Phantom preparation

Two phantoms were utilized in this study. Firstly, one cylindrical phantom was filled with a homogeneous distribution of 166Ho-chloride dissolved in demineralized water (HolmiumSolution, Quirem Medical B.V., Deventer, The Netherlands). This phantom had an inner diameter of 20 cm, an inner height of 20 cm, a volume of 6283 mL, and an activity concentration of 0.049 MBq/mL at the injection time point. The second phantom was a flanged, rod-less, Jaszczak phantom with six fillable spheres, see Fig. 1 for sphere numbering and configuration. The background compartment of the Jaszczak phantom had a volume of approximately 6.7 L and the fillable spheres had inner diameters of 9.9, 15.4, 19.8, 24.8, 31.3, 60 mm (and approximate volumes 0.5, 2.0, 4.0, 8.0, 16.0, 113 mL). The Jaszczak phantom was also filled with homogeneous solutions of 166Ho-chloride. The activity concentration was 4.10 MBq/mL in the spheres and 0.41 MBq/mL in the background compartment at the injection time point, resulting in a sphere-to-background activity concentration ratio (\(\:\text:\text}_\text\text\text\text}\)) of 10:1. The total activity in the Jaszczak phantom ranged from 3.26 GBq to 61 MBq throughout the experiment, see Table 1. The 166Ho activities were measured in a dose calibrator (manufactured in 2019, equipped with ionization chamber VIK-202, Comecer, Joure, The Netherlands). In both phantoms the 166Ho-chloride solution was saturated with 50 mM ethylenediaminetetraacetic acid to bind the holmium ions, forming water-soluble complexes.

Fig. 1

CT images of the Jaszczak phantom with the fillable spheres. Axial view on the left and sagittal view on the right. The sphere numbering presented in this image is used throughout this paper

SPECT/CT system

Both phantoms were imaged using a Symbia Intevo Bold SPECT/CT scanner equipped with the proprietary absolute quantification software Broad Quantification and the additional TrueCalc software (Siemens Healthineers, Erlangen, Germany). The purpose of TrueCalc is to improve the detector response at high count rates by reducing the impact of detector dead-time and give consistent quantitative accuracy across a wide range of activities [17, 19, 20]. The SPECT/CT scanner was manufactured and installed in 2019, uses software version VB22A, features a dual-headed detector configuration with a field-of-view of 53.3\(\:\times\:\)38.7 cm2 and a NaI crystal with a thickness of 9.5 mm. Prior to the measurements the SPECT/CT scanner had been peaked with a ~ 5 MBq 166Ho point source, and the Broad Quantification calibration procedure for 166Ho had been carried out in accordance with the operator manual, see supplementary information.

Data acquisition

Imaging of the homogeneous phantom was acquired at one time point (total activity of 250 MBq at scanning). Imaging of the Jaszczak phantom was acquired at 14 different time points with three repetitions at the 10th, 12th, 13th, and 14th time point. The dead-time [%] estimate was read from the workstation during the acquisition of the data (‘Tomo Acquisition’-activity, ‘Analyzer’-tab), see Table 1. All SPECT data were acquired with the following settings: a photopeak energy window at 81 keV (15% width), two adjacent scatter windows (8% width), non-circular orbit over 360°, step and shoot, 2 × 60 projections, 20 s projection time, and a 128 × 128 matrix size. Parallel hole, Medium Energy Low Penetration (MELP) collimators were used, and the checkbox for ‘Enable Quantitative Acquisition’ had been ticked. When acquiring quantitative data, with the additional dead-time correction software (TrueCalc), the SPECT scanner generates two different projection datasets per SPECT acquisition; one dataset that is corrected for the estimated count losses due to dead-time effects, and a second dataset that is uncorrected. The measured counting rate performance per time point, for these two projection datasets, can be found in the Supplemental information. The dead-time estimates, presented in Table 1, are unaffected by the TrueCalc software. Additionally, low-dose CT data for attenuation correction and structural information were acquired for each dataset. The positioning of the Jaszczak phantom was standardized across all measurements, see Fig. 1.

Image reconstruction

The acquired SPECT data for both phantoms were reconstructed using two different Siemens proprietary algorithms; Flash3D and xSPECT. The widely used Flash3D method is a 3D ordered subset expectation maximization (OSEM) method (utilized the uncorrected projection data). For Flash3D, the data were reconstructed with 10 iterations 8 subsets, and a voxel size of \(\:4.80\times\:4.80\times\:4.80\:\text}^}\). The xSPECT algorithm utilizes an ordered subset conjugate gradient (OSCG) method and Broad Quantification was enabled, meaning that the images were reconstructed in the unit of Bq/mL. Additionally, the xSPECT algorithm also applied the TrueCalc count loss correction in the image reconstruction (utilized the projection data corrected for count losses). For xSPECT, the data were reconstructed with 36 iterations 1 subset, a voxel size of \(\:4.88\times\:4.88\times\:4.88\:\text}^}\), and decay corrected back to the injection time point. Triple energy window scatter correction (automatic scatter window weight of 0.94) and CT based attenuation correction was applied for both reconstruction methods. If nothing else is indicated, no post-reconstruction filtering was applied to the Flash3D data and a 15 mm full width at half maximum (FWHM) post-reconstruction filtering was applied to the xSPECT data. See supplementary information for the choice of image reconstruction parameters.

