Nannan Yuan

Lihui Wang
email: lhwang2@gzu.edu.cn

Chen Ye

Zeyu Deng

Jian Zhang

Yuemin Zhu

Self-supervised Structural Similarity-based Convolutional Neural Network for Cardiac Diffusion Tensor Image Denoising

Keywords: self-supervised-learning, image denoising, cardiac diffusion tensor imaging, structural edge-weighted loss, similarity matching

Background: Diffusion tensor imaging (DTI) is a promising technique for non-invasively investigating the myocardial fiber structures of human heart. However, low signal-to-noise ratio has been a major limit of cardiac DTI to prevent us from detecting myocardium structure accurately. Therefore, it is important to remove the effect of noise on DW images.

Purpose: Although the conventional and deep learning-based denoising methods have shown the potential to deal with effectively the noise in diffusion weighted (DW) images, most of them are redundant information dependent or require the noise-free images as golden standard. In addition, the existed DW image denoising methods often suffer from problems of over-smoothing. To address these issues, we propose a self-supervised learning model, structural similarity based convolutional neural network with edge-weighted loss (SSECNN), to remove the noise effectively in cardiac DTI.

Methods:

Considering that the DW images acquired along different diffusion directions have structural similarity, and the noise in these DW images is independent and identically distributed, the structural similarity-based matching algorithm is proposed to search for the most similar DW images. Such similar noisy DW image pairs are then used as the input and target of the denoising network SSECNN, which consists of several convolutional and residual blocks. Through the selfsupervised training with these image pairs, the network can restore the clean DW images and retain the correlations between the denoised DW images along different directions. To avoid the over-smoothing problem, we design a novel edge-weighted loss which enables the network to adaptively adjust the loss weights with iterations and therefore to improve the detail preserve ability of the model. To verify the superiority of the proposed method, comparisons with state-ofthe-art (SOTA) denoising methods are performed on both synthetic and real acquired DTI datasets.

Results:

Experimental results show that SSECNN can effectively reduce the noise in the DW images while preserving detailed texture and edge information and therefore achieve better performance in DTI reconstruction. For synthetic dataset, compared to the SOTA method, the root mean square error (RMSE), peak signal to noise ratio (PSNR) and structure similarity (SSIM) between the denoised DW images obtained with SSECNN and noise-free DW images are improved by 6.94%, 1.98% and 0.76% respectively when the noise level is 10%. As for the acquired cardiac DTI dataset, the SSECNN method could significantly improve signal to noise ratio (SNR) and contrast to noise ratio (CNR) of cardiac DW images and achieve more regular helix angle (HA) and transverse angle (TA) maps. The ablation experimental results validate that using the structure similarity-based method to search the similar DW image pairs yield the smallest loss, and with the help of the edge-weighted loss, the denoised DW images and diffusion metric maps can preserve more details.

Conclusions:

The proposed SSECNN method can fully explore the similarity between the DW images along different diffusion directions. Using such similarity and an edge-weighted loss enable us to denoise cardiac DTI effectively in a self-supervised manner. Our method can overcome the redundancy information dependence and over-smoothing problem of the SOTA methods.

Introduction

Magnetic resonance diffusion tensor imaging (DTI) is currently the unique technique that can noninvasively detect three-dimensional structure of in vivo myocardium by measuring the diffusion displacement distribution of water molecules therein. It is well known that water molecules in the tissue do not diffuse equally along all directions, for instance, in myocardium, water diffuses quickly along the direction parallel to the myocyte and diffuse slowly in the perpendicular direction, accordingly, diffusion weighted (DW) signal is more attenuated in the parallel direction while less attenuated along the perpendicular direction. In DTI, such anisotropic diffusion property in each voxel is described with a diffusion tensor, which is estimated with least square method from the DW signals acquired along at least six gradient directions [START_REF] Tournier | Diffusion tensor imaging and beyond[END_REF] . However, due to the signal attenuation caused by water molecular diffusion, the acquired DW images usually have low signal-to-noise ratio, which influences accordingly the estimation accuracy of diffusion tensors and diffusion metrics. Therefore, it is important to remove the effect of noise on DW images for accurately calculating the diffusion tensor images and analyzing the structure of myocardial fibers.

Conventionally, noise reduction is usually achieved by averaging the images from multiple acquisitions [START_REF] Madore | A new way of averaging with applications to MRI[END_REF] . However, this method undoubtedly increases the acquisition time and cannot satisfy the clinical requirements. To deal with this problem, researchers have proposed several postprocessing methods for DW image noise reduction. These post-processing methods can be generally classified into two categories, i.e., traditional methods and deep learning-based methods.

Typical traditional denoise methods include nonlocal mean algorithms [START_REF] Chen | Noise reduction in diffusion MRI using non-local selfsimilar information in joint x-q space[END_REF] , the sparse dictionary learning-based denoising algorithms [START_REF] Kong | Noise reduction of diffusion tensor images by sparse representation and dictionary learning[END_REF][START_REF] Wang | Medical Image Fusion and Denoising Algorithm Based on a Decomposition Model of Hybrid Variation-Sparse Representation[END_REF] , the total variance optimization denoising algorithms [START_REF] Zhu | Removal of high density Gaussian noise in compressed sensing MRI reconstruction through modified total variation image denoising method[END_REF] , the self-similarity-based denoising algorithms [START_REF] Chen | Joint low-rank prior and difference of Gaussian filter for magnetic resonance image denoising[END_REF] , and the Bayesian methods [START_REF] Liu | Diffusion tensor imaging denoising based on Riemannian geometric framework and sparse Bayesian learning[END_REF][START_REF] Juneja | Denoising of magnetic resonance imaging using bayes shrinkage based fused wavelet transform and autoencoder based deep learning approach[END_REF] etc.. Since these traditional methods usually require setting manually multiple hyperparameters and optimizing iteratively to achieve good performance on a particular task, they are time-consuming, difficult for generalization, and prone to introduce denoising artifacts [START_REF] Sagheer | A review on medical image denoising algorithms[END_REF] . To solve these problems, fourdimensional (4D) image-based noise reduction algorithms were proposed, such as AONLM method [START_REF] Coupé | Adaptive multiresolution non-local means filter for three-dimensional magnetic resonance image denoising[END_REF] , which achieves noise reduction by exploiting the self-similarity between local patches;

Local-PCA (LPCA) [START_REF] Manjón | Diffusion weighted image denoising using overcomplete local PCA[END_REF] and Marchenko-Pastur PCA [START_REF] Veraart | Denoising of diffusion MRI using random matrix theory[END_REF] methods, denoising through a low-rank approximation by thresholding the eigenvalues of the noisy signal matrix; and Patch2Self 14 model, which uses the regression fitting with multi-directional neighborhood information to denoise. These methods fully consider the characteristics of multi-directional DW images and therefore can promote the noise reduction performance. However, the operations of patch similarity searching, the low rank approximation and the regression fitting are highly related with the number of diffusion directions, if the number of diffusion directions is reduced, the number of similar patches, the redundancy of multidimensional information, and the regression fitting accuracy will be decreased, accordingly, the denoising performance will be influenced.

To overcome the shortcomings of traditional denoising methods, medical image denoising methods based on deep learning have been rapidly developed in recent years. Gondara et al. [START_REF] Gondara | Medical image denoising using convolutional denoising autoencoders[END_REF] achieved CT image denoising for different noise types by training sparse autoencoders using a small number of samples. Based on residual networks, CNN-DMRI [START_REF] Tripathi | CNN-DMRI: a convolutional neural network for denoising of magnetic resonance images[END_REF] and MCDNCNN 17 models can effectively remove noise for low signal-to-noise ratio MR images. Inspired by these works, Wang et al. [START_REF] Wang | High -field mr diffusion -weighted image denoising using a joint denoising convolutional neural network[END_REF] proposed a multichannel CNN model JD-CNN, which combined the multi-b-value DW images information to effectively remove the noise. Subsequently, Tian etc. proposed a DeepDTI [START_REF] Tian | DeepDTI: High-fidelity six-direction diffusion tensor imaging using deep learning[END_REF] model, which uses three-dimensional (3D) CNN to denoise DW image volumes with the synthesized noise-free DW images as target, it not only achieves the satisfactory denoising performance, but also minimizes the data requirement of DTI to only six DW image volumes.

Based on DeepDTI, the authors proposed further a SDnDTI model [START_REF] Tian | SDnDTI: Self-supervised deep learning-based denoising for diffusion tensor MRI[END_REF] , which uses the same method as DeepDTI to synthesize multiple repetitions of noisy DW image volumes, and then removes the noise using a 3D CNN with the average of multiple repetitions as training target. Although the supervised deep learning models achieved promising denoising results, their requirement for the ground-truth of noise-free images prohibits their clinical applications since the noise-free images are not available. To address this issue, unsupervised deep learning models for image noise reduction were proposed. Lin et al. [START_REF] Lin | Denoising of multi b-value diffusion-weighted MR images using deep image prior[END_REF] modified deep image prior (DIP) model so that it can be applied to the multi-b-value DW image denoising task, its main idea was to use the prior information to restore the noise-free images. However, noise reduction results of DIP depend heavily on the iteration numbers of CNN, which causes that different optimal parameters must be set again for different DW images to get effective denoising results. In addition to DIP, many unsupervised deep learning noise reduction models have been proposed successively in the field of natural image noise reduction, such as Noise2Noise 22 , Noise2Void 23 , Noise2Self 24 , Neighbor2Neighbor [START_REF] Huang | Neighbor2neighbor: Self-supervised denoising from single noisy images[END_REF] , and Self2Self 26 etc. Most of these methods use image pairs with different noisy observations to train models for achieving unsupervised noise reduction, such as using the different noisy images of the same scene, the adjacent image patches of the same noisy image, or the image pairs obtained with blind point strategies etc.. These unsupervised denoising methods can get satisfactory denoising result for a single DW image, however, to calculate the right diffusion tensor images from the denoised DW images, it requires that the DW signals along all the diffusion directions at each voxel are all correctly denoised, this cannot be guaranteed with the current existing methods since they do not consider the relationship between DW images along different directions during denoising.

