Voxel-Based Dosimetry for Radiopharmaceutical Therapy

Introduction

A single number cannot describe a dose that is not uniform. In radiopharmaceutical therapy, the radioactive drug concentrates unevenly — more in some tumor regions than others, differently across the kidneys, variably in marrow — yet traditional organ-level dosimetry collapses all of that into one mean absorbed dose per organ. Voxel-based dosimetry keeps the spatial detail, turning a patient's own images into a three-dimensional map of absorbed dose. ^{1, 2}

That shift matters clinically. As radiopharmaceutical therapy (RPT) moves from fixed-activity administration toward personalized treatment planning, the field increasingly wants the same quantity radiation oncology has always used: a dose distribution, with a dose-volume histogram (DVH) for tumors and organs at risk. Voxel-based dosimetry is how nuclear medicine gets there, built on quantitative SPECT/CT, voxel S-values or Monte Carlo transport, and careful handling of time. ^{2, 3}

This article explains the physics and workflow of voxel-based dosimetry, how it differs from organ-level MIRD, when Monte Carlo is warranted, and where it fits in the regulatory and clinical picture. DRPS supports facilities building quantitative imaging and dosimetry programs through its PET/CT and nuclear medicine physics and medical physics consulting services across Florida, Maryland, Virginia, Washington DC, California, Nevada, Pennsylvania, New York, New Jersey, and Delaware.

Topic Explanation

From mean organ dose to a dose map

Voxel-based dosimetry is internal dosimetry performed on a three-dimensional grid of small volume elements (voxels), producing an absorbed-dose distribution rather than a single mean value per organ. It is the spatial generalization of the MIRD schema that underlies all internal dosimetry. For the organ-level foundation, see the MIRD schema for internal dosimetry.

In the classic MIRD formulation, the mean absorbed dose to a target region is the sum over all source regions of the time-integrated activity multiplied by an S-value:

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

where $\tilde{A} (r_{S})$ is the time-integrated (cumulated) activity in source region $r_{S}$ and $S (r_{T} \leftarrow r_{S})$ converts that activity into mean dose to target region $r_{T}$ . This gives one number per organ. ¹

Voxel-based dosimetry applies the same equation at the voxel scale. Each voxel is both a potential source and a target, so the dose to voxel $v_{k}$ is: ²

D (v_{k}) = j \sum \tilde{A} (v_{j}) S (v_{k} \leftarrow v_{j})

Because the voxel S-value depends only on the displacement between source and target in a homogeneous medium, this sum is a convolution of the time-integrated activity map with a single voxel S-value kernel — computationally fast and the reason voxel dosimetry is practical at the bedside. ²

Why nonuniformity is the whole point

Organ-level dosimetry assumes activity is uniformly distributed in a reference-phantom organ. Real uptake is not uniform: a tumor may have a necrotic, low-uptake core and an avid rim; a kidney may receive dose unevenly along the cortex; marrow uptake varies. A mean dose can be identical for two very different distributions, one of which under-treats the tumor core while the other over-irradiates a region of an organ at risk. The DVH that voxel dosimetry produces exposes exactly those differences. ^{2, 9}

Key Technical Principles

Voxel S-values and dose point kernels

A voxel S-value is the mean absorbed dose to a target voxel per unit time-integrated activity in a source voxel, tabulated for a specific radionuclide and voxel size in a homogeneous soft-tissue medium. MIRD Pamphlet No. 17 introduced voxel-level S-values and the use of dose point kernels and Monte Carlo methods for nonuniform distributions. ¹ A dose point kernel is the continuous radial description of absorbed dose around an isotropic point source of the radionuclide; voxel S-values can be derived from it.

