### PET/CT system

The whole study was conducted using the PET/CT Biograph® mCT 40 (Siemens Healthcare Molecular Imaging, Hoffman Estates, IL, USA). The patient bore aperture was 78 cm (inner diameter 84.2 cm) with an axial field of view (FOV) of 22 cm. The system was equipped with 32,448 LSO crystals (4 × 4 × 20 mm^{3}). The detection energy window was set to 435 to 650 keV for a coincidence window of 4.1 ns. The system was able to record TOF information between two events in coincidence. Given the sufficient count rate capacity of the system [21] confirmed by in-house performance measurements of count losses according to the NEMA NU 2–2007 methods [22], it was chosen to not incorporate a copper ring between the source and the LSO crystals to lower the count rate originating from the bremsstrahlung [19, 23].

### Phantom study

#### Source preparation and acquisition protocol

A standard IEC/NEMA 2001 torso-shaped phantom (PTW Freiburg GmbH, Freiburg, Germany) was used with five spheres (internal diameters 10, 13, 17, 22, and 28 mm). The spheres were initially filled with free ^{90}Y (8100 ± 5% kBq mL^{−1}). The phantom volume (9.1 L) was also filled uniformly with an initial activity of ^{90}Y (200 ± 5% kBq mL^{−1}) to simulate a sphere-to-background ratio (SBR) of approximately 40:1. This SBR was chosen to simulate a high tumor uptake relative to the background typically encountered in a RAIT procedure. Acquisition of the phantom was performed nine times over 14 days, starting from an initial activity concentration in the spheres of 6,740 kBq mL^{−1} decreasing to 490 kBq mL^{−1}. All measurements were performed over a duration of 30 min using a single-bed position including the whole phantom in the FOV.

#### Reconstruction

The acquisitions were reconstructed with the proprietary implementation of the point spread function (PSF) ordinary Poisson (OP) ordered subset expectation maximization (3D OP-OSEM PSF) available for this scanner [24]. We have used both TOF and non-TOF reconstructions with respectively 21 and 24 subsets, which are the clinical default settings. One or three iterations were used for both TOF and non-TOF reconstructions to assess the impact of increasing the number of iterations on the sphere detection and quantification accuracies. A maximum of three iterations was set in order to limit noise amplification. Additional parameters such as the impact of two iterations were omitted as the study was limited to evaluating the trade-off between detectability and quantification. Datasets were reconstructed into standard 200 × 200 × 109 matrix size using a 4 × 4 × 2 mm^{3} voxel size. A 3D Gaussian post-smoothing of 2 mm full-width at half maximum (FWHM) was applied. To allow direct comparison, all reconstructed images were coregistered to the image corresponding to the first acquisition. This was facilitated by placing the phantom at identical axial and transaxial positions using laser lights of the system and markings made on the phantom.

### Data processing

#### Detectability

The detectability was assessed using a contrast-to-noise ratio (CNR) based figure of merit (FOM), and its formalism is given below. As mentioned before, the branching ratio of internal pair creation for ^{90}Zr is remarkably small compared to usual PET tracers. The detection of lesions incorporating ^{90}Y, therefore, is challenged by very low levels of radioactive distribution, or signal. In this respect, the determination of a MDA has been the subject of several studies in preclinical situations [25, 26]. The MDA may be evaluated using the Rose criterion [27]. It states that an object is discernable when CNR > 5, with:

\mathrm{CNR}=\frac{{C}_{\mathrm{L}-}{C}_{\mathrm{B}}}{{\sigma}_{\mathrm{B}}},

(1)

where *C*
_{L}, *C*
_{B}, and *σ*
_{B} are the lesion, the background, and the background noise intensities, respectively.

The background noise
{\sigma}_{B}^{r}
measured inside a given region of interest (ROI) *R*
_{r} of *V* voxels of a given slice was defined as:

{\sigma}_{\mathrm{B}}^{\mathrm{r}}=\sqrt{\frac{1}{V}{\displaystyle \sum _{j\in {R}_{\mathrm{r}}}{\left({\widehat{m}}_{r}-{f}_{j}\right)}^{2}}}.

(2)

Here, {\widehat{m}}_{\mathrm{r}} is the average of activity for the *V* voxels inside the ROI *R*
_{r} in the reconstructed image *f*. The final noise FOM was measured in *R* ROIs in the background of a given slice, and was defined as:

{\sigma}_{\mathrm{B}}=\frac{1}{R}{\displaystyle \sum _{r=1}^{R}{\sigma}_{\mathrm{B}}^{\mathrm{r}}}.

(3)

The *R* = 20 ROIs localized in the background were randomly chosen, in such a way that they were separated by at least two voxels from each other and at least three voxels from the phantom border. Each ROI consisted of *V* = 32 voxels. The transverse slice aligned with all sphere centers was chosen for analysis.

