MIRD Pamphlet No. 29: MIRDy90—A ⁹⁰Y Research Microsphere Dosimetry Tool

• selective internal radiation therapy (SIRT)
• radioembolization
• partition model dosimetry
• ⁹⁰Y-microspheres
• MIRD dual-compartment dosimetry

Selective internal radiation therapy (SIRT), or ⁹⁰Y-microsphere radioembolization, is a therapy indicated for primary or metastatic hepatocellular carcinoma. Treatment entails use of a catheter positioned in a hepatic artery under fluoroscopic guidance to deliver glass or resin microspheres containing ⁹⁰Y. The microspheres may become selectively entrapped within the tumor microvasculature to impart therapeutic radiation to the immediately adjacent tissue. Current SIRT protocols involve patient-specific prescribed activities—necessary because of variations in arterial vasculature and anatomy among different patients. Individualized treatment plans support optimization of therapeutic outcomes while minimizing radiation-induced side effects (1). Treatment planning is also part of the Food and Drug Administration–approved and Conformité Européenne–marked use of this modality. ^99mTc-macroaggregated albumin (^99mTc-MAA) is used as a surrogate agent for mapping the expected distribution of ⁹⁰Y-microspheres before the therapeutic administration (2). The ^99mTc-MAA imaging provides estimates of the ⁹⁰Y-microsphere distribution via 2-dimensional planar γ-camera or 3-dimensional SPECT imaging—the latter preferred since planar imaging may overestimate the lung shunt fraction (LSF) (3,4). ^99mTc-MAA images are used to evaluate extrahepatic shunting to the lung (5,6) to ensure that healthy lung tissue does not receive an absorbed dose greater than 30 Gy per treatment or a 50 Gy cumulative absorbed dose (for TheraSphere; Boston Scientific) (7) or to ensure that the procedure does not result in greater than a 20% lung shunt (for SIR-Spheres; Sirtex Medical Inc.) (8).

Historically, and currently, use of ⁹⁰Y-microspheres has been approved with simple models for activity personalization, namely body surface area (BSA) and MIRD single compartment. Looking forward, increasingly customized dose models for greater levels of personalization in ⁹⁰Y therapies are being introduced and evaluated. The ^99mTc-MAA mapping images can be used in conjunction with various model-based dose calculation methods to determine a patient-specific administered activity for the ⁹⁰Y-microsphere therapy. The recent standard operational procedures publication from the European Association of Nuclear Medicine dosimetry committee endorses the concept of integrating ^99mTc-MAA mapping for therapy optimization (2), as does the International Commission on Radiation Units and Measurements (9) and other international scientific advisory bodies (10).

The BSA model for therapy planning was developed in the early 2000s (11) and is the established prescription activity model for the SIR-Spheres device (8). The BSA model has advantages of simplicity and ease of use (12). The BSA model assumes that the size of the patient’s total liver volume is proportional to the patient’s BSA, thereby enabling adjustment of prescribed activity to a patient’s malignant liver volume (13). Although the BSA approach has the advantage of simplicity (Fig. 1), the limited personalization may increase the risk of undertreatment or overtreatment of patients (14,15). One limitation of the BSA method is that it assumes the BSA correlates with liver volume in the general population; however, the validity of this assumption may vary depending on body habitus and disease burden (13). Consequently, the BSA model for ⁹⁰Y treatment planning may lead to substantial interpatient variability in both the normal-liver–absorbed dose and the tumor-absorbed dose. For example, large patients with a disproportionately small liver volume may receive elevated absorbed doses to the nontumor regions of the liver, whereas smaller patients with larger livers may receive comparatively low absorbed doses when BSA-based planning is used (12,13). A second limitation is that neither tumor nor normal-liver parenchyma target absorbed doses are calculated or considered. Rather, the prescribed activity calculation formula is empiric, based on BSA, tumor volume, perfused liver volume, and whole liver volume. The calculation does allow for activity reduction of prescribed activity for clinical reasons or if the lung-absorbed dose, based on estimated LSF and lung mass, is estimated to exceed 30 Gy. Finally, the BSA model disregards the tumor–to–normal-liver activity concentration ratio (TNR). Nonetheless, the BSA model is still widely used to prescribe ⁹⁰Y activity in the treatment of liver cancer, as this model remains the vendor-recommended dosimetry method in the United States for the SIR-Spheres device in the treatment of unresectable metastatic liver tumors (8). However, other factors such as tumor burden and liver function should also be considered to ensure optimal treatment outcomes (16).