Data analysis

All image delineation and all data analysis were performed using MATLAB (R2021a, The MathWorks Inc., Natick, Massachusetts).

Image delineation

All volumes-of-interests (VOIs) for spheres, background and whole phantom volumes, were semi-automatically created based on the known phantom geometry and CT based positioning on a high resolution CT (voxel size \(\:0.98\times\:0.98\times\:1.5\:\text}^}\)). The background VOI in the Jaszczak phantom was defined by subtracting the sphere VOIs from the whole phantom VOI. To minimize loss of data precision in the analysis, the reconstructed SPECT data were transformed to the high resolution CT voxel space by means of an affine transformation and nearest neighbor interpolation. All analyses were carried out using the high resolution grid.

SPECT quantification

Three methods for quantifying the SPECT data for the Jaszczak phantom were compared in this study;

1.

Scanner-specific conversion factor measured in the Flash3D-reconstruction of the cylindrical homogeneous phantom (CFhomogeneous) [12,13,14,15,16],

2.

Self-calibration based on the Flash3D-reconstruction and delineation of the Jaszczak phantom for each dataset (CFself) [4, 15], and.

3.

Broad Quantification absolute quantification software (based on xSPECT-reconstruction).

For the two Flash3D-based quantification methods, the conversion factor (CF) was calculated using the following formula;\(\:\text\text=\frac}\cdot\:\text\cdot\:}_\text\text\text\text}}\right)}}}_\text\text}}\right)}\hspace\hspace\left[\frac\text\text}\text\text}\right],\hspace\)

where \(\:\) is the mean counts in the VOI to be quantified, \(\:\text\) is the time per projection [s], \(\:\text\) is the number of projections, \(\:_\) is the voxel volume [mL], \(\:A\) is the true total activity in the VOI [MBq], and \(\:_\) is the volume of the VOI [mL]. The CFhomogeneous was calculated based on the activity present at scanning in a two liter cylindrical VOI centered in the homogeneous phantom. The CFself was calculated based on the total activity present in the Jaszczak phantom at the start of each SPECT acquisition, and a VOI encompassing the whole phantom. Each Flash3D-reconstruction was processed to have the unit of counts per second per milliliter [cps/mL], and was thereafter quantified by dividing each voxel in the image with either the CFhomogeneous or CFself. Lastly, the quantified images [MBq/mL] were decay corrected to the injection time point.

The Broad Quantification-based quantification method directly quantifies the xSPECT-reconstruction in units of Bq/mL and decay corrects it to the injection time point, see supplementary information for information about the calibration procedure.

Homogeneity evaluation in cylindrical phantom

Based on the quantitative SPECT images of the cylindrical homogeneous phantom, the homogeneity of the reconstructions were evaluated through assessment of activity concentration profiles (ACPs) parallel to the phantom’s symmetry axis. Three voxel row profiles and two cylindrical VOIs were evaluated. The ACPs for the cylindrical VOIs were obtained by averaging the activity concentration values, for all voxels within a specified radius, per slice in the SPECT data. Furthermore, cumulative activity-volume histograms (cAVH) have been calculated for one VOI encompassing the whole phantom volume, and two cylindrical VOIs centered in and having the same length, but with a smaller radius (either 30 mm or 70 mm), as the cylindrical phantom. The cAVHs were qualitatively compared to the theoretical ideal cAVH for a homogeneous distribution, which is a step function. Images without post-reconstruction filtering and with a 15 mm FWHM Gaussian filter were compared in this analysis.

Activity recovery in Jaszczak phantom

The percentage of recovered activity was computed for each of the three SPECT quantification methods and each time point of the Jaszczak phantom measurements. All the voxels in a VOI encompassing the whole phantom, i.e. the same VOI as was used for the determination of CFself, was considered for this calculation.

Activity concentration recovery coefficient

The activity concentration recovery coefficients (ACRC) were calculated for the sphere VOIs, and the background VOI for each SPECT quantification method and for each time point of the Jaszczak phantom measurements. The ACRC was defined as\(\:ACRC=\frac_}_},\)

where\(\:_\) is the mean activity concentration of the sphere or background VOI in the quantified SPECT image [MBq/mL], and \(\:_\) is the true activity concentration in the same VOI [MBq/mL].

Recovery curve

Recovery curves that can be used for correcting images for losses related to partial volume effects (PVEs), i.e. ACRC as a function of sphere diameter (d), were created. The ACRCs for the three repeated measurements at time point 10, 12, 13 and 14 were averaged for each quantification method and the dependency of the activity level was visualized. A 3-parameter (a, b, c) logistic function on the form

$$\:ACRC\left(d\right)=a\left(1-\frac\right)}^}\right)$$

was fitted to the data [13]. The a-coefficient represents the asymptote that the fitted curve is converging towards when increasing the spherical diameter of a hot object, indicating the theoretically highest ACRC possible for each quantification method and activity level.