G Gallardo

G Zanitti

M Higger

S Bouix

D Wassermann

Inferring the Localization of White-Matter Tracts using Diffusion Driven Label Fusion

Inferring which pathways are affected by a brain lesion is key for both pre and post-treatment planning. However, many disruptive lesions cause changes in the tissue that interrupt tractography algorithms. In such cases, aggregating information from healthy subjects can provide a solution to inferring the affected pathways. In this paper, we introduce a novel label fusion technique that leverages diffusion information to locate brain pathways. Through simulations and experiments in publicly available data we show that our method is able to correctly reconstruct brain pathways, even if they are affected by a focal lesion.

Introduction

Pathologies such as infiltrative tumors or focal lesions disrupt the structure of white matter, resulting in cognitive deficits. Depending on the type and severity of the pathology, fiber bundles can be displaced, infiltrated or directly interrupted [START_REF] Schonberg | Characterization of displaced white matter by brain tumors using combined DTI and fMRI[END_REF][START_REF] Huisman | Tumor-like lesions of the brain[END_REF][START_REF] Won | White Matter Change Revealed by Diffusion Tensor Imaging in Gliomas[END_REF]. Inferring which pathways are closely located to the lesion or being directly affected by it is key for palliative care, as well as pre and post-treatment planning. With this knowledge, neurologists and neurosurgeons can decide if a lesion should be treated more aggressively or conservatively [START_REF] Huisman | Tumor-like lesions of the brain[END_REF][START_REF] Mcgirt | Independent association of extent of resection with survival in patients with malignant brain astrocytoma[END_REF]. However, the most common method to reconstruct brain pathways, tractography, fails in the presence of brain lesions [START_REF] Jellison | Diffusion Tensor Imaging of Cerebral White Matter: A Pictorial Review of Physics, Fiber Tract Anatomy, and Tumor Imaging Patterns[END_REF]. Therefore, having a non-tracking method to locate brain pathways which is robust to lesions is key to successfully treat patients with disruptive brain lesions.

In the presence of a disruptive brain pathology, the directionality commonly present in a Diffusion Weighted Image (DWI) can be severely reduced [START_REF] Jellison | Diffusion Tensor Imaging of Cerebral White Matter: A Pictorial Review of Physics, Fiber Tract Anatomy, and Tumor Imaging Patterns[END_REF]. This is directly reflected as a decrease in the fractional anisotropy (FA) in the affected regions. Since tractography algorithms rely on directionality information in order to reconstruct tracts, areas with significantly decreased FA will hamper or completely stop the tracking. This impedes reconstructing tracts in the brain, and therefore detecting those being affected by the lesion [START_REF] Schonberg | Characterization of displaced white matter by brain tumors using combined DTI and fMRI[END_REF][START_REF] Jellison | Diffusion Tensor Imaging of Cerebral White Matter: A Pictorial Review of Physics, Fiber Tract Anatomy, and Tumor Imaging Patterns[END_REF]. In such cases where tracking is not feasible, one possible solution is to rely on information from healthy subjects. Assuming we identified major bundles in a group of healthy subjects, we can register them to our patient's brain and aggregate them to infer the affected pathways.

Label fusion is a family of techniques to infer a region's location in a target subject, based on its characteristics in a group of control subjects [START_REF] Asman | Non-local statistical label fusion for multi-atlas segmentation[END_REF]. One well known label fusion technique is Majority Voting [START_REF] Xu | Methods of Combining Multiple Classifiers and Their Applications to Handwriting Recognition[END_REF]. Given a voxel on a brain image, each template subject "votes" for a label. The resulting label for the voxel will be that with the most votes. Majority Voting is simple to implement and has been shown to generate accurate brain segmentations even when using few template subjects [START_REF] Asman | Non-local statistical label fusion for multi-atlas segmentation[END_REF]. Majority Voting weights the vote of each template subject equally, despite how (dis)similar they are from the target subject. However, among the templates there will be subjects more accurate in predicting a region's location, and those less accurate [START_REF] Rohlfing | Performance-based classifier combination in atlas-based image segmentation using expectation-maximization parameter estimation[END_REF]. Because of this, it has been proposed to weigh the vote of each template based on some similarity function with the target [START_REF] Sabuncu | A Generative Model for Image Segmentation Based on Label Fusion[END_REF]. The underlying intuition is that the label choice should be driven by those subjects who resemble the most to the one being labeled. The practical advantages of various strategies based on this idea have been demonstrated by Artaechevarria et al. [START_REF] Artaechevarria | Combination strategies in multi-atlas image segmentation: Application to brain MR data[END_REF].