This FOM proved to be equivalent to a rigorous noise assessment using multiple statistically independent replicates while avoiding the correlation between voxels that results from iterative reconstruction [28].

The relation (1) is established for a signal present in a single voxel. However, it can be extended to a lesion covering *N* voxels [25] using the equation:

\mathrm{CNR}=\frac{{C}_{\mathrm{L}}-{C}_{\mathrm{B}}}{{\sigma}_{\mathrm{B}}}\times \sqrt{N}\times \mathrm{PVE},

(4)

where PVE is the partial volume effect calculated for each sphere. The PVE was evaluated with an ^{18} F-based acquisition with similar phantom preparation, by drawing a circular ROI with an internal diameter equal to the actual diameter of the spheres. For this setup, the SBR was chosen identical to that of the ^{90}Y-based acquisitions. The measurement was repeated 30 times to supply 30 independent datasets. The mean PVE was derived from these 30 datasets.

As the spheres were close to a circular-shaped object, we chose to modify the limit of detectability for CNR according to a previous work based on human observers [29]. Although determined in the different context of simulated noisy micrographs, they have suggested that circular-shaped object was detected if CNR > 8 for an area equivalent to those considered in the present work. Thus, this limit will be considered in this work.

#### Recovered activity in the spheres

The total activity in each sphere was calculated for each of the nine ^{90}Y-based acquisitions and was compared to the theoretical value as a percentage of recovered activity. The total activity in a sphere was computed as the mean intensity of all voxels within the volume of interest (VOI) corresponding to the sphere. The VOI for each sphere was determined from the sum image of the 30 ^{18} F-based independent acquisitions mentioned earlier for PVE determination. The five VOIs were calculated using a threshold relative to the maximum value in the VOI. The intensity threshold was chosen to obtain the smallest difference between the true volume and the measured volume.

#### Spatial distribution of the signal in spheres

The reconstruction of a very weak signal can be significantly biased when assessing its spatial distribution. The change in the distribution of the signal within the spheres according to the radioactive concentration was evaluated by calculating the root mean square error (RMSE) using the following equation:

\mathrm{RMSE}\left({\mathrm{S}}^{90\mathrm{Y}}{,\mathrm{S}}^{18\mathrm{F}}\right)=\sqrt{\frac{1}{N}{\displaystyle \sum _{k=1}^{N}{\left({B}_{\mathrm{k}}^{{\mathrm{S}}^{90\mathrm{Y}}}-{B}_{\mathrm{k}}^{{\mathrm{S}}^{18\mathrm{F}}}\right)}^{2}}},

(5)

where {B}_{\mathrm{k}}^{{\mathrm{S}}^{90\mathrm{Y}}} denotes the contents of voxel *k* in a sphere for the yttrium-based acquisition, and {B}_{\mathrm{k}}^{{\mathrm{S}}^{18\mathrm{F}}} represents fluorine-based acquisition. The signal considered for the fluorine-based acquisition was measured from a mean image computed from the 30 independent acquisitions described in the ‘Recovered activity in the spheres’ section. For the RMSE calculation, the images were first normalized by the mean signal for each acquisition and for each sphere considered.

#### Count rate

The acquisition of a weak signal may be masked by natural radioactivity of ^{176}Lu in LSO crystals (about 2.59% of the lutetium element). The background signal generated by ^{176}Lu can contribute to the amount of random and true coincidences [26, 30]. For each acquisition, prompt and random coincidence rates were measured. A long acquisition (approximately 900,000 registered true coincidences) with no activity present in the field of view was performed to determine the ^{176}Lu background count rate.

### Patient study

A clinical study was performed on ten patients, including six patients with HCC treated by hepatic SIRT using TheraSphere® (MDS Nordion) or SIR-Spheres® (Sirtex Medical), and four patients with B lymphoma treated using anti-CD20 Zevalin® (Bayer) or anti-CD22 epratuzumab (Immunomedics, Inc., Morris Plain, NJ, USA) ^{90}Y-based RAIT. Among the six HCC patients, five had macroscopic lesions, and one had a diffuse liver disease. Among the four lymphoma patients, two had a diffuse large B-cell lymphoma, and one had a follicular lymphoma receiving RAIT as consolidation treatment after an induction therapy. The other patient had a follicular lymphoma and was undergoing first-line treatment with Zevalin® (Bayer). All patients underwent a 30-min PET imaging session with all acquisition parameters identical to those of the phantom study. Reconstructions were performed with or without TOF information with one or three iterations. For those who underwent radioembolization, the total amount of reconstructed activity was compared to the theoretical activity injected to the patient, as measured by the dose calibrator before injection.

All patients gave informed written consent in accordance with institutional guidelines, including the declaration of Helsinki. The trials were approved by the responsible ethics committee.