A 3D printed fillable liver phantom was used in this study to emulate IDIF measurements of a PV and compare with the ground truth. A contrast enhanced Computed Tomography (CT) image was used as the basis for the design of the liver 3D model. To fit the model within the printer limits, the overall dimensions of the liver were scaled down to approximately half of its original dimensions in each direction. By contrast, the portal vein was modelled at original dimensions to maintain the same PET/MR acquisition characteristics in the experiments. The inferior vena cava was also included in the model, as it touches with the liver. Wall size thickness of the PV and vena cava were kept below 1.5 mm to avoid influence of the non-visible plastic material on PET images.

The final model, shown in Fig. 1, consists of 3 fillable compartments which are sealed with luer locks. The total volume of the 3D printed liver is 465 cm3. The included portal vein compartment measures between 15 mm and 10 mm in diameter, as it continuously changes in size while entering the liver. The portal vein compartment measures 75 mm across its maximum length. These values are representative of the expected portal vein dimensions [12]. The scaled vena cava measures approximately 15 mm in diameter across its modeled length.

Illustration and dimensions of the designed 3D liver model with Inferior-Posterior (A), Anterior-Posterior (C) view and an axial cut-view through the portal vein insert of the model (B)

The model was printed in a 3D printer (Form 3B+, Formlabs, USA) using the clear resin V5 material (Formlabs, USA) and attached to the torso-section of a custom-built MR phantom that was used to simulate respiratory motion, as described in the phantom experiments section below.

The suggested PET/MR acquisition protocol in this study is summarized in Fig. 2. This was designed based on the available capabilites of the mMR PET/MR scanner (Siemens Healthineers, Erlangen, Germany). In this protocol, before tracer administration, high-resolution anatomical MR images are acquired using a breath hold protocol to avoid motion artifacts. An accelerated gradient echo sequence (True Fast Imaging with Steady-State Free Precession, TRUFI-3D) is used with isotropic 1.2 mm voxel resolution (repetition time (TR): 478.91 ms, echo time (TE): 1.92 ms, flip angle (FA): 29 °, FOV: 265 × 273 mm), in which blood vessels have high contrast and can be easily segmented.

Timeline diagram of a PET-MR acquisition protocol using the proposed methodology for image derived portal vein input function estimation of the initial 4 min post PET tracer injection. Following the completion of the BodyCOMPASS™ sequence, PET acquisition and other MR sequences can proceed for the duration needed in the protocol

Following this short acquisition, an MR attenuation correction (MRAC) DIXON sequence (TR: 3.96 ms, TE: 1.23 ms, FA: 9 °, FOV: 312 × 500 mm) is acquired synchronously with the start of PET acquisition for producing the necessary attenuation maps. Following these two acquisitions, the BodyCOMPASS™ (Siemens Healthineers, Erlangen, Germany) motion tracking sequence is performed with free breathing for approximately 4 min (TR: 2.97 ms, TE: 1.32 ms, FA: 10 °, FOV: 400 × 400 mm). This is a stack-of-stars MRI sequence that radially samples the k-space while also recording a respiratory trace from the center of k-space (referred to as self-gating signal) [17]. The signal is recorded at a frequency of approximately 7 Hz and saved in the BodyCOMPASS™ acquisition raw data. The acquired MR data are automatically split and reconstructed in 5 respiratory gates by the mMR system, which are then used to estimate deformations between gates for use with PET reconstruction and obtain motion-free PET images. In this work we did not reconstruct the PET data using the PET/MR system, as the PET motion correction implementation of the BodyCOMPASS™ is limited to static PET reconstructions only. Instead, we made use of the recorded respiratory trace for offline PET reconstruction with motion compensation.

In a hypothetical clinical protocol using the proposed methodology, PET tracer administration would be set to start with the BodyCOMPASS™ sequence in order to have motion tracking data available from the beginning of tracer arrival to the liver (by its blood supplying vessels).

After the completion of the BodyCOMPASS™ sequence, PET acquisition and other MR sequences can proceed for the duration needed in the study. For the phantom experiments in this work, no further PET or MR acquisitions were made after the run of the BodyCOMPASS™ sequence.