In this work, we introduce the first label fusion technique that leverages diffusion data, as represented in DWI, to weights the vote of each template subject. Since the presence of a path constrains the diffusion of water particles, adding diffusion information can help to better delineate fiber bundles [START_REF] Girard | AxTract: Toward microstructure informed tractography[END_REF]. Particularly, we have subjects voting for the presence of a specific tract in a region. Our technique then weighs the votes based on how much the voted pathway is supported by the target's diffusion data (Fig. 1). In this way, we give higher weights to the voted pathways which directionality better agrees with the target's diffusion.

We validate our technique through simulations and experiments in publicly available data. First, we validate that our technique correctly weights votes using synthetic data. For this we generate three types of synthetic DWIs (phantoms) representing: a single fiber phantom, a 90 degrees fiber crossing phantom, and a phantom with no fibers. We generate tracts from the DWIs and test how our technique weighs them and their planar rotations on each phantom. We show that our technique assigns higher weights to the votes for tracts aligned with the DWI's diffusion. After, we randomly select 50 subjects from the Human Connectome Project (HCP) and reconstruct 6 major brain pathways on each of them. We use the reconstructed tracts as ground truth to benchmark the inferences made by our technique and Majority Voting on a leave-one-out cross-validation experiment. Our results show that our proposed technique has a lower sensitivity than Majority Voting, but a higher specificity. Meaning, our technique obtains less false positives at the cost of obtaining more true negatives. Finally, we simulate focal lesions with different degrees of severity in the white matter of one HCP subject. Particularly, we target a spherical region where the Superior Longitudinal Fasciculus passes by. We do so by iteratively decreasing the FA of each voxel in the spherical region, until obtaining isotropic diffusion. We show that, while a tractography-based reconstruction technique fails to reconstruct, our technique is able to identify the affected tract. Furthermore, our technique is always able to correctly label the voxels surrounding the lesion, while labeling less voxels within the lesion as it worsen. This helps not only to detect the affected tract, but also to know how much it is affected.

Methods

Majority Voting.

Let labels = {l i } be the set of labels representing tracts in the brain. Let L s , s ∈ S represent the labeling of a set of template subjects S, where each L s ∈ labels vx×vy×vz is a 3D volume with dimension (v x , v y , v z ) representing the labeling of template subject s. Majority Voting [START_REF] Rohlfing | Performance-based classifier combination in atlas-based image segmentation using expectation-maximization parameter estimation[END_REF] infers the label of each voxel x in a target subject by computing:

L * (x) = argmax l∈labels s∈S p(L(x) = l|L s (x)),
where

p(L(x) = l|L s (x)) =    1, if L s (x) = l 0, otherwise. (1)
In this case, each subject votes for a label, and the label with the most votes is assigned to the target voxel. It is important to notice that no information from the target subject is being used to infer the label L * (x).

Diffusion Based Voting

Majority Voting (Eq. 1) decides the label of a target voxel based on the "votes" of template subjects, without using any information from the target subject. However, when inferring the location of white matter pathways, we can profit from the fact that water molecules tend to diffuse in the direction of the pathways. This means that we can use diffusion information to weigh the voting process and help locate the bundles. In particular, votes for tracts aligned with the diffusion of the target subject should get higher weights.

One way to characterize the directionality on a diffusion weighted image (DWI) is by means of fiber orientation distribution functions (fODFs) [START_REF] Tuch | Q-ball imaging[END_REF]. Now, we will first explain how to estimate a fODF from both DWI and tracts. Then, we will show how to leverage them in order to compute weights for each vote.

Fiber Orientation Density Function from dMRI Data.

By fitting the diffusion information into a Constrained Spherical Deconvolution (CSD) model, it is possible to estimate a fiber orientation density function [START_REF] Tournier | Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution[END_REF] (fODF). The fiber ODF F x (θ, φ) represents the estimated fraction of fibers within the voxel x that are aligned along the direction (θ, φ), expressed in spherical coordinates.

Fiber Orientation Density Function from Tractography.

A tract can be described as a set of streamlines, where a streamline is a discretized 3-dimensional curve. Assuming that a streamline doesn't have sharp turns within a voxel, we can estimate its directionality by looking at the entry and exit points (Fig. 1 A). Repeating this for each streamline on a tract, we obtain a set of directional vectors, representing the directionality of the tract within the voxel. As with the diffusion data, we can once more use the CSD model to estimate an fODF representing the directionality of a tract in the voxel.

