Pharmacokinetic digital phantoms for accuracy assessment of image-based dosimetry in ¹⁷⁷Lu-DOTATATE peptide receptor radionuclide therapy

Three adult phantoms with different anatomical characteristics from the XCAT phantom population (Segars et al 2010, 2013) were used in this work. The phantoms are comprised of anatomical templates for different organs, part of organs, various tissues and organ contents (hereafter referred to as phantom structures). The anatomical templates were used in the XCAT computer program to generate three-dimensional (3D) voxel maps where each accessible structure was assigned a unique code integer. This enabled association of each structure to an individual mass density value and time-activity curve, as described earlier (Brolin et al 2013). Mass-density values, required for the simulation of photon and electron transport in the phantom, were obtained from (ICRU 1988). The voxel phantoms were realized with cubic voxels of 2.5³ mm³, and the 3D matrix sizes were adjusted to encompass the entire phantom bodies. The phantoms were modified to better mimic typical patients by adding new structures representing tumours. Eight tumours from three different patients were outlined using an in-house developed semi-automatic segmentation program (Gustafsson et al 2012). The tumours were inserted at the approximate locations where originally situated in the patients, i.e. in the liver and abdomen. The properties of the phantoms are summarised in table 1. Their 3D mass density distribution are shown in figure 1, illustrating the different anatomical features.

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Patient time-activity data was acquired from 10 patients after their first therapy cycle with ¹⁷⁷Lu-(DOTA0,Tyr3)-Octreotate (DOTATATE). The treatment was performed with an intravenous infusion of 7.4 GBq in 100 mL saline by intravenous infusion during 30 min, in combination with a simultaneous co-infusion of 2000 mL amino-acid solution (Vamin 14 g N L⁻¹ electrolyte-free; Fresenius Kabi). The specific activity of the radiopharmaceutical was approximately 40 MBq μg⁻¹. The imaging protocol consisted of conjugate-view whole-body (WB) planar scans at 1, 24, 96 and 168 h post-infusion (p.i.), including a CT scout image for attenuation correction, as well as a quantitative SPECT/CT study performed at 24 h p.i. The camera system used was a Discovery VH SPECT with a Hawkeye CT unit (General Electric). The emission studies were performed using medium-energy general-purpose (MEGP) collimators, and an energy window of 208 keV  ±  10%. Planar image activity quantification was performed using a pixel-based implementation of the conjugate-view method (Sjögreen Gleisner and Ljungberg 2012). The SPECT reconstructions were performed using OS-EM (Ordered-Subset Expectation Maximization) with 8 iterations and 10 subsets, including CT-based attenuation correction, model-based scatter correction (Frey and Tsui 1996) and distance-dependent resolution compensation.

Activity concentrations in the kidneys, liver, spleen and tumours at each time-point were determined by a hybrid method, utilizing data from both SPECT and WB images (Garkavij et al 2010). In this method, the organ activity concentration curve is assumed to follow the time-activity curve determined from the WB data. The curve is then normalised to the 24 h p.i. activity concentration measured in the SPECT image. Liver data from two patients were excluded since the normal liver parenchyma could not be reliably delineated in the planar images due to excessive tumour infiltration. In addition, spleen data could not be obtained for one patient due to a prior splenectomy.

The total-body activity was determined from the WB scans. In addition, the activity content in the urinary bladder was determined from the whole-body scan at 1 h p.i. Since none of the included patients voided between the infusion and the first imaging session, the urinary bladder activity provided a measure of the urinary clearance. Faecal activity was estimated in three patients with prominent intestinal activity at 24 h p.i. The activity was calculated from the SPECT/CT image acquired at 24 h, using the CT for intestinal volume-of-interest (VOI) delineation. Time-activity data for plasma, required for reliable model fitting, were not available for the patients treated at our centre. Therefore, published plasma data from a study employing a similar administration protocol (Esser et al 2006) were used.