The physical range of the emissions sets how far dose spreads from a source voxel:

Lu-177 emits a low-energy beta with a short, roughly sub-2-millimeter range in soft tissue, so most dose is deposited within a few voxels — voxel convolution works well.
Y-90 emits a higher-energy beta reaching on the order of a centimeter, spreading dose across many voxels, which makes accurate kernels and cross-voxel dose essential.
Alpha emitters such as Ac-225 deposit energy over sub-cellular distances, so standard millimeter-scale voxel S-values are inadequate and small-scale or Monte Carlo methods are required. ^{1, 2}

Time: the time-integrated activity map

Dose is driven by the total number of decays, not the instantaneous activity, so each voxel (or region) needs its time-integrated activity — the area under its activity–time curve: ^{2, 8}

\tilde{A} (v_{j}) = \int_{0}^{\infty} A (v_{j}, t) d t

In the common case of uptake followed by single-exponential clearance, the activity decays with an effective rate constant combining physical decay and biological clearance:

λ_{eff} = λ_{phys} + λ_{bio}, \tilde{A} = \frac{A _{0}}{λ _{eff}}

Worked example. Lu-177 has a physical half-life of 6.647 days, so $λ_{phys} = ln 2/6.647 = 0.1043 d^{- 1}$ . If a lesion clears biologically with a 3.0-day half-life, $λ_{bio} = ln 2/3.0 = 0.231 d^{- 1}$ , giving:

λ_{eff} = 0.1043 + 0.231 = 0.335 d^{- 1}, T_{eff} = \frac{ln 2}{0.335} = 2.07 days

The effective half-life (2.07 days) is shorter than either the physical or biological half-life alone, and it determines how much dose the lesion accumulates. Capturing it requires imaging at multiple time points, which is why dosimetry protocols acquire serial SPECT/CT. ^{4, 8}

Quantitative SPECT/CT is the foundation

Voxel dose is only as accurate as the activity map it starts from. Converting SPECT counts into activity concentration (becquerels per milliliter) requires calibration, CT-based attenuation correction, scatter correction, and resolution recovery — the methods formalized in MIRD Pamphlet No. 23 and the radionuclide-specific guidance of MIRD Pamphlets No. 24 (I-131) and No. 26 (Lu-177). ^{2, 3, 4} For the calibration side of this, see quantitative SPECT/CT calibration.

The three tiers of internal dosimetry

Approach	Spatial output	Tissue heterogeneity	Computational cost	Typical use
Organ-level MIRD	One mean dose per organ	Reference-phantom only	Low	Standard reporting; whole-organ constraints
Voxel-based (S-value convolution)	3D dose map and DVH	Assumes homogeneous soft tissue	Moderate	Patient-specific tumor and organ dose maps
Direct Monte Carlo	3D dose map and DVH	Full patient geometry and density	High	High-density heterogeneity; alpha emitters; reference accuracy

Voxel S-value convolution is the practical middle ground: far more informative than a single organ number, and far faster than full Monte Carlo. Monte Carlo remains the reference standard where tissue density varies sharply (lung, bone, air) or where the physics demands it. ^{2, 9}

Clinical Impact

The clinical argument for voxel dosimetry is that absorbed dose predicts outcome, and mean organ dose can mislead. In peptide receptor radionuclide therapy (PRRT) with Lu-177 DOTATATE, tumor-absorbed doses spanning roughly 10 to 340 Gy showed a significant dose–response relationship, with the correlation strongest for larger lesions (a reported coefficient of determination of 0.91 for tumors larger than 4 cm). ⁵ Higher absorbed dose was associated with greater tumor shrinkage — exactly the kind of relationship that personalized planning aims to exploit.

On the safety side, individualized dosimetry in Lu-177 DOTA-octreotate therapy found kidney absorbed doses of about 2 to 10 Gy per 7.4 GBq cycle, with the kidney the dose-limiting organ in 197 of 200 patients when applying constraints near 23 Gy to the kidney and 2 Gy to the marrow. Roughly half of patients could safely receive more than four cycles, while others reached the limit sooner. ⁶ A fixed four-cycle regimen — as used in the registration trial that established Lu-177 DOTATATE for midgut neuroendocrine tumors ⁷ — therefore under-treats some patients and approaches organ limits in others. Voxel-based dosimetry is the tool that distinguishes the two.

