CT images of the CT Electron Density Phantom Model 062 M (computerized imaging reference systems, CIRS) were acquired with a SPECT/CT system (Symbia Intevo Bold, Siemens Healthineers) with adjustable CT voltage (80 kVp, 110 kVp, and 130 kVp). All CT reconstructions were performed with the I31s kernel (Sinogram AFfirmed Iterative REconstruction, SAFIRE at strength S3), which utilizes a weighted FBP for initial reconstruction, followed by two correction loops [16]. The Segment Editor module of 3D Slicer (version 4.8.1) [18, 19] was used to analyze the CT images. All mathematical calculations were performed in Python (version 3).

Comparison between CT-based linear attenuation coefficients and the national institute of standards and technology linear attenuation coefficients database

Seventy CT acquisitions of the Electron Density Phantom equipped with seventeen inserts of nine different tissue-equivalent materials (exhale lung, inhale lung, adipose, breast, muscle, liver, bone 200 mg/cm3 hydroxyapatite (HA), bone 800 mg/cm3 HA, and bone 1250 mg/cm3 HA) were acquired. These measurements included seven different combinations of kVp and QRM (80kVp with 20mAs, 35mAs, and 50mAs, 110kVp with 20mAs and 35mAs, and 130kVp with 20mAs, and 35mAs), each repeated ten times. All acquisitions were performed with a pitch of 1.5. A 177Lu μ-map based on the I31s CT reconstruction kernel was generated using the standard manufacturer reconstruction (Flash3D, Siemens Healthineers) with a voxel size of 4.8 mm. The mean μ value (μmeasured) of each insert was quantified in cubic volumes of interest (VOIs) of 3 × 3 × 8 voxels (Fig. 1). To identify a potential radial dependency of the attenuation (e.g., due to the CT beam hardening conditions), the μmeasured values for the inserts located on the inner and outer section of the Electron Density Phantom were evaluated independently: two datasets (dataset 1: nine inner inserts excluding the 1250 mg/cm3 HA bone insert; dataset 2: eight outer inserts) were used for statistical tests of normality (Shapiro–Wilk normality test) and mean difference (unpaired t-test). Next, for each insert, μmeasured was compared against the theoretical μ value (μtheoretical) for 208.4 keV 177Lu gamma emission (peak with highest emission probability) from the National Institute of Standards and Technology (NIST) standard reference database 8 [17], which allows the calculation of the attenuation coefficient of a mixture (a combination of elements) using the elemental material composition and mass density provided by the manufacturer of the Electron Density Phantom [18]. Moreover, the CTDIvol for each combination of kVp and QRM was extracted from the DICOM header of each image.

Fig. 1

Positioning of the cubic volume of interest of 3 × 3 × 8 voxels in the bone insert with 1250 mg/cm3 hydroxyapatite in 130 kVp and 35 mAs image. A whole phantom. Blue dotted line indicates position of inner inserts, orange dotted line indicates position of outer inserts. B Zoom over the bone insert and placing of the cubic volume of interest

Calculation of the attenuation correction factor image for 177Lu from the μ-map

In this section, a theoretical approach was applied to evaluate the influence of the kVp and QRM on 177Lu SPECT/CT-based activity quantification. Specifically, the Chang algorithm [19] was implemented using measured 177Lu μ-maps in combination with the equation described in Bailey et al. [20]. First, to create a theoretical μ-map, a digital version of the Electron Density Phantom was generated based on one of the 130 kVp and 35 mAs CT images of 512 × 512 × 86 voxels with a voxel size of 0.977 × 0. 977 × 3 mm3. All inserts, the contour of the phantom, and all voxels outside the phantom (air plus bed) were separately segmented in 3D Slicer (Fig. 2A). Then, these segmentations were downscaled to the voxel size (4.8 mm) of the μ-map (128 × 128 × 55). Next, the μtheoretical values for the 208.4 keV 177Lu gamma emission were assigned to each segment (19 segments comprising 17 material inserts, the water plastic phantom material, and air) using the 3D Slicer segmentation color table (Fig. 2B).

