# Temporal footprint reduction via neural network denoising in 177Lu radioligand therapy

Max Celio Nzatsi, Nicolas Varmenot, David Sarrut, Grégory Delpon, Michel Cherel, Caroline Rousseau, Ludovic Ferrer

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Max Celio Nzatsi, Nicolas Varmenot, David Sarrut, Grégory Delpon, Michel Cherel, et al. Temporal footprint reduction via neural network denoising in 177Lu radioligand therapy. Physica Medica European Journal of Medical Physics, 2025, 137, pp.105071. 10.1016/j.ejmp.2025.105071. hal-05367947

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# Temporal footprint reduction via neural network denoising in 177Lu radioligand therapy

Max Celio Nzatsi<sup>a,b</sup>, Nicolas Varmenot<sup>a,b,c</sup>, David Sarrut<sup>d</sup>, Grégory Delpon<sup>a,e</sup>, Michel Cherel<sup>a,b</sup>, Caroline Rousseau<sup>a,b ID</sup>, Ludovic Ferrer<sup>a,b,* ID</sup>

## ARTICLE INFO

**Keywords:**

MSE-WCGAN

SPECT/CT

Deep-learning

177Lu

Dosimetry

PSMA

DOTATATE

Internal radiotherapy

## ABSTRACT

**Background:** Internal vectorised therapies, particularly with [177Lu]-labelled agents, are increasingly used for metastatic prostate cancer and neuroendocrine tumours. However, routine dosimetry for organs-at-risk and tumours remains limited due to the complexity and time requirements of current protocols.

**Method:** We developed a Generative Adversarial Network (GAN) to transform rapid 6 s SPECT projections into synthetic 30 s-equivalent projections. SPECT data from twenty patients and phantom acquisitions were collected at multiple time-points.

**Results:** The GAN accurately predicted 30 s projections, enabling estimation of time-integrated activities in kidneys and liver with maximum errors below 6 % and 1 %, respectively, compared to standard acquisitions. For tumours and phantom spheres, results were more variable. On phantom data, GAN-inferred reconstructions showed lower biases for spheres of 20, 8, and 1 mL (8.2 %, 6.9 %, and 21.7 %) compared to direct 6 s acquisitions (12.4 %, 20.4 %, and 24.0 %). However, in patient lesions, 37 segmented tumours showed higher median discrepancies in cumulated activity for the GAN (15.4 %) than for the 6 s approach (4.1 %).

**Conclusion:** Our preliminary results indicate that the GAN can provide reliable dosimetry for organs-at-risk, but further optimisation is needed for small lesion quantification. This approach could reduce SPECT acquisition time from 45 to 9 min for standard three-bed studies, potentially facilitating wider adoption of dosimetry in nuclear medicine and addressing challenges related to toxicity and cumulative absorbed doses in personalised radiopharmaceutical therapy.

## 1. Introduction

Radioligand therapy (RLT) consists in delivering to the patient a radiopharmaceutical therapeutic activity whose specificity is to target and destroy tumour cells while saving as much healthy tissue as possible [1]. In the era of personalised medicine, this implies prescribing a patient-specific activity that guarantees both tumour-killing efficacy and preservation of healthy tissues. The personalised approach currently used in RLT for a patient is achieved by pre-therapy imaging, typically with [$^{68}$Ga]Ga or [$^{18}$F]F positron emitters. These images make it possible to evaluate the biodistribution of the radiopharmaceutical injected, the expected therapeutic efficacy, and the optimal therapeutic

targeting for an individual patient. The theranostic approach uses the same radiopharmaceutical vector for both imaging and therapy, while the companion approach uses a slightly different radiopharmaceutical for those procedures. The theranostic and companion approaches are relevant because they avoid injecting the patient with a radiopharmaceutical that could ultimately be ineffective [1].

These therapies could benefit from further personalisation if SPECT/CT exams were carried out with radiopharmaceutical tracer activity. This would make it possible to estimate the therapeutic activity to be administered for a given absorbed dose to the organs-at-risk or tumours [2,3]. Patients could also benefit from dosimetry procedures with therapeutic activities. In this case, the cumulative absorbed doses to

<footnote><sup>a</sup> Institut de cancérologie de l'Ouest, Saint-Herblain, France</footnote>

<footnote><sup>b</sup> CRCI2NA, INSERM UMR1307, CNRS-ERL6075, Université d'Angers, Université de Nantes, Nantes, France</footnote>

<footnote><sup>c</sup> GIP ARRONAX, Saint-Herblain, France</footnote>

<footnote><sup>d</sup> Université de Lyon, CREATIS, CNRS UMR5220, Inserm U1294, INSA-Lyon, Léon Bérard Cancer Centre, Lyon, France</footnote>

<footnote><sup>e</sup> Université de Nantes, IMT Atlantique, Laboratoire SUBATECH CNRS UMR 6457, Nantes, France</footnote>

<footnote>* Corresponding author at: Institut de cancérologie de l'Ouest, Saint-Herblain, France.</footnote>

<footnote>E-mail address: ludovic.ferrer@ico.unicancer.fr (L. Ferrer).</footnote>
organs-at-risk could also be used to verify if they are eligible for another therapeutic course [3].