To address the above-mentioned problems, we propose a self-supervised denoising model (SSECNN) for cardiac DTI based on self-similarity in DW images along different diffusion directions. Specifically, we search the similar noisy DW images along different directions to serve as training inputs and targets by maximizing the structural similarity. Following that, inspired by Noise2Noise method, a network was designed to learn the noise-free DW images with the matched noisy DW image pairs. For better reserving the texture details of the denoised images, we propose a novel edge-weighted loss which enables the network to adaptively adjust the loss weights with iterations and therefore to improve the detail reserve ability of the noise reduction model. Considering that the DW images acquired along different diffusion gradient directions have structural similarity, and the noise in these DW images is independent and identically distributed. Therefore, the structural similarity matching algorithm proposed in this paper searches for the most similar DW image pairs among images with different diffusion directions at the same b value. Suppose that the size of a 4D DW image data is ( , , , ) l h w n , which represents the image slice width, height, numbers of slices and gradient directions, respectively. Note that in the case of multiple acquisitions, n represents the number of gradient directions multiplied by the number of repeated acquisitions. For every 3D volume with the size of ( , , ) l h n , the structural similarity SSIM [START_REF] Wang | Image quality assessment: from error visibility to structural similarity[END_REF] is calculated with each other volume. SSIM is defined as follows modules is 3×3, padding=1, and stride=1.

Denoising principle of SSECNN method

1 2 2 2 2 2 1 2 (2 )(2 ) ( , ) ( )( ) x y xy x y x y x y c c SSIM DW DW c c               (1)

Loss function of SSECNN model

Since the noise in DW images with lower b-value conforms to the Gaussian distribution [START_REF] Wiest-Daesslé | Rician noise removal by nonlocal means filtering for low signal-to-noise ratio MRI: applications to DT-MRI[END_REF] , according to the findings of Noise2Noise 22 and IMC-Denoise [START_REF] Lu | IMC-Denoise: a content aware denoising pipeline to enhance Imaging Mass Cytometry[END_REF] , taking the similar noisy DW image pairs that we selected from the different diffusion directions as the input and target of the network, and using the mean square error (MSE) as the loss can achieve the same denoising effect as that of the supervised learning. Accordingly, the loss function is formulated as: thus the edge region will be not over smoothed when denoising. This weighting strategy is like an attention mechanism that allows the network to pay more attention to fine details such as edges.

Quantitative evaluation metrics

For the synthetic data, we used root mean square error (RMSE), peak signal to noise ratio (PSNR) and structure similarity index (SSIM) as the performance evaluation metrics. For the acquired data, since there is no noise-free image serving as the ground-truth, to quantitatively verify the effectiveness of the proposed method for myocardial DW image noise reduction, we calculated signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR), respectively. Among them, SNR reflects the image signal to noise ratio in a given region, and CNR indicates contrast ratio between the region of interest (ROI) and the background, which can reveal the detectability of the ROI in denoised images. Bigger SNR and CNR mean the better noise reduction performance. The calculation of SNR and CNR are as follows 1 ( ) 1 ( )

n i i i s SNR n s      , (4) 1 ( ) 1 (
)

n i b i b s s CNR n s       , (5)
where n represents the number of ROIs, i s and b s represent the signal intensity of the i th ROI and the background, ( )   and ( )   represent the corresponding mean intensity and standard deviation, respectively.

In addition to evaluate the noise reduction effect on diffusion tensor images, tensor reconstruction with the denoised DW images was performed, from which, the diffusion anisotropy fraction (FA), mean diffusion coefficient (MD), fiber orientation (FO), helix angle (HA) and transverse angle (TA) of cardiac fibers are derived. FA represents the degree of anisotropy of diffusion process of water molecules in the tissue, with a value ranging from 0 to 1, which can reflect the tissue structure organizations. FA of zero indicates that the diffusion is isotropic, which means that the diffusion process in the tissue is unrestricted or equally restricted in all directions. If FA is near one, it means that the diffusion of water molecules in the tissues prefers to diffuse along a given direction and is restricted along all other directions. MD reflects the overall diffusion of water molecules in the tissues, the bigger MD indicates the less restriction for diffusion in tissues. FA and MD are defined as follows

2 2 2 1 2 1 3 2 3 2 2 2 1 2 3 ( ) ( ) ( ) 1 2 FA                  , ( 6
) 1 2 3 ( ) 3 MD       , (7)
where λ1, λ2, and λ3 indicate three eigenvalues of the diffusion tensor, respectively [START_REF] Kingsley | Introduction to diffusion tensor imaging mathematics: Part II. Anisotropy, diffusion-weighting factors, and gradient encoding schemes[END_REF][START_REF] Grover | Magnetic resonance imaging: principles and techniques: lessons for clinicians[END_REF] . FO reflects the arrangement pattern of cardiac myocytes, which is determined by the direction of the eigenvector associated with the largest eigenvalue of the diffusion tensor. To quantitatively describe the myocyte arrangement, HA and TA are usually calculated from FO, where HA is the angle between the projected direction of myocardial FO in the ventricular tangent plane and the ventricular short axis, and TA is the angle between the projected direction of myocardial FO in the ventricular short axis and the ventricular tangent plane, both of which range from -90°to 90°. The detailed calculation process of HA and TA can be found in the work of Healy et al. [START_REF] Healy | Quantitative comparison of myocardial fiber structure between mice, rabbit, and sheep using diffusion tensor cardiovascular magnetic resonance[END_REF] .The variations of HA and TA ranges can be used to characterize some cardiac disease.

3 Experiments and results

Datasets description and experimental implementations

Since there is no ground-truth for noise-free cardiac DW images, to subjectively evaluate the performance of the proposed method, we first generated synthetic noise-free DW images using Phantomas [START_REF] Caruyer | Phantomas: a flexible software library to simulate diffusion MR phantoms[END_REF] . The image size was 55 × 55 × 55 with a resolution of 1.5 × 1.5 × 1.5 mm

Denoising results for synthetic dataset

Denoised results for synthetic DW images

In the first row of Fig. 2 shows the synthetic noise-free DW image, noisy DW image (noise level is 10%) and DW image with six diffusion directions denoising results obtained with different methods; in the second row shows the zoom-in images for the regions outlined in red box; in the third row illustrates the RMSE maps between noise-free images and denoising results, and in the fourth row corresponds to the zoomed-in RMSE maps for the region outlined in red box. We can observe that, AONLM and BM3D methods blur the boundaries, Neighbor2Neighbor (Nei2Nei)

and DIP methods remain more noise, and Patch2Self (P2S) results in higher RMSE values.

Although the denoising results obtained with LPCA are comparable to our method, SSECNN produces sharper boundaries and gets lower RMSE values. This can also be found in the quantitative comparison results in Table 1, for all the noise levels, SSECNN achieves the highest SSIM and PSNR, as well as the lowest RMSE. Compared with the suboptimal method LPCA, the RMSE, PSNR and SSIM obtained with SSECNN are improved by 6.94%, 1.98% and 0.76% when the noise level is 10%. Fig. 3 shows the reconstructed diffusion tenor images and the corresponding diffusion metrics using the denoised synthetic DW images, including fiber tracking (FT), FO, FA and MD maps. Our proposed method SSECNN achieves the best performance since its FT, FO, FA, and MD are closest to the ground-truths, while the Nei2Nei and DIP methods obtain the worst performance, which cannot reconstruct well the fiber orientations and fiber tracks, in addition, the derived FA and MD maps are far away from the ground-truths. Although AONLM, BM3D, LPCA and P2S can yield the acceptable denoising results, there is a partial error in the direction of their FO and their RMSEs for FA and MD maps are much larger than our methods, especially at the edge regions. with the dataset of 6 diffusion directions and single acquisition. To observe the details, the second, fourth and sixth rows zoom in the local regions highlighted in red rectangle in the first, third and fifth rows respectively. It can be seen that averaging multiple acquisitions can only be used when the multiple acquisitions are available. In addition, its noise reduction effect is not effective, not only remaining the obvious noise but also smoothing the edge information after denoising.

Traditional method BM3D and deep learning method DIP introduce redundant image artifacts in the process of denoising, and the denoising effect of Nei2Nei method is not obvious. The other three methods AONLM, LPCA, and P2S can remove noise effectively to some extent, but their results depend on the number of acquisitions and diffusion directions, the more acquisitions and diffusion directions, the better the denoising results. From the columns of AONLM and LPCA of Fig. 4, we observe that when the number of acquisitions decreases, the denoising results are too smooth to loss the structural details, and when the number of diffusion directions decreases, the noise cannot be effectively removed and the denoised image is blurred. For P2S method, we notice that when the number of diffusion directions are fewer, its denoising image is more blurred.

Compared with all the other methods, the proposed SSECNN model can visually remove noise effectively and retain the detail information such as tissue edges. Furthermore, SSECNN is insensitive to the number of acquisitions and the number of diffusion directions, that means it can achieve almost the same noise reduction results no matter how many diffusion directions and acquisitions are provided. To quantitatively evaluate the noise reduction performance of different methods on acquired data, the SNR and CNR of different methods obtained with different diffusion directions and acquisitions are given in Table 2. When calculating the SNR and CNR, we manually selected four distinct regions per volume corresponding to the four different myocardial fibers as ROIs and one region which contains almost no structural information as background. It can be seen that our method achieves the highest SNR and CNR for all the cases, which indicates that our method can remove the noise effectively and protect the image sharpness simultaneously.

Denoising results for acquired cardiac DT images

Cardiac diffusion tensor (DT) image denoising requires not only to denoise effectively on DW images but also to guarantee the correctness of the diffusion tensor metrics calculated from the denoised DW images. Fig. 5 and Fig. 6 show the reconstructed DT metrics after denoising with different methods using multiple acquisitions and single acquisition, respectively, which mainly include myocardial FT, FO, FA, MD, HA, and TA. It can be seen from Fig. 5 To further illustrate the sensitivity of different denoising methods to the number of acquisitions and diffusion directions, Fig. 6 shows the DT image denoising results obtained by different methods based on the dataset with single acquisition and six diffusion directions.

