, 96 and 168 hours with the area under the curve shaded as trapezoids plus an extrapolated tail; the right panel shows the same data on a log scale with a straight-line fit through the late points.
Figure. Time-integrated activity is the area under the time–activity curve. Trapezoids between measured points miss the tail after the last scan, which is added by fitting an exponential (right, log scale: a straight line). The single-time-point shortcut (A at 96 h × 2t/ln2) gives a similar area here (simulated kidney data).
Flow diagram of the MIRD chain from quantitative imaging at several time points, through time–activity curves and time-integrated activity, S values, summation over sources to absorbed dose and comparison with limits, with a side panel showing self-dose and cross-dose between two organs.
Figure. The MIRD chain: activity measured over time in each source region is integrated to Ã, multiplied by the S value for each target (self-dose within an organ, cross-dose from penetrating photons) and summed; therapy doses are then compared with organ limits.
Three panels of simulated data: an activity map of a tumour with a necrotic centre, the corresponding absorbed-dose map, and a dose–volume histogram with the mean dose and D90 marked.
Figure. Simulated data. Voxel dosimetry turns a quantitative activity map into a dose map and a dose–volume histogram. The mean tumour dose hides the under-dosed necrotic centre, which D90 (the dose received by at least 90% of the volume) reveals.

The MIRD schema

  • Dose to a target is the sum over source regions of Ã × S: D(r_T) = Σ Ã(r_S)·S(r_T←r_S).
  • S values come from Monte Carlo transport in reference phantoms, using each nuclide's emission energies and yields and the absorbed fraction φ reaching the target.
  • For β, α and Auger emitters φ ≈ 1 within the source and ≈ 0 elsewhere, so self-dose dominates; photons add cross-dose between organs.
  • Organ S values assume uniform activity in reference-mass organs; scaling self-dose by reference/patient mass is the simplest personalisation.

Effective dose and its limits

  • E = Σ w_T·H_T, with H_T = Σ w_R·D_T,R (w_R 1 for photons and electrons, 20 for α).
  • ICRP 128 tabulates dose coefficients for reference adults and children; effective dose serves justification, optimisation and comparison of procedures, not an individual's dose or risk.
  • Therapy causes tissue reactions that depend on organ absorbed dose and dose rate, so effective dose has no role there (see radiation protection).

Software and voxel methods

  • OLINDA/EXM and IDAC-Dose 2.1 (ICRP voxel phantoms, sphere module for tumours) calculate organ doses from organ à values.
  • Voxel dosimetry convolves the 3-D Ã map with voxel S values or dose-point kernels, or assumes local deposition when the β range is shorter than the voxel (¹⁷⁷Lu about 2 mm maximum vs 4–5 mm voxels).
  • Monte Carlo on the patient's CT handles lung and bone interfaces; voxel methods yield dose maps and dose–volume histograms that reveal heterogeneity.

Quantitative SPECT/CT and time points

  • Quantification needs attenuation, scatter and resolution modelling, a phantom-derived calibration factor (cps/MBq), dead-time correction and recovery coefficients for small objects (see quantification).
  • Use at least three well-separated time points; for kidneys after the first ¹⁷⁷Lu cycle EANM advises three SPECT/CT scans between day 1 and day 7.
  • Fit the curve and integrate to infinity — trapezoids alone miss the tail; single-time-point methods rely on known population kinetics.

Therapy dosimetry in practice

  • ¹³¹I thyroid cancer: blood ≤2 Gy and 48-h whole-body retention ≤4.44 GBq (≤2.96 GBq with diffuse lung metastases); ablation succeeded more often with ≥300 Gy to remnants and ≥80 Gy to metastases (see thyroid cancer).
  • Benign thyroid (Marinelli-type): activity = target dose × mass / (energy per decay × time-integrated uptake); EANM rule of thumb (T_eff 5.5 d) is 6, 8 or 12 MBq × mass (g) / 24-h uptake for 150, 200 or 300 Gy.
  • ¹⁷⁷Lu-DOTATATE: kidneys and marrow are the organs at risk; ¹⁷⁷Lu-PSMA: salivary and lacrimal glands and marrow, with no established salivary tolerance dose (see theranostics).
  • ⁹⁰Y SIRT partition model from ⁹⁹ᵐTc-MAA SPECT/CT: lung ≤30 Gy per treatment and ≤50 Gy cumulative; resin whole-liver: non-tumoural liver ≤40 Gy, tumour ≥100–120 Gy.
  • EU: Directive 2013/59/Euratom Article 56 requires therapy to be individually planned and its delivery verified. US: NRC requires a written directive for therapeutic administrations but not patient-specific dosimetry.
  • BED for instantaneous uptake and mono-exponential clearance: BED = D[1 + D·λ/((μ + λ)·α/β)], μ = repair rate, λ = clearance rate.
In depth
  • MIRD 21 replaced 'cumulated activity' and 'residence time' by à and ã, and adopted effective dose only for comparing stochastic risk.
  • Models differ: IDAC-Dose 2.1 with ICRP 103 weighting gives 0.016 mSv/MBq for FDG, against 0.019 mSv/MBq in ICRP 128.
  • Single time point: a kidney measurement at about 96 h reproduced à with median error +5% (−9 to +17%); 24-, 48- and 144-h measurements underestimated kidney dose unacceptably in some patients.
  • Kidney doses are 0.54–1.00 Gy/GBq for ¹⁷⁷Lu-somatostatin analogues and 0.4–0.8 Gy/GBq for ¹⁷⁷Lu-PSMA, with up to three-fold spread between patients.
  • EANM reads Article 56 in three levels: standardised treatments within 10% of the intended activity; off-label activities more than 25% above label need patient-specific organ-at-risk dosimetry; dosimetry-guided prescription.
  • In DOSISPHERE-01 (glass ⁹⁰Y, HCC), ≥205 Gy to the index lesion gave a 71% response rate against 36% with 120 ± 20 Gy to the lobe.

Sources: MIRD 21 (PMID 19258258) · Andersson 2017 (PMID 29098485) · Hänscheid 2018 (PMID 28588150) · EANM 2022 (PMID 35284969) · Konijnenberg 2021 (PMID 33057773) · Garin 2021 (PMID 33166497)

Sources

  1. Bolch WE, Eckerman KF, Sgouros G, Thomas SR. MIRD pamphlet No. 21: a generalized schema for radiopharmaceutical dosimetry. J Nucl Med. 2009;50:477–84.
  2. ICRP Publication 103: the 2007 Recommendations. Ann ICRP. 2007;37(2–4).
  3. ICRP Publication 128: radiation dose to patients from radiopharmaceuticals. Ann ICRP. 2015;44(2S).
  4. Andersson M, et al. IDAC-Dose 2.1, an internal dosimetry program for diagnostic nuclear medicine. EJNMMI Res. 2017;7:88.
  5. Ljungberg M, et al. MIRD pamphlet No. 26: quantitative ¹⁷⁷Lu SPECT for dosimetry. J Nucl Med. 2016;57:151–62.
  6. Sjögreen Gleisner K, et al. EANM dosimetry committee recommendations for ¹⁷⁷Lu-labelled SSTR and PSMA ligands. Eur J Nucl Med Mol Imaging. 2022;49:1778–1809.
  7. Campennì A, et al. The EANM guideline on radioiodine therapy of benign thyroid disease. Eur J Nucl Med Mol Imaging. 2023;50:3324–48.
  8. Levillain H, et al. International recommendations for personalised SIRT with ⁹⁰Y resin microspheres. Eur J Nucl Med Mol Imaging. 2021;48:1570–84.
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