A first-order linear compartment model, shown in figure 2, was developed to simulate typical pharmacokinetics observed in ¹⁷⁷Lu-DOTATATE patients. The primary objective was to construct a PK model that could be used for defining time-varying activity distributions in the phantoms, and thereby provide basis for simulation of realistic and representative images. The PK model was constructed as a closed system to force consistency between the time-activity curves for the different organs and the total-body activity curve.

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The plasma volume was represented by a single compartment into which the activity was assumed to be infused at a constant rate during 30 min. The rapid clearance of activity from plasma, reported in e.g. (Kwekkeboom et al 2001, Esser et al 2006), could not be attributed to renal elimination alone. It was thus assumed that there is a rapid transfer of activity into the extravascular space. The liver, spleen, tumour and remaining body were therefore each modelled by at least two compartments respectively, where the first compartment represented an extravascular volume with rapid plasma equilibration, while the second compartment represented a slower component of uptake and release, for instance mediated by somatostatin receptor binding. For the tumours, an additional third compartment was included to account for long-term activity retention due to internalization of the radiolabelled peptide (Waser et al 2009). During model development, it was found that release of internalized activity had to be included to get a good fit to tumour data. To avoid the need of explicit modelling of radioactive metabolites, this release was accounted for by modelling the internalisation as a reversible process.

The kidneys were modelled by two compartments, where the first (rapid) represented activity in the renal filtrate, i.e. activity that had accumulated in the kidneys due to glomerular filtration but had not yet been reabsorbed or excreted into the urinary tract. The second compartment (slow) represented the long-term renal activity retention, mainly due to peptide reabsorption in the proximal tubular cells (Melis et al 2005, Rolleman et al 2010). The tubular uptake was thus modelled as a transfer from the first to the second renal compartment, whereas urinary excretion was modelled as transfer from the first renal compartment to the urinary bladder. To achieve a good fit of the model to renal data, for which a long-term (>24 h p.i.) decrease was seen, a biological washout was included from the second renal compartment. The washout was included as a transfer to the plasma compartment. Although physiologically implausible, this approach maintained the total-body activity and bypassed the need to model radioactive metabolites. Furthermore, the choice of target for this transfer had no discernible impact on the model fit.

Hepatobiliary elimination was included in the model, since intestinal activity is of concern in planar-based dosimetry as it overlaps with renal activity in the anterior–posterior (AP) direction (Garkavij et al 2010). A compartment representing hepatocytic uptake and subsequent biliary excretion was therefore included in the model.

Mathematically, the compartment model was described by a system of first-order linear differential equations following:

$$\begin{eqnarray}&&\frac{\text{d}{{A}_{i}}(t)}{\text{d}t}=\underset{j=1}{\overset{N}{\sum}}\left({{k}_{j,i}}\,{{A}_{j}}(t)-{{k}_{i,j}}\,{{A}_{i}}(t)\right)\end{eqnarray} \tag{ 1 }$$

where $~{{A}_{i}}(t)$ denotes the decay-corrected activity content of compartment i as a function of time t, ${{k}_{j,i}}~$ is the transfer rate constant from compartment j to compartment i and N is the number of compartments.

The patient time-activity data were decay corrected to infusion time, normalized to the injected activity, and interpolated to nominal imaging times at 1, 24, 96 and 168 h p.i. Since the aim of this work was to establish typical pharmacokinetics, geometrical-means of the organ activity concentrations and urinary bladder activity at the different time points were calculated. The total-body long-term activity retention was found to be highly dependent on the tumour burden and associated uptake. Therefore, the total-body activity curve was selected from two of the patients that had a total tumour volume comparable to the phantoms. Utilizing blood-activity data (Esser et al 2006) and vascular volume fractions for tumours and organs of interest (Baxter et al 1995, ICRP 2002), contributions from vascular activity to the measured organ activity concentrations at 1 h p.i. were subtracted. For the remaining time-points, this contribution was considered negligible.