There are currently many challenges to overcome before the clinical use of dosimetry becomes part of routine patient care. One of them is the limited number of SPECT/CT systems in nuclear medicine departments and their already high occupation rate [2]. Moreover, precise absorbed dose estimations require multiple imaging sessions lasting typically 15 min per bed acquisition on a span of days that increases the load on nuclear medicine departments and their patients.

To reduce the dosimetry burden for both patients and imaging departments, several approaches have been proposed [4]. Some authors [5-7] suggested reducing the number of imaging time-points required to estimate absorbed doses. By using different modelling techniques, they were able to predict the uptake, biodistribution, and elimination of therapeutic agents in the patient with sufficient accuracy using fewer imaging sessions. These approaches typically gave less than 10 % of error [5] compared to the conventional multi-time point approach for organs-at-risk when carefully choosing the imaging time-point. Conversely, they showed greater uncertainty for the absorbed doses of tumours. Another approach is to reduce the time required to obtain images by reducing the duration of each projection and/or the number of projections. The consequences are quantitative biases due to the increased noise in the images and unwanted distortions in the reconstructed images [8].

Recent progress in deep learning methods has demonstrated new nonlinear denoising approaches that have shown their value over classical linear or adaptive filtering approaches [8]. In nuclear cardiology, several groups [9,10] have proposed different types of convolutional neural network architectures to reduce the SPECT or PET acquisition duration and, alternatively, patients' injected activity. In oncology, one team [11] reduced the number of projections by a factor 4 for patients that benefited from [¹⁷⁷Lu]Lu-DOTATATE treatments. They were able to predict the unseen projections from the acquired projections using 3 convolution neural networks (CNN). Their results showed the feasibility of this approach for estimating radioactive concentrations in patients' kidneys while limiting quantitative biases.

In our study, we aimed to reduce the duration of SPECT acquisitions from 30 to 6 s per projection using a GAN architecture, as good performances in SPECT image denoising have been reported [10]. It was paramount that the architecture was able to handle SPECT images, even acquired late after the injection, to allow for quantitative analysis in a dosimetric context.

## 2. Materials and methods

In this study, a conditional generative adversarial network (GAN), named MSE-WCGAN, was used to improve low-statistic SPECT/CT projections by generating high-statistic projections from noisy 6 s acquisitions, using patient and phantom data for validation. We will present the data, then the proposed network we developed, and finally the different stages we used to evaluate the performance of the network.

### 2.1. Patient data

In this study, we used SPECT/CT scans centred on the chest and abdomen of sixteen patients with metastatic prostate cancer (mPCa) who had received [¹⁷⁷Lu]Lu-PSMA treatment. To supplement our image database, we also used SPECT/CT images of four patients with neuroendocrine tumours (NETs) treated with [¹⁷⁷Lu]Lu-DOTATATE. These twenty patients underwent one to four imaging sessions. The first image acquisitions were performed at 4 and 24 h post-therapeutic injection for the mPCa and NETs patients respectively, whereas the following imaging time-points ranged from 24 to 192 h. Of the twenty patients, five benefited from four time-point acquisitions. As our main focus was to assess the quantitative accuracy of our network in challenging noisy conditions, we kept those five patients as a final test for the network.

Additionally, a second evaluation was performed on SPECT/CT acquired 4 h after the injection of 7.4 GBq of [¹⁷⁷Lu]Lu-PSMA on 35 mPCa patients. We were able to gather more patients for this study because, in our department, SPECT/CT images are collected for every therapeutic procedure in which a [¹⁷⁷Lu]Lu-PSMA patient is involved. This led to more robust evaluation of the network, at least for the first images.

The requirement to obtain informed consent for inclusion in this analysis was waived by the Ethics Committee of the University Hospital of Angers (N° 2023-059, 13 April 2023).

### 2.2. Phantom data

To assess absolute quantitative biases, four acquisitions were carried out 4, 76, 150, and 245 h after the preparation of a LIQUI-PHIL phantom (The Phantom Laboratory Inc.). This object contained fillable volumes mimicking kidneys and liver as well as 3 spheres to simulate tumours as depicted in Fig. 1. The volume, radioactivity and radioactive concentration of the different volumes are presented in Table 1. The biggest sphere was located inside the liver whereas the 2 others were set in the background part of the tank. The apparent contrast was thus lower for the former than the two others. Despite the favourable contrast of the 2 remaining spheres, the challenge remained for the network to enhance the projection in noisy conditions, chiefly for the smallest one (~1 mL). The radioactive concentrations were chosen to mimic the average contrast observed in reconstructed images of patients 24 h after a therapeutic injection of [¹⁷⁷Lu]Lu-PSMA.

### 2.3. Image acquisition

Each acquisition consisted of 60 projections of 256x256 pixel wide frames and acquired over 30 s on an NM670 SPECT/CT gamma camera (General Electric HealthCare) equipped with medium-energy general purpose (MEGP) collimators. The energy window was centred on 208 keV (+/- 7.5 %) with two adjacent windows (+/- 4.0 %) used for Compton scattering correction [12]. In parallel, the gamma-camera also recorded list-mode files that we binned into 6 s projections with the same geometric and energetic parameters as described above. This made it possible to create a paired dataset of 30 s and 6 s projections.