Comparing with the denoising results obtained with multiple acquisitions (Fig. 5), it can be seen that, when using single acquisition and fewer diffusion directions, the FO obtained by BM3D, Nei2Nei, DIP and P2S methods show an irregular distribution which cannot reveal the helical structure of the cardiac fibers, especially the Nei2Nei, DIP and P2S methods, in which, FO are disarranged and the helix/transverse angle maps (Fig. 6 (f) and (g)) are too noisy. In contrast, the proposed method SSECNN, AONLM and LPCA can still reconstruct the cardiac fiber structures even only using the dataset with single acquisition and fewer diffusion directions to denoise, especially for SSECNN, it achieves the smoothest HA and TA maps. From the FA map illustrated in Fig. 6(d), we see that the noise influence on FA is not effectively removed with BM3D, Nei2Nei, and DIP methods, resulting in a larger fluctuation for FA values, however, AONLM, LPCA and our method SSECNN can deal well with the noise in FA map. As to the MD maps (Fig. 6 (e)), the P2S obtains the highest MD values while Nei2Nei obtains the lowest, the LPCA yields the smoothest MD variations, and for the rest methods generate almost the same MD maps. The box plots of FA and MD values obtained with different methods using multiple acquisitions and single acquisition are given in Fig. 7. Since averaging-based denoising method cannot be implemented with single acquisition, in the Fig. 7, average method is not considered. It can be observed that, for all the methods, denoising with multiple acquisitions generally generate lower FA and both smaller range values of FA and MD. In addition, the range of FA values derived by AONLM, LPCA, and our proposed SSECNN methods are consistent, but the FA values obtained by the other methods are either too big or too small. Moreover, regarding to the difference in FA values between multiple scans and single scans, we notice that SSECNN achieves the smallest difference between multiple scans and single scan, followed by AONLM and LPCA.

As to the range of MD values, the SSECNN model is more robust to the variations of acquisition times and diffusion direction numbers than AONLM and LPCA, which validates that our SSECNN is not sensitive to the number of diffusion directions and acquisitions.

Ablation experiments

Influences of Similar Slice Matching Strategies

To verify the effectiveness of the similar slice matching strategy of SSIM used in this paper, we compared it with three other similarity measures, including Cosine similarity, Euclidean distance and Histogram. Besides the differences in similarity measures, all the experimental conditions are kept unchanged. Fig. 8 (a) shows the DW image denoising results obtained with different similar image matching strategies. It can be seen that the denoising results using SSIM and Cosine as similarity measures are significantly better than those using Euclidean and

Histogram, with the denoised DW images having clearer edge structure. From the residual maps between the input and output images, it is obviously observed that using SSIM and Cosine as the similarity measures lead to the residual maps full of random noise, while using Euclidean and

Histogram results in the residual maps with myocardial structure information, which means that the latter two matching strategies influence the edges and details of the denoised images. Fig. 8 (b) shows the loss curves of denoising for different matching strategies. The Euclidean and Histogram strategies converge to larger loss values, and the SSIM and Cosine strategies eventually converge to almost the same smaller loss values, but the Cosine loss curve is not as stable as that of SSIM.

From these loss curves, we can see that matching strategy of similar slices will influence the denoise results and convergence speed of the model. Although SSIM and Cosine matching strategies achieve comparable denoising effects, the SSIM matching strategy is preferred because its convergence performance is faster and more stable than that of Cosine.

Ablation in loss function

To verify the effectiveness of the edge-weighted loss proposed in this paper, we illustrated the edge maps detected with Sobel operator during the training in Fig. 9. We found that, at the beginning, the edge detected with Sobel operator is influenced greatly by the noise, but with the increasing of iteration numbers, the denoising performance of the model becomes better and Sobel operator tends to detect the real edges. Therefore, using it as the loss weight can make the model focus on the denoising performance at the edge regions. that the proposed method can effectively remove the noise of cardiac DW images without using the noise-free images as the labels. SSECNN can well preserve the details and texture information of DW images, and the myocardial fiber structure can be accurately reconstructed from these noise-reduced DW images, which is of great significance for investigating the myocardial fiber structure using DW images with low SNR.

Currently, averaging the multiple acquisitions is the commonly used method for DW image denoising, it is highly limited in the real applications since it cannot be used when multiple acquisitions are not available. ANOLM and BM3D methods address this limitation by using the self-similarity between the image blocks to achieve noise reduction. However, due to the low resolution of DW images and the limitation of fewer similar blocks, these block-similarity based methods are easy to blur the denoised images, accordingly, some important texture information is lost, as shown in Fig. 2 (3 rd and 4 th columns) and Fig. 4 (2 nd and 3 rd columns). LPCA explores the redundancy of the multi-dimensional information of DW images and performs a low-rank approximation for denoising by thresholding the eigenvalues of the noisy signal matrix. Its performance depends on the degree of redundancy of the local signals and the selection of threshold. When the diffusion directions are not enough, the redundancy of DW images are not obvious so that the denoising performance of LPCA is not as well as expected, as shown in Fig. 4 (4 th column, 6 th row).

Deep learning method DIP assumes that the network itself can describe priori information of an image, so that it must exist certain network parameters that allow us to produce the clean image corresponding to a given noisy input. DIP requires only one image to learn, but its denoising performance is highly related with the iteration times. The objective of DIP is to minimize the mean square error between the output and the noisy images, accordingly the denoising result is dependent on the number of optimization iterations, which means that stopping the training too early or too late cannot remove the noise effectively. In cardiac DTI reconstruction, it requires that the denoised DW images along all the diffusion directions to be optimal to ensure that the reconstructed DTI metrics are correct. Since the prior of each DW image is different, the corresponding optimal iteration number should be different when using DIP noise reduction.

However, in practice, to remove the noise in a DW image volumes, the number of iterations is fixed, accordingly, the DW image denoising with DIP cannot achieve optimal results, as illustrated in Fig. 2

List of Tables

2. 1

 1 Overall architecture of SSECNN The overall architecture of the SSECNN denoising model is shown in Fig.1, which mainly consists of a similar image matching module (Matcher, M) and a denoising module (Denoiser, D). After matching the noisy DW images with the matcher M, we can get the noisy training pairs ij s and ij s , which are used as the input and expected output of the denoiser D to optimize the parameters  of the model.

Fig. 1

 1 Fig. 1 Schema of the proposed SSECNN architecture.

  target DW volume and other volume along different diffusion directions, respectively, x  and y  are the local mean intensity of and c2 are two constants. By maximizing the SSIM, the similar DW image pairs are found and form the training set of the self-supervised denoising model. Let the origin slice group being { } S , and the corresponding similar slice group being { } S  . Slices in { } S are the input of denoiser D, and slices in { } S  are taken as the target of D. In this work, the denoiser D uses the residual network as the backbone. Batch normalization (BN) and RuLU activation function are used to improve the denoising performance. The network consists of one CR (Conv2d+ReLU) module, 16 CBR (Conv2d+BN+ReLU) modules, 17 CB (Conv2d+BN) modules and one C (Conv2d) module. The skip-connection between the different modules is used to ensure the model learn consistent features about the noise distribution. The 2-D convolutional kernel size in all

  f  represents the network, mn s and ' mn s represents the voxel intensity of the input noisy image and the expected network output image for the voxel (m,n), respectively. This loss treats all voxels equally, resulting in some edge regions being over-blurred. To deal with this issue, we propose a weighted loss to suppress the over-smoothing phenomenon based on the edge sharpness information, denotes the loss weight for the voxel (m,n), its value is obtained with Sobel operator computed on the denoised results. Since the weight of m n w is larger at the edge position, it can make the model prefer to denoise in the edge region, while for the smooth region m n w is smaller,

Fig. 2

 2 Fig. 2 Denoising results of DW images on synthetic data and RMSE obtained by various methods.

Fig. 3

 3 Fig. 3 Denoising results for synthetic DTI with various methods.

3. 3 Denoising results for real acquisitions 3 . 3 . 1

 3331 Fig.4 shows the denoising results for myocardial DW images obtained with different methods. The last column of Fig.4 demonstrates the original noisy image, we observe that the detailed structure of LV has been severely damaged by the noise. The first row shows the DW image denoising results obtained by different methods with the dataset of 12 diffusion directions and 6 repeated acquisitions; the third row shows the denoising results obtained with dataset of 12 diffusion directions and single acquisition; the fifth row shows the DW image denoising results

Fig. 4

 4 Fig. 4 Denoising results for DW images obtained by various methods with different diffusion directions and acquisitions.

  (a) and (b) that the signal loss in the original image is obvious due to the presence of noise, resulting in disarranged FT and FO. After denoising using different methods, the FT and FO distribution become more regular and well arrangement, especially in LV where the cardiac fiber orientations show a helical distribution. From the zoom-in details of the local fiber orientation in Fig.5(c), we see that multiple post-processing denoising methods are superior to the averaging method that commonly used in clinical applications. Although Nei2Nei and P2S methods can correct the cardiac FO to some extent, they still have some wrong FO, especially at crossing regions between LV and right ventricle, as shown in the zoom-in images. The FA and MD maps are given in Fig.5(d) and (e), from which we observe that the FA maps obtained by Average and Nei2Nei methods have obvious noise effects, and the FA obtained by BM3D, Nei2Nei and DIP have a larger fluctuation range, while the FA values obtained by AONLM, LPCA, P2S and the proposed method have a smaller range. For the MD maps, no significant difference in MD values is found among different methods, except for the extreme large MD values obtained by P2S and extreme small MD values obtained by Nei2Nei. To further compare the effects of different denoising methods on cardiac FO, HA and TA of fiber orientations are calculated and shown in Fig.5(f) and (g). It is evident that the regular distribution of HA and TA could not be observed under the influence of noise. Although the HA and TA distributions can be recovered to some extent by using Average and P2S methods, the interference of noise still exists. BM3D, Nei2Nei and DIP methods can effectively recover the helical distribution of HA, that means HA changes from positive to negative from endocardium to epicardium, but for TA, it is still affected by noise at the Septum and free lateral regions. In contrast, the HA and TA obtained by the proposed method SSECNN, LPCA and AONLM are consistent with positive HA at endocardium and negative HA at epicardium, as well as the TA angle is close to 0°, reflecting the circular arrangement of cardiomyocytes.