The PK model was implemented in SAAM II software for kinetic analysis (v. 1.2, University of Washington). The SAAM II software is a tool for pharmacokinetic modelling with a graphical user interface that facilitates interactive development of compartment models and subsequent curve fitting to experimental data. In this work, SAAM II was used to fit the transfer rate constants of the PK model (figure 2) by a non-linear least square fit to the acquired patient data (tables 2 and 3). Since the dependent variable of the PK model was compartmental activity (decay corrected), volumes were assigned to the various organs to convert the measured activity concentrations to total organ activity. As the organ volumes differed between the phantoms, an individual fit of the model parameters was performed for each phantom. To increase the generalizability of results obtained using these phantoms, it was considered appropriate that at least one of them would differ from the other in terms of renal activity uptake. Therefore, the input renal activity concentration for phantom 3 was increased with 1 standard deviation (SD), as determined from patient data, before fitting.

The compartmental activity contents given by the solution to (1), with associated transfer rate constants, could not be used directly for defining the source distribution within the phantoms since there was not a one-to-one match between the compartments and the XCAT phantom structures. For instance, the phantom has two kidneys with defined renal substructures, whereas both kidneys were merged in the PK model.

To model the passage of the radiolabeled peptide through the kidneys and urinary tract of the phantoms, additional compartments were added. The first (rapid) kidney compartment was subdivided into eight compartments representing activity in renal filtrate and urine residing in the left and right renal cortex, medulla, pelvis and ureter, respectively. The second (slow) kidney compartment was subdivided into two compartments, one for each kidney. The values of the additional transfer constants that were introduced were derived from parameter values obtained from the original fit. The renal uptake rate, $~{{k}_{1,9}}$, was divided equally between the two kidneys, and the transfer constants governing the transport of activity through the renal parenchyma and renal pelvis were set to maintain the renal transit time, given by ${{\left(k_{9,11}^{{}}\right)}^{-1}}$ in the original model. The reabsorption constants in the extended model were rescaled such that the reabsorption fraction, given by the ratio ${{k}_{9,10}}/\left({{k}_{9,10}}+{{k}_{9,11}}\right)$ in the original model, was maintained.

The full PK model, including the extended renal transport model, was implemented and solved numerically using the fourth-order Runge-Kutta (RK4) algorithm in IDL (v.8.2, Exelis Visual Information Solutions, Boulder, USA), to yield the activity of each compartment as a function of time. The step-size, $\Delta t$, was 0.07 min and the number of samples, n, was 2²¹. The numerical solutions provided time-activity data up to approximately 101 d p.i. corresponding to approximately 15 physical half-lives of ¹⁷⁷Lu.

To define the dynamic activity distribution of the phantoms, the time-activity curves for each structure was calculated as a weighted sum of compartmental activities according to:

$$\begin{eqnarray}&&A_{q}^{\text{p}}\left({{t}_{k}}\right)=~\underset{i=1}{\overset{N}{\sum}}{{A}_{i}}\left({{t}_{k}}\right)\cdot {{w}_{q,i}},\end{eqnarray} \tag{ 2 }$$

where $A_{q}^{\text{p}}\left({{t}_{k}}\right)$ is the activity in phantom structure q at time ${{t}_{k}}$ and ${{w}_{q,i}}$ is the fraction of activity in compartment i localized in structure q. For the spatial activity distribution to be consistent with the PK model, the total activity in the phantom should equate the total activity of all compartments at all points in time, i.e. $\sum\nolimits_{q=1}^{M}A_{q}^{p}=\sum\nolimits_{i=1}^{N}{{A}_{i}}~$, where M is the number of phantom structures (see table 1). The factors ${{w}_{q,i}}$ were assigned to obtain the desired anatomical distribution of each compartment, while explicitly ensuring that $\sum\nolimits_{q=1}^{M}{{w}_{q,i}}=1,\forall i$. Most compartments were associated with a single phantom structure by setting ${{w}_{q,i}}$ equal to one for that compartment-phantom structure pair. The plasma compartment (i = 1) was distributed in accordance with the vascular fractions of the phantom structures, $V{{F}_{q}}$, i.e. ${{w}_{q,1}}=\frac{{{V}_{q}}\cdot V{{F}_{q}}}{{{V}_{\text{b}}}}~,~$ where ${{V}_{\text{b}}}~$ is the total-body vascular volume given by ${{V}_{\text{b}}}=\sum\nolimits_{q=1}^{M}{{V}_{q}}\cdot V{{F}_{q}}$. The vascular fraction $V{{F}_{q}}$ of phantom structure q was defined as $V{{F}_{q}}={{V}_{\text{b},q}}/{{V}_{q}}$ where ${{V}_{\text{b},q}}~$ and ${{V}_{q}}~$ is the vascular volume and total volume of phantom structure q, respectively. For the major structures, vascular fractions were derived from reference data on organ mass, mass density and total and regional blood volumes from ICRP publication 89 (ICRP 2002). Tumour data were obtained from Baxter et al (1995). For the remaining structures the vascular fraction was assumed to be 0.05.

