# Pre-therapy dose prediction in targeted radionuclide therapy using semi-supervised learning: An in-silico preliminary study

J. Zhang, A. Bousse, Y. Li, S. Xue, K. Shi, D. Visvikis, J. Bert

► To cite this version:

J. Zhang, A. Bousse, Y. Li, S. Xue, K. Shi, et al. Pre-therapy dose prediction in targeted radionuclide therapy using semi-supervised learning: An in-silico preliminary study. 2024 IEEE Nuclear Science Symposium (NSS), Medical Imaging Conference (MIC) and Room Temperature Semiconductor Detector Conference (RTSD), Oct 2024, Tampa, France. pp.1-1, 10.1109/NSS/MIC/RTSD57108.2024.10655434. [hal-04940102](https://hal.science/hal-04940102v1)

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# Pre-therapy dose prediction in targeted radionuclide therapy using semi-supervised learning: An in-silico preliminary study

Jing Zhang, Alexandre Bousse, Yihao Li, Song Xue, Kuangyu Shi, Dimitris Visvikis, and Julien Bert

**Abstract**—Targeted Radionuclide Therapy (TRT) is a modern strategy in radiation oncology that aims to administer a potent radiation dose specifically to cancer cells using cancer-targeting radiopharmaceuticals. Accurate radiation dose estimation tailored to individual patients is crucial. Deep learning, particularly with pre-therapy imaging, holds promise for personalizing TRT doses. However, current methods require large time series of SPECT imaging, which is hardly achievable in routine clinical practice, and thus raises issues of data availability. Our objective is to develop a semi-supervised learning (SSL) solution to personalize dosimetry using pre-therapy images. The aim is to develop an approach that achieves accurate results when PET/CT images are available, but are associated with only a few post-therapy dosimetry data provided by SPECT images. In this work, we introduce an SSL method using a pseudo-label generation approach for regression tasks inspired by the FixMatch framework. The feasibility of the proposed solution was preliminarily evaluated through an in-silico study using synthetic data and Monte Carlo simulation. Experimental results for organ dose prediction yielded promising outcomes, showing that the use of pseudo-labeled data provides better accuracy compared to using only labeled data.

**Index Terms**—Targeted radionuclide therapy, personalized dosimetry, deep learning, semi-supervised learning, Monte-Carlo simulation

## I. INTRODUCTION

Targeted Radionuclide therapy (TRT) is a contemporary approach in radiation oncology, aiming to deliver maximal destructive radiation doses via cancer-targeting radiopharmaceuticals. Radioactive ligands targeting the prostate-specific membrane antigen (PSMA) have emerged for treating metastatic castration-resistant prostate cancer (mCRPC) [1]. Despite the early success of TRT, concerns have been raised about the risks of an inadequate trade-off between therapeutic dose and side effects. An essential requirement of TRT is optimizing radiation dose tailored for individual patients. Therefore, absorbed doses must be estimated in advance of therapy [2]. Deep learning approaches may play a key role in personalizing the dose in TRT using pre-therapy imaging (Ga-68 or F-18). However, doses are typically evaluated through a large quantity of time-series imaging of whole-body single-photon emission computed tomography (SPECT) scans at various time points (days) after each treatment cycle. In routine clinical practice, acquiring such extensive imaging data is hardly achievable, and only a few patients undergo post-therapy dosimetry. This raises an issue of data availability to train deep learning solutions.

Our objective is to develop a semi-supervised learning (SSL) solution for personalizing patient dosimetry using pre-therapy images [3]. The aim is to develop an approach that achieves accurate results when PET/CT images are available,

This work was partially funded by the European Union through the SECURE project under the grant HORIZON-EURATOM-2021 N° 101061230 and by the French National Research Agency with the project MoCaMed under reference ANR-20-CE45-0025.

The authors are with LaTIM, INSERM-UMR1101, University of Brest, 29200 Brest, France (e-mail: jing.zhang@univ-brest.fr). Y. Li is with Shanghai United Imaging Healthcare Co., Ltd., Shanghai 200232, China, and S. Xue and K. Shi are with University of Bern, Switzerland.

but are associated with only a few post-therapy dosimetry data provided by SPECT images. To address this challenge, we adapted the FixMatch method [4] for regression tasks to consider dose prediction. The feasibility of the proposed solution was preliminarily evaluated through an in-silico study using synthetic data and Monte Carlo simulation.

## II. MATERIALS AND METHODS

### A. Semi-supervised learning

<figure><img src="image_2.png" /><figcaption>Fig. 1: Diagram for the proposed pseudo-label generation in SSL for regression. The model is trained on weakly augmented unlabeled data, consisting of computed tomography (CT) and positron emission tomography (PET) images, to generate a pseudo-label. A predicted dose value is then inferred from strongly augmented data. Finally, the model is updated using the Mean Absolute Error (MAE) loss for regression.</figcaption></figure>

The FixMatch method [4] is a simple yet powerful approach that effectively leverages unlabeled data for training. Our objective is to predict dose values (output) from PET/CT images (input) using only a few unlabeled data points, i.e., dose values associated with the PET/CT images. While the FixMatch method was originally designed for classification tasks, we adapt the pseudo-labeling technique and extend it to the regression task of dose prediction.