Label Fusion Weighted by Diffusion

Majority Voting (Eq. 1) decides the label of a voxel based on how many subjects "vote" for it. Given that we are inferring brain pathways, we want to introduce a weight that denotes how much the voted tract resembles the target's diffusion data:

L * (x) = argmax l∈labels s∈S p(L(x) = l|L s (x))p(D(x)|D sl (x)).
(2)

In our segmentation scheme, the term p(L(x) = l|L s (x)) is modeled as in the voting scheme (eq. 1). Our second term, p(D(x)|D sl (x)) express the probability of seeing the diffusion of our target subject, D(x), on voxel x, given the diffusion of subject s generated by tract l on the same voxel, D sl (x). Since registering DWIs is a highly time consuming task [START_REF] O'donnell | Advances in computational and statistical diffusion MRI[END_REF], we want to avoid it. Instead, we can register tracts, for which efficient algorithms exist, and use them as an estimator of the diffusion of each template subject. Knowing that water particles in the brain diffuse along tracts, we can estimate D sl (x) by computing the fODF of the registered tract l as explained in 2.2.2 . Simultaneously, we can characterize D(x) with the fODF computed from the DWI of the target subject as explained in 2.2.3. In order to reflect how much the fODF of our target subject's diffusion resembles the fODF of the voted tract on a voxel, we model p(D(x)|D sl (x)) as:

p(D(x)|D sl (x)) =              F (x), F sl (x) , if L s (x) = l,
and l = 0

F (x), U , if L s (x) = 0 0, otherwise (3)
where F (x) is the fiber ODF on voxel x estimated from the target's DWI, and is normalized such that F (x), F (x) = 1. F sl (x) is the fiber ODF of the tract l registered from subject s and normalized as F (x). U is a uniformly distributed fiber ODF, this is the diffusion assumed for either the label 'no-tract', representing the background or a gray matter structure. By computing the inner product between normalized ODFs, we can estimate how much they look alike. In this way, we weight the vote of each subject accounting for the white-matter structure of both the voting and target subjects.

Experiments and Results

In section 2 we presented how to add diffusion information to Majority Voting (Eq. 2). This allows us to weigh the vote for a tract by how much the diffusion of the target supports it. Now, we validate our technique using both synthetic data and subjects from the Human Connectome Project (HCP). We start by assessing our techniques correctly weighs votes using DWI phantoms. Then, we proceed to infer the location of white-matter pathways in subjects of the HCP, and compare them with their ground-truth as reconstructed with the white-matter query language (WMQL) [START_REF] Wassermann | The white matter query language: a novel approach for describing human white matter anatomy[END_REF]. Finally, we simulate a lesions in the white matter and test how our method behaves in its presence.

Data and Preprocessing

We created three types of diffusion weighted image phantoms using Phantomas [START_REF] Caruyer | Phantomas: a flexible software library to simulate diffusion MR phantoms[END_REF]. The first phantom possess only one tract, traveling from one side to the other of the image horizontally (Fig. 2 A). The second possess two crossing tracts, forming a 90 degrees angle between them (Fig. 2 B). The last has no fibers on it, representing isotropic diffusion (Fig. 2 C). From each phantom we generated 30 diffusion weighted images (DWIs). All the DWIs were generated using a signal to noise ratio (SNR) of 20, and a resolution of 1mm per voxel. The final images are 3-dimensional matrices with 10 voxels in each dimension. Having such small images allows us to test our label fusion on a controlled environment. We estimated fiber orientation distributions (FODs) in each voxels by means of constrained spherical deconvolution (CSD) [START_REF] Tournier | Robust determination of the fibre orientation distribution in diffusion MRI : Non-negativity constrained super-resolved spherical deconvolution[END_REF] using Dipy [START_REF] Garyfallidis | Dipy, a library for the analysis of diffusion MRI data[END_REF]. The fODFs were discretized on a sphere with n = 100 vertices. A uniform fODF, U , was created by assigning to each vertex of the sphere the value (n)/n, making U, U = 1.

To test our technique in more realistic scenarios, we randomly selected 50 subjects from the HCP500 dataset from the Human Connectome Project. For each subject, we first estimated FODs by means of CSD from they diffusion data. Then, we leveraged the FODs to perform whole-brain probabilistic tractography. For the tractography we used each voxel in the whitematter as a seed, and simulated 8 particles per seed [START_REF] Garyfallidis | Dipy, a library for the analysis of diffusion MRI data[END_REF]. Finally, we extracted four tracts from the left hemisphere using the implementation of the white-matter query language (WMQL) [START_REF] Wassermann | The white matter query language: a novel approach for describing human white matter anatomy[END_REF]. For each subject we computed non linear registrations to the rest using as reference their T1w images [START_REF] Jenkinson | Fsl[END_REF]. Using the resulting warp transformations, we registered the tracts between every pair of subjects.

Assessing the Correctness of Voting Weights in Synthetic Data

In order to study how the tract's directionality influences its vote weight, we started by reconstructing the tract present in the first phantom (Fig. 2 A). For this, we took one of the 30 generated DWIs, and computed 1000 streamlines by means of probabilistic tracking from the voxels through which the tract passes. If our technique behaves correctly, the tract we reconstructed should obtain a high vote weight in the DWIs derived from phantom A. At the same time, any change in its directionality, should decrease the received weight. To assess this, we computed weights in 30 DWIs for the reconstructed tract, and for planar rotations of it around the central voxel. Figure 3 A shows the obtained weights on the first phantom. Effectively, the weight starts to rapidly decrease as the angle increments and the directionality of the tract moves away from that of the diffusion.