The activity in the two compartments representing the 'remainder-of-body' were assigned to the set of phantom structures that were not associated with a specific compartment in the PK model. Since these compartments represented extravascular localization, the structures containing only air (e.g. the lung airway tree) or blood (e.g. arteries and veins) were excluded. The brain was also excluded from this set of structures due to the poor permeability of somatostatin analogues through the blood-brain barrier (Haldemann et al 1995).

The compartments representing the long-term renal uptake (kidney slow) were associated with both the cortex and medulla since it has been shown that the cortex-to-medulla activity ratio 2–4 d after administration is approximately 70/30 (de Jong et al 2004, Konijnenberg et al 2007). Given that the renal cortex comprises approximately 70% of the total renal volume, the activity in these compartments was distributed in accordance with the fractional volumes of the renal substructures for each phantom. The inhomogeneous activity distribution within the renal substructures reported by de Jong et al (2004) would require a partition of the renal substructures in the XCAT phantom and was therefore not considered.

Elimination of activity from the body by urinary and faecal excretion was accounted for by setting the activity content to zero for the urinary bladder and the intestinal contents every fourth and twenty-fourth hour, respectively.

The mean absorbed dose rate R to a phantom target structure q was calculated according to

$$\begin{eqnarray}&&{{R}_{q}}({{t}_{k}})=\underset{s=1}{\overset{M}{\sum}}A_{s}^{\text{p}}({{t}_{k}}){{\text{e}}^{-\lambda {{t}_{k}}}}\cdot S(q\leftarrow s),\end{eqnarray} \tag{ 3 }$$

where $~A_{s}^{\text{p}}\left({{t}_{k}}\right)$ denotes the activity located in source organ s at time ${{t}_{k}}$, λ is the ¹⁷⁷Lu decay constant, and $S\left(q\leftarrow s\right)$ denotes the S value, i.e. the mean absorbed dose rate contribution to phantom structure q per unit activity in s. The absorbed dose rate functions were numerically integrated to yield the total absorbed dose according to

$$\begin{eqnarray}&&{{D}_{q}}=\Delta t\underset{k=1}{\overset{n-1}{\sum}}{{R}_{q}}({{t}_{k}})~.\end{eqnarray} \tag{ 4 }$$

