# Deep learning-enhanced 3D real-time photoacoustic imaging using experimental ground truths obtained from fluctuation imaging

Ivana Falco, Guillaume Godefroy, Maxime Henry, Véronique Josserand,
Emmanuel Bossy, Bastien Arnal

► To cite this version:

Ivana Falco, Guillaume Godefroy, Maxime Henry, Véronique Josserand, Emmanuel Bossy, et al. Deep learning-enhanced 3D real-time photoacoustic imaging using experimental ground truths obtained from fluctuation imaging. Physics in Medicine and Biology, 2025, 70 (20), pp.205016. 10.1088/1361-6560/ae0f70. hal-05281185v2

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# Deep learning-enhanced 3D real-time photoacoustic imaging using experimental ground truths obtained from fluctuation imaging

Ivana Falco, Guillaume Godefroy, Maxime Henry, Véronique Josserand,
Emmanuel Bossy, Bastien Arnal

► To cite this version:

Ivana Falco, Guillaume Godefroy, Maxime Henry, Véronique Josserand, Emmanuel Bossy, et al. Deep learning-enhanced 3D real-time photoacoustic imaging using experimental ground truths obtained from fluctuation imaging. Physics in Medicine and Biology, 2025, 70 (20), pp.205016. 10.1088/1361-6560/aeof70. hal-05281185v2

HAL Id: hal-05281185

https://hal.science/view/index/docid/5315598

Submitted on 15 Oct 2025
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# Deep learning-enhanced 3D real-time photoacoustic imaging using experimental ground truths obtained from fluctuation imaging

Ivana Falco¹, Guillaume Godefroy²,*, Maxime Henry³, Véronique Josserand³, Emmanuel Bossy¹ and Bastien Arnal¹,†

¹ Université Grenoble Alpes, CNRS, LIPhy, Grenoble 38058, France

² Université Grenoble Alpes, CEA Leti, 17 av. des Martyrs, Grenoble F-38000, France

³ Université Grenoble Alpes, INSERM U1209, CNRS UMR5309, Optimal platform, Institute for Advanced Biosciences, Grenoble 38000, France

* Author to whom any correspondence should be addressed.

E-mail: bastien.arnal@univ-grenoble-alpes.fr

**Keywords:** photoacoustic imaging, visibility artifacts, deep learning, photoacoustic fluctuation imaging, real-time, transfer learning, chicken embryo model

Supplementary material for this article is available [online](#)

## Abstract

3D conventional photoacoustic (PA) imaging often suffers from visibility artifacts caused by the limited bandwidth and constrained viewing angles of ultrasound transducers, as well as the use of sparse arrays. PA fluctuation imaging (PAFI), which leverages signal variations due to blood flow, compensates for these visibility artifacts at the cost of temporal resolution. Deep learning (DL)-based PA image enhancement has previously demonstrated strong potential for improved reconstruction at a high temporal resolution. However, generating an experimental training dataset remains problematic. Herein, we propose creating an experimental training dataset based on single-shot 3D PA images (input) and corresponding PAFI images (ground truth) of chicken embryo vasculature, which is used to train a 3D ResU-Net neural network. The trained DL-PAFI network predictions on new experimental test images reveal effective improvement in visibility and contrast. We observe, however, that the output image resolution is lower than that of PAFI. Importantly, incorporating only experimental data into training already yields a good performance, while pre-training with simulated examples improves the overall accuracy. Additionally, we demonstrate the feasibility of real-time rendering and present preliminary *in vivo* predictions in mice, generated by the network trained exclusively on chicken embryo vasculature. These findings suggest the potential for achieving real-time, artifact-free 3D PA imaging with sparse arrays, adaptable to various *in vivo* applications.