Figure 3 B shows the weights obtained when computing weights of the reconstructed tract in 30 DWIs derived from the second phantom (Fig. 2 B), which have a fiber crossing in the central voxel. In this case, the weight is higher when the reconstructed tract aligns with one of the crossing fibers (at 0 degrees or 90 degrees), while rapidly decaying in between them. Finally, figure 3 C shows the weights when using 30 DWIs with isotropic diffusion (Fig. 2 C). In this case, the weight is always low, driven by the discrepancy between the directionality of the tract and the free diffusion present in the DWIs.

To assess that the proposed model is not over-weighing tracts, we also computed the weight that a "non-tract" label would receive in each of the phantoms. This is, when the user votes that there is no tract present in the voxel. As explained in section 2, equation 3, when a subject is voting for a non-tract label, a uniform fiber ODF is compared against the diffusion fODF. Figure 2 A, B, andC show the weight obtained in the central voxel when a subject is voting for the label "non-tract". In figure 2 A, we can see that the weight of "non-tract" is low, specially when compared with the high weight of the correctly aligned tracts (low angle rotations). This is driven by the highly directional underlying diffusion data of the phantom. Figure 2 B shows that the weight of a "non-tract" vote is similar to that of an aligned tract. Finally, figure 2 C shows always a higher weight for the "non-tract" than for any tract, consistent with the isotropic diffusion of our third phantom.

Inferring Tracts in Human Connectom Project Subjects

To validate our technique in a more realistic but still controlled scenario, we used our technique to infer the location of specific white-matter tracts in 50 HCP subjects. We selected the following tracts to work with: Inferior Fronto-Occipital Fascicle (IFOF), Corticospinal Tract (CST), Inferior Longitudinal Fasciculus (ILF), and Superior Longitudinal Fasciculus (SLF I, II, and III). These 6 tracts provide a fair diversity of directionality, shape, and position in the brain.

For each tract we performed a leave-one-out cross-validation experiment. At each step, we inferred the tract of one subject from the registered tracts of the others using both Majority Voting and our technique. Then, we quantified the performance of both techniques using as ground truth the target's bundle. In particular, we computed their confusion matrix. A confusion matrix is a matrix M ∈ R labels×labels , where each entry M ij represents the number of times the label in the ground truth was i and the technique labeled j. In this experiment, since we are only inferring one tract, we have two labels: tract and non-tract. We computed the sensitivity, and specificity of each confusion matrix [START_REF] Kuhn | Applied Predictive Modeling[END_REF]. Sensitivity measures the proportion of voxels in the ground-truth tract that were "discovered". Specificity measures the proportion of voxels that were correctly labeled, over all the labeled voxels. Table 1 shows the results obtained for each technique and tract. In all of the tracts, our technique shows on average a 5% a lower sensitivity than Majority Voting. This means that we label a smaller portion of the ground-truth bundle. On the other hand, our diffusion weighted label-fusion achieves on average a 13% higher specificity. Therefore, our technique is discovering less voxels, but those which are labeled can be trusted more.

Inferring Tracts in the Presence of Simulated Lesions

To test how our technique behaves on an injured brain, we simulated lesions at different degrees of severity in the white matter of one of our subjects. Given that some brain lesions directly affect Fractional Anisotropy (FA) [START_REF] Schonberg | Characterization of displaced white matter by brain tumors using combined DTI and fMRI[END_REF][START_REF] Huisman | Tumor-like lesions of the brain[END_REF], we simulated lesions by adding isotropic signal to a set of voxels, therefore lowering their FA. We targeted the SLF bundle, in order to compare how the labeling changes with lesion of different degrees. We did so by selecting a spherical region of 4mm where the SLF passes, and mixing the diffusion signal there with signal from the ventricles. Since the ventricles are regions filled with cerebrospinal fluid (CSF), their diffusion is approximately isotropic. In particular, for each voxel x in the affected region, we chose a voxel v in the ventricle and mixed their DWI signals, S(•), as follows:

S(x) = S(x)(1 -α) + S(v)α, α ∈ [0, 1], ( 4
)
where α manages the severity of the lesion. In this case, α = 0 represents healthy tissue, and α = 1 represents a total disruption of the white-matter, resulting in pure isotropic diffusion.