Fig. 5

 5 Fig. 5 Cardiac diffusion tensor image denoising results using different methods with multiple repeated acquisitions.

Fig. 6

 6 Fig.6 Denoising results of myocardial DTI using different algorithms based on the dataset with single acquisition and fewer diffusion directions.

Fig. 7

 7 Fig. 7 Box plots of FA (a) and MD (b) values obtained by different methods with multiple and single scans.

Fig. 8

 8 Fig. 8 Comparison of multiple similarity matching strategies. (a) Denoising results and corresponding residual maps for different matching strategies, (b) Loss curves of denoising model with different matching strategies.

Fig. 9

 9 Fig. 9 Edge maps extracted by Sobel operator for different epochs.This can also be validated with the ablation results in Fig.10, where we compared the denoising results obtained with weighted loss and non-weighted loss learning in terms of synthetic dataset. We observe that the denoising results with the weighted loss can retain more detail information for simulated images (PSNR=33.98, SSIM=0.9872), as shown in the first two columns of Fig.10. The denoised DW image obtained with non-weighted loss is blurred at the regions marked by the red arrows in the zoom-in image (PSNR=33.37, SSIM=0.9861), and its edges are not as sharp as those obtained with weighted loss. For the simulated diffusion tensor metrics, edge-weighted loss results in the closest FO, FA and MD to the ground-truths.

Fig. 10

 10 Fig.10 Comparison of the denoising results with and without edge-weighted loss.

Fig. 1

 1 Fig. 1 Schema of the proposed SSECNN architecture.

Fig. 2

 2 Fig. 2 Denoising results of DW images on synthetic data and RMSE obtained by various methods.

Fig. 3

 3 Fig.3 Denoising results for synthetic DTI with various methods.

Fig. 4

 4 Fig. 4 Denoising results for DW images obtained by various methods with different diffusion directions and acquisitions.

Fig. 5

 5 Fig. 5 Cardiac diffusion tensor image denoising results using different methods with multiple repeated acquisitions.

Fig. 6

 6 Fig.6 Denoising results of myocardial DTI using different algorithms based on the dataset with single acquisition and fewer diffusion directions.

Fig. 7

 7 Fig. 7 Box plots of FA (a) and MD (b) values obtained by different methods with multiple and single scans.

Fig. 8

 8 Fig. 8 Comparison of multiple similarity matching strategies. (a) Denoising results and corresponding residual maps for different matching strategies, (b) Loss curves of denoising model with different matching strategies.

Fig. 9

 9 Fig. 9 Edge maps extracted by Sobel operator for different epochs.

Fig. 10

 10 Fig.10 Comparison of the denoising results with and without edge-weighted loss.

  training set and testing set with a ratio of 4:1, in the other words, the training set includes DW images of 12 volunteers and the testing set includes DW images of the rest 3 volunteers. According to the number of slices and the number of diffusion directions of each subject, it can be calculated that the training set contains 36186 DW image slices and the testing set contains 8544 slices. During the training, data augmentation strategies, such as random flipping, cropping, and scaling, were used to overcome the overfitting problem.To verify the superiority of proposed method, it is compared with traditional methods (Multiple acquisitions averaged 2 , AONLM[START_REF] Coupé | Adaptive multiresolution non-local means filter for three-dimensional magnetic resonance image denoising[END_REF] , BM3D[START_REF] Dabov | Image denoising by sparse 3-D transformdomain collaborative filtering[END_REF] , LPCA[START_REF] Manjón | Diffusion weighted image denoising using overcomplete local PCA[END_REF] ) and deep learning methods (Neighbor2Neighbor 25 , DIP[START_REF] Ulyanov | Deep image prior[END_REF] , Patch2Self[START_REF] Fadnavis | Patch2Self: Denoising Diffusion MRI with Self-Supervised Learning[END_REF] ). The hyperparameters of all the comparison models

	Additionally, multiple acquisitions of cardiac DW images for 15 volunteers were also used in
	this work. All DW images were acquired using a 1.5T MRI scanner (MAGNETOM Avanto,
	Siemens AG) with EPI sequences, the detailed acquisition parameters are: TR/TE = 6500/71 ms,
	in-plane image matrix size = 128 × 128, and spatial resolution = 1.6 × 1.6 mm 2 . Diffusion
	weighting factor b value = 1000 s/mm 2 , and the number of diffusion gradient directions changes

[START_REF] Chen | Noise reduction in diffusion MRI using non-local selfsimilar information in joint x-q space[END_REF]

. Diffusion weighting factor b value = 1000 s/mm 2 , and the number of diffusion gradient directions is 64. To generate the noisy DW images, Gaussian noise with variance of 0.0036, 0.0064 and 0.01 (corresponding standard deviations are 6%, 8% and 10%) was added respectively to the noise-free DW images.

with each volunteer, with a minimum value of 12 and a maximum value of 72. Since the slice thickness changes for each individual acquisition, the number of image slices for each volunteer varies from 22 to 56, and the number of repeated acquisitions varies from 1 to 6 times. We divided this dataset into are consistent with their original ones. All experiments in this work were implemented with Pytorch framework and trained on a Nvidia Tesla V100 GPU, and the optimizer was ADAM with a learning rate of 0.0001, β1 of 0.5, and β2 of 0.999. During the training process, the batch size and epoch number of the model were set to 64 and 500, respectively.

Table 1

 1 RMSE, PSNR and SSIM of the denoised DW images obtained by various methods for different noise levels

	Noise levels Metrics	Noisy	AONLM	BM3D	LPCA	Nei2Nei	DIP	P2S	SSECNN
		RMSE	0.0361	0.0260	0.0262	0.0139	0.0411	0.0272	0.0348	0.0130
	6%	PSNR	28.83	31.68	30.86	37.10	29.72	31.32	29.16	37.69
		SSIM	0.9545	0.9857	0.9796	0.9893	0.9710	0.9733	0.9804	0.9923
		RMSE	0.0482	0.0300	0.0313	0.0177	0.0472	0.0346	0.0413	0.0170
	8%	PSNR	26.33	30.46	29.37	35.02	27.51	29.20	27.67	35.37
		SSIM	0.9360	0.9816	0.9740	0.9848	0.9642	0.9623	0.9767	0.9901
		RMSE	0.0603	0.0337	0.0358	0.0216	0.0547	0.0539	0.0385	0.0201
	10%	PSNR	24.39	29.43	28.27	33.32	25.24	25.38	28.28	33.98
		SSIM	0.9177	0.9770	0.9683	0.9797	0.9553	0.9462	0.9752	0

.9872 3.2.2 Denoised results for synthetic DT images

Table 2

 2 SNR and CNR of the denoised DW images obtained by various methods with different diffusion directions and acquisitions

	Cases Metrics Noisy	Average AONLM	BM3D	LPCA	Nei2Nei	DIP	P2S	SSECNN
	12d+6s	SNR 3.21±0.30 4.08±0.27 4.73±0.65 4.49±0.48 4.15±0.52 4.76±0.49 3.99±0.57 4.44±0.30 5.24±0.57 CNR 1.75±0.24 2.85±0.68 3.79±1.79 3.64±1.95 4.27±2.40 2.77±0.70 2.31±0.66 3.72±0.95 4.69±2.45
	12d	SNR 3.24±0.20 CNR 1.74±0.20	4.83±0.39 4.54±0.30 4.40±0.29 4.81±0.33 4.11±0.46 4.45±0.10 5.29±0.34 3.75±1.61 3.46±1.17 4.05±1.83 2.70±0.68 2.31±0.51 3.80±0.27 4.47±1.84
	6d	SNR 3.23±0.19 CNR 1.74±0.20	4.70±0.38 4.50±0.32 4.28±0.29 4.78±0.32 4.11±0.38 4.04±0.09 5.25±0.30 3.62±1.26 3.51±1.12 3.07±0.93 2.70±0.68 2.34±0.48 2.81±0.19 4.45±1.82

Note: d represents the diffusion directions, s represents the scans or acquisitions.

Table 1

 1 RMSE, PSNR and SSIM of the denoised DW images obtained by various methods for different noise levels

	Noise level Metrics	Noisy	AONLM	BM3D	LPCA	Nei2Nei	DIP	P2S	SSECNN
		RMSE	0.0361	0.0260	0.0262	0.0139	0.0411	0.0272	0.0348	0.0130
	6%	PSNR	28.83	31.68	30.86	37.10	29.72	31.32	29.16	37.69
		SSIM	0.9545	0.9857	0.9796	0.9893	0.9710	0.9733	0.9804	0.9923
		RMSE	0.0482	0.0300	0.0313	0.0177	0.0472	0.0346	0.0413	0.0170
	8%	PSNR	26.33	30.46	29.37	35.02	27.51	29.20	27.67	35.37
		SSIM	0.9360	0.9816	0.9740	0.9848	0.9642	0.9623	0.9767	0.9901
		RMSE	0.0603	0.0337	0.0358	0.0216	0.0547	0.0539	0.0385	0.0201
	10%	PSNR	24.39	29.43	28.27	33.32	25.24	25.38	28.28	33.98
		SSIM	0.9177	0.9770	0.9683	0.9797	0.9553	0.9462	0.9752	0.9872

Table 2

 2 SNR and CNR of the denoised DW images obtained by various methods with different 630 diffusion directions and acquisitions 21±0.30 4.08±0.27 4.73±0.65 4.49±0.48 4.15±0.52 4.76±0.49 3.99±0.57 4.44±0.30 5.24±0.57

	Cases Metrics Noisy	Average AONLM	BM3D	LPCA	Nei2Nei	DIP	P2S	SSECNN
	12d+6s	SNR 3.CNR 1.75±0.24 2.85±0.68 3.79±1.79 3.64±1.95 4.27±2.40 2.77±0.70 2.31±0.66 3.72±0.95 4.69±2.45
	12d	SNR 3.24±0.20 CNR 1.74±0.20	4.83±0.39 4.54±0.30 4.40±0.29 4.81±0.33 4.11±0.46 4.45±0.10 5.29±0.34 3.75±1.61 3.46±1.17 4.05±1.83 2.70±0.68 2.31±0.51 3.80±0.27 4.47±1.84
	6d	SNR 3.23±0.19 CNR 1.74±0.20	4.70±0.38 4.50±0.32 4.28±0.29 4.78±0.32 4.11±0.38 4.04±0.09 5.25±0.30 3.62±1.26 3.51±1.12 3.07±0.93 2.70±0.68 2.34±0.48 2.81±0.19 4.45±1.82

Note: d represents the diffusion directions, s represents the scans or acquisitions.