### 2.4. Training and validation datasets

One of the objectives of this study was to test our model with images acquired late after therapeutic injections. To fill this objective, we used 5 patients (3 mPCa and 2 NET) for which 3 to 4 time-points were available. In order to complete our evaluation with a larger cohort of patients, we used the images of 33 mPCa patients who had only one time-point SPECT image 24 h post-injection (as this is a regular case in our department). So, these 33 patients were not part of the training nor evaluation phase of the network.

The 10,320 projections were those we got from the twenty patients acquired over all the time-points. For 15 of these patients, we picked 6660 and 1380 projections for training and validation respectively for which we used the data augmentation, resulting in a total of 19,980 and 4140 projections for training and validation phases, respectively. The 2280 remaining projections of the five patients were used for the testing phase.

### 2.5. The proposed neural network

We developed a conditional Generative Adversarial Network (GAN), as illustrated in Fig. 2, and which is composed of two parts: the generator (G) and the discriminator (D), which are trained against each other [13]. This architecture is an image-to-image network trained to consider low-statistic 6 s projections as conditional input to generate higher-statistic 30 s projections as output.

The generator part was composed of 5 down-convolutional layers
<figure><img src="image_3.png" /><figcaption>Fig. 1. The LIQUI-PHIL phantom and the 3 spheres used to evaluate the accuracy of absolute radioactive concentration.</figcaption></figure>

<table><caption>**Table 1**
Radioactive concentrations and activities filled in the different volumes of the LIQUI-PHIL phantom.</caption><thead><tr><th></th><th>Volume [mL]</th><th>Activity concentration [kBq/mL]</th><th>Activity [MBq]</th><th>Contrast</th></tr></thead><tbody><tr><td>Tank</td><td>11416.0</td><td>56.8</td><td>648.1</td><td>1.0</td></tr><tr><td>Liver</td><td>1526.0</td><td>250.3</td><td>382.0</td><td>4.4</td></tr><tr><td>Kidneys</td><td>168.0</td><td>1024.8</td><td>172.2</td><td>18.0</td></tr><tr><td>Sphere</td><td>20.3</td><td>685.7</td><td>5.6</td><td>2.7</td></tr><tr><td>Sphere 1</td><td>8.2</td><td>685.7</td><td>5.6</td><td>12.1</td></tr><tr><td>Sphere 2</td><td>1.0</td><td>685.7</td><td>0.7</td><td>12.1</td></tr></tbody></table>

and as many up-convolutional layers. Each convolution and deconvolution operation was followed by a batch normalisation. ReLU and Leaky ReLU activation functions were used for convolution and deconvolution respectively. We defined skip connections at each deconvolution stage. All convolution and deconvolution operations used 3x3 convolution kernels with a stride and padding of 1. To manage model complexity and reduce overfitting risks, we limited the number of convolutional layer channels to 64.

## 2.6. Ablation study

The GAN architecture is known to be difficult to train, notably due to, in some cases, unstable convergence (or worse, divergence) between the generator and discriminator [14]. Based on recent publications, we modified in turn certain parts of our network and evaluated their effects on its performance in generating 30 s projections from those acquired in 6 s.

The first model, A, used Binary Cross Entropy (BCE) for the discriminator loss function because it is often chosen in image task classifications [15]. The last layer was a fully connected layer with a sigmoid as an activation function to estimate the probability of the image being real or generated. In the second model, B, the discriminator loss function was replaced by the Wasserstein distance as some publications reported better performance in terms of convergence and collapsing issues [16,17]. In addition, we replaced the sigmoid activation function of the last fully connected layer by a LeakyRelu function as the task changed from classification to distance evaluation between the 2 pixel distributions of the real and generated images. In the generator, we also added a term in the loss function measuring the mean squared

error (MSE) between the 30 s and generated projections to preserve details during the network training process [18]. In the last model studied, C, BCE was used as the loss function of the discriminator and the last fully connected layer and associated activation functions were removed from the discriminator. This last change allowed the discriminator to produce a prediction map at the pixel level whether the pixels are real or inferred by the generator.

## 2.7. Model training, validation, testing and optimisation

During the training iterative process, each input projection was normalised by the maximum pixel value and weights updated. The generator used mini-batches of three 6 s projections (one photopeak and two scatter images) as inputs, inferring three 2D projections that mimic the 30 s and 2 adjacent energy windows projections. After each iteration, the batches were shuffled to prevent the network from becoming dependent on sequential data. The synthetic 30 s projections were compared to real 30 s projections using the generator's loss function. The discriminator loss was calculated by passing both the generated and real 30 s projections through the discriminator and the gradient of the discriminator loss function was passed back to the generator to update its weights for the next iteration. This process was repeated until both the training and validation cost functions converged together, indicating a stabilised model performance.

The models were trained using the Torch (v. 1.11.0) python library on a computer equipped with 16 GB of RAM and an NVIDIA Tesla T4 GPU (8 GB). To balance our computer RAM and GPU memory, we set the mini-batch size to 3. The Adam optimiser [19] was used for its efficiency and stability. Using a heuristic process, we set the values $10^{-5}$, 0.5, 0.9 to the learning rate, $\beta_1$ and $\beta_2$ respectively. We fixed the LeakyReLU slope to 0.02.

## 2.8. Analyses

The ablation study was conducted by using PSNR and SSIM metrics [20] as commonly performed in this field [18,21]. Once the model was selected, we tested it on the 6 s projections of the 33 patients kept aside. To recall, their acquisitions were performed 4 h after the therapeutic injection.