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FIGURE 1.

Summary of various ⁹⁰Y prescription activity models with associated compartments and assumed distribution. (A) Ground truth sphere distribution. (B) BSA model—considers volumes of 3 regions, including tumor, perfused liver, and whole liver volumes. (C) MIRD single compartment—considers only target region volume. (D) MIRD dual compartment—considers perfused normal-liver region volume and tumoral liver volume. (E) MIRD multicompartment—considers perfused normal-liver region volume, tumoral liver volume, and individual tumor volumes. (F) Voxel-level distribution.

The MIRD Committee of the Society of Nuclear Medicine and Molecular Imaging developed a standardized method for calculating absorbed radiation dose to macroscopic anatomic regions from β-particles emitted by radionuclides (17). This model, referred to in this paper as the MIRD single-compartment model (Fig. 1) for ⁹⁰Y dosimetry, was predicated on the assumption that the distribution of ⁹⁰Y within the liver can be approximated as a single region with a spatially uniform activity distribution and an absorbed fraction equal to 1.0 (17). This model suggests that a given activity concentration can be used to ascertain absorbed dose to the tissue by modeling the energy deposited per unit mass (absorbed dose, where 1 J/kg = 1 Gy). Thus, operators may calculate the prescribed activity required to deliver a certain absorbed dose (Gy) to a target tissue. This model uses volumetric measurements from anatomic imaging to determine the anticipated mass (volume × density) of distribution, from which the expected activity concentration (activity per unit mass) and absorbed dose may be derived. Vendor implementation of the single-compartment model incorporates uptake measurements from surrogate ^99mTc-MAA imaging to account for anticipated microspheres shunted to the lungs. The MIRD single-compartment model is relatively simple, easy to implement, and more advanced than the BSA model because it uses a measurement of the mass of the patient-specific treatment region and allows for absorbed dose estimates to be integrated into the treatment procedure. However, its limitations include the inability to account for different distributions of ⁹⁰Y within the healthy and diseased tissue in the treatment volume. This model is widely used today for ⁹⁰Y dosimetry in liver cancer treatment and remains the approved method for TheraSphere treatment planning (7).

The partition model for ⁹⁰Y SIRT treatment planning addresses the limitations of the BSA model and the MIRD single-compartment model (18). The partition model, here and in the MIRDy90 software, is called the MIRD dual-compartment model. The dual-compartment model accounts for differences in ⁹⁰Y activity concentration within normal liver and subliver treatment regions to provide a more accurate method for computing absorbed dose in the various tissue compartments. Calculated absorbed doses may then be used to tailor the patient’s prescribed activity. The MIRD dual-compartment model defines the treatment volume as 2 compartments: the tumor region and the perfused liver region (Fig. 1D). In addition to using mass (volume × density) information for each region that is derived from volumetric anatomic imaging, the model also uses a TNR determined from the ^99mTc-MAA SPECT images; from this information the absorbed dose in each region may be calculated (12). Thus, the model is more complex than the BSA and MIRD single-compartment models because it incorporates more patient-specific information, yet it still can be implemented with a small number of measurements and calculation parameters. The MIRD dual-compartment model can be used to deliver a threshold absorbed dose to tumor while maintaining safe absorbed doses to the liver and lungs. Limitations of the MIRD dual-compartment model are that it assumes uniform distribution of ⁹⁰Y within the 2 regions (15) and cannot handle multiple tumor regions. To overcome these limitations, multicompartment models have been developed extending the dual-compartment model to accommodate individual tumors (19,20). Alternative voxel-based approaches have also been proposed for ⁹⁰Y treatment planning (21–23), leading to the integration of voxel-based solutions by several vendors.

