Patient Selection

We retrospectively reviewed a cohort of 63 patients with metastatic castration-resistant prostate cancer who underwent radioligand therapy with [177Lu]Lu-PSMA-617, including routine multi-time-point (MTP) dosimetry imaging at 0 h, 4 h, 24 h, 48 h, and 72 h post injection between February 2021 and March 2023. Patients were included if they presented with clearly delineated, SPECT-positive, and segmentable lymph node metastases. Based on these inclusion criteria, a total of ten patients were selected for personalized phantom fabrication.

CT in Lu-177 SPECT/CT Dosimetry

The patient´s CT data were acquired using a Siemens Symbia Intevo Bold System (Siemens Healthineers, Germany). The SPECT/CT acquisition was performed at about 24-h post injection as part of routine dosimetry workflow. The CT parameters were as follows: tube voltage of 110 kV; tube time–current 24 mAs reference; slice collimation 16 × 1.2 mm; and pitch 1.5. The CT images were reconstructed using the manufacturer`s implementation of the iterative reconstruction algorithm with an I31s kernel and a slice thickness of 5 mm. An overview of the lymph node phantoms is shown in Fig. 1.

Fig. 1The alternative text for this image may have been generated using AI.

The 10 3D-printed lymph node phantoms used for validating the correction graph. In the top row, from left to right, the phantoms are Pat63, Pat13, Pat47, Pat14 and Pat62. In the bottom row, from left to right, the phantoms are Pat61, Pat33, Pat21, Pat60 and Pat40

Segmentation and Design of the Lymph Node Phantoms

LNM were segmented from the patient`s CT data using ITK-Snap software (version 4.0.2). For this purpose, LNM were manually contoured voxel by voxel in the transverse slices of the CT images. The resulting segmentation was then exported as surface mesh in STL format and further processed in the CAD software Meshmixer (Version 3.5). In Meshmixer, the segmentation of LNM was smoothed using the “Smooth” function. This function was employed to generate a smoothed, anatomically realistic surface model from the voxelized segmentation. The smoothing mode “Shape Preservation” was applied in this process. The smoothing scale was set between 1 and 5, depending on the volume of LNM, with the smoothing factor set to 1 and “Constrain Rings” to 3. The smoothing scale parameter controls the intensity of the smoothing, where 0 represents no smoothing, and 100 represents the maximum possible smoothing. For very small LNM with low volumes, lower values were used to minimize the impact on model volume and to remain as close as possible to the original segmentation. Higher smoothing values were applied for models with larger volumes, as the effect on volume was less pronounced in these cases. To quantify whether CAD smoothing altered lesion volume, volumes of the original CT-based segmentations (ITK-Snap) were measured and compared with the volumes of the smoothed STL models (Meshmixer). A wall with a thickness of 1 mm was added around the segmentation to create a hollow structure. For fixation and filling of the models, a filling-connector was attached at the lower end. The connector has a total length of 50 mm and includes a threaded screw for attachment to the torso phantom. The connector contains a small hole through which the LNM-phantoms can be filled. The manufacturing process of the lymph node phantoms is shown in Fig. 2. 

Fig. 2The alternative text for this image may have been generated using AI.

Manufacturing process of lymph node phantoms from segmentation on CT to the printed phantom, exemplified by Pat47

Determination of the Surface-to-Volume Ratios (SA:V)

The lymph node phantoms' surface-to-volume ratio (SA:V) was determined after the previously described smoothing process in Meshmixer. For this purpose, the "Stability" module was used, which calculates both the surface area and the volume of the models.

Printing of the Lymph Node Phantoms

All lymph node phantoms were produced using a Keyence Agilista-3200W 3D printer. The phantom walls were printed using the printer-specific Keyence material AR-M2, a rigid translucent polyacrylate resin, while the water-soluble Keyence material AR-S1 was used as support material during the printing process. After printing, the support material was thoroughly removed by repeatedly flushing the phantoms with water through the filling connector.

SPECT/CT Measurement and Evaluation

For the phantom scans, five phantoms were placed in a torso phantom (similar to the body phantom NEMA-NU 2007, PTW-Freiburg, Freiburg, Germany) using a base plate. The placement was arranged so that each lymph node phantom maintained an equal distance from the wall to the center of the torso phantom. The ten printed lymph node phantoms were divided into two measurement series, each conducted with four different target-to-background ratios (TBR). Measurement series 1 included the phantoms P13, P14, P21, P33 and P47, while measurement series 2 included the phantoms P40, P60, P61, P62 and P63. The phantoms were all filled with the lutetium compound [177Lu]Lu-DOTATOC to prevent adhesion to the model walls, which occurs more frequently when using pure lutetium.