We created four datasets by setting α to 0.25, 0.5, 0.75 and 1. On each dataset we performed a whole-brain probabilistic tractography, and filtered the resulting streamlines using WMQL to reconstruct the SLF. We found that for the values of α = 0.75 and α = 1 WMQL failed to recover the SLF, since it was interrupted by the simulated lesion. Then, we used both majority voting and our technique to aggregate the SLF from the rest of the subjects. Since Majority Voting for all datasets. Moreover, both Majority Voting and our technique obtained a high overlap in the result for α = 0.25. However, our technique labeled less voxels within the lesion as the alpha value increased (making FA to decrease). This is a good behaviour, since by lowering the FA we make the diffusion more isotropic, loosing the underlying tract. In particular, for α = 1, our technique results in two disconnected sets of voxels being labeled as SLF. This is correct, because for α = 1 the diffusion is completely isotropic, meaning that the tract was interrupted. This behaviour allows not only to know which tract was affected, but also at which degree it is affected, informing if the tract is interrupted or not.

Discussion

In this work we presented a label-fusion technique that leverages diffusion information to better infer the location of brain pathways. Our technique allows to correctly locate white-matter pathways even in the presence of a lesion that disrupts tractography algorithms. Furthermore, being based on a label-fusion algorithm, our technique can achieve accurate segmentations even when the inference is made from few subjects [START_REF] Asman | Non-local statistical label fusion for multi-atlas segmentation[END_REF].

Our technique adds diffusion information in the process of label-fusion. Given that fiber bundles constrains the diffusion of water particles in the brain, our technique uses diffusion information to improve Majority Voting [START_REF] Xu | Methods of Combining Multiple Classifiers and Their Applications to Handwriting Recognition[END_REF]. More specifically, we weight each vote based on how the voted pathway is supported by the target's diffusion data. In this way, voted pathways that better resemble the white matter of the target subject obtain a higher weight. The weights come from comparing how much the diffusion fODF of our target subject's resembles the fODF of the voted tract on a voxel. In this way, we can compare the white-matter structure of our target subject with that of the voting subject, without having to register DWIs. Adding diffusion weights to Majority Voting, allowed us to profit from its robustness while improving the labeling of white-matter bundles, as shown by our results in synthetic data and subjects from the Human Connectome Project.

Our Technique Creates Weights Consistent With the Underlying Diffusion Data.

To assess that our technique correctly weighed votes, we created three different phantoms, and derived DWIs from them. The phantoms had: (A) a single bundle running straight, (B) a 90 degrees crossing bundles, and (C) no bundles. We reconstructed the tract in the phantom A, and computed the weights obtained by the tract and planar rotations of it in the 3 phantoms.

Our results show that our technique assigns high weights when the tract aligns with the bundles represented in the underlying diffusion data. Furthermore, when the directions differ by more than 10 degrees, the weight starts to drop rapidly. Our results also show that in the phantom C, where there is no bundle, the 'no-tract' vote receives a higher weight than any rotation. These results show that our technique is able to correctly weight each label based on diffusion directionality.

Our

Technique Shows Lower Sensitivity but Higher Specificity than Majority Voting.

To test our technique in realistic data, we registered tracts between different subjects of the HCP. Using these registered tracts, we inferred the position of individual tracts in each subject. Table 1 shows that in each inferred tract, our technique achieved on average a 13% higher specificity at the trade off of obtaining a 5% lower sensitivity. Hence, our techniques presents less false positives at the cost of more false negatives, making it more conservative than Majority Voting. Furthermore, our specificity is always higher than 0.7. This means that our technique was able to discover less voxels belonging to the tracts, but at least 70% of those labeled are correct.

Our Technique Allows to Infers Which Tract is Affected by a Focal Lesion, and How Affected the Area Is

We further characterized the behaviour of our technique by simulating non-deforming lesions in the white-matter of a HCP subject. Particularly, we defined a spherical region on the path of the Superior Longitudinal Fasciculus, and increased its Fractional Anisotropy until achieving isotropic diffusion. In doing so, we effectively simulated a focal lesions ranging from an infiltration to the interruption of a tract. Under these common scenarios in which the diffusion data is affected, reconstruction techniques such as WMQL are not able to recover the tract. This is because, as the diffusion data losses directionality, the tracking becomes more and more hampered. Indeed, in our experiment WMQL was not able to dissect the affect SLF, since the process of tractography was stopped by the lesion. On the other hand, both majority voting and our technique were able to correctly label the affected tract. However, as shown by our results (Figure 4), only our technique was able to label less voxels as the tract became more interrupted. This is the expected behaviour in the presence of a lesion, since the more damaged an area is, the less it is expected for the tract to be present. When the tract is completely interrupted, our technique is still able to label the voxels surrounding the lesions, thus enabling to detect the affected tract. Therefore, our technique not only allows to detect the affected tracts, but also gives information on how altered the tract is.

Conclusions

We presented a label fusion technique that leverages diffusion data to infer the localization of white-matter tracts. The results show that our technique is well suited to create subject specific segmentation of the brain. Our method could be use in specificity medicine to interrogate diffuse pathologies like TBI, even in the presence of small lesions (as shown in fig. 4). Our technique could be used in the study of infiltrative brain tumors, where registration is less of a problem, and in the future, could be extended to larger tumors, due to the growing advances in registration based on tumor growth models.