The BSA, single-compartment, and dual-compartment models rely on surrogate ^99mTc-MAA imaging for estimating the lung-absorbed dose. The dual-compartment model relies on this surrogate for estimating the anticipated ⁹⁰Y TNR. Riveira-Martin et al. showed that dual-compartment treatment planning using ^99mTc-MAA resulted in projected absorbed dose metrics having a high correlation with posttherapy ⁹⁰Y bremsstrahlung SPECT imaging, highlighting the utility of ^99mTc-MAA surrogate imaging for ⁹⁰Y treatment planning (24). Other studies reported important limitations when using ^99mTc-MAA as a surrogate for ⁹⁰Y-microspheres that influenced absorbed dose projections. For example, these limitations included different physical and biologic properties of ^99mTc-MAA and microspheres (particle size and shape, and number of particles administered), catheter placement, and the different imaging modalities used for evaluation (e.g., partial-volume effects) (25–27). Despite the uncertainty regarding concordance between pretherapy ^99mTc-MAA and ⁹⁰Y-microsphere distributions, ^99mTc-MAA imaging is readily available as a common diagnostic radiopharmaceutical, and its use is a required step in current treatment protocols.

There is significant emerging motivation for adopting more complex dosimetry models for ⁹⁰Y SIRT treatment planning; several studies have suggested that the increased accuracy of the partition model may improve ⁹⁰Y treatment planning compared with the simpler MIRD single-compartment and BSA models (18,27,28). For example, Garin et al. described a randomized multicenter study that assessed the benefit of personalized dosimetry (target tumor-absorbed dose with limited absorbed doses to the healthy liver and lungs) and standard dosimetry (target absorbed dose to the perfused lobe) in patients with hepatocellular carcinoma. The study of Garin et al. reported that personalized dosimetry in SIRT resulted in a significantly higher objective response rate than did the standard dosimetry approach, suggesting that personalized dosimetry could be beneficial in clinical practice and should be implemented in future clinical trials (29). In addition, recent recommendations from an international multidisciplinary workgroup explicitly recommend use of the dual-compartment model in certain clinical scenarios (10).

To the best of our knowledge, no MIRD dual-compartment model calculation tools are currently approved by the U.S. Food and Drug Administration. Approved voxel-level dosimetry software is available and can effectively provide dual-compartment dosimetry. Therefore, centers that do not use vendor software but wish to use the MIRD dual-compartment or multicompartment models are constrained to in-house calculation tools. There are several smartphone applications that have been available to prepare microsphere treatment plans. These apps have demonstrated the utility of having shared tools to support SIRT programs, where physicians, physicists, and others can review and compare dose calculations and prescribed activities. However, the apps provide black-box calculations, and neither the apps nor their function are well documented. Thus, the need remains for vetted MIRD dual-compartment and multicompartment model calculation tools.

In this article, we describe MIRDy90, a committee-tested and endorsed activity/absorbed dose calculation worksheet to support SIRT dosimetry calculations as one of the MIRDsoft.org suite of research dosimetry tools. The MIRDy90 worksheet has been tested and validated against other absorbed dose calculation tools.

MATERIALS AND METHODS

⁹⁰Y-Microsphere Activity Calculation Models

The SIR-Spheres BSA model requires several input parameters: total treatment volume, tumor volume, LSF, patient height and weight, and total liver volume. As input for the BSA model, a BSA needs to be calculated. Although several published equations provide BSA, the equation used in the SIR-Spheres package insert is shown in Equation 1. The patient BSA is determined from the patient’s height and body mass: Eq. 1

The BSA model-prescribed activity can be calculated using Equation 2 with treatment, tumor, and total liver volumes obtained from the patient’s CT or MR images. Eq. 2where V(tumor) is the volume of the tumor, V(PLV) is the volume of the perfused liver being treated, and V(total liver) is the volume of the whole liver. Along with the prescribed activity, the BSA model requires that the absorbed dose to the lung also be calculated and considered. This is achieved by first determining the zero-time activity within the lung (30): Eq. 3