The PET data were extracted and reconstructed off-line using the CASToR open-source reconstruction platform [18]. During reconstruction, for each update using the data of each gate a forward and backward transformation was used to result in reconstructed images at the reference position. This strategy ensures the use of all data statistics within the reconstruction loop for each frame of the dynamic series and produces motion-compensated PET images. The respiratory trace extracted from the MR BodyCOMPASS™ sequence was used to split the data into gates of different respiratory phases, as described further in the Motion estimation section.

The PET data were reconstructed into a dynamic series of 12 × 20 s frames using the OSEM algorithm (2it21sub). The framing duration was chosen on the rationale that after input function dispersion, 20 s frames would be adequate for capturing the input function shape characteristics (see supplementary material).

All available corrections were applied during reconstruction, namely normalization, attenuation, scatter and random corrections. Due to the image transformation accounted within the reconstruction, corrections that were initially calculated for the reference position can be used during these gated reconstructions. The attenuation maps for each acquisition were generated using a previous CT scan of the phantom, after manual registration to anatomical MR images of each experiment. The use of the CT image was necessary as the phantom contains several plastic components which do not produce MR signal and therefore are not visible in the generated MRAC. Normalization, scatter and random corrections were extracted from Siemens off-line reconstruction tools and used in CASToR off-line reconstructions. The applied corrections are matching the corrections used in standard clinical PET/MR practice. No time-of-flight was used in the reconstruction as the mMR system does not offer time-of-flight information. For comparison with standard PET reconstructions without motion compensation, reconstructions of a single gate at end-expiration were performed for all experiments and included in the analysis.

The BodyCOMPASS™ sequence provides MR images for each gate position, which can be used for subsequent registration of gated images or within static PET reconstruction as described above. In this work, the MR visible components of the phantom did not produce a strong MR signal, such as the signal expected from a human torso with tissue surrounding the liver. As a result, the MR images for each gate were deteriorated by strong streak artifacts. Therefore, in our experiments, we made use of the MR respiratory trace to reconstruct static PET images for each gate, as seen for in a single acquisition example in the middle row of Fig. 6. Motion between gates was estimated using a well validated tool for registration using PET data [19], and since in our experiments motion was limited to linear translations in the cranio-caudal direction, only rigid registration parameters were estimated. In particular, the gate that represented end-expiration was used as the target, to which all other gates were registered to.

For comparison with the ground truth phantom displacement, the location data from the piezoelectric controller were averaged over individual gate positions and reported for comparison. PET count-rate data (prompts) were also extracted from the PET list-mode data to evaluate if they could be a suitable alternative to the MR trace for retrospective data driven gating using PET data alone.

The 3D printed phantom was fitted within the abdomen section of a custom-built dynamic torso phantom, as seen in Fig. 3, which has been developed for MRI motion simulations [20, 21]. The dynamic torso phantom is designed to simulate 3 different motion types (i.e., breathing motion of the chest wall, the heart and the abdominal organs, as well as heartbeat motion) using non-magnetic linear piezoelectric motors (Xeryon, Belgium) and a full-plastic pneumatic system. In our experiments we made use of a single piezoelectric motor to emulate respiratory motion of the liver along the cranio-caudal direction.

The experimental setup of the 3D printed liver phantom, positioned within the abdomen section of a phantom designed to simulate respiratory motion in the cranio-caudal direction. The motion is driven by the displayed piezoelectric motors

Measurements with the proposed PET/MR protocol were made initially without motion and then repeated for 3 different motion patterns. The motion patterns differed in respiratory cycle period and the range of motion. Namely the experiments 5s20mm, 5s35mm and 7s20mm were conducted with 5 s, 5 s and 7 s respiratory cycle period and 20 mm, 35 mm and 20 mm range of motion respectively. All measurements were made on an mMR PET/MR scanner (Siemens Healthineers, Erlangen, Germany). The motion patterns were limited to linear shifts between selected maximum-expiration and -inspiration points, with varying respiration periods. Real time feedback from the piezoelectric controller enabled precise recording of the displacement over time with 0.1 s sampling rate.

The liver compartment was filled with an [18F]FDG activity concentration of 4.1 kBq/cm3, the portal vein with 78.8 kBq/cm3 and the vena cava with 17.6 kBq/cm3. These values were approximately selected based on a range of expected values from arterial IF sampling and liver uptake in FDG studies. The activity used to fill the various compartments of the phantom was prepared in separate stock solutions. The activity used in the preparation of each solution was measured using a dose calibrator, which was cross-calibrated with the PET/MR system. All activity values in this work are reported with decay correction to the start of the first experiment.