## 1. Introduction

Traditional high-fidelity photoacoustic (PA) imaging typically relies on scanning systems with broadband ultrasound (US) transducers (Yao and Wang 2011), whereas clinical settings favor handheld devices (Taruttis and Ntziachristos 2015). These devices, however, often face artifacts caused by the limited bandwidth and limited view (Paltauf et al 2007). While these artifacts already affect 2D imaging, 3D imaging encounters further challenges due to the increased number of required transducers. Advances in massively parallel acquisition and wide-band matrix arrays offer potential solutions (Na et al 2022), but these technologies remain limited in availability. Hence, we explore ways to enhance image quality using a limited number of receivers—that is, a *sparse* array with restricted bandwidth. In a sparse array, transducers typically do not cover the whole receiving surface, potentially leading to degraded reconstructions affected by background signals around the absorbing structures. Model-based inversion schemes have been proposed to enhance image quality (Bu et al 2012, Dean-Ben et al 2012). Still, these
algorithms require precise calibration, are sensitive to experimental conditions, and are highly compu-
tationally demanding, which limits their applicability in real-time settings. As an alternative, our group
proposed *PA fluctuation imaging* (PAFI) (Vilov *et al* 2020). Based on the acquisition of several subsequent
PA images, PAFI leverages natural red blood cell fluctuations to simultaneously compensate for limited
bandwidth and view, even with sparse arrays. However, 1000 acquisitions per PAFI images are needed
for adequate quality, limiting temporal resolution (Godefroy *et al* 2023). Nowadays, when considering
accelerating and optimizing computational resources, deep learning (DL) approaches are widely adopted.
Notably, DL is applied in medical imaging to model correlations between input data and high-quality
ground truth (GT) images. While DL has been extensively used in various stages of image reconstruc-
tion, this study specifically focuses on DL as a post-processing tool to enhance PA imaging. In this con-
text, an impressive amount of work has been published (Antholzer *et al* 2019, Davoudi *et al* 2019, Guan
*et al* 2020, Kim *et al* 2020, Dehner *et al* 2023), ranging from simpler to more sophisticated algorithms
and architectures (Hauptmann and Cox 2020, Yang *et al* 2021). In previous research, our group applied
a 2D ResU-Net to mitigate visibility artifacts in a leaf-skeleton model, with PA images and photographs
serving as input and GT, respectively (Godefroy *et al* 2021). This new work aims to extend these findings
into 3D imaging. An ongoing challenge is generating reliable training datasets with high-quality GT data.
Some studies rely solely on simulations (Kim *et al* 2020, Deng *et al* 2021), while others use experimental
GT data obtained with densely populated arrays, such as a 1024-element probe (Davoudi *et al* 2019,
Choi *et al* 2023), or with specialized probes like Fabry-Pérot cavities (Hauptmann *et al* 2018). Some
studies use model-based reconstructions to build their GT images (Hauptmann *et al* 2018, Dehner *et al*
2023). Recent networks including transformers combined with convolutional neural networks (CNN)
(He *et al* 2025) give promising results, although we will stick to a well established CNN architecture for
this study due to its stability, lower data requirements and suitability for relatively small experimental
datasets.

We use a 3D ResU-Net architecture which is ideal for task requiring precise localization and multi-scale features extraction in the presence of noise. Its residual connections enhance convergence and generalization. The 3D nature of the network creates spatial-contextual awareness, capturing volumetric texture patterns and noise correlations. In this letter, we propose using experimental PAFI images as GT for training neural networks. PAFI images are obtained from a series of straightforward delay-and-sum reconstructions which offers a practical alternative to model-based reconstructions. PAFI provides reliable artifact correction which comes at the cost of temporal resolution. In this approach, both input and GT pictures are obtained from the same imaging device which offers multiple advantages that will be further discussed. After describing sample preparation and dataset acquisition, we assess the neural network performance when trained exclusively on experimental data recorded in chicken embryos. We then analyze the impact of transfer learning from simulated data of blood vasculature. We further present a practical real-time demonstration and finally, we investigate the network potential to generalize to *in vivo* mouse vasculature.