The S values for all source-target combinations in the three phantoms were calculated using a Monte Carlo program for voxel-based internal dosimetry (Liu et al 2001). The program is essentially a wrapper routine for the EGS4 Monte Carlo code (Nelson et al 1985), but includes calculation of beta spectra, sampling of decay positions and spatial energy deposition scoring as further described in (Ljungberg et al 2003). Cross-sections for lung tissue, soft tissue and bone, normalised to unit density, were generated from the EGS4-related utility code PEGS4. In the simulations, the voxel cross-sections were obtained by multiplying the voxel mass density with the suitable normalised cross-section, i.e. lung tissue (ρ  ⩽  0.8 g cm⁻³), soft tissue (0.8 g cm⁻³  >  ρ  ⩽  1.2 g cm⁻³) or bone (ρ  ⩾  1.2 g cm⁻³). The simulations were performed with a homogeneous activity distribution in each source structure, and the resulting energy deposition in all target structures was scored and subsequently divided with the target region mass. The emission spectra and half-life of ¹⁷⁷Lu were obtained from the Nudat2 database provided by the National Nuclear Data Center (NNDC 2014). Electron transport was simulated using the PRESTA (Parameter Reduced Electron-Step Transport Algorithm) (Bielajew and Rogers 1986). The cut-off energies, i.e. the energy at which particle tracking is terminated and the remaining kinetic energy is locally absorbed, was 50 keV and 10 keV for electrons and photons, respectively. Five separate simulation batches, each with 10⁶ particle emissions per source structure, were performed with different random number generator seeds to evaluate the numerical uncertainty. The final S values were taken as the average value of the five batches. The numerical uncertainties of ${{D}_{q}}$ due to discretisation and truncation were heuristically assessed by halving the step-size with the integration interval fixed, and by doubling the integration interval for a fixed step-size, respectively.

To exemplify the intended use of the phantoms for method validation and accuracy assessment of image-based dosimetry in ¹⁷⁷Lu PRRT, a virtual dosimetry study was performed. This sub-study was designed to mimic a dosimetry method that is readily available in most clinics. It should be noted a more exhaustive study will be undertaken in a separate work, and results presented herein are to be regarded as a clinically relevant example.

2.7.1. Imaging simulations.

2.7.2. Image-based dosimetry calculations.

The methods used for quantitative SPECT reconstruction and planar image quantification of the simulated studies were the same as used for the patient studies (section 2.2). However, the required attenuation maps that were derived from patient CT data in real studies, were instead calculated by mapping the true mass-density distribution of the phantoms to linear attenuation coefficients at 208 keV (Berger and Hubbell 1987). The CT scout images used for planar attenuation correction in the pixel-based conjugate-view method (Sjögreen Gleisner and Ljungberg 2012) were obtained by projecting the 3D attenuation maps onto the coronal plane.

The reconstructed SPECT images were rescaled with the camera system sensitivity and voxel volume to obtain images in units of MBq mL⁻¹. Activity concentrations in the kidneys, liver, spleen and tumours were acquired in small single-slice VOIs to minimise the impact of the partial volume effect (PVE). Rather than using the specific values for the phantom organs to calculate the absorbed doses, S values were obtained from OLINDA (Vanderbilt University, Nashville, Tennessee, USA) (Stabin et al 2005), using the adult female model for the kidneys, liver and spleen; and using the spherical model of appropriate size for each of the tumours. This approach was chosen in order to mimic a real-world scenario where the patient S values are unknown and where Monte Carlo programs for explicit radiation transport calculations are unavailable. One common approach in ¹⁷⁷Lu dosimetry is to assume negligible cross-dose contributions from other source organs (Sandström et al 2013). This assumption is reasonable for organs with high uptake given that the ¹⁷⁷Lu emission spectrum is dominated by short-range beta particles (maximum range ~2 mm). Using this approximation, the absorbed dose rate estimate $\widehat{R}$ at 24 h p.i. was calculated according to

$$\begin{eqnarray}&&\widehat{R}=\frac{\widehat{C}\cdot {{S}_{\text{self}}}\cdot m}{\rho}\end{eqnarray} \tag{ 5 }$$

where $\widehat{C}~$ is the SPECT-based activity concentration estimate, $~{{S}_{\text{self}}}$ is the OLINDA self-dose S value, m is the mass of the target organ in the OLINDA model, and ρ is the mass density of the target organ, assumed to be 1.06 g mL⁻¹.

Time-activity values for the organs of interest were determined from the planar images, by delineating region-of-interests and correcting for activity in background and overlapping tissues. The absorbed-dose rate at 1, 96 and 168 h was then calculated as the SPECT-derived absorbed dose-rate 24 h p.i. multiplied with the relative organ activity for each time-point, as determined from the planar image data. A mono-exponential curve was fitted (Wehrmann et al 2007, Bodei et al 2008, Sandström et al 2013), and the absorbed dose calculated by analytical integration.