Fig. 2

Digital phantom from the CIRS electron density phantom. A Segments from the high resolution CT image. B µ-map based on theoretical values from NIST database [17]. C Theoretical attenuation correction factor (ACFtheoretical) image. \(I_\) is the image with attenuation correction and \(I\) is the image without attenuation correction

Second, to generate the attenuation correction factor (ACF) images, an existing Python script [21] was extended to implement a modified Chang method [20] using the theoretical μ-map (ACFtheoretical) (Fig. 2C and Additional file 2: material) and measured μ-maps for each kVp and QRM combination (generated in section 1 of “Materials and methods”) (Additional file 3: material).

Next, ACFmeasured and ACFtheoretical were analyzed using the same VOI sizes and localizations as defined in section 1 of “Materials and methods”. Subsequently, the change in 177Lu activity quantification (\(\Delta A\left[ \% \right]\)) to be expected was assessed using Eq. 1 (derivation in Additional file 1):

$$\Delta A\left( _}^}} }} \right)}\left( }_}}} }}}_}}} }}} \right) \cdot }$$

(1)

Lastly, a Shapiro–Wilk normality test followed by a one-way analysis of variance (parametric or nonparametric depending on the normality test) for comparing multiple independent samples were performed to compare the changes in 177Lu activity quantification based on the seven kVp and QRM combinations.

Noise assessment in CT-based 177Lu μ-map

To evaluate the influence of kVp and QRM of the CT-AC on the noise in the attenuation map, eight cubic VOIs of 1,000 voxels each were drawn on the homogeneous plastic water section of the Electron Density Phantom in the CT-AC-based 177Lu μ-map (the positioning is described in Fig. 3). This process was repeated for all ten repetitions of each kVp and QRM combination. First, a mean μ value \(\left( }}} } \right)_\) over all eight cubic i VOIs was calculated for each repetition j:

$$\left( }}} } \right)_ = \frac^ \left( }}} } \right)_ }}$$

(2)

Fig. 3

Segmented VOIs for the noise analysis. Illustration performed on imageJ [28]

Subsequently, total mean (\(\mu_}}}\)) and standard deviation (\(\mu_}}}\)) over all ten repetitions j was calculated for each combination of kVp and QRM:

$$\mu_}}} = \frac^ \left( }}} } \right)_ }},$$

(3)

$$\mu_}}} = \sqrt \mathop \sum \limits_^ \left( }}} } \right)_ - \mu_}}} } \right)^ }$$

(4)

Finally, the coefficient of variation (COV) was calculated as:

$$} = \frac}}} }}}}} }}$$

(5)

Influence of different attenuation materials on activity quantification accuracy

In this section, the influence of kVp, QRM, and the SPECT reconstruction algorithm on the SPECT/CT-based 177Lu quantification was evaluated experimentally. To compare different attenuation materials, a phantom consisting of four radioactive sources (syringes of volume 1 mL / diameter 0.7 cm or 10 mL / diameter 1.6 cm), each surrounded by a different attenuation medium, was designed. It consisted of the IEC NEMA body phantom container and a 3D-printed mounting system for four cylinders made of different attenuation materials, each of which had a hollow cylinder drilled in its center for axial syringe insertion (Fig. 4A and B). The attenuation materials included lung (Polystyrene, PS, diameter: 5 cm, density: 0.023 g/cm3), bone (polytetrafluoroethylene, PTFE, diameter: 3 cm, density: 2.18 g/cm3), soft tissue (polyamide, PA, diameter: 3 cm, density: 1.02 g/cm3), and fat tissue equivalent materials (polypropylene, PP, diameter: 3 cm, density: 0.91 g/cm3). These densities are based on the manufacturer specifications [22, 23]. To compensate for the low mass density of Polystyrene, a cylinder with a larger diameter was used in comparison to the other three cylinders.