ACKNOWLEDGMENTS

This work was supported by the National Nature Science Foundations of China (Grant No.62161004), Guizhou Provincial Science and Technology Projects (QianKeHe ZK [2021] Key 002), Nature Science Foundations of Guizhou Province (QianKeHe [2020]1Y255).

CONFLICT OF INTEREST

515

The authors have no conflicts to disclose.


Guillermina Hernandez-Raquet

Fabienne Gas
email: fabienne.gas@cea.fr

Esther Le Toquin

Sylvain Faure

Nicole Orange

New Biocide Foam Containing Hydrogen Peroxide for the Decontamination of Vertical Surface Contaminated With Bacillus thuringiensis Spores

Keywords: Bacillus thuringiensis, spores, decontamination, hydrogen peroxide, foam, biocide

Despite scientific advances, bacterial spores remain a major preoccupation in many different fields, such as the hospital, food, and CBRN-E Defense sector. Although many disinfectant technologies exist, there is a lack for the decontamination of difficult to access areas, outdoor sites, or large interior volumes. This study evaluates the decontamination efficiency of an aqueous foam containing hydrogen peroxide, with the efficiency of disinfectant in the liquid form on vertical surfaces contaminated by Bacillus thurengiensis spores. The decontamination efficiency impact of the surfactant and stabilizer agents in the foam and liquid forms was evaluated. No interferences were observed with these two chemical additives. Our results indicate that the decontamination kinetics of both foam and liquid forms are similar. In addition, while the foam form was as efficient as the liquid solution at 4 • C, it was even more so at 30 • C. The foam decontamination reaction follows the Arrhenius law, which enables the decontamination kinetic to be predicted with the temperature. Moreover, the foam process used via spraying or filling is more attractive due to the generation of lower quantity of liquid effluents. Our findings highlight the greater suitability of foam to decontaminate difficult to access and high volume facilities compared to liquid solutions.

INTRODUCTION

Certain Gram-positive bacteria, like Bacillus and Clostridium species, are able to protect themselves from environmental stress or nutrient depletion by a sporulation process. Vegetative cells that pass into a dormant spore state are known to be much more resistant to the environment and to disinfection treatments than growing cells of the same species [START_REF] Nicholson | Resistance of Bacillus endospores to extreme terrestrial and extraterrestrial environments[END_REF][START_REF] Driks | Overview: development in bacteria: spore formation in Bacillus subtilis[END_REF][START_REF] Piggot | Sporulation of Bacillus subtilis[END_REF][START_REF] Higgins | Recent progress in Bacillus subtilis sporulation[END_REF][START_REF] Wood | Environmental persistence of Bacillus anthracis and Bacillus subtilis spores[END_REF]. Several factors have been identified as responsible for the increased spore resistance. A thick spore coat protects the inner layers from lytic enzymes and from many chemicals, including chlorine dioxide and sodium hypochlorite [START_REF] Driks | Bacillus subtilis spore coat[END_REF](Driks, , 2002a)). The extremely low spore permeability enables the protection of the inner spore membrane against hydrophilic agents and possible UV and γ-radiation [START_REF] Riesenman | Role of the spore coat layers in Bacillus subtilis spore resistance to hydrogen peroxide, artificial UV-C, UV-B, and solar UV radiation[END_REF][START_REF] Doona | Fighting Ebola with novel spore decontamination technologies for the military[END_REF]. The reduced water content in the core protects the spore from dry and wet heat, enabling it to survive for longer periods of time in a hostile environment [START_REF] Setlow | Spores of Bacillus subtilis: their resistance to and killing by radiation, heat and chemicals[END_REF][START_REF] Leggett | Bacterial spore structures and their protective role in biocide resistance[END_REF]. The spore DNA is saturated with small acidsoluble proteins (SAPS) of the α/β type and the high presence of calcium-dipicolinic acid chelate inside the spore core makes spore destruction more difficult by UV radiation, heat, and some genotoxic chemicals [START_REF] Setlow | Role of dipicolinic acid in resistance and stability of spores of Bacillus subtilis with or without DNA-protective alpha/beta-type small acid-soluble proteins[END_REF][START_REF] Moeller | Roles of small, acidsoluble spore proteins and core water content in survival of Bacillus subtilis spores exposed to environmental solar UV radiation[END_REF]. Finally, the DNA repair mechanisms occur just at the beginning of germination when the spore returns to growth-cell life [START_REF] Setlow | I will survive -protecting and repairing spore DNA[END_REF]. Bacterial spores have always been considered as a threat either through their potential for use as biological weapons (e.g., the 2001 anthrax attack in the United States) [START_REF] Schmitt | Total decontamination cost of the anthrax letter attacks[END_REF], or because of food and hospital contaminations [START_REF] Faille | Sporulation of Bacillus spp. within biofilms: a potential source of contamination in food processing environments[END_REF][START_REF] Yi | A pilot study on using chlorine dioxide gas for disinfection of gastrointestinal endoscopes[END_REF][START_REF] Fernandes | Formation of multi-species biofilms by Enterococcus faecium, Enterococcus faecalis, and Bacillus cereus isolated from ricotta processing and effectiveness of chemical sanitation procedures[END_REF].

Several decontamination technologies have been proposed in the past and different sporicidal treatments are known. UV radiation and genotoxic chemicals damage spore DNA [START_REF] Tennen | Mechanisms of killing of spores of Bacillus subtilis by iodine, glutaraldehyde and nitrous acid[END_REF]; strong acid disrupts spore integrity; peroxynitrite and other chemicals damage the spore inner membrane [START_REF] Genest | Killing of spores of Bacillus subtilis by peroxynitrite appears to be caused by membrane damage[END_REF], and heat or peroxides disrupt the spore germination apparatus by targeting key proteins [START_REF] Loshon | Analysis of the killing of spores of Bacillus subtilis by a new disinfectant, Sterilox[END_REF][START_REF] Melly | Studies on the mechanism of killing of Bacillus subtilis spores by hydrogen peroxide[END_REF]. The choice of a decontamination treatment depends on the way to use the technology, the biocide efficiency of the treatment, the type of contaminated surfaces, the energy quantity and basic materials needed for the decontamination, and the quantity of waste products after treatment [START_REF] Sagripanti | Bacterial spores survive treatment with commercial sterilants and disinfectants[END_REF][START_REF] Wood | Efficacy of liquid spray decontaminants for inactivation of Bacillus anthracis spores on building and outdoor materials[END_REF][START_REF] Ryan | Effect of inoculation method on the determination of decontamination efficacy against Bacillus spores[END_REF][START_REF] Van Bokhorst-Van De Veen | Inactivation of chemical and heat-resistant spores of Bacillus and Geobacillus by nitrogen cold atmospheric plasma evokes distinct changes in morphology and integrity of spores[END_REF]. Each treatment presents different advantages: different means of implementation for a method applying chemical products (wet wipes, sprays, or fumigation) [START_REF] Otter | Survival of nosocomial bacteria and spores on surfaces and inactivation by hydrogen peroxide vapor[END_REF][START_REF] Kenters | Effectiveness of cleaning-disinfection wipes and sprays against multidrug-resistant outbreak strains[END_REF], no waste after treatment with UV radiation, good dispersion of biocide products by fumigation for closed areas. But few processes are able to efficiently decontaminate, without extra costs or high quantities of waste, outdoor, and indoor sites with large volumes or hard to access areas like ventilation pipes [START_REF] Schmitt | Total decontamination cost of the anthrax letter attacks[END_REF][START_REF] Edmonds | Decontamination efficacy of three commercial-off-the-shelf (COTS) sporicidal disinfectants on mediumsized panels contaminated with surrogate spores of Bacillus anthracis[END_REF].

To date several laboratories offer commercial foaming solutions and sprayers to decontaminate surfaces. These disinfecting formulations contain foaming surfactants and an active substance, sodium hypochlorite or hydrogen peroxide, but not a stabilizing agent (Environmental Protection Agency, 2006). A stabilizing agent enables the foam to be stabilized in time, thus decreasing the foam drainage and increasing the contact time with the contamination [START_REF] Dame | Relations between physicochemical properties and instability of decontamination foams[END_REF]. Foams with a controlled liquid fraction, containing a stabilizing agent and able to reduce spore contamination by six logs, have been successfully developed and patented in our laboratory [START_REF] Faure | Disinfecting aqueous foam, process for preparing same and use thereof[END_REF]. These foaming solutions are used with a dedicated foam generator that maintains the foam liquid fraction between 3 and 5%. These long-lifetime foams could be used to statically decontaminate outdoor and indoor facilities and equipment such as ventilation pipes, offices, cold-rooms, trains, and containers. Two ways of use were developed: sprayer application depositing a centimeter-thick layer of the decontamination foam on accessible contaminated surfaces, or a filling application for all volumes, even facilities difficult to access. Without treatment, all such places could become contamination exchange areas contributing to contamination propagation.