The absorbed dose to the lung is calculated as follows: Eq. 4where M(lung) is the mass of the lungs, typically assumed to be 1 kg, and DCF is the ⁹⁰Y dose conversion factor. The DCF relates the energy deposited locally in tissue per unit of activity, expressed in units of J/GBq. In the ⁹⁰Y dosimetry models described herein, the DCF values commonly used assume charged particle equilibrium and complete self-absorption; this assumption results in a slight overestimate of the absorbed dose depending on the microsphere distribution volume (Fig. 4 in reference 2). Various publications provide different values for the DCF: American Association of Physicists in Medicine report 144 and International Commission on Radiation Units and Measurements report 96 use 49.38 J/GBq (9,31), the SIR-Spheres package insert uses 49.67 J/GBq (8), the TheraSphere treatment calculator uses 50 J/GBq (7), and the European Association of Nuclear Medicine dosimetry committee recommends a value of 49.75 J/GBq (2). Values of 49.67 J/GBq and 49.77 J/GBq can be derived from National Nuclear Data Center (32) and MIRD (33) decay data, respectively. The differences appear to be due to small variations in the source nuclear data, such as the average energy emitted per nuclear transition and isotope half-life. MIRDy90 is prepopulated with the MIRD decay data–derived DCF of 49.77 J/GBq.

The MIRD single-compartment model assumes that the activity of ⁹⁰Y is distributed uniformly throughout the target treatment site. The absorbed dose and prescribed activity are calculated using the activity of ⁹⁰Y and physical half-life, dose deposition characteristics, and the volume of the liver region being treated. The model requires the target region (perfused liver/treatment volume) mass (mass = volume × density), the LSF, and the desired absorbed dose to the target region. The desired absorbed dose is defined in Equation 5: Eq. 5

The prescribed activity is then calculated using Equation 6, which accounts for shunting of spheres by including a correction for the LSF: Eq. 6

The MIRD dual-compartment model requires several patient-specific inputs: the desired absorbed dose to the tumoral liver compartment (Gy), target volume (the perfused normal liver volume plus tumor volume), tumor volume, LSF, and TNR. To calculate the ⁹⁰Y prescribed activity, the MIRD dual-compartment model requires the volumes of the tumor and normal perfused liver in the lobe being treated and the anticipated uptake in the tumor, perfused normal liver, and lung, typically measured using the pretreatment ^99mTc-MAA SPECT. The TNR is the ratio of activity concentration in the tumoral liver to that in the perfused normal liver tissue (Eq. 7). The TNR calculation is imperfect; segmented volumes of interest on SPECT/CT images can vary with segmentation technique and have inter- and intraoperator variability or can be subject to partial-volume effects (34). The TNR in Equation 7 is unitless: Eq. 7where A(tumor) is the activity in the tumoral liver, M(tumor) is the mass (kg) of the tumoral liver, A(PNL) is the activity in the perfused normal liver, and M(PNL) is the mass (kg) of the perfused normal liver. The absorbed dose to the tumor is Eq. 8where D(PNL) is the mean absorbed dose to the perfused normal liver tissue. The prescribed activity of ⁹⁰Y is calculated as follows: Eq. 9where A_0,DC is the prescribed activity of microspheres calculated using the MIRD dual-compartment model. Using Equations 8 and 9, one can tailor prescribed activity to deliver a target absorbed dose to the tumoral liver, normal liver, or lung tissue.

The MIRD dual-compartment model can be extended to a multicompartment tumor model by considering individual tumors that make up the tumoral liver compartment as separate compartments: Eq. 10where D_i is the absorbed dose to the individual tumor (tumor_i), which is scaled according to the tumor TNR (TNR_i) relative to the absorbed dose to the perfused normal liver. For the model to be implemented as presented in Equation 10, the absorbed dose to the perfused normal liver, D(PNL), needs to be calculated a priori. In MIRDy90, D(PNL) is calculated by implementing the dual-compartment model and must be determined before multicompartment calculations.

MIRDy90 Calculation Worksheet

The MIRDy90 calculation worksheet was built as a tool for evaluating ⁹⁰Y SIRT prescribed activity calculation models. Features of MIRDy90 include parallel implementation of BSA, MIRD single-compartment, MIRD dual-compartment, and MIRD multicompartment tumor model dosimetry; a simple-to-use single-screen interface; instant calculations for an interactive user experience, provided with supporting graphics; informative model summaries; straightforward and simple comparisons of activity calculation models; and easy-to-review (open-source) code and calculations.

The MIRDy90 worksheet was built on the Excel (Microsoft) platform, which allows an organized input–output user interface and reviewable calculations. The worksheet has been designed to be straightforward and uses the formatting and graphical capabilities of Excel. A screenshot of the MIRDy90 interface is shown in Figure 2.