Measurement Series 1

The lymph node phantoms were filled with a 216.8 kBq/ml concentration of [177Lu]Lu-DOTATOC. The background in the first scan remained cold, i.e., without activity. For the subsequent scans, the background was filled with 10.7, 21.6, and 42.5 kBq/ml, respectively. As a result, the actual target-to-background ratios for the planned 20:1, 10:1, and 5:1 were 20.7:1, 10.0:1, and 5.1:1, respectively.

Measurement Series 2

The lymph node phantoms were filled with a 197.2 kBq/ml concentration of [177Lu]Lu-DOTATOC. The background in the first scan remained cold, i.e., without activity. For the subsequent scans, the background was filled with 10.6, 20.9, and 42.1 kBq/ml, respectively. As a result, the actual target-to-background ratios for the planned 20:1, 10:1, and 5:1 were 18.6:1, 9.4:1, and 4.6:1, respectively.

To facilitate the later segmentation of the reconstructed SPECT/CT images, the lymph node phantoms were additionally filled with CT contrast agent (Imeron 350, Bracco Imaging, Konstanz, Germany) in a 1:20 ratio. This slightly increased this compartment's Hounsfield units (HU) to approximately 362.25 HU.

SPECT/CT Scanner

All phantom scans were performed using a clinical SPECT/CT system (Symbia Intevo Bold, Siemens Healthineers, Germany) with a medium-energy low-penetration (MELP) collimator. The scans were carried out with the following configurations: 180° detector configuration, 120 projections over 360° (3° sampling) in 60 views at 30 s per view, a projection matrix of 256 × 256 and a pixel spacing of 1.95 × 1.95 mm. The energy window was set between 187.56 to 229.24 keV, with a lower scatter window from 166.72 keV to 187.56 keV and an upper scatter window from 229.24 keV to 250.08 keV. To obtain quantitative values, the SPECT system was calibrated using Se-75 precision reference sources as part of the Siemens xSPECT Quant technology (Siemens). The CT parameters of the hybrid SPECT/CT acquisition were set as follows: tube voltage 130 kV; tube time–current 78 mAs reference; Siemens Care Dose 4D tube current modulations; slice collimation 0.6 × 9.6 mm and pitch 1.1. The CT images were reconstructed using the manufacturer’s recommended iterative reconstruction algorithm with the I31s kernel and a slice thickness of 1 mm. The SPECT projection data was reconstructed using the Siemens xSPECT Quant technology, based on an ordered-subset conjugate-gradient (OSCG) algorithm. Corrections were performed according to the manufacturer`s implementations. In brief, scatter radiation was corrected using a dual-energy window method and attenuation correction was performed based on CT. The reconstructed SPECT images had a matrix size of 256 × 256 with a voxel size of 1.95 × 1.95 × 1.95 mm. Four reconstructions were performed with 12, 24, 48, 72 iterations, all using one subset, resulting in fully quantitative SPECT data. The recovery coefficient (RC) for each lymph node phantom was determined from these reconstructions. The ratio of the concentrations obtained with SPECT to the actual concentrations (known from the phantom filling) was calculated. Finally, the activity was extracted using a Python script after manually segmenting the respective volumes in ITK-Snap.

Single Volume-of-Interest (VOI) Method

The single VOI method calculates the activity of a structure based on a larger volume of interest surrounding the actual structure. This approach includes the activity within the structure itself and that which has been washed out from these structures due to the partial volume effect. Additionally, this method can include activity from the background within the VOI. For this, a VOI was placed around the visually observed uptake in the SPECT image using the MM Oncology workflow in the software Syngo.via (Version: VB60A, Siemens Healthineers, Germany).