The inferred and real 30 s projections were then reconstructed on our clinical reconstruction workstation (Xeleris v. 3.0514, GEHC) using our standard clinical parameters (OSEM, 4 iterations, 8 subsets) and corrected for attenuation, scatter and collimator response and ultimately normalised in radioactive concentration with the camera sensitivity
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** GAN architecture. Each blue and green area corresponds to a multi-channel feature map. The number of channels is indicated at the top of the box. The dashed lines represent the skip connections, i.e., the copy feature maps. The small up and down arrows indicate the difference operations. Other colours are defined in the legend. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

factor.

We extracted the activities on both reconstructed datasets (inferred and real) inside volumes of interest (kidneys) that were delineated on the patient's CT with 3DSlicer (v. 5.6.1) [22] and its plugin Total-Segmentator (v. a716dd3) [23]. We estimated the relative difference between both activities using as reference the one measured on the 30 s reconstructed images. We then compared our findings to those from a similar study [11].

Additionally, we used the images of the five patients acquired over a week to test the network's capacity in challenging noisy images. We evaluated at each time-point the activities of the delineated organs-at-risk (liver, kidneys) as well as tumours following the same protocol as described above. We used the thresholding tool of *3DSlicer's Segment Editor* module to delineate the tumours on images presenting the best contrast. We used a fixed thresholding approach similar to a previously published method [24]. The delineations were then propagated on to the other time-point images and eventually moved via the *3DSlicer's transform* module. In addition, we extracted the activities on the reconstructed images from the 6 s projections. This allowed us to compare the three approaches (acquired 30 s, predicted 30 s and 6 s) and state whether using the network was worthwhile. We also estimated the cumulated activities between the first and last time-point using the trapeze method. Apart from this quantitative evaluation, a visual qualitative analysis was also carried out on the projections and reconstructed images.

Finally, we conducted the same analysis on the LIQUI-PHIL phantom except that, given that we had the exact value of the decay constant, we used a mono-exponential fitting model between 0 and infinity to estimate the cumulated activity. Radioactive concentration and cumulated activities were assessed in each organ-like structure and sphere. We repeated this experiment 5 times because, as the phantom acquisition was acquired in list-mode, we were able to generate as many 6 s projections as we wanted and ultimately use the MSE-WCGAN to produce

the inferred 30 s projections.

## 3. Results

We compared three models of GAN with architecture variations as well as loss function: (A) GAN with Binary Cross Entropy (BCE) loss and a fully connected layer, (B) GAN with Wasserstein distance loss and a fully connected layer, and (C) GAN with BCE loss without a fully connected layer. As illustrated in Fig. 3, the loss function of model A exhibited a rapid decrease and reached a plateau after 20 epochs. However, after 70 epochs, the loss function started to increase, indicating potential overfitting for the training. Moreover, the loss function for the validation dataset also started to oscillate. Model B achieved a convergence after 80 epochs for both training and validation datasets as their loss functions moved in parallel, suggesting effective control of the over-fitting. In contrast, model C displayed significant oscillations in the validation loss, indicating instabilities in training.

The PSNR and SSIM comparison of three models was grouped by the patients' acquisition day and presented in Fig. 4. The PSNR of model B achieved the highest values across all acquisition days, notably at later time points compared to the others, suggesting that this model would produce less noisy images than the 2 others compared to the 30 s images. Regarding the SSIM metric, models B and C performed equally well compared to A. Based on these findings, we have chosen the GAN architecture based on the *Wasserstein* distance loss function and the fully connected layers, that we refer to hereafter as MSE-WCGAN (Mean Square Error Wasserstein Conditional GAN).

We then estimated the relative difference in radioactive concentration of 33 patients' kidneys between the real 30 s and inferred 30 s acquisitions acquired 4 h post-therapeutic injection. MSE-WCGAN was able to predict the left and right kidneys' radioactive concentrations with 0.6% ± 2.6% and 1.03% ± 1.9% compared to the ones we would have obtained with an acquisition performed with 30 s per projection.
<figure><img src="image_5.png" /><figcaption>Fig. 3. Evolution of loss function with respect to the number of epochs for the three variants of the GAN model.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. PSNR and SSIM for GAN models A, B and C across all imaging days, D0, D1, D5, D6.</figcaption></figure>

These results were close to those reported (3.0 % and 2.5 % respectively for left and right kidneys) on 15 patients in the group that developed a convolutional neural network to reduce the number of projections in

acquisitions performed with [¹⁷⁷Lu]Lu-DOTATATE [11].

We performed a qualitative assessment of MSE-WCGAN generated projections and their associated reconstructed images on the five

<figure><img src="image_7.png" /><figcaption>Fig. 5. Comparison between 6 s, MSE-WCGAN and 30 s projections (posterior view) of [¹⁷⁷Lu]Lu-PSMA patients. D0 and D6 are images at injection day and 6 days after. A, B, and C are tumours localised in one spine vertebra, the right shoulder and right adrenal respectively.</figcaption></figure>
patients unseen during the training and validation phases. As illustrated in Fig. 5, showing the posterior view of one of these mPCa patients, MSE-WCGAN was able to generate inferred 30 s projections comparable to real ones, even 6 days after the therapeutic injection. We also added the corresponding 6 s projections to the figure. Lesions A (vertebrae), B (shoulder) and C (adrenal) were present in MSE-WCGAN images at D0 but A and B were comparable to the one detected in real 30 s. Overall, the MSE-WCGAN were able to produce similar noisy images as the real acquisition. However, we observed that when the 6 s projections failed to present counts in some lesions, MSE-WCGAN failed to recover the counts in the same location as exemplified in lesion A in D6.