Fig. 4

Quantitative SPECT: A Frontal view of 10-mL syringe insert. B Lateral view of 10-mL syringe insert. C Segmentation boundaries using 10-mL syringe insert with sources inside of NEMA Phantom

A 100-mL radioactive stock solution consisting of 177Lu-chloride dissolved in 0.1 M HCl with 100 ppm of stable lutetium [13] was prepared. Eight syringes (four syringes of 1 mL and four syringes of 10 mL) were weighted before and after the filling process for a weight-based determination of the contained activity. A VDC-405 radionuclide calibrator equipped with a VIK-202 ionization chamber (Comecer SpA) was used for estimating the activity added to the stock solution during the phantom filling process. The reference activity concentration was obtained from a 1-mL aliquot of the stock solution, which was measured in a high-purity germanium (HPGe) detector (model GR4020 [Canberra]), whose energy-dependent efficiency had previously been calibrated with several NIST-traceable standards over the energy range considered [13].

SPECT/CT images of both phantom setups (four 1-mL syringes, four 10-mL syringes) placed inside a water-filled (to simulate soft tissue attenuation) IEC NEMA body phantom were acquired (Fig. 4C). The images were acquired with a Siemens Intevo Bold SPECT/CT system with 9.5-mm crystal thickness, medium-energy low-penetration collimation, 180° detector configuration, automatic contouring, continuous mode, 60 views, 30 s per view, 256 × 256 matrix, and 3 energy windows (20% around the main photopeak of 208 keV and two adjacent 10% scatter windows). After SPECT acquisition, seven CT acquisitions were performed using the same combinations of kVp and QRM as described in the previous Sects. (80kVp with 20mAs, 35mAs, and 50mAs, 110kVp with 20mAs and 35mAs, and 130kVp with 20mAs, and 35mAs). The CT-AC images were reconstructed with the I31s kernel in a 512 × 512 × 133 matrix with a resolution of 1.0 × 1.0 × 3.0 mm3. Next, 7 × 3 SPECT reconstructions were performed, one for each kVp and mAs combination (seven CT-based μ-maps) using three different reconstruction algorithms: (1) xSPECT Quant (Siemens Healthineers), an ordered-subset conjugate gradient minimization (OSCGM) reconstruction providing images in activity concentration (Bq/mL) based on a NIST traceable calibration source; the calibration is performed as part of the quality controls of the SPECT/CT system; reconstruction was performed using 24 iterations, 1 subset, and no postfilter [24]. (2) Flash3D (Siemens Healthineers), ordered-subset expectation maximization (OSEM) with attenuation correction, scatter correction, and depth-dependent 3D resolution recovery, which generates reconstructed images in counts; as recommended by the manufacturer, images were downsampled to a matrix size of 128 (voxel size: 4.8 mm); reconstruction was performed using 6 iterations, 6 subsets and no postfilter; an image calibration factor (ICF) of 20.3 cps/MBq (counts-per-second-per-Megabecquerel) as described in Tran-Gia et al. [13] for the same setup was used for conversion from counts to activity concentration. (3) STIR (Open Source software) [25], OSEM with attenuation correction, scatter correction, and a depth-dependent 3D resolution recovery method; as for Flash3D, images were downsampled to a matrix size of 128; reconstructions were performed using 6 iterations, 6 subsets and no postfilter; here, an ICF of 20.0 cps/MBq (determined as described by Tran-Gia et al. [13]) was used for conversion from counts to activity concentration.

After SPECT reconstruction, cylindrical VOIs were drawn on the 130 kVp and 35 mAs CT images of each phantom. In addition to the syringes and the attenuation material, the VOIs included were extended to a portion of the water phantom (Fig. 4C) to account for the activity distributed outside the walls of the syringe due to the limited spatial resolution of SPECT imaging [26]. These VOIs were applied to all SPECT reconstructions to ensure that the evaluation of activity was performed comparably between the different reconstructions.