Multi VOI Method

To use the oversized VOI method, an enlarged VOI is first placed around the target structure to contain the entire activity of the source. Additionally, two concentric VOIs with increasing volume are placed around the initial VOI to include surrounding radioactivity. Assuming that the contribution of activity from the surrounding tissue increases linearly with the VOI size, the actual activity in the target region can be determined by extrapolating the activity against the VOI volume [27]. To apply this correction method, the images of the phantom scans were loaded with the MM Oncology workflow in Syngo.via (Version: VB60A, Siemens Healthineers, Germany), and three VOIs were manually placed around each lymph node phantom. The second and third VOIs correspond to twice and three times the volume of the first VOI, respectively. Using the VOI parameters in Syngo.via, the corrected activity of the structure can be calculated using formula (1) from the Volume (X) and activity within the VOIs (Y). Here, YX0 denotes the y-intercept at X = 0 and represents the estimated true lesion activity at zero added background.

$$_)= \frac^- \sum \left(X \times Y\right) \times \sum X}^-^}$$

(1)

Single Target Correction (STC)

The single target correction (STC) method was developed for cases where only a single image region requires correction. STC operates on a voxel-based level and does not require the definition of background regions. The STC algorithm involves several steps, during which the target volume and the background are corrected voxel by voxel. Using STC requires precise segmentation of the target volume as well as knowledge of the point-spread function (PSF), which describes the extent of image blurring. After each correction step, a new image estimate is generated, serving as the basis for further iterations, thereby increasing correction accuracy. Compared to some other PVC approaches, an advantage of STC is that only a single region needs to be segmented, whereas other methods often require segmentation of the entire image. Furthermore, with accurately performed segmentation, STC provides voxel-level corrected images with improved edge sharpness, potentially enhancing the detection of tumor lesions [28]. The single target correction was applied to individual lymph node phantoms using the PETPVC toolbox developed by Thomas et al. [29]. For this purpose, the phantoms were manually segmented again on the CT image using ITK-snap. To approximate the point-spread function, three rod sources were placed in the same arrangement as the lymph node phantoms within the torso phantom, with one source each positioned along the X, Y, and Z axes. This setup allowed the approximate determination of the PSF in the X, Y, and Z directions at the position of the lymph node phantoms. The PSF values used were 17.30 mm, 17.77 mm, and 16.86 mm for the X, Y, and Z axes. The number of iterations was set to 10, which has been identified as optimal in other studies [30]. After STC correction, the recovery coefficient (RC) for each phantom was determined from the STC-corrected images using a Python script.

Recovery Coefficient-Based Method

This method represents the first and simplest algorithm for correcting measurements by applying a correction factor known as the recovery coefficient (RC). It was initially introduced by Hofman et al. for a single region [21]. The RC is defined as the ratio of the measured activity concentration of an object to its actual concentration [26]. To use this method, phantom measurements are first conducted, examining known volumes of different sizes, shapes, or surface-area-to-volume ratios (SA:V). These phantoms can represent organs, tumors, or geometric shapes. The resulting phantom data are analyzed to calculate an RC for each volume/SA:V. The RC indicates how much activity is lost due to the object`s size. In practice, the RC determined for a specific object size can be used to correct measurements of similar objects, thereby improving the accuracy of the determined activity. We selected the NEMA IEC body phantom set to apply an RC-based method to our lymph node phantoms because the spheres in this phantom were standardized in shape and size, making this phantom widely used. The phantom is acrylic (PMMA) and contains six fillable spheres with inner diameters of 10 mm, 13 mm, 17 mm, 22 mm, 28 mm, and 37 mm. All scans were conducted using the same camera as the lymph node phantoms, with identical technical parameters and the same setup. Similar to the lymph nodes, scans were performed with four different target-to-background ratios. The spheres of the phantom were filled with a concentration of 202.5 kBq/ml of [177Lu]Lu-DOTATOC. The background during the first scan remained cold, without activity. For subsequent scans, the background was filled with concentrations of 10.1, 20.2, and 40.7 kBq/ml, resulting in actual ratios of 20.0:1, 9.9:1, and 4.9:1 for the initially planned 20:1, 10:1, and 5:1 acquisitions, respectively. Finally, the spheres were manually segmented on the CT using ITK-snap. The RC for each sphere was extracted using a Python script. From the RCs and the background ratio, a non-linear regression was used, the function used an exponential decay with plateau using a least squares optimization with no weighting, it is shown in formula (2). The parameter Ym represents the lower asymptote (or plateau) of the function and was fixed for each fit according to the respective target-to-background ratio (TBR) of the measurement. In contrast, Y0​ denotes the intersection with the y-axis, and was derived using GraphPad Prism via non-linear regression. The rate constant \(k\) determines the steepness of the curve (how rapidly the RC decreases from Y0​ to YM​ as the SA:V increases).

$$Y=_-\left(_-_\right)\times ^$$

(2)