This study measured the disinfectant efficiency of a new biological decontamination foam using hydrogen peroxide as the disinfectant. The work was carried out on both foam and liquid (no air bubbles) forms to determine the decontamination efficiency. In addition, the study gave data related to the negative or positive contribution of each chemical product contained in the solution. For both foam and liquid forms, the decontamination impact from the stabilizer agent was evaluated. Further tests were performed by using the liquid form containing only the hydrogen peroxide. Bacillus thuringiensis (Bt) spores, biological indicators for decontamination tests in the field of CBRN Defense, were used for all tests. Moreover, to simulate difficult case of decontamination, all tests were performed on vertical surfaces contaminated with Bt spores. Different contact times and temperatures were tested for each decontamination technologies liquid and foam. Foam formulations with or without stabilizer agent were tested at three temperatures to study how the behavior of the foam is affected by temperature variations.

MATERIALS AND METHODS

Bacterial Spore Preparation B. thuringiensis DSM 5815 (provided by Leibniz-Institute DSMZ Co., Braunschweig, Germany) were used for this study, and prepared according to the protocol described by [START_REF] Wood | A simple decontamination approach using hydrogen peroxide vapour for Bacillus anthracis spore inactivation[END_REF]. Briefly, frozen B. thuringiensis was inoculated into 10 mL of lysogeny broth media (LB, Becton Dickinson Co., Sparks, MD, United States) at 30 • C for 16-18 h with continuous agitation at 160 rpm. Aliquots of 150 µl were then transferred into fresh media and incubated for 5 h at 30 • C with continuous agitation at 160 rpm. The inoculum was spread onto a nutrient agar [0.5% (w/v) Tryptone, 0.3% (w/v) beef extract, 0.3% (w/v) NaCl, 2% (w/v) agar, and 0.01% (w/v) glucose], completed with 10 mL of metal solution

[0.025% (w/v) MnSO 4 •H 2 O, 0.03% (w/v) CaCl 2 , 0.04% (w/v) (NH 4 ) 2 SO 4 , 0.004% (w/v) MnCl 2 •4H 2 O, 0.0025% (w/v) CuSO 4 •5H 2 O, and 0.0025% (w/v) ZnSO 4 •7H 2 O]
and incubated at 30 • C. The sporulation progression in the petri dishes was checked by optical microscopy after 7-9 days. When the sporulation reached ≥95%, the spores were harvested from the plates using a rake and sterile distilled water, and washed four times in sterilized water by centrifugation and resuspension (4500 rpm at 4 • C, two times 30 , 20 , and 15 min) to remove cell debris and media co-contaminants. The spore suspension was heat-treated at 70 • C for 15 min with continuous agitation at 300 rpm. For heat-shock, the heat-treated spores were plunged into ice for 20 min and sonicated for 4 min at 45 Hz. The final titer of the suspension was determined by 1:10 and 1:5 serial dilutions, prepared using LB media and covered on a petri dish with appropriate solid growth media. The plates were incubated at 30 • C overnight before CFU evaluation. 1) were tested both in the foam and in the liquid form. The solution S1 was tested only as liquid.

A static generator was used to mix air and foaming solutions to generate foam. A tube filled with glass balls generated the foam just before the coupon treatment. The generator parameters were set to obtain a foam with a liquid fraction between 3 and 6% (volume liquid/volume foam), with an average of 5.5%.

Test Materials

Tests were performed with coupons of polystyrene (petri dish polystyrene, Greiner Bio-one Co., Ltd., Frickenhausen, Germany) which is transparent and non-reactive with our disinfectant. The coupons were calibrated at 2.5 cm by 12 cm. Each coupon was sterilized overnight in a chemical bath containing hydrogen peroxide (ANIOS Co., Lille-Hellemmes, France), washed with 70% (v/v) ethanol to remove all disinfectant traces, and stored at 60 • C in a sterile container until use.

Disinfection Efficiency Test on Coupon

A bacterial suspension of B. thuringiensis spores was prepared in distilled water at a concentration of 10 9 CFU/mL. An aliquot of 100 µL (10 8 CFU/mL) was inoculated, in droplets, on the surface of each coupon with the help of a micropipette (Figure 1). After inoculation, the coupons were air dried in a biosafety cabinet (2 h maximum before use).

The inoculated coupons were then immersed in a 50 mL Falcon© tube containing approximately 25 mL of foam or 20 mL of liquid solution. The Falcon© tubes containing coupon were kept in vertical position at different controlled temperatures: 20 • C inside a biosafety cabinet, 30 • C inside a climatic chamber and 4 • C in a refrigerator, for various times (5, 10, 15, 20, 25, and 35 min).

After the incubation each coupon was transferred into a new 50 mL Falcon© tube containing 10 mL of neutralizer solution of phosphate buffered saline (PBS) + 0.04% catalase (Sigma-Aldrich, St. Louis, Mo., United States) to stop the biocide activity. 20 mL of this neutralizer solution were added also to the Falcon© tubes containing only the foam (Figure 1).

To isolate the spores from the coupons, each tube was centrifuged at 4500 rpm for 15 min at 4 • C. After removing the supernatant, the pellet containing spores was re-suspended with 10 mL of liquid LB. Each Falcon© tube containing coupon was incubated for 1 h at 30 • C. Serial dilutions were plated for each Falcon© tube in LB media and covered with LB agar. Experiments were performed in duplicate. After drying, the plates were incubated for 18-24 h at 30 • C and CFU were counted manually.

Disinfection Efficiency Test Without Coupon

Bacterial suspension of B. thuringiensis at a concentration of 10 9 CFU/mL, was used to test the decontamination efficiency of solutions without coupon. 100 µL droplets of this suspension were applied directly inside 20 mL of foam or 1 mL of liquid solution inside a 50 mL Falcon© at 20 • C. After different contact times, these Falcons© were treated following the protocol described in Figure 1.

Validation of Disinfectant Tests

Controls tests were carried out in parallel for each disinfectant test: (1) Blank control: coupons were not inoculated, but decontaminated as the inoculated ones. These coupons were used as control for issue related to cross-contamination during the test.

(2) Positive control: each experiment included an assay where the solution did not contain disinfectant (S4 and S5 in Table 1). Protocol described in Figure 1 was followed for both the foam and the liquid form without disinfectant. These tests indicated the amount of spores transferred in the liquid or in the foam by the coupon and the amount remained adhered on coupon. (3) Recovery of microorganisms: the same tests with solutions S4 and S5 were performed without coupon to evaluate the impact of the protocol on the recovery.

Data Processing

Recovery rate and log 10 reduction (LR) were determined at last three times in duplicate for each preparation. Recovery data were calculated for each preparation with and without coupons following the equation (1):

Mean % recovery = [Mean CFU pc /CFU spike ] × 100 (1)
where mean CFU pc is the mean of CFU recovered from at last three duplicate positive controls (pc) for each preparation with or without coupons, and CFU spike is the number of CFU spiked (inoculated) on the coupon, or inside the liquid or foam. Decontamination efficacy for each treatment was calculated to measure the efficacy of the foam treatment in terms of the spore log 10 reduction (LR). This was calculated by dividing the number of viable spores extracted after the decontamination tests by the number of spores originally spiked. The decontamination efficacy for biological agents was expressed in terms of a log reduction using the equation (2):

Log Reduction (LR) = log(CFU t /CFU spike ) (2)
where CFU t is the mean number of viable organisms recovered from either each coupon or the foam or liquid solution used for a test, after decontamination. Test coupons in which no CFU was recovered, were assigned a CFU count of 1, resulting in a log CFU of zero. Standard deviations were calculated from the mean results of the replicated experiments.

For each mean, the standard error of the mean (SEM) was calculated. Student t tests were performed using XLStat software (Addinsoft, Paris, France) to determine if two data sets of mean were significantly different from one another. A p-value<0.05 was considered to be significant.

Evaluation of the Rate Constant for Inactivation and Arrhenius Law

In order to evaluate the effects of temperature on the decontamination efficacy for bacterial spores, the rate constant for inactivation k was deduced with a mathematic model based on first-order kinetics:

dN/dt = -kN, or, in the integration form, log(N/N 0 ) = -kt

(3) where N 0 is CFU control and N is CFU t at time t (including time zero). The slope of the linear regression of log (N/N0) versus time t is equal to -k.

In the Arrhenius equation, k is related to the inactivation energy of each decontamination parameter E a (kJ/mol -1 ) [START_REF] Watanabe | Inactivation of Geobacillus stearothermophilus spores by high-pressure carbon dioxide treatment[END_REF] by the equation: k = A 0 e(-E a /RT), or, in the integration form,

ln k = ln A 0 -(E a /RT) ( 4
)
where k is the rate constant for inactivation, which is a function of temperature T, A 0 is the frequency factor and R is the gas constant (8.314 J/mol.K -1 ).

A survival curve for each foam and liquid parameter was plotted for each temperature to measure k. For each foam and liquid parameter, the slope of the linear regression of ln k versus 1/T enabled the determination of E a /R and A 0 .

RESULTS

Determination of Spores Recovery Inside the Foam or Liquid Solutions in the Absence of Disinfectant

The spores recovery injected inside foam or liquid forms was determined with S5 solution that did not contain disinfectant (Table 1). The mean recovery from foam form was higher than the liquid solution with respectively means of 8.03 ± 0.03 log and 7.70 ± 0.10 log, and statistically significant (p-value = 0.01; t-test on mean). This significant difference justifies the amount used in equation ( 1) (CFU spike = 10 8 CFU/mL).

Determination of the Spores Recovery in the Absence of Disinfectant on Coupon

The recovered amount of spores from coupon (adherent spores) was not statistically different when the coupon was in contact with foam or with liquid solution (p-value = 0.086). Similarly, the fraction of spores recovered inside foam or liquid (transferred spores) was not statistically different (p-value = 0.295). However, the total recovery of these controls was lower than for control tests without coupons. The recovered amount of spores from both adherent and transferred parts was 7.42 ± 0.15 log.

A fraction of bacterial spores was rapidly transferred inside the foam or the liquid solution (Figure 2). Within 5 min, 5% average of the inoculated bacterial spores were transferred inside the liquid solution. For the transfer within foam, 10 min were needed to obtain 3% of the spores transferred. After 20 min, the quantity transferred from coupon to foam or liquid solution did not change and stabilized at 5%. Moreover, the total foam recoveries were always higher than the total liquid solution recoveries. After 25 min of treatment with our foam, 90% of spores still adhered on the surface. The surface was considered still contaminated with more than 10 7 CFU. This value is considered dangerous for human health in the case of spores from bacterial pathogens.