Overall, the LIQUI-PHIL phantom analysis demonstrated a superior performance of MSE-WCGAN over 6 s in estimating radioactive concentration and cumulated activities in organ-like volumes. As illustrated in Table 2, we observed that MSE-WCGAN presented higher radioactive concentrations (i.e: negative values respective to our calculation) than 30 s in the early days for the organs-at-risk. At D10, the highest median observed discrepancy was 7.5 % for the left kidney for the MSE-WCGAN approach. On the contrary, the 6 s organ-at-risk radioactive concentrations were always lower than those deduced from the 30 s reconstructed projections. Moreover, except at D0, all 6 s radioactive concentrations presented higher discrepancies respective to 30 s than those observed with the MSE-WCGAN. It is worth noting that these results were emphasised for the liver where higher median relative error, up to 16.4 %, was observed.

These results led to better estimation of the organs' cumulated activities relative to 30 s for MSE-WCGAN than for the 6 s approach. Right and left kidneys and liver values were 4.4, 7.2 and 3.4 %. The 6 s approach led to values of 8.6, 8.6 and 15.6 % for the respective organs-at-risk.

Interestingly, the same analysis performed on the spheres was also conclusive in favour of MSE-WCGAN with regard to 6 s. The 20 mL sphere presented relative differences between -5.5 to 11.6 % from D0 to D10 when MSE-WCGAN was used, whereas we observed 6.5 to 16.7 % for 6 s. The same behaviour was observed for the 8 mL sphere. Radioactive concentration values ranged from 0.5 to 12.5 % for MSE-WCGAN and from 17.5 to 24.4 % for 6 s respectively. For the smallest sphere, MSE-WCGAN performed slightly better than 6 s (cf. Table 2) but the gains were not as much as those observed for the previous spheres.

<caption>**Table 2**</caption>

6 s and MSE-WCGAN organs and spheres radioactive concentration differences respective to 30 s.

<table><thead><tr><th rowspan="2">Organ</th><th rowspan="2">Day</th><th colspan="3">6 s</th><th colspan="3">MSE-WCGAN</th></tr><tr><th>Min.</th><th>Median</th><th>Max.</th><th>Min.</th><th>Median</th><th>Max</th></tr></thead><tbody><tr><td rowspan="4">Liver</td><td>0</td><td>10.6</td><td>10.9</td><td>11</td><td>-4.7</td><td>-4.4</td><td>-4.3</td></tr><tr><td>3</td><td>12.6</td><td>12.7</td><td>12.8</td><td>-1.8</td><td>-1.5</td><td>-1.3</td></tr><tr><td>6</td><td>13.7</td><td>13.8</td><td>14.3</td><td>0.3</td><td>0.9</td><td>1.4</td></tr><tr><td>10</td><td>16.1</td><td>16.4</td><td>16.6</td><td>3.4</td><td>4.5</td><td>5.6</td></tr><tr><td rowspan="4">Left kidney</td><td>0</td><td>3.9</td><td>4.1</td><td>4.4</td><td>-4.5</td><td>-4.4</td><td>-3.6</td></tr><tr><td>3</td><td>6.0</td><td>6.1</td><td>6.4</td><td>1.5</td><td>1.9</td><td>2.6</td></tr><tr><td>6</td><td>7.2</td><td>7.2</td><td>7.4</td><td>2.9</td><td>3.7</td><td>4.1</td></tr><tr><td>10</td><td>8.4</td><td>8.7</td><td>9.1</td><td>6.4</td><td>7.5</td><td>7.7</td></tr><tr><td rowspan="4">Right kidney</td><td>0</td><td>4.9</td><td>5.2</td><td>5.7</td><td>-6.8</td><td>-6.3</td><td>-6.0</td></tr><tr><td>3</td><td>7.1</td><td>7.3</td><td>7.4</td><td>-4.4</td><td>-2.3</td><td>-1.1</td></tr><tr><td>6</td><td>6.7</td><td>6.9</td><td>7.1</td><td>0.2</td><td>1.4</td><td>2.6</td></tr><tr><td>10</td><td>8.6</td><td>8.8</td><td>9.2</td><td>4.7</td><td>5.9</td><td>7.7</td></tr><tr><td rowspan="4">Sphere 1 mL</td><td>0</td><td>34.4</td><td>36.7</td><td>39.1</td><td>26.6</td><td>30.5</td><td>34.4</td></tr><tr><td>3</td><td>26.3</td><td>28.2</td><td>35.0</td><td>15.8</td><td>23.0</td><td>30.0</td></tr><tr><td>6</td><td>8.8</td><td>9.1</td><td>12.1</td><td>3.0</td><td>12.1</td><td>14.7</td></tr><tr><td>10</td><td>45.0</td><td>60.0</td><td>68.4</td><td>45.0</td><td>50.0</td><td>52.6</td></tr><tr><td rowspan="4">Sphere 8 mL</td><td>0</td><td>17.3</td><td>17.5</td><td>17.8</td><td>-0.7</td><td>0.5</td><td>1.4</td></tr><tr><td>3</td><td>17.1</td><td>18.7</td><td>19.5</td><td>2.1</td><td>3.4</td><td>4.0</td></tr><tr><td>6</td><td>16.5</td><td>17.7</td><td>18.2</td><td>0.4</td><td>1.9</td><td>3.6</td></tr><tr><td>10</td><td>23.3</td><td>24.4</td><td>25.7</td><td>11.7</td><td>12.5</td><td>14.8</td></tr><tr><td rowspan="4">Sphere 20 mL</td><td>0</td><td>6.4</td><td>6.5</td><td>7.2</td><td>-6.1</td><td>-5.5</td><td>-3.5</td></tr><tr><td>3</td><td>16.4</td><td>16.7</td><td>16.9</td><td>3.2</td><td>3.3</td><td>4.3</td></tr><tr><td>6</td><td>6.9</td><td>7.2</td><td>8.1</td><td>-0.9</td><td>0.0</td><td>0.7</td></tr><tr><td>10</td><td>8.2</td><td>9.2</td><td>9.7</td><td>11.2</td><td>11.6</td><td>12.2</td></tr></tbody></table>