Figure 1 :

 1 Figure 1: We use a label fusion technique to infer the location of white matter bundles by aggregating information of healthy subjects. After registering the tracts, each subject "votes" for either a tract or a non-tract structure (gray matter or background). Our technique adds diffusion based weights to each one of these votes. The weights are computed based on the similarity between the fiber Orientation Distribution Function of the structure being voted and the DWI of the target subject.

Figure 2 :

 2 Figure 2: In order to test our technique, we created three types of synthetic DWIs, known as phantoms. (A) A phantom with only one tract in the white matter. (B) A phantom with two fibers crossing. (C) A phantom with no tracts, representing isotropic diffusion.

Figure 3 :

 3 Figure 3: In order to study how a tract's directionality influences its vote weight, we estimated the fiber bundle by means of tractography in the Phantom A. Then, we computed the weights obtained by the tract and planar rotations of it in: (A) Phantom A. (B) Phantom B. (C) Phantom C. The figures show that our technique gives the highest weights to structures that are aligned with the underlying diffusion.

Figure 4 :

 4 Figure 4: We tested how our technique behaves in the presence of simulated lesions. Lesions were simulated in a specific region (red circle) by following eq. 4 to lower the FA of the region. The SLF passes through such a region. The figures show the result of applying our technique in order to determine the SLF at different values of the parameter α in eq. 4: (A) α = 0.2, (B) α = 0.5, (C) α = 0.75, and (D) α = 1. Results show that while the value of α increases, the amount of voxels labeled within the affected region decreases.

Table 1 :

 1 Sensitivity and specificity of our proposed method (Weighted) and a non-weighted voted (Majority) when inferring single bundles from 9 subjects. The inferred bundles are: Superior Longitudinal Fasciculus (SLF) I, II and III, Inferior Longitudinal Fasciculus (ILF), Cortico Spinal Tract (CST), and Inferior Occipito-Frontal Fascicle (IOFF).

		Sensitivity	Specificity
		Weighted	Majority	Weighted	Majority
	IOFF	0.10 (0.04) 0.13 (0.04) 0.71 (0.15) 0.55 (0.15)
	CST	0.38 (0.03) 0.42 (0.03) 0.80 (0.04) 0.70 (0.04)
	ILF	0.22 (0.01) 0.27 (0.02) 0.77 (0.04) 0.63 (0.04)
	SLF I	0.19 (0.01) 0.27 (0.01) 0.80 (0.04) 0.66 (0.05)
	SLF II	0.23 (0.01) 0.31 (0.01) 0.82 (0.04) 0.68 (0.04)
	SLF III 0.11 (0.01) 0.17 (0.02) 0.71 (0.04) 0.58 (0.05)


Sergine Even

Lucie Rault

Pierre-Alexandre Lévêque

Sarah Barbey

Frederic Launay

Hélène Larroque

Yves Le Loir

Pierre Germon

Jocelyne Guinard-Flament

Bovine mammary gland microbiota et immune response

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Bovine mammary gland microbiota et immune response

Sergine Even 1 (sergine.even@inrae.fr), Lucie Rault 1 , Pierre-Alexandre Lévêque 1,2 , Sarah Barbey 3 , Frederic Launay 3 , Hélène Larroque 4 , Yves Le Loir 1 , Pierre Germon 5 , Jocelyne Guinard-Flament 2

Introduction and aims

Bovine mastitis is an inflammation of the mammary gland generally due to an infection. It is responsible for considerable economic losses in dairy farms. Preventive and curative strategies that mainly rely on antibiotic therapies are not totally effective and contribute to antibiotic resistance dissemination, prompting the need for alternative or complementary strategies. We previously established a link between teat cistern microbiota composition and bovine mastitis in quarters which had different histories regarding mastitis [1]. In this study, to further decipher the relationships between teat cistern microbiota and immune and microbial responses, a switch from twice-to once-daily milking (ODM) was used to trigger an udder perturbation.

Material and methods

A switch to ODM was used in 31 initially healthy quarters of dairy cows. Immune and microbial responses including determination of teat microbiota were monitored just prior to the transition (day 0), and 3 and 14 days following transition to ODM.