**2. Material and methods**

**2.1. Experimental dataset**

We use the chorioallantoic membrane (CAM) model of chicken embryos, chosen for its rich vascular
structure, accessibility, and semi-transparency. Fertilized eggs were incubated at 37 °C with 65% humid-
ity, with optimal imaging occurring after 9 or 10 days. This protocol was performed according to the
ethical local policies, indicating that no approval is required for experiments conducted before day 16 of
incubation. The preparations included rotating the egg to detach the CAM, extracting the yolk, creating
an eggshell window, and adding warm PBS for acoustic contact. The egg was placed in a plastic bowl
with a central hole, which was filled with water at 37 °C maintained by a heating plate. Top illumination
was provided by 5 ns laser pulses at 100 Hz and λ = 730 nm, generated by a Nd:YAG-OPO laser (Innolas
SpitLight), as in figure 1(A). RF signals are captured from a custom 256-channel spherical array (8 MHz,
f = 35 mm, f/D = 0.7, elements diameter 2 mm) connected to a high-frequency Vantage Verasonics scan-
ner (256 channels). The input images are generated using 3D delay-and-sum (DAS) without apodization
in receive. The GT pictures are computed as slow-time standard deviations of 1500 PA images after SVD
(singular value decomposition) filtering (Vilov et al 2020). Details on setup, acquisition, conventional PA,
and PAFI computation can be found in Godefroy et al (2023). The final dataset included 107 volumet-
ric images pairs (89 × 89 × 89 voxels representing a field of view of 8 × 8 × 8 mm³), taken from about 40
embryos, and divided into 81 training images, 9 validation images, and 17 test images.
<figure><img src="image_6.png" /><figcaption>**Figure 1.** Data acquisition, reconstruction, and training framework. (A) Experimental dataset acquisition and processing of chicken embryo model vasculature. The reconstruction algorithm is Delay-and-Sum (DAS) beamforming. *N* = 1500. (B) One of the 3D DAS photoacoustic images is chosen as input, with the corresponding photoacoustic fluctuation image (PAFI) 3D image serving as ground truth. Both go through a standardization process (normalization and noise removal). The input is iteratively processed by the 3D ResU-Net to minimize the difference between the output and the ground truth. The training ideally continues until this difference is minimized. Although the shown images represent experimental examples of chicken embryo vasculature, this framework applies to experimental and simulated data.</figcaption></figure>

## 2.2. Numerical dataset

A numerical dataset is created for transfer learning, leveraging a similar blood vascular dataset. This dataset is generated by transforming 2D retinal vessel images into 3D structures, where vessels are ‘thickened’, randomly oriented, and filled with particles (1 voxel = 1 particle at a 10% volume fraction) mimicking the red blood cells before being assembled for 3D PA image simulation. We do not consider any optical background properties as the medium surrounding the blood vessels in the chicken embryo model is transparent. The fluence is then uniform in the simulations. RF signals are modeled as a sum of signals from individual absorbers, with each particle treated as a distinct source on a finely discretized grid (λ/2 steps defined at the central frequency of the probe of 8 MHz (Vilov et al 2020)). We use the experimentally measured US probe impulse responses at the focal point as a reference, which was obtained using a 50 µm black polyethylene microsphere (Cospheric) (Falco et al 2024). For each absorber, RF signals are computed by temporally shifting these reference responses to account for the relative transducer position. Time shifts are applied in the Fourier domain across all frequencies, capturing time-of-flight variations across point sources. Signals are then summed to form the final RF data, representing the simulated PA acquisition of the entire object. The single-shot 3D PA images, serving as inputs of the neural network, are obtained through a delay-and-sum algorithm without any apodization in reception. Finally, PAFI images are generated analytically by convolving the object with the squared modulus of the PSF at the focal point (Vilov et al 2020). The numerical training set comprises 200 examples, while the test set includes 30 examples. Four examples of the training set are shown in the supplementary materials. The neural network model trained on this simulated training set is used as a starting point to train the neural network on experimental data.

## 2.3. DL framework

The DL framework is summarized in figure 1(B). A single-shot 3D conventional PA image is chosen as input, paired with the corresponding PAFI image as GT, both undergoing standardization (mean value removal and normalization). We use a 3D ResU-Net (Residual U-Net (Zhang et al 2018)), adapting the architecture from (Luke et al 2019). The activation function used after each convolution is the rectified linear unit. The ADAM optimizer is implemented with a learning rate of 1·10⁻⁴, using mean squared error as the loss function, and a batch size of 8. To improve generalization and accelerate convergence, batch normalization (Ioffe and Szegedy 2015) and dropout layers (Srivastava et al 2014) are added. Early stopping, set to 60 iterations, monitors performance to prevent overfitting. The upsampling is performed through nearest-neighbor interpolation followed by convolution. Training and evaluation are conducted on a desktop PC equipped with dual Intel Xeon Gold 6240 R CPUs (2.40 GHz), a Quadro RTX 6000 GPU, and 256 GB RAM. Training takes approximately 2 h on the simulated dataset and about 60 min on the experimental dataset.
<figure><img src="image_7.png" /><figcaption>**Figure 2.** Four representative predictions from the experimental test set with the neural model pre-trained with numerical data and then trained with experimental data. (a) Maximum intensity projections (MIPs) of the 3D inputs, ground truth images, and deep learning (DL) predictions are represented along one of the XY, XZ, or YZ planes and normalized between 0 and 1. First column: input photoacoustic image obtained by conventional delay-and-sum reconstruction (DAS-PA). Second column: ground truth given by photoacoustic fluctuation imaging (PAFI). Third column: DL predictions of the network trained on experimental data only (DL-PAFI exp). Fourth column: DL predictions of the network pre-trained on simulated data and trained on experimental data (DL-PAFI simu+exp). Blue arrows indicate structures not well recovered and mistakes made by the neural model. The yellow arrow indicates differences in output sensitivity compared to PAFI. (b), (c) and (g), (h) Profiles plotted along the dashed lines B–C and G–H, respectively. The orange arrow highlights a significant difference in vessel intensity. (d), (e) Cross-sections demonstrating visibility artifact correction. (k) Resolution profiles along the two transversal axis for a small vessel.</figcaption></figure>