Decontamination Efficiency on Coupon at Room Temperature

To compare the decontamination efficiency on vertical surface between foam and liquid containing disinfectant, reaction inactivation kinetics were performed (S1, S2, and S3 in Table 1). Experiments in liquid solutions enabled to characterize the effect of the foaming surfactant (Glucopon 215UP) and stabilizing agent (Xanthan) on the inactivation kinetic (LR) (Figure 3). After twenty-five minutes of contact time in a vertical position, the adhered spores on the coupons were not completely inactivated. The decontamination efficiency ranged from 3.68 log for the liquid solution without additive (S1), to 4.47 log for the liquid solution with all additives (S3). The decontamination kinetic of liquid solutions on spores adherent to the coupon can be seen in Figure 3, with the lines for first-order kinetic-model [START_REF] Murdoch | Evaluating different concentrations of hydrogen peroxide in an automated room disinfection system[END_REF]. The equation of these lines enabled the determination of the inactivation coefficients for each treatment at "room temperature" (equal 293.15 K and 20 • C). The model did fit satisfactorily the result of each treatment, with R 2 ranging from 0.94 to 0.98. Nevertheless, as can be seen in Table 2, no positive effect of Glucopon and Xanthan (S3) was revealed [difference not statistically significant compared to other treatments (S1 and S2) (p-value >0.05)].

Figure 4 shows the LR as a function of time, for solutions containing hydrogen peroxide S2 and S3 in the both forms: liquid and foam. The same statistical model used for the liquid solution (Figure 3), was applied to determine the inactivation coefficients at "room temperature". This model fitted correctly with the results, with R 2 of 0.96 and 0.98 for the decontamination foam without (S2), and with stabilizing agent (S3) respectively. Using foam with an average of 5.5% of liquid fraction was enough to satisfactorily wet the surface with a liquid film that enables the spores to be inactivated. Also, the decontamination efficacy kinetic for both decontamination foams was almost similar and after twenty-five minutes of contact time, the mean LR was equal for both (4.5 log). However, after 45 min of contact time no CFU were retrieved on the surface of the coupons. The inactivation coefficients (k s -1 ) of the spores transferred inside the foam were 0.209 with stabilizing agent (S3) and 0.288 without (S2). However, control tests with solutions S4 and S5 showed that only 5% of the bacterial spores were transferred within the foam after twenty-five minutes of contact time. The decontamination kinetic inside foam with (S3) and without (S2) the stabilizing agent was not statistically different (p-value >0.05). After twenty-five minutes, the decontamination was not completed in both foam fractions, but no CFU were retrieved after at least 35 min from the foam fractions even if they were found on the coupon (data not shown).

Decontamination Efficiency at Different Temperatures

To determine the effect of the temperature on decontamination efficacy, the spore inactivation was assessed at three temperatures after twenty-five minutes of exposure. This efficacy was evaluated for solution S3 in the foam and liquid form. At the lowest temperature (4 • C = 277.15 K) the values of LR were very low and ranged from 1.44 to 2.25 LR (Figure 5). Cold temperatures drastically slowed down the decontamination kinetic on surface. On the contrary, a different behavior was found at higher temperature (30 • C = 303.15 K). The LR results were different between the decontamination by foam and by liquid solution. For the foam, no bacterial spores were recovered on coupon after twenty-five minutes of contact time at 303.15 K, at the limit of detection. For the liquid solution, after the same contact time, the bacterial spore recovery was nearly 5.5 LR. The difference between both forms (foam and liquid solution) at 303.15 K was statistically significant (p-value >0.05).

Activation Energy of Foams S2 and S3 (Arrhenius law)

The activation energy was determined for foams S2 and S3. For this comparison, CFU control (CFU pc ) were used to calculate LR. To determine if results were fitted by the Arrhenius law, the reciprocal of absolute temperature was plotted as a function of the natural logarithm of the inactivation coefficient (Figure 6). The two foam curves were fitted by the Arrhenius law. The activation energies ranged from 46.85 KJ/mol -1 for foam without stabilizing agent (S2) to 67.55 KJ/mol -1 for foam with stabilizing agent (S3).

DISCUSSION

The efficiency to decontaminate Bacillus thuringiensis spore had already been proven for the described, newly patented, foam containing hydrogen peroxide. This efficiency was particularly tested on horizontal coupons [START_REF] Faure | Disinfecting aqueous foam, process for preparing same and use thereof[END_REF]. Hydrogen peroxide was selected as disinfectant for its antibacterial and sporicidal activity, and for its surface-and additive-friendly characteristics [START_REF] Sagripanti | Bacterial spores survive treatment with commercial sterilants and disinfectants[END_REF][START_REF] Melly | Studies on the mechanism of killing of Bacillus subtilis spores by hydrogen peroxide[END_REF][START_REF] Raber | Decontamination options for Bacillus anthracis-contaminated drinking water determined from spore surrogate studies[END_REF][START_REF] Eryilmaz | In vitro antimicrobial activity of three new generation disinfectants[END_REF]. The hydrogen peroxide was known to be neutralized by catalase positive bacteria [START_REF] Mcdonnell | Antiseptics and disinfectants: activity, action, and resistance[END_REF][START_REF] Pottage | Meticillin-resistant Staphylococcus aureus is more resistant to vaporized hydrogen peroxide than commercial Geobacillus stearothermophilus biological indicators[END_REF]. However, previous studies had shown that with high hydrogen peroxide concentration and a sufficient contact time this bacterial defense can be overwhelmed [START_REF] Otter | Survival of nosocomial bacteria and spores on surfaces and inactivation by hydrogen peroxide vapor[END_REF][START_REF] Rios-Castillo | Bactericidal efficacy of hydrogen peroxide-based disinfectants against grampositive and gram-negative bacteria on stainless steel surfaces[END_REF]. Recently in our laboratory, the Xanthan foam described in this study was already successfully tested on different bacteria used in French standard NF T 72-194: Enterococcus hirae, Staphylococcus aureus, Salmonella typhimurium and Pseudomonas aeruginosa (data not shown). Moreover, the sporicidal capacity of this foam was checked on horizontal surface on Bacillus thuringiensis, Geobacillus stearothermophilus (biological indicator for biosafety level 3 decontamination) and Bacillus anthracis (biological weapon). The foam enabled to reduce more than 6 log of these spores in 30 min of contact time on horizontal coupons (data not shown). Therefore, in this paper we investigate the decontamination behavior of this new foam solution with coupons in a vertical position.

Firstly, the formulation impact on the decontamination efficiency had been validated by experiments on liquid solution. The surfactant agent (Glucopon) enables the generation of a foam with an appropriate generator. The use of a stabilizing agent (Xanthan) in the foam allows the achievement of a sufficient contact time for decontamination in vertical position and by filling [START_REF] Dame | Relations between physicochemical properties and instability of decontamination foams[END_REF]. Indeed, Dame et al. already showed the increase of a radiological decontamination foam stability and the duration of the wetting film on the wall. This effect is attributed to presence of Xanthan which delays the beginning of the drainage and after decreases the drainage kinetic. Moreover, our results proved that both products, Glucopon and Xanthan, have no negative impact on the decontamination efficiency of hydrogen peroxide. The comparison of results revealed that the disinfectant quantity in the foam with liquid fraction at 5.5%, is sufficient to obtain the same decontamination efficiency measured for the liquid solution. Thus, the wetting-film from a foam with a liquid fraction of average 5.5% is thick enough to wet the spore layer on the coupon to decontaminate. Furthermore, at this liquid fraction of the foam, only 5.5 L of liquid solution were needed to produce 100 L of foam. Therefore the quantity of effluent is also considerably reduced at the end of treatment compared to liquid solution treatment, for the same efficiency. Moreover, the Xanthan foam process is advantageous due to the sticking properties of the stabilizing agent in the foam. This one ensures a sufficient contact time in vertical position to neutralize all spores (spores reduction of 8 log for 45 min in this study). Thus, it is not necessary to apply the solution several times to ensure the manufacturer's recommended contact times for vertical decontamination (Environmental Protection Agency, 2010; [START_REF] Edmonds | Decontamination efficacy of three commercial-off-the-shelf (COTS) sporicidal disinfectants on mediumsized panels contaminated with surrogate spores of Bacillus anthracis[END_REF]. All these results in vertical position show that the foam could neutralized spores below 1 h and could be adapted to decontaminate rapidly sites where access is difficult, for example pipes, ceiling, walls with or without crevices, and areas behind equipment.