The cumulated activity results were 8.2, 6.9 and 21.7 % for the 20 mL, 8 mL and 1 mL spheres when MSE-WCGAN was used on the image whereas these values were respectively 12.4, 20.4 and 24.0 % for the 6 s approach.

Ultimately, we performed the analysis on the five test-patients' images where we delineated tumours, liver and both kidneys, except one patient who had had a left kidney nephrectomy. Similarly to the test-object analysis, we observed closer radioactive concentrations obtained with the MSE-WCGAN than the 6 s approach compared to 30 s reconstructed images for the organs-at-risk. In particular, at later time points, MSE-WCGAN was still able to estimate the radioactive concentration with a deviation close to 10 % whereas the 6 s approach presented deviations as high as 76 % as illustrated in Fig. 6. More precisely, kidneys' median values were in the range 0.7 to 10.2 % for MSE-WCGAN between D0 to D8 whereas these values ranged from 6.5 to 43.0 % when 6 s approach was used. Liver median values extracted from MSE-WCGAN images ranged from -9.8 to 10.1 % and 7.6 to 75.7 % for 6 s approach. We delineated 37 lesions (14 bone metastasis, 15 hepatic metastasis, 8 nodes) and reported them on every image. The lesions' mean volume was 2 ± 1.6 mL. Surprisingly, we found that MSE-WCGAN performed worse than 6 s to restore the radioactive concentration in tumours. Indeed, the median value was 26.0 % [12.3–60.0] over the days of acquisition for MSE-WCGAN whereas it was 7.2 % [3.2–21.8] using 6 s approach. Only three lesions had volume that were close or higher to 5 mL. Their median error was still superior for the MSE-WCGAN approach than 6 s one but to a lesser extent (8.5 vs 6.4 % respectively).

The cumulated activity differences were consequently smaller for MSE-WCGAN than 6 s for the organs-at-risk. We observed that the median kidney and liver differences compared to the 30 s approach were 5.9 % and -1.0 % for MSE-WCGAN whereas these values were respectively 10.1 % and 15.8 % for 6 s approach. The differences in the median lesion cumulated activities relative to 30 s were higher for the MSE-WCGAN than the 6 s approach (15.4 vs 4.1 % respectively).

## 4. Discussion

Nuclear medicine has taken on a pivotal role in patient care management with the development of new theragnostic agents such as [¹⁷⁷Lu]Lu-PSMA or [¹⁷⁷Lu]Lu-DOTATATE to treat a high volume of patients. This puts a lot of constraints on nuclear medicine departments. Reducing the temporal footprint of image procedures is thus a major stake for allowing physicians to control that a radiopharmaceutical treatment is effectively targeting the tumours revealed in screening imaging. Unfortunately, the limited sensitivity of imaging devices, chiefly SPECT systems, combined with low amounts of radioactivity (or low radioactive emission yield) are the most common contributing factors to lengthy imaging procedures. This study is, to our knowledge, the first analysis conducted on either real patients or phantom acquisitions that evaluates a deep neural network model in the different challenging conditions of noise that are encountered in the clinical images acquired for dosimetry procedures conducted in [¹⁷⁷Lu]Lu-PSMA or [¹⁷⁷Lu]Lu-DOTATATE treatments.

Deep learning techniques have been attractive for enhancing noisy PET images. Recently, software has been cleared by the American FDA and used in clinical departments to generate higher quality PET images or to lessen patient injected activities [25,26]. New promising deep learning approaches have been developed lately to perform PET [27] or SPECT [28,29] image reconstruction but they are still in the early stage of their development and have not yet been implemented or tested in clinical environments. In SPECT, several publications have reported the use of deep learning techniques to reduce the impact of shortened acquisitions in clinical scenarios where two main strategies were explored. The first reduced both the number of projections [9,11] and the neural network, and was used to infer missing projections whereas the projections were acquired with a normal number of counts. The second
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** MSE-WCGAN and 6 s kidney and liver radioactive concentrations differences relative to 30 s for all acquisition days.</figcaption></figure>

reduced the time per projection [9] and the network task was to recover the normal number of counts as well as its spatial distribution from the reduced number of detected counts.