The whole-body absorbed dose was calculated by fitting and integrating a bi-exponential function (Wehrmann et al 2007) to the total-body activity values determined from the quantitative whole-body scans, and multiplying the cumulated activity with the OLINDA S value rescaled linearly to the phantom mass.

The patient dataset used for fitting the PK model parameters (figure 2) are summarized in tables 2 and 3. Measured activity concentrations in kidneys, liver and spleen for the individual patients are shown in figure 3, together with the resulting curves for the three phantoms according to (2). Note that the kidney curves are averaged of the renal cortex and medulla. The concentration of the left and right kidney differ since they have different volumes in all phantoms and were assigned equal uptake rate constants. In addition, the renal activity concentration for phantom 3 is higher than for 1 and 2 as the input dataset was chosen as 1 SD above the mean concentration (table 2). For the other organs, the time-activity curves are virtually identical. It can be noted there is a good agreement between patient and phantom data and that the pharmacokinetics for normal organs are reasonably consistent between patients. It should however be pointed out that the total tumour volume of the phantoms is small relative to the tumour volume of the patients. Since the long-term whole-body activity retention is mainly determined by the tumour burden and associated uptake, the whole-body activity of the phantoms shown in figure 3 should not be considered representative of patients with high tumour burden.

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The prominent initial peak in the kidney time-activity data is mainly caused by activity that is in the process of being eliminated through renal filtration, as illustrated in figure 4. Approximately 17% of the activity is located in the urinary bladder one hour after the start of infusion and has thus passed through the kidneys. The height of the peak is dependent on the renal transit time, ${{\left(k_{9,11}^{{}}\right)}^{-1}}$, which was determined from the model fitting and found to be in the range 5–10 min for the three phantoms. The initial, smaller, peaks for the other organs are a result of vascular and interstitial activity which is rapidly cleared after the end of infusion. The activity concentrations in the renal cortex and medulla are obtained following the extended renal transport model, as described in section 2.5.

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The reference values of absorbed dose to the kidneys and renal substructures, liver, spleen tumours and whole-body are given in table 4, assuming a standard activity administration of 7.4 GBq. The mean absorbed doses to the phantom kidneys are in the range 3.05–4.78 Gy, with an expected variation due to the different activity concentration curves, illustrated in figure 3. The mean absorbed dose to the spleen is higher, approximately 5.2 Gy; and for the liver, approximately 1.7 Gy. The tumour absorbed doses are between 26.1–26.9 Gy. The small variation indicates that differences in target volume has minor impact on the absorbed fraction of radiation energy from ¹⁷⁷Lu, and that irradiation from activity in other organs is negligible.

The fractional uncertainties of the reference values due to the Monte Carlo statistics in the EGS4 calculations are in the order of 0.01%. The step-size and integration interval was also found acceptable, with results changing less than 0.1% in the numerical testing described in section 2.6. The combined numerical uncertainty was thus in the order of 0.1%.

The simulated SPECT studies for the three phantoms corresponding to 24 h p.i. are shown in figure 5, illustrating the different anatomical features of the phantoms as well as the drawback of planar imaging due to overlapping activity in the AP direction. The sequence of WB planar images are shown for phantom 3 in figure 6, also including corresponding images of one patient to enable visual comparison.

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The absorbed-dose estimates to the kidneys, liver, spleen and tumours are summarized in table 5, as percentage deviations from the corresponding reference value in table 4. The whole-kidney absorbed dose was used as references value for the renal absorbed-dose estimates. In summary, the deviations for all organs and tumours are between  −24 and 14%, and for the whole-body absorbed doses between 2 and 4%. The deviations for the tumours are approximately in the same range as the deviations for the organs investigated, and there is no trend of increased accuracy of the absorbed-estimates with increasing tumour volume.