The broader field is actively building toward image-based, increasingly automated dosimetry, including machine-learning methods for segmentation and dose estimation layered on the organ-level and voxel-based foundations. ⁹ For the therapy context, see our discussions of Ra-223 therapy physics and safety and Y-90 radioembolization dosimetry.

Practical Optimization Tips

1. Calibrate before you compute

Establish and document the SPECT/CT calibration factor (counts to Bq/mL), attenuation and scatter corrections, and resolution recovery before attempting dosimetry. An uncalibrated activity map produces a precise-looking but wrong dose. ^{3, 4}

2. Image at enough time points

Acquire serial imaging that samples both uptake and clearance so the time-integrated activity is well determined. Too few points, or points clustered at one phase, bias the effective half-life and the dose. ^{4, 8}

3. Register images carefully

Voxel dosimetry sums over co-registered time points, so misregistration between serial SPECT/CT studies smears the activity map and the dose. Rigid or deformable registration quality should be checked.

4. Match the method to the radionuclide

Use voxel S-value convolution for Lu-177 and similar short-range betas in soft tissue; reach for Monte Carlo where there is high-density heterogeneity, for Y-90 near lung, and for alpha emitters where voxel S-values do not apply. ^{1, 2}

5. Report DVHs, not just means

The value of voxel dosimetry is the distribution. Report tumor and organ-at-risk DVHs and relevant metrics, and state the method, voxel size, corrections, and time points, consistent with good-practice dosimetry reporting. ⁸

6. Correct for partial-volume effects

Small lesions near or below the scanner's spatial resolution lose apparent activity to partial-volume effects, underestimating dose. Document the recovery approach, especially for sub-centimeter targets. ⁵

Common pitfalls to avoid

Trusting a mean dose for heterogeneous uptake. Two very different distributions can share one mean.
Single-time-point dosimetry without justification. It assumes a fixed effective half-life that may not hold.
Using soft-tissue voxel S-values across lung or bone. Density changes break the homogeneity assumption.
Applying millimeter voxel S-values to alpha emitters. The range mismatch makes the result meaningless.
Omitting the methodology. A dose number without its corrections, voxel size, and time points cannot be interpreted or compared.

Regulatory Considerations

Radiopharmaceutical therapy is governed primarily through the written-directive and medical-use framework, while dosimetry methodology is guided by professional consensus. The two interact: good dosimetry supports safe, documentable, defensible therapy, but much of RPT is still delivered at fixed or weight-based activity rather than a prescribed absorbed dose. ^{10, 11}

Key frameworks to reference:

10 CFR Part 35 — Medical Use of Byproduct Material governs authorized users, written directives, patient-specific records, and the radiation safety program for therapeutic radiopharmaceuticals. The authorized user determines the administered activity; voxel-based dosimetry typically operates as an optimization and research layer above the minimum requirement. ¹⁰
ICRP Publication 140 — Radiological Protection in Therapy with Radiopharmaceuticals frames the dosimetric and protection principles for these treatments. ¹¹
MIRD Pamphlets No. 17, 23, 24, and 26 provide the methodological backbone: voxel S-values, quantitative SPECT, and radionuclide-specific guidance. ^{1, 2, 3, 4}
EANM Dosimetry Committee good-practice reporting defines what a dosimetry report should contain so results are interpretable and comparable. ⁸

Jurisdiction note: radioactive material used in these therapies is regulated by the NRC or the equivalent Agreement State program. Of the states DRPS serves, Florida, Maryland, Virginia, California, Nevada, Pennsylvania, New York, and New Jersey are NRC Agreement States, while Washington, DC and Delaware are regulated directly by the NRC. Facilities should verify which authority issues their license and align dosimetry documentation with their medical-use program. Connect dosimetry work to PET/CT and nuclear medicine physics and medical physics consulting.