## 2.4. Animal preparation

All animal experiments were carried out according to the institutional guidelines of the European Community (EU Directive 2010/63/EU) for the use of experimental animals and were approved by an ethics committee (Cometh38 Grenoble, France) and the French Ministry of Higher Education and Research under the reference: APAFIS#19706-2019030114369271 v2. A six weeks old NMRI female nude mouse (Janvier labs, France) was anesthetized (air/isoflurane 4% for induction and 1.5% thereafter) and positioned on a heated platform, with a rectal thermometer monitoring body temperature. The snout was placed in a nose cone connected to the anesthetic gas supply. US gel was applied to the imaging area to ensure optimal probe contact.

# 3. Results

## 3.1. Results in Chicken embryo model

Normalized cross-correlation (NCC) and structural similarity index measure (SSIM) are used to quantify the similarity between predictions and GT images. Considering a threshold on PAFI to define the object, we also provide the contrast-to-noise ratio values to quantify global image enhancement (CNR = $\langle\langle A\rangle\rangle_{\text{obj}} - \langle\langle A\rangle\rangle_{\text{BG}}/\sigma[A]_{\text{BG}}$). When tested on the experimental test-set examples, the model trained with experimental data alone achieves scores of NCC = 0.75 ± 0.11, SSIM = 0.75 ± 0.11. However, despite this relatively high score, errors persist. We illustrate four test-set representative cases in figure 2 as maximum intensity projections (MIPs). Specifically, the network does not achieve sufficient sensitivity to recover capillary beds and struggles in reconstructing vertical structures (see figure 2(a), third column). To improve performance, we combine the numerical with the experimental dataset, employing
<table><caption>**Table 1.** Similarity, correlation metrics and CNR based on the test-set experimental GT images (PAFI), conventional DAS (DAS-PA) and DL reconstructions. DL-PAFI exp: training on experimental data only. DL-PAFI simu+exp: pre-training on simulated data, training on experimental data.</caption><thead><tr><th></th><th>DAS-PA</th><th>DL-PAFI<br>exp</th><th>DL-PAFI<br>simu + exp</th></tr></thead><tbody><tr><td>NCC</td><td>0.32 ± 0.07</td><td>0.75 ± 0.11</td><td>0.78 ± 0.12</td></tr><tr><td>SSIM</td><td>0.17 ± 0.14</td><td>0.80 ± 0.06</td><td>0.83 ± 0.07</td></tr><tr><td>CNR</td><td>1.53 ± 0.40</td><td>12.01 ± 2.94</td><td>13.39 ± 3.25</td></tr></tbody></table>