In this study, we opted for this last approach and developed and evaluated an original GAN network for generating synthetic 30 s from 6 s projections in the context of lutetium therapies. We were more keen on implementing noise reduction on projections than on reconstructed images as some authors have already performed [9,11]. It was expected that reducing noise in multiple projections would help preserve small features during tomographic reconstruction, even though some loss of low contrast details might be revealed [8]. Another concern could have been the violation of the statistical Poisson model assumed by the iterative reconstruction. Sampled MSE-WCGAN inferred projections were found to be consistent with Poisson statistics similarly to the real 30 s projections. Therefore, we decided to follow our regular dosimetric workflow by using our clinical reconstruction software.

Quantitatively, we conducted several experiments based on patients and phantom acquisitions. In 33 patients, we estimated radioactive concentrations as precisely as if regular 30 s projections had been used. We showed similar results as already reported [11]. Our phantom analysis showed that MSE-WCGAN images led to cumulated activity errors for both the organs-at-risk and the spheres mimicking the tumours, but less than those observed with the 6 s approach. The maximal observed median relative errors were 7.5 % and 12.5 % (16.1 % and 23.3 % resp.) for the organs-at-risk and the 2 largest spheres (8 and 20 mL) with the MSE-WCGAN approach (6 s resp.). The radioactive concentration in the smallest sphere (1 mL) was not correctly rendered in either approach. The phantom study contrasted with the patient study, where MSE-WCGAN still performed well with organs-at-risk, but the opposite was true for tumours. We hypothesized that the small lesion size was mostly responsible for this behaviour. With the non-spherical shapes, 3/4 of the lesion volumes were less than 2.5 mL. Few counts could be detected in the 6 s frame duration in regard to these lesions' positions. So, MSE-WCGAN might have struggled to compensate for these sparse image counts. We should also take into account that the CNN based generator used in GAN architectures might have contributed by adding some smoothness inherently (although with some control via the *wasserstein* loss function). In this context, most of the authors developed U-shape CNN based architectures with MSE as a loss function

[8,9,11]. In our GAN model, we used loss functions for the generator and discriminator based on a combination of MSE and the *Wasserstein* distance. We showed that this architecture and loss functions were able to predict, at least visually, projections that were similar to those that were genuinely acquired, even on latest acquired projections as described previously.

Finally, the analysis conducted on the five patients’ organs-at-risk showed convincing abilities for MSE-WCGAN to restore cumulated activities. These results suggested that the MSE-WCGAN was suitable for both enhancing image quality and predicting the activities in the organs.

Despite promising results, this work has some limitations. Firstly, we trained and evaluated the MSE-WCGAN on a number of projections that were not evenly distributed over the acquisition days. We could have probably expected better results if the network had been trained and evaluated with more projections acquired at a later time-point. These latter images are more challenging to compensate for noise reduction due to the fewer detected counts. Expanding our dataset with more patient projections would hopefully be advantageous. As a future perspective, we plan to explore advanced deep learning techniques such as transfer learning and fine-tuning to facilitate the adaptation and validation of our network across datasets acquired at a later time-point. By leveraging pre-trained models and subsequently refining them on target datasets, we aim to reduce the time typically required for training from scratch. These strategies have been applied recently in SPECT denoising with small sample sizes, improving image quality metrics [30].

Secondly, recovery coefficient correction was not applied to the different datasets. A more comprehensive approach, involving specific recovery factors for each dataset could further improve quantitative accuracy. This will be explored in future work. Regarding lesion delineation, contours were defined on the reconstructed images based on the 30 s projections. Maybe, it would have been more relevant for the demonstration of this work to delineate the tumours on the 3 different types of images (i.e 30 s, MSE-WCGAN, 6 s). But, in some situations, lesions were hardly visible on 6 s reconstructed images making the segmentation a really challenging task. So, we decided to use the 30 s segmentation for all datasets, guaranteeing that the observed differences come from variations induced by the model and not artefacts linked to diverse segmentations. It is also worth emphasising that, to date, no
consensual method is used to segment lesions in SPECT imaging. In addition, segmentation has been identified as one of the most impactful processes on tumours and/or organs-at-risk absorbed dose uncertainties. A recent paper [31] deployed the EANM guideline [32] to evaluate the uncertainties of tumour dosimetry calculation performed on [¹⁷⁷Lu]Lu-DOTATATE therapies. Notably, they showed how the system spatial resolution (SR) influences the absorbed dose uncertainty, i.e: better SR leads to lesser absorbed dose uncertainties. Hence, defining lesions (or organs-at-risk) contours on CT (assuming a 0.5 mm FWHM SR) led to absorbed dose uncertainties between 20 % to 40 % for lesion volume sizes between 100 and 5 mL respectively. For the SPECT system (i.e SR ~ 10.0 mm FWHM), they showed that the absorbed dose uncertainties increased to values between 30 % and 80 % for the same respective volume sizes. These findings highlight the inherent variability in absorbed dose estimation in molecular radiotherapy, particularly for small lesions and low-volume organs, and our results are consistent with the range of uncertainties already documented for SPECT-based dosimetry.