Results and discussion

A temporal relationship was reported between initial teat cistern microbiota composition and richness, the immune response to ODM, and mastitis development. Quarters with a low initial microbiota richness and taxonomic markers such as Bacteroidetes and Proteobacteria were associated with a higher rate of mastitis during ODM. Quarters with a higher richness and taxonomic markers such as Firmicutes, Bifidobacterium and Corynebacterium displayed early inflammation following transition to ODM but without developing mastitis (no infection). Short-term evolution of microbiota indicates that microbiota with a higher initial richness were more strongly altered by transition to ODM, with notably the disappearance of rare OTUs. Microbiota modifications were associated with an early innate immune system stimulation, which, in turn, may have contributed to the prevention of mastitis development [2]. These results suggest a role of the bovine teat microbiota composition and richness in the immune response of the mammary gland during perturbations such as transition to ODM or pathogen entrance. They invite us to consider strategies that can preserve teat microbiota diversity and taxa associated to a healthy status for the design of next-generation probiotics. Key words: mastitis, mammary gland microbiota, immune response

  1-Falentin H, Rault L, Nicolas A, Bouchard DS, Lassalas J,Lamberton P, et al. 2016. Bovine Teat Microbiome Analysis Revealed Reduced Alpha Diversity and Significant Changes in Taxonomic Profiles in Quarters with a History of Mastitis. Front Microbiol. 7:480. 2-Rault L, Lévêque P-A, Barbey S, Launay F, Larroque H, Le Loir Y, et al. 2020. Bovine Teat Cistern Microbiota Composition and Richness Are Associated With the Immune and Microbial Responses During Transition to Once-Daily Milking. Front Microbiol.11:602404.


domain: chim sdv

text:
Hippolyte Durand

Isabelle Baussanne

Martine Demeunynck

Jasmine Viger-Gravel

Lyndon Emsley

Michel Bardet

Elisa Zeno

Naceur Belgacem

Julien Bras

Jasmine Vigier-Gravel

Two-step immobilization of metronidazole prodrug on TEMPO cellulose nanofibrils through thiol-yne click chemistry for in situ controlled release

Keywords: Cellulose nanofibrils, drug release, click chemistry, DNP-NMR

Introduction

Among cellulosic nanomaterials, cellulose nanofibrils (CNF) are considered as one of the best biosourced starting platform material for the development of unique systems. The tremendous enthusiasm in the scientific community for this material arises from the general characteristics of cellulose nanomaterials such as widespread availability, biodegradability, biocompatibility, excellent mechanical properties and tunable surface chemistry [START_REF] Kargarzadeh | Advances in cellulose nanomaterials[END_REF]. Today, such CNF can be used in several and various applications ( i.e. paper and packaging [START_REF] Aulin | Oxygen and oil barrier properties of microfibrillated cellulose films and coatings[END_REF][START_REF] Bardet | Cellulose Nanofibers and Their Use in Paper Industry[END_REF][START_REF] Boufi | Nanofibrillated cellulose as an additive in papermaking process: A review[END_REF][START_REF] Lavoine | Antibacterial paperboard packaging using microfibrillated cellulose[END_REF], electronics [START_REF] Hoeng | Use of nanocellulose in printed electronics: A review[END_REF], composites [START_REF] Dufresne | Biopolymer Nanocomposites: Processing, Properties, and Applications[END_REF] medical and cosmetics [START_REF] Halib | Potential Applications of Nanocellulose-Containing Materials in the Biomedical Field[END_REF][START_REF] Jorfi | Recent advances in nanocellulose for biomedical applications[END_REF][START_REF] Laurén | fi%2Fbitstrea m%2[END_REF][START_REF] Lin | Nanocellulose in biomedicine: Current status and future prospect[END_REF] industries) as reinforcement agent, rheology modifier or nanostructured networks and membranes. Among identified CNF grades, TEMPO oxidized CNF (CNF-t) has enhanced features such as its chemical reactivity together with its specific rheological properties, both explained by the presence of carboxylic acid and aldehydes moieties along the cellulose nanofibers.

Industrial production of CNF-t is under development in different places of the globe. Pioneer research investigations on TEMPO oxidation of cellulose by the group of Professor Akira Isogai in Japan [START_REF] Isogai | TEMPO-oxidized cellulose nanofibers[END_REF][START_REF] Saito | Homogeneous Suspensions of Individualized Microfibrils from TEMPO-Catalyzed Oxidation of Native Cellulose[END_REF] led to the apparition of CNF-t production facilities while in Europe and North America, small companies are starting to sell CNF-t. The growing production facilities come along with novel and promising applications of CNF-t such as the biomedical field. A couple of reviews deal with the use of CNF-t (together with other cellulose nanomaterials) for biomedical application and describe the potential of this material for the design of new innovative healthcare systems [START_REF] Du | Cellulose nanocrystals and cellulose nanofibrils based hydrogels for biomedical applications[END_REF][START_REF] Jorfi | Recent advances in nanocellulose for biomedical applications[END_REF][START_REF] Lin | Nanocellulose in biomedicine: Current status and future prospect[END_REF][START_REF] Syverud | SciFinder-Potential of cellulose nanofibrils in tissue engineering-ACS abstract[END_REF]. CNF-t draws specific attention since it is possible to produce it in an ultrapure form with low endotoxin content making them suitable for wound healing when freeze-dried into aerogels: low cytotoxicity was also confirmed in addition with really high water holding capacity [START_REF] Nordli | Producing ultrapure wood cellulose nanofibrils and evaluating the cytotoxicity using human skin cells[END_REF]. CNF-t were also investigated to be used as drug carriers. The ability to deliver Ibuprofen through the skin from CNF-t-Ibuprofen gel formulations was assessed in-vitro and in-vivo. CNF-t systems were able to match with commercial references while including five times lower drug loading proving a more efficient and optimized use of drug [START_REF] Celebi | Ibuprofen delivery into and through the skin from novel oxidized cellulose-based gels and conventional topical formulations[END_REF]. Aerogels of different kinds of cellulose nanofibrils suspensions mixed with beclomethasone dipropionate (BDP) nanoparticle coated with hydrophobin proteins were also produced through freeze drying. CNF-t based systems showed a sustained drug release. The CNF three-dimensional structure was tunable by varying the freeze drying parameters allowing for a controlled release of the drug [START_REF] Valo | Drug release from nanoparticles embedded in four different nanofibrillar cellulose aerogels[END_REF].