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FIGURE 2.

Screenshot of MIRDy90 software graphical user interface. User input area is on left, and worksheet calculations are on right. In this example, MIRD dual-compartment model is selected, and target absorbed dose is prescribed to achieve 205 Gy to tumor. (A) Input data fields for each model. Input parameters used in selected model are highlighted. (B) Model summary box, which displays user’s selected calculation outputs. (C) Selected model graphical display and dose summary table. (D) MIRD dual-compartment dosimetry model outputting display activity and absorbed dose summaries for each of 4 prescribed activity targets. (E) MIRD multicompartment input (TNR_i) and projected tumor-absorbed doses (for up to 5 tumors) (optional). (F) Single-compartment (MIRD) and BSA dosimetry model outputs providing conventional model summaries. DL = dose limit; PNL = perfused normal liver.

Workflow and Model Selection

Users may enter data based on simulation or case measurements, review and compare model estimates, select the desired model, and save the case or print the screen. The requisite parameters to support each model are displayed on the input screen. As users enter data into the fields, the available models become activated, and respective calculations are displayed. The user may navigate and select one of the models from the drop-down menu, as shown in Figure 3. The prescribed activity for the selected model is shown in the model summary box on the bottom left of the interface (Fig. 2B).

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FIGURE 3.

MIRDy90—selecting prescribed activity calculation model.

Once a model is selected, the requisite inputs required for the calculations are highlighted, along with the respective output dosimetry module. The dose summary table and graphical display (Fig. 2C) will show a summary of the prescribed activities and compartment doses, as well as indicators confirming whether the treatment exceeds any of the specified dose limits relevant to the selected model. The plot presents an overview of prescribed activity (GBq) versus absorbed dose (Gy), as well as relative doses in each of the compartments in the respective models.

MIRD Single-Compartment and BSA Models

If the MIRD single-compartment or BSA model is selected, the respective dosimetry module is highlighted (Fig. 2F). The dose summary table and graphical display (Fig. 2C) will show the conventional outputs for the single-compartment and BSA models. The MIRDy90 BSA model presents outputs akin to the SIR-Spheres ⁹⁰Y Resin Microspheres Activity Calculator (SMAC; Sirtex Medical Inc.), a dose prescription calculator available online (35). The BSA model has the option for BSA activity reduction (%) or for dosing to the lung limit by selecting the model “BSA dose to lung limit.” The single-compartment dosimetry module summarizes the conventional single-compartment (MIRD) model inputs and outputs akin to the TheraSphere calculator (36).

MIRD Dual- and Multicompartment Models

If the MIRD dual-compartment model is selected, the MIRD dual-compartment dosimetry module (Fig. 2D) will be highlighted. The dose summary Table (Fig. 2C) and MIRD dual-compartment dosimetry module will display a summary of the prescribed activities and compartment doses, as well as indicators confirming whether treatment exceeds any of the specified liver-, lung-, and cumulative lung-absorbed dose limits. Users can refine calculations by adjusting parameters, aided by graphical display of the output absorbed doses. Users can select 1 of 4 target constraints: prescribed target absorbed dose to the tumor (Gy), absorbed dose limit to the liver, absorbed dose limit to the lung, or user-defined administered activity (GBq). In each scenario, the worksheet calculates the required prescribed activity. The displayed plot presents prescribed activity (GBq) versus dose (Gy), as well as the relative doses in each of the compartments. The plot updates automatically, depending on which of the 4 MIRD dual-compartment model targets is selected. Additionally, MIRDy90 facilitates calculation of individual tumor-absorbed doses in the multicompartment module, where users can provide individual tumor TNRs. In MIRDy90, individual tumor doses are scaled relative to the perfused normal-liver–absorbed dose according to Equation 10. If an individual tumor TNR is entered into the multicompartment table (Fig. 2E), an additional target constraint will be available in the prescribed activity calculation model drop-down list (Fig. 3). This model, “multicompartment (min target tumor dose),” calculates the prescribed activity required to deliver a minimum tumor-absorbed dose. In Figure 2, the dual-compartment model (target tumor dose) is selected, and the graphical display shows the prescribed activity of ⁹⁰Y (dashed red line), as well as the absorbed doses to the tumor (dark blue line), perfused normal liver tissue (light blue line), and lung (green line). The dual-compartment dosimetry module also displays the prescribed activity and the compartment absorbed doses and activities for all target constraints simultaneously, highlighting only the model that is selected.