Frequently Asked Questions (FAQs)

What is voxel-based dosimetry?

Voxel-based dosimetry calculates absorbed dose on a three-dimensional grid of small volume elements (voxels) rather than as a single average value for a whole organ. It uses a patient's time-integrated activity distribution from quantitative SPECT/CT or PET/CT and either voxel S-values (precomputed dose contributions between voxels) or Monte Carlo radiation transport to produce a dose map that reflects nonuniform uptake.

How does voxel-based dosimetry differ from organ-level MIRD?

Organ-level MIRD assigns one mean absorbed dose to an entire organ using whole-organ time-integrated activity and standardized S-values from reference phantoms. Voxel-based dosimetry keeps the spatial detail, producing a dose distribution and dose-volume histogram instead of a single number. This matters when uptake is heterogeneous, such as in tumors or partially infiltrated organs, where the mean can hide hot and cold regions.

What are voxel S-values and dose point kernels?

A voxel S-value is the mean absorbed dose to a target voxel per unit time-integrated activity in a source voxel, for a given radionuclide and voxel size, usually in a homogeneous soft-tissue medium. A dose point kernel is the related continuous description of dose around a point source. Convolving the time-integrated activity map with the voxel S-value kernel gives the voxel dose distribution quickly, though it assumes tissue homogeneity.

Why is quantitative SPECT/CT a prerequisite for dosimetry?

Absorbed dose accuracy depends directly on the accuracy of the activity estimates at each imaging time point. Quantitative SPECT/CT with proper calibration, attenuation correction, scatter correction, and resolution recovery converts image counts into activity concentration in becquerels per milliliter. Without that calibration, the time-integrated activity, and therefore the dose, is unreliable.

When is Monte Carlo needed instead of voxel S-values?

Voxel S-value convolution assumes a homogeneous medium, so it is less accurate across large density changes such as lung, bone, or air cavities, and at interfaces. Direct Monte Carlo transport models the actual patient geometry and tissue densities and is the most accurate approach, at a higher computational cost. It is preferred for high-density heterogeneity and for alpha emitters, where energy is deposited over sub-cellular distances.

What dose limits guide radiopharmaceutical therapy dosimetry?

Commonly referenced constraints from the peptide receptor radionuclide therapy literature include roughly 23 Gy to the kidneys and about 2 Gy to the bone marrow as organs at risk, with tumor control improving at higher absorbed doses. These values come from the clinical dosimetry literature and should be applied with the patient's individual data rather than assumed; the kidney is frequently the dose-limiting organ.

Does the NRC require patient-specific dosimetry for these therapies?

Under 10 CFR Part 35, therapeutic radiopharmaceuticals require a written directive and patient-specific documentation, and the authorized user determines the prescribed activity. Many approved therapies are administered as fixed or weight-based activities rather than a prescribed absorbed dose, so individualized voxel-based dosimetry is often an optimization and research practice beyond the minimum regulatory requirement. The medical physicist supports both the regulatory records and any dosimetry program.

Key Takeaways

A mean dose hides nonuniformity. Voxel-based dosimetry produces a 3D dose map and DVH that organ-level MIRD averages away.
The math is the MIRD schema at voxel scale. Convolving the time-integrated activity map with voxel S-values gives dose quickly in homogeneous tissue.
Time drives dose. Serial quantitative SPECT/CT determines the time-integrated activity and effective half-life that set the absorbed dose.
Match the method to the physics. Voxel S-values suit short-range betas like Lu-177; Monte Carlo is needed for density heterogeneity and alpha emitters.
Dose predicts outcome. Tumor dose–response and organ-at-risk limits (around 23 Gy kidney, 2 Gy marrow) argue for individualized planning over fixed activity.
Document everything. Report corrections, voxel size, time points, and DVHs so dosimetry is interpretable, comparable, and defensible.