Most studies based on liquid and foam decontamination process were performed between 20 and 24 • C (293-297 K) [START_REF] Young | Mechanisms of killing of Bacillus subtilis spores by Decon and OxoneTM, two general decontaminants for biological agents[END_REF][START_REF] Ryan | Effect of inoculation method on the determination of decontamination efficacy against Bacillus spores[END_REF] or "room temperature" [START_REF] Rogers | Decontamination assessment of Bacillus anthracis, Bacillus subtilis, and Geobacillus stearothermophilus spores on indoor surfaces using a hydrogen peroxide gas generator[END_REF][START_REF] Eryilmaz | In vitro antimicrobial activity of three new generation disinfectants[END_REF]. For certain studies the experimental temperature has not been described [START_REF] Andersen | Decontamination of rooms, medical equipment and ambulances using an aerosol of hydrogen peroxide disinfectant[END_REF][START_REF] Gonzalez | Ability of cleaning-disinfecting wipes to remove bacteria from medical device surfaces[END_REF]. Whereas some papers advised to take this parameter into account for the evaluation of the decontamination efficiency [START_REF] Russell | Bacterial spores and chemical sporicidal agents[END_REF][START_REF] Edmonds | Decontamination efficacy of three commercial-off-the-shelf (COTS) sporicidal disinfectants on mediumsized panels contaminated with surrogate spores of Bacillus anthracis[END_REF]. The influence of temperature on the decontamination efficiency of our foam is studied. Indeed, this foam could be used at different temperatures especially for the decontamination of outdoor sites (4 • C = 277.15 K and 30 • C = 303.15 K). The results show the decontamination kinetic of our hydrogen peroxide foam increases with raising temperatures. This observation is coherent with another foam preparation containing sodium hypochlorite [START_REF] Guan | Influence of temperature and organic load on chemical disinfection of Geobacillus stearothermophilus spores, a surrogate for Bacillus anthracis[END_REF] and other works on liquid hydrogen peroxide on horizontal surface [START_REF] Hilgren | Inactivation of Bacillus anthracis spores by liquid biocides in the presence of food residue[END_REF]. However, to our knowledge, this is the first time that a foam containing hydrogen peroxide is studied at these temperatures and in vertical surface. At 30 • C the foam neutralized all bacterial spores after 25 min of contact time in a vertical position. However, the reaction inactivation kinetic is not linear with the increase of temperatures. At this temperature, the viscosity decrease speeds up and seems to produce a positive effect on the drainage inside the wetting film directly in contact with the spores. This effect enables the detachment of bacterial spores, which are neutralized inside the foam, as well as the disinfectant replenishment. This hydrodynamic effect is not found for liquid treatment, which is more static. This effect could explain the difference between foam and liquid solution efficiency when the temperature increases.

At 4 • C the foam did not enable complete decontamination of the surface in 25 min. As the foam reaction follows the Arrhenius law, the decontamination kinetic can be predicted at any temperature. Therefore, it is possible to adapt the contact time between the foam and the contamination. A contact time of 2h30 at 4 • C appears to be required to reach 8 log of reduction of spores. The adherent properties of the foam and the stabilizing agent ensure a sufficient wetting film thickness during this contact time. Thus, using the Arrhenius law, it is possible to adjust the contact time depending on the environmental temperature for the best use of the foam. For example, to decontaminate a vehicle in a garage, it is possible to calculate the contact time required, depending on the ambient temperature in different seasons [START_REF] Andersen | Decontamination of rooms, medical equipment and ambulances using an aerosol of hydrogen peroxide disinfectant[END_REF]. In conclusion, the temperature plays a role in decontamination efficiency kinetic and should be taken into account before carrying out the assays, especially to compare the efficiency of different products [START_REF] Wood | Efficacy of liquid spray decontaminants for inactivation of Bacillus anthracis spores on building and outdoor materials[END_REF].

In addition, this study demonstrated that bacterial spores were not only decontaminated on the coupon but also after being transferred inside the foam thanks to the wetting film. Previous studies have already discussed the complex issues of biological sampling and recovery from surfaces after testing [START_REF] Rastogi | Quantitative method to determine sporicidal decontamination of building surfaces by gaseous fumigants, and issues related to laboratory-scale studies[END_REF][START_REF] Tomasino | Use of alternative carrier materials in AOAC official method[END_REF][START_REF] Edmonds | Decontamination efficacy of three commercial-off-the-shelf (COTS) sporicidal disinfectants on mediumsized panels contaminated with surrogate spores of Bacillus anthracis[END_REF]. Tomasino et al. found that recovery from different materials ranged from approximately 20 to 70%. They studied the recovery from three different fractions. The first fraction remains on the sampling tool surfaces, i.e., tube. A second one was not retrieved, due to spore adhesion to the surface matrix. Finally, the third fraction corresponded to the spores retrieved from a coupon by sampling tools. These three fractions correspond well to those analyzed here by the recovery tests with and without coupons. However in our study, we measured also the amount of spores detached from the coupon and transferred within the foam. Even if there is a high rate of spore adhesion to the surface, the spore upper layer is transferred inside the foam by the wetting film. After 20 min, the fraction of spores transferred in the foam reached a maximum (Figure 2). However, all spores transferred into the foam are neutralized after 35 min with disinfectant. Finally, a recovery difference was also found between foam and liquid solutions. For the foam, the recovery is higher than the liquid solution. It would appear that the foam bubbles could facilitate the capture of hydrophobic spores, due to the attachment of the spores to the air-liquid interface. Consequently, the liquid effluents are safe after 35 min foam treatment, avoiding the contamination of other surfaces.

Major foam decontamination properties have been highlighted in this study. First, the formulation's stability, wetting, and hydrodynamic properties improve the decontamination effects on adherent spore. Secondly, the foam process allows to inactivate the transferred spores into the foam. Finally, the temperature plays a key role on the decontamination kinetic and should be taken into account to compare the efficiency of disinfectants. This process was developed in context of CBRN-E Defense sector because it could treat large and complex shape facilities in case of biological attack or accident. But it could be useful also for other applications i.e., hospital, food, as can be seen from the many articles published on this topic [START_REF] Benga | Survival of bacteria of laboratory animal origin on cage bedding and inactivation by hydrogen peroxide vapour[END_REF][START_REF] Mott | Comparison of sampling methods to recover germinated Bacillus anthracis and Bacillus thuringiensis endospores from surface coupons[END_REF][START_REF] Szabo | Decontamination of Bacillus spores adhered to iron and cement-mortar drinking water infrastructure in a model system using disinfectants[END_REF].

FIGURE 1 |

 1 FIGURE 1 | Step-by-step diagram of the foam and liquid solution decontamination method.

FIGURE 2 |

 2 FIGURE 2 | Mean log CFU (±SD) for tests without disinfectant (solution S5 in Table 1); foam form: (A) adherent on coupons ( ) and (B) transferred inside foam (=); liquid solution: (C) adherent on coupons ( ) and (D) transferred inside liquid solution (=), at various contact times and room temperature. CFU, colony forming units.

FIGURE 3 |

 3 FIGURE 3 | Spore survival adherent on coupon curves, at 293.15 K (20 • C) at different contact times. (A) Solution H 2 O 2 with Glucopon and Xanthan (S3) in liquid form (R 2 = 0.98) ( ). (B) Solution H 2 O 2 (S2) with Glucopon without Xanthan in liquid form (R 2 = 0.94) (X). (C) Solution H 2 O 2 without Glucopon and Xanthan (S1) in liquid form (R 2 = 0.96) ( ). Unbroken lines for first-order kinetics.

FIGURE 4 |

 4 FIGURE 4 | Spore survival adherent on coupon curves, at 293.15 K (20 • C) at different contact times. (A) Solution H 2 O 2 with Glucopon and Xanthan (S3) in foam form (R 2 = 0.98) ( ). (B) Solution H 2 O 2 with Glucopon and without Xanthan (S2) in foam form (R 2 = 0.96) (•). (C) Solution H 2 O 2 with Glucopon and Xanthan (S3) in liquid form (R 2 = 0.98) ( ). (D) Solution H 2 O 2 with Glucopon and without Xanthan (S2) in liquid form (R 2 = 0.94) (X). Unbroken lines for first-order kinetics for foam and broken lines for first-order kinetics for liquid solution.

FIGURE 5 |

 5 FIGURE 5 | Spore survival adherent on coupon curves, at different temperatures after 25 min of contact time. (A) Solution H 2 O 2 with Glucopon and Xanthan (S3) in foam form (X). (B) Solution H 2 O 2 with Glucopon and Xanthan (S3) in liquid form ( ) unbroken lines for foam and broken lines for liquid solution.

FIGURE 6 |

 6 FIGURE 6 | Effect of temperature on Arrhenius plots of the rate constant for spore inactivation. (A) Foam H 2 O 2 with Glucopon and Xanthan ( ). (B) Foam H 2 O 2 with Glucopon and without Xanthan (•). Unbroken lines for first-order kinetics for foam.

TABLE 1 |

 1 Tested solutions formulated with Hydrogen peroxide, Xanthan, and Glucopon 215 UP.

	Solution		Formula
	S1	12%	Hydrogen peroxide
	S2	12%	Hydrogen peroxide
		1.1%	Glucopon 215 UP
	S3	12%	Hydrogen peroxide
		1.1%	Glucopon 215 UP
		0.3%	Xanthan
	S4	1.1%	Glucopon 215 UP
	S5	1.1%	Glucopon 215 UP
		0.3%	Xanthan
	Values are presented in percentages (volume/volume for hydrogen peroxide et
	weight/volume for Glucopon and Xanthan).
	Disinfectant Solutions
	Five solutions were prepared with or without hydrogen peroxide
	at 12% (v/v) and with or without Xanthan 0.3% (w/v) (Sigma-
	Aldrich, St. Louis, Mo., United States), and Glucopon 215 UP
	commercial solution 1.1% (w/v) (BASF Canada Inc., Mississauga,
	Canada) respectively (

Table 1). Solutions

containing Glucopon 215UP (S2, S3, S4, and S5 in Table

TABLE 2 |

 2 The constant inactivation rate k for adherent spores on coupon, in accordance with different treatments at 293.15 K (20 • C).

	Treatment	Constant
		inactivation k
		(s -1 )
	Foam:H 2 O 2 with Glucopon and Xanthan (S3 in foam form)	0.1927
	Foam: H 2 O 2 with Glucopon and without Xanthan (S2 in	0.1848
	foam form)
	Liquid: H 2 O 2 with Glucopon and Xanthan (S3 in liquid form)	0.1715
	Liquid: H 2 O 2 with Glucopon and without Xanthan (S2 in	0.1427
	liquid form)
	Liquid: H 2 O 2 solution without Glucopon and without	0.1503
	Xanthan (S1)

Frontiers in Microbiology | www.frontiersin.org

September 2018 | Volume 9 | Article 2295

ACKNOWLEDGMENTS

We thank our lab members for helpful discussions.

FUNDING

This work was jointly funded by the inter-ministerial program of R&D against CBRNE risks and the Normandy Region.

AUTHOR CONTRIBUTIONS

ELT, FG, NO, and SF designed and supervised the study. ELT, FG, and SF designed the experiments. ELT performed the experiments. ELT, FG, and SF analyzed the data. ELT, FG, NO, and SF wrote the manuscript.

Conflict of Interest Statement:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.