One another concern would have been the imaging protocol itself as we used only 60 projections for 256 squared matrices. This limited radial sampling compared to the more standard 120 projections seen with these matrices could have limited the results we obtained notably on tumours. But, doubling the number of projections would have doubled the acquisition time which was not desirable. Another option could have been to half the matrix size. This would have implied more blurry projections but with lesser noise. This was not tested in this present work but could be in a later stage by feeding the network with downsampled projections.

Moreover, we have only trained and tested the network with images obtained from one constructor's camera for which we had access to the list-mode. It would have been interesting to evaluate our network with SPECT projections acquired on a camera model from another constructor or even a different camera type equipped with large pixelated semiconductor detectors. In principle, our network is agnostic of the system as long as it is able to provide the same set of projections performed over 30 and 6 s. This is where mode-lists are interesting because we are certain that the radioactive distribution observed in the shortest acquisition time (6 s) is the same as that detected during a full acquisition. Without this feature, it would be necessary to perform 2 acquisitions delayed by the time required to perform the first one, which could be a concern (e.g: bladder filling). Nonetheless, this concern could be leveraged for later time-point images where the radiopharmaceutical is more or less in a steady state and its effective radioactive decay should be low compared to the time required for the first acquisition. In addition, these procedures also enhance the burden on the nuclear medicine department and the patients. As a future perspective, we plan to explore advanced deep learning techniques such as transfer learning and fine-tuning to facilitate the adaptation and validation of our network across datasets acquired from different SPECT systems. By leveraging pre-trained models and subsequently refining them on target datasets, we aim to reduce the extensive computational resources and time typically required for training from scratch. These strategies have been effective in enhancing [¹⁸F]-FMISO and [⁶⁸Ga]Ga-DOTATATE noisy PET images from a network trained initially to enhance noisy [¹⁸F]FDG PET images [33].

The current implementation of our MSE-WCGAN demonstrated suboptimal performances in recovering activity within small lesions. To address this limitation, future work could focus on two complementary strategies. First, synthetic projections could be simulated with Monte-Carlo techniques, incorporating variable lesions size and heterogeneous backgrounds. This approach requires the development of a computationally efficient and quantitatively accurate gamma camera model to ensure that the synthetic projections reflect closely clinical ones. Second, the MSE-WCGAN loss function could be modified to incorporate gradient-preserving constraints, explicitly maintaining image gradients to preserve contrast transitions and edge definition as

successfully applied in low-dose CT denoising [34]. These approaches are expected to improve the network's robustness and its ability to detect and quantify small lesions, thereby supporting more reliable clinical applications.

New 3D-fully SPECT cameras are used to explore patients faster than conventional SPECT cameras without sacrificing quantitative accuracy for dosimetry purposes [35,36]. As a future work, it would be interesting to quantitatively challenge images generated by our network against those obtained by this new type of camera, where images would be acquired with the same acquisition durations for both types of system.

Regulatory considerations represent a significant challenge for the clinical integration of AI-generated synthetic SPECT images. While the use of such synthetic images is feasible, it necessitates rigorous validation to ensure safety and performance compliance. Adherence to relevant medical device regulations, such as the European Union Medical Device Regulation (EU MDR), is mandatory. These regulatory aspects were beyond the scope of the present study and they will need to be carefully considered by clinical partners and industry stakeholders in the context of future clinical implementation.

Our method made it possible to reduce the time spent by patients on the camera even for broader patient coverage. Typically, a whole-body 3-bed acquisition needed for metastatic castration resistant prostate cancer (mCRPC) patients, taking up to 45 min, would last less than 10 min, which is good news for fragile patients. This approach has improved image quality and could provide medical physicists with quantitative images suitable for dosimetric workflows. The shortened acquisition time allows for an optional extended field coverage to make possible measurement of radioactive concentration in organs-at-risk such as the salivary glands or lumbar region which are of particular interest in the context of mCRPC treated with [¹⁷⁷Lu]Lu-PSMA. However, the accuracy of quantification in these low-volume regions warrants further investigation. As radiopharmaceutical therapy is now a full-fledged therapeutic option for mCRPC, organs-at-risk absorbed doses have become important, especially as these same patients often also benefit from hematotoxic therapies such as external radiotherapy, targeted therapy, chemotherapy. Hence, one has to pay attention to the accumulation of absorbed doses to best manage these different treatments throughout the chronic disease that is mCRPC. Lesion dosimetry is also a concern in nuclear medicine but practically it seems difficult to derive the amount of therapeutic activity on the basis of absorbed dose to one lesion. This raises interesting questions regarding the choice of the lesion for which the activity should be prepared or what amount of absorbed doses should be given to particular lesions.

## 5. Conclusion

We developed a neural network that reduced by five the time spent by patients on the examination couch without sacrificing much quantitative accuracy. We hope that these promising results will pave the way to greater generalization of dosimetry in the field of nuclear medicine.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This work was supported in part by the French National Research Agency (ANR) "France 2030 investment plan" under the references Equipex Arronax-Plus (ANR-11-EQPX-0004), Labex IRON (ANR-11-LABX-18-01), I-SITE NExT (ANR-16-IDEX-0007), and Labex DHOLMEN, and by financial support from the Pays de la Loire Region. This work benefited from the funding from The Fondation Persée hosted by The "Fondation de France" and The "Fonds de dotation REALITES" and
"Agence National de Bourses du Gabon".

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