transfer learning to increase dataset size and feature diversity. This process begins with pre-training the model on the numerical dataset—which achieves a high score (NCC = 0.94 ± 0.03, SSIM = 0.94 ± 0.02) when tested on the simulated test set—providing an initial model state for further training with experimental data. Notably, pre-training accelerates convergence: the initial cost function drops 76-fold compared to the case without pre-training, reducing the total training iterations from 300 to 170. Overall, image quality improves markedly, with enhanced contrast and reduced noise. The score metrics increase (NCC = 0.78 ± 0.11, SSIM = 0.78 ± 0.12). The significance of performance improvement provided by the pre-training was confirmed using a paired t-test on NCC ($p = 2.1 \cdot 10^{-4}$) and on SSIM ($p = 3.7 \cdot 10^{-6}$). The feature space alignment between the experimental and simulated datasets were analyzed on the testset examples using the tSNE method. The two types of data share a common domain which strengthen our methodology. Visibility artifacts are effectively corrected by the neural network, as shown in MIPs (figure 2(a), fourth column) and cross-sections (figures 2(d) and (e)). Despite a few errors, marked by light blue arrows (representing missing structures or inaccuracies) and orange arrows (representing differences in intensity), vessel size and pixel intensity are well preserved. Profile alignment along the dashed lines (B–C) and (H–G) is represented in figures 2(b)–(c) and (h)–(g), respectively. Resolution is improved compared to DAS-PA, but remains slightly lower than that of PAFI, which benefits from 1500 acquisitions and second-order moment computation for super-resolution (Chaigne et al 2017). Particularly, the yellow arrow in Ex.3 illustrates that the network is now sensitive to the capillary bed. To compare resolutions obtained with PAFI and DL-PAFI, we consider a small vessel of Ex.4 indicated by the arrow labeled ‘K’. The frame is rotated to align the vessel along one axis and the two transverse profiles are displayed in figure 2(k). The two full widths at half maximum (FWHM) were evaluated in the transverse plane: $FWHM_1 = 0.27$ mm, $FWHM_2 = 0.18$ mm and $FWHM_1 = 0.47$ mm, $FWHM_2 = 0.34$ mm, respectively for PAFI and DL-PAFI. This confirms qualitative observations that PAFI resolution is superior to DL-PAFI. To investigate the effect of noise, we performed predictions on Ex.2 and Ex.4 by adding different noise amplitude to the signals. These results are described in the supplementary materials.

Similarity metrics scores are summarized in table 1. We threshold the images at 0.05 to avoid potential bias in the structural metric due to background noise. Both metrics increase by ≈0.5 with DL-PAFI compared to conventional PA imaging. A real-time rendering demonstration using our DL model is provided in the supplementary materials (Link to video). Note that for this rendering, the imaged object consisted in a tube knot filled with static ink. Hence, the model provides an enhanced image of both flowing and static object contributions without possible discrimination. The present implementation uses the CPU Verasonics beamformer (MATLAB), then passes the input image to python through the harddrive before the inference. Once the image is loaded, the inference time was 15 ms. Thus, a future implementation could achieve a display rate similar than the beamforming rate (currently 10 Hz), which could also be improved through the use of GPUs. An end-to-end GPU implementation would indeed further accelerate real-time imaging.

## 3.2. *In vivo* preliminary results

We further investigated this approach by evaluating whether our model trained on a chicken embryo dataset (simu + exp) could generalize to another type of data. Specifically, we tested the network *in vivo* on the femoral vein and brain of an NMRI nude mouse. Using the same imaging setup as for the chicken embryos, with 730 nm illumination, 1500 images were captured. The outputs observed in figure 3 show enhanced contrast and significant noise reduction. Considering PAFI as GT, we provide NCC and SSIM scores in table 2 along with CNR results. Concerning visibility enhancement, the green arrow in figure 3(Ex.1) indicates a structure in which the limited bandwidth artifact appears corrected, according to the GT, despite a slight mismatch in size and intensity. In figure 3(Ex.2), structures marked by the yellow arrow are recovered in DL-PAFI and appear consistent with those in PAFI. It is important to note that, for the superficial femoral vein, PAFI can still serve as a reliable reference, even though
<figure><img src="image_8.png" /><figcaption>**Figure 3.** Two experimental *in vivo* results. The neural network is the same trained with chicken embryo data. Images are displayed as MIPs normalized between 0 and 1. (Ex.1) Femoral vein. Green arrow: limited bandwidth artifact corrected. (Ex.2) Mouse brain, transcranial imaging. Yellow arrow: recovered structures not visible in the input.</figcaption></figure>