Conclusion

Radiopharmaceutical therapy is converging with external-beam radiation oncology on a shared language of absorbed dose and dose-volume histograms. Voxel-based dosimetry is the bridge: it takes a patient's quantitative SPECT/CT, builds a time-integrated activity map, and convolves it with voxel S-values — or transports it with Monte Carlo — to produce a dose distribution that reflects how the therapy actually deposited energy in that patient.

The method is only as good as its inputs: calibrated quantitative imaging, enough time points to pin down the effective half-life, careful registration, and a radionuclide-appropriate dose engine. Facilities that invest in those fundamentals can move from "how much activity did we give" toward "how much dose did the tumor and the kidneys receive" — the question personalized theranostics is ultimately trying to answer.

How DRPS Can Help

Diagnostic Radiation Physics Services helps nuclear medicine and theranostics programs build the quantitative-imaging and dosimetry infrastructure that voxel-based dosimetry requires. This includes PET/CT and nuclear medicine physics support, quantitative SPECT/CT calibration guidance, dosimetry workflow and reporting review, and medical physics consulting aligned with NRC and Agreement State medical-use requirements.

DRPS supports facilities across our service locations, including Florida, Maryland, Virginia, Washington DC, California, Nevada, New York, Pennsylvania, New Jersey, and Delaware. Good dosimetry turns a dose number into a decision the clinical team can act on.

Related Resources

References

Bolch WE, Bouchet LG, Robertson JS, et al. MIRD pamphlet No. 17: the dosimetry of nonuniform activity distributions — radionuclide S values at the voxel level. Journal of Nuclear Medicine. 1999;40(1):11S-36S. PubMed
Dewaraja YK, Frey EC, Sgouros G, et al. MIRD pamphlet No. 23: quantitative SPECT for patient-specific 3-dimensional dosimetry in internal radionuclide therapy. Journal of Nuclear Medicine. 2012;53(8):1310-1325. doi:10.2967/jnumed.111.100123. PubMed
Dewaraja YK, Ljungberg M, Green AJ, et al. MIRD pamphlet No. 24: guidelines for quantitative 131I SPECT in dosimetry applications. Journal of Nuclear Medicine. 2013;54(12):2182-2188. doi:10.2967/jnumed.113.122390. 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
Ilan E, Sandström M, Wassberg C, et al. Dose response of pancreatic neuroendocrine tumors treated with peptide receptor radionuclide therapy using 177Lu-DOTATATE. Journal of Nuclear Medicine. 2015;56(2):177-182. doi:10.2967/jnumed.114.148437. PubMed
Sandström M, Garske-Román U, Granberg D, et al. Individualized dosimetry of kidney and bone marrow in patients undergoing 177Lu-DOTA-octreotate treatment. Journal of Nuclear Medicine. 2013;54(1):33-41. doi:10.2967/jnumed.112.107524. PubMed
Strosberg J, El-Haddad G, Wolin E, et al. Phase 3 trial of 177Lu-Dotatate for midgut neuroendocrine tumors. New England Journal of Medicine. 2017;376(2):125-135. doi:10.1056/NEJMoa1607427. PubMed
Lassmann M, Chiesa C, Flux G, Bardiès M. EANM Dosimetry Committee guidance document: good practice of clinical dosimetry reporting. European Journal of Nuclear Medicine and Molecular Imaging. 2011;38(1):192-200. doi:10.1007/s00259-010-1549-3. PubMed
Woo SK. The role of artificial intelligence in advancing theranostics dosimetry for cancer therapy: a review. Nuclear Medicine and Molecular Imaging. 2025;59(5):329-341. doi:10.1007/s13139-025-00939-9. PubMed
International Commission on Radiological Protection. ICRP Publication 140: Radiological Protection in Therapy with Radiopharmaceuticals. Annals of the ICRP. 2019;48(1). icrp.org
U.S. Nuclear Regulatory Commission. 10 CFR Part 35: Medical Use of Byproduct Material. ecfr.gov