Default Parameters

MIRDy90 is prepopulated with default parameters required for the program to run, derived from reference publications. These include a liver tissue density of 1.03 g/cm³ (7), a DCF of 49.77 J/GBq (33), a default lung volume of 5,525 cm³ (equivalent to a lung mass of 1.0 kg based on an assumed mean lung density of ρ = 0.181 g/cm³ (37)), a perfused normal-liver dose limit of 70 Gy (38), a single-treatment lung dose limit of 30 Gy (7,8), and a cumulative lung dose limit of 50 Gy (7). The user may choose to modify these default parameters.

Benchmarking MIRDy90 Against Vendor Dose Prescription Tools

The MIRDy90 worksheet was designed to use the same equations as those provided with various vendor dosimetry tools. For the BSA model validation, the MIRDy90 worksheet results were compared with those from SMAC (35). The SMAC tool uses the BSA model to calculate the suggested prescribed activity for use of the product and estimates the lung-absorbed dose based on either the default 1-kg or entered patient-specific lung mass.

For the MIRD single-compartment model comparison, the MIRDy90 results were compared with those of the Boston Scientific iDOC online calculator used to determine TheraSphere prescribed activities. The iDOC tool (36) provides the TheraSphere ⁹⁰Y-microsphere prescribed activity for treatment planning as well as the projected lung-absorbed dose; TheraSphere has recently removed this tool from its website indefinitely. For the dual-compartment model, benchmarking MIRDy90 results against a vendor-provided standard was not possible because no vendors currently have software for this region-based model. For external comparison of the dual-compartment model, MIRDy90 calculations were benchmarked against the Cancer Y90 Calculator (Softmills Technology International), a smartphone app currently available for android and iOS that provides single-compartment and dual-compartment model dosimetry (39).

A series of 10 example patient cases was generated by selecting typical clinical values determined from local experience. The example data were entered into the MIRDy90 worksheet, and the results of the various calculation models were compared with the respective available online calculators or app. The target volumes (perfused normal liver + tumoral liver) ranged from 400 to 850 cm³; tumor volumes, from 30 to 330 cm³; TNR values, from 2.8 to 5.4; LSF values, from 1% to 10%; patient heights, from 150 to 186 cm; patient weights, from 55 to 118 kg; and total liver volumes, from 1,000 to 1,603 cm³. The MIRD single-compartment target dose to the treatment volume was chosen to be 150 Gy, and the dual-compartment model desired absorbed dose to tumor was chosen to be 205 Gy. Each tool uses similar but slightly different DCFs, and the MIRDy90 tool allows adjustment of this factor by the user. For comparative purposes, the DCF used in MIRDy90 was adjusted to match the value used in the software tool to which it was compared (e.g., the SIR-Spheres SMAC and Cancer Y90 Calculator [partition] app use a DCF of 49.67 J/GBq, and the TheraSphere iDOC uses a DCF of 50 J/GBq).

The assumed soft-tissue density (tumoral and nontumoral liver) also varies among the tools, and this was adjusted in MIRDy90 to facilitate direct comparisons. For reference, the vendor-supplied TheraSphere instructions for use adopts a soft-tissue density of 1.03 g/cm³, and International Commission on Radiological Protection (ICRP) publications 110 and 145 use densities of 1.05 and 1.06 g/cm³, respectively (ICRP 110 considers only the parenchyma, whereas ICRP 145 considers contributions from both blood and parenchyma (40)); the Cancer Y90 Calculator app uses the ICRP 145 soft-tissue density of 1.06 g/cm³. Alternatively, lung density may be obtained directly from patient CT. The parameters for each of the simulated cases are shown in Table 1.

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TABLE 1.

Simulated Patient Input Parameters

• © 2024 by the Society of Nuclear Medicine and Molecular Imaging.

• Received for publication October 3, 2023.
• Accepted for publication January 23, 2024.