<table><caption>**Table 2.** Similarity, correlation metrics and CNR based on the PAFI GT images for conventional DAS (DAS-PA) and DL reconstructions calculated for the *in vivo* mouse cases.</caption><thead><tr><th></th><th></th><th>DAS-PA</th><th>DL-PAFI</th></tr></thead><tbody><tr><td rowspan="3">Femoral</td><td>NCC</td><td>0.46</td><td>0.58</td></tr><tr><td>SSIM</td><td>0.54</td><td>0.70</td></tr><tr><td>CNR</td><td>3.75</td><td>6.80</td></tr><tr><td rowspan="3">Brain</td><td>NCC</td><td>0.41</td><td>0.63</td></tr><tr><td>SSIM</td><td>0.14</td><td>0.60</td></tr><tr><td>CNR</td><td>2.70</td><td>7.94</td></tr></tbody></table>

lower signal fluctuations are detected by the probe in turbid media due to light attenuation. However, in brain imaging, PAFI does not offer the same image quality or reliability due, in addition, to optical and acoustic losses caused by passage through the skull. Thus, these preliminary results suggest further work to be conducted.

## 4. Conclusions

This letter demonstrates that the PAFI technique can provide experimental GT images to train a 3D convolutional network for enhanced PA imaging using a sparse array with limited bandwidth. The PAFI technique provides full visibility pictures of media exclusively composed of blood vessels. From a broad variety of blood vessels, the network efficiently learns to correct for the physics of the propagation and the detector properties. The process of obtaining both the input data and this straightforward GT with the same device ensures consistency while minimizing generalization challenges. This method eliminates the need for more expensive or complex configurations, as well as additional steps like registration, making it an efficient way to generate a dataset that is otherwise difficult to produce.

Training exclusively on experimental data already results in good structural similarity and correlation between PAFI and DL-PAFI. However, transfer learning from numerical data training accelerates convergence and enhances the sensitivity to blood capillaries and the overall accuracy. The final DL predictions present significantly improved image quality, notably in contrast and noise reduction, with most reconstructed vessels appearing with accurate size and amplitude. Nevertheless, there could be some variability introduced by the embryo development stage which was restricted between 9 and 10 days. Including older embryos could have resulted in including larger vessels, improving the network capacities. Most importantly, DL predictions—performed in real time—outperform the low temporal resolution of PAFI.

The PAFI technique relies on 1000–1500 acquisitions per image, making the process resource-intensive and potentially less feasible for *in vivo* applications where motion is present. To address this, future work could explore self-supervised learning strategies (Xiao et al 2025) that do not require explicit high-quality GT, or domain adaptation techniques to transfer models trained on PAFI data to more practical, low-acquisition regimes (Susmelj et al 2024). However, although initially developed to enhance PAFI temporal resolution for real-time imaging, our DL approach shows potential for *in vivo* applications where PAFI alone struggled. This suggests that a model trained with PAFI data acquired in favorable conditions could be applied in contexts where PAFI falls short because of low sensitivity or large
physiological motion. Furthermore, while PAFI is only sensitive to flowing blood, DL predictions are based on single shot images and cannot differentiate between static or dynamic contrasts. Then, predictions can also enhance static absorbers features, making them interesting for pathological explorations showing optical absorption contrasts. Future work will explore if the network is able to improve images of objects that have different shapes than blood vessels. However, we note the potential inconsistency in the dataset if some static contrast is imaged with DAS-PA and not showing on PAFI images. In this chicken embryo model, this case is met where there is a hemorrhage while opening the egg shell. The dataset must be carefully considered in this regard. The inconsistent examples can either be excluded manually or automatically using similarity criteria between predictions and GT images, thus implying retraining with a refined dataset. In conclusion, while this initial proof-of-concept shows promises, it also outlines the need for further development. The metrics we used (NCC, SSIM and CNRS) could be limited to capture the perceptual or clinical quality of the reconstructed images and more advanced task-specific or perceptual metrics could be used (segmentation accuracy, LPIPS (Zhang et al 2018)) to provide a more comprehensive assessment. As the dataset is currently limited, it could be worth expanding it. Further work will aim at using a more recent architecture, and enhancing the pre-processing of training images could all contribute significantly to achieving the same high resolution as PAFI, fully correcting the visibility artifact, and further improving overall performance. Other developments are needed regarding the PAFI technique to make it more robust in vivo and to allow the recording of a training dataset directly on the targeted in vivo application.

## Data availability statement

Data will be made available upon reasonable request.

## Acknowledgment

This work was supported by the Agence National de la Recherche (ANR) under the FULBOX Project (ANR-21-CE19-0003-01).

## ORCID iDs

Guillaume Godefroy 0000-0002-0538-7967

Bastien Arnal 0000-0002-4905-2915

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