The first part of the method involves constructing pseudo-labeled data from unlabeled data (Fig. 1). Inspired by the FixMatch method, we developed an approach that learns to produce consistent labels using input data with both weak and strong data augmentation, achieved by applying different transformations, such as disturbances, to the images. Let $\mathcal{F}\theta$ be the training model with learnable parameters $\theta$ (Fig. 1). For the unlabeled data $\lambda_{ulb}$, it predicts multiple values $z_i$ from a set of weakly augmented input images $\lambda'_i$, as shown in Eq. (1).

$$z_i = \mathcal{F}_{\theta}(\lambda'_i) \qquad (1)$$

We take the mean value of those predictions $\bar{z} = \mu(z_i)$ as the pseudo-label when the consistency of those predictions is within a threshold. Then, the model is updated by minimizing the difference between the pseudo-label and the predicted value from strongly augmented image $\lambda'_s$, as shown in Eq. (2), where $L$ refers to the Mean Absolute Error (MAE) loss.

$$\min_{\mathcal{E}} [L(\mathcal{F}_{\theta}(\lambda'_s), \bar{z}(\sigma(z_i) < \tau))] \qquad (2)$$

At this point, this method imbues the unlabeled data with meaningful labels, facilitating its utilization in the regression training process. The final training consists of two stages. Firstly, pre-training the model with labeled data $\mathcal{F}\theta(\lambda_{lbl})$ using a supervised loss (MAE). This ensures that the model has the capability to forecast a value with tolerable error. Secondly, refining the training using the pseudo-labels with the same loss function.
### III. EXPERIMENTS AND RESULTS

#### A. Data generation

The XCAT phantom [5] was used to generate synthetic data. The morphology of the phantom was randomly sampled to encompass various sizes and weights representative of patients. For each sample, the XCAT phantoms produced a voxelized phantom featuring different human tissues for each voxel. Based on this phantom, we generated an attenuation map for each sample, which was used for both image and dosimetry simulation. Additionally, for simulating the pre-therapy PET image (Ga68-PSMA), an activity map at 2 hours post-injection (1500 MBq) was generated using a physiologically based pharmacokinetic (PBPK) model for PSMA [6]. Similarly, for calculating the total dose of Lu177-PSMA treatment, the PBPK model was employed to obtain the Time Integrated Activity (TIA) map.

For efficient generation, the pre-therapy PET image was simulated using an iterative method that accounted for both attenuation and the associated activity map. This method involved steps of projection, spatial filtering, and backprojection using the expectation maximization reconstruction method, which allowed for realistic resolution and noise levels. To manage memory efficiently, the network architecture was tailored for 2D images, after which the 3D PET image was projected using maximum intensity. For determining the total therapy dose, a Monte Carlo simulation was conducted using GATE10 [7] with the TIA map incorporating Lu177. Subsequently, the total absorbed dose value for each organ was calculated.

#### B. Training

We conducted experiments on 1000 synthetic samples using 5-fold cross-validation. The samples were divided into a training set (800 samples) and validation and testing sets (100 samples each). We used pre-trained models (trained on ImageNet), fine-tuned them in a semi-supervised manner, and used a learning rate of $10^{-4}$ for 300 epochs. The AdamW optimizer [8] was used. For weak augmentation, horizontal flipping and random rotation were applied, while for strong augmentation, horizontal flipping, random rotation, and color distortions were used. Data augmentation was applied dynamically to the training set during training.

#### C. Evaluations and results

We tested different amounts of labeled and unlabeled images by considering various ratios of unlabeled ($N_{ulb}$) and labeled ($N_{tbl}$) images. This was defined using a ratio $\alpha$, where $N_{ulb} = (100 - \alpha)\% \times N$ and $N_{tbl} = \alpha\% \times N$ relative to the total number of data $N$. This value ranged from 5% to 100%. For each ratio value, the predicted doses were compared using three methods: fully supervised learning (FSL), considering all labeled images ($N$), considering only $N_{tbl}$; the SSL approach with the split ($N_{ulb}, N_{tbl}$); and Monte Carlo simulation. Only six organs were considered in this study (see Fig. 2-a).

The Pearson correlation coefficient (PCC), denoted by $\rho$, was used and defined as follows:

$$ \rho(z, \hat{z}) = \frac{\operatorname{cov}(z, \hat{z})}{\delta_z, \delta_{\hat{z}}} \quad (3) $$

Where $z$ and $\hat{z}$ represent the predicted and Monte Carlo dose values, respectively, and $\delta$ is the standard deviation. The PCC

ranges from -1 to 1, measuring the linear correlation between the doses across all test cases and providing a better view of the quality of the prediction.

The experimental results for $\alpha = 50\%$ (see Fig. 2-a) show that SSL performed slightly better than FSL for the same amount of labeled data, especially for some organs. However, as expected, the results were lower compared to FSL using all the data. The robustness of the method was evaluated by estimating the PCC of the SSL for the complete range of $\alpha$ (see Fig. 2-b). As expected, the lower the fraction of labeled images, the lower the PCC becomes, until it drops rapidly when $\alpha < 25\%$.

<figure><img src="image_3.png" /><figcaption>Fig. 2: Comparison of dose prediction performance for (a) FSL vs. SSL ($\alpha=50\%$) and (b) for the SSL for all range value of $\alpha$.</figcaption></figure>

### IV. CONCLUSIONS

In this work, we introduce an SSL method that uses pseudo-label generation for regression tasks. This approach allows us to predict personalized doses in TRT using pre-therapy PET/CT images, even when only a limited number of SPECT images are available. Initial results for organ dose prediction on synthetic phantoms are promising. We are actively conducting a deeper investigation for a more comprehensive evaluation and are also working to further improve the results. Ultimately, our goal is to apply this approach to real clinical data.

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