The antibacterial metronidazole is used to fight diseases concerning different organs and especially in gastrointestinal tract and reproductive system, mainly against anaerobic micro-organisms. Its mechanism of action involves the penetration into the anaerobic bacteria, its chemical transformation (reduction) by proteins to an active product that will cleave DNA strands, and thereby inhibits the replication mechanism thus preventing cell growth (Metronidazole, n.d.; Pubchem, n.d.). Since the 1980's, metronidazole has been successfully used with cellulose derivatives tableting compounds such as hydroxypropyl methyl cellulose (Campos-Aldrete & Villafuerte-Robles, 1997), methyl cellulose [START_REF] Itiola | Tableting characteristics of metronidazole formulations[END_REF] and cellulose acetate phthalate [START_REF] Gates | A New Bioerodible Polymer Insert for the Controlled Release of Metronidazole[END_REF]. Up to our knowledge, only a very few publications deal with the use of CNF-t and metronidazole. CNF-t hydrogels were used as matrix for encapsulation of 6 different active principle ingredients, including metronidazole. Researchers investigated the effect of freeze drying and subsequent rehydration on rheological properties and the drug release profiles. Results suggested that the CNF-t hydrogels were successfully rehydrated and release profiles were equivalent, before and after freeze drying, confirming their potential for controlled release applications [START_REF] Paukkonen | Nanofibrillar cellulose hydrogels and reconstructed hydrogels as matrices for controlled drug release[END_REF]. These uses of metronidazole relied only on physical adsorption of the drug onto the cellulosic substrates. Micro and nano-sized three dimensions structures of the developed systems allowed for a diffusion-controlled release mechanism.

The purpose of this work is to prepare an enhanced CNF based drug vehicle that can be integrated in innovative implantable medical devices with controlled drug release properties. This requires a complementary anchoring strategy of the drug to the cellulosic substrates in order to achieve in situ controlled drug release. For this purpose, metronidazole was chosen as drug model as it offers two advantages. First, its chemical versatility with the pending hydroxyl group makes easy to design a new prodrug that will contain a cleavable ester linker necessary to obtain the in situ release, and a reactive thiol end-group for anchoring to the CNF. Secondly, as mentioned already, metronidazole is of first choice for anaerobic conditions, those that are met in the targeted implantation site. The presence of ester link will allow the liberation of the drug by ester-specific enzymes (present in fat tissues and on infection sites [START_REF] Schakenraad | Enzymatic activity toward poly(L-lactic acid) implants[END_REF]) on the targeted site of treatment.

On the CNF side, efficient chemical modification is required to bind the end-group of the prodrug. It should be noted that surface modification of CNF is still an intense and challenging field of research.

The very large specific area of CNF, together with their high amounts of reactive hydroxyls (along with carboxylic acids and aldehydes groups in the case of CNF-t) lead to a wide range of strategies for surface modifications. Reactions such as etherification, esterification, silylation and amidation have been performed to covalently bind small molecules or polymer chains to CNF as described in relevant reviews [START_REF] Habibi | Key advances in the chemical modification of nanocelluloses[END_REF][START_REF] Missoum | Nanofibrillated Cellulose Surface Modification: A Review[END_REF][START_REF] Rol | Recent advances in surface-modified cellulose nanofibrils[END_REF]. Characterization of resulting modified CNF substrates is often challenging and calls for cross characterizations, covering both chemical and physical approaches, and also functionality evaluation. The use of sustainable materials such as CNF goes hand in hand with the increasing need for low-environmental impact processes and green chemistry procedures for CNF surface functionalization. In this context, click chemistry is of particular interest. Sharpless et al. introduced in 2001 the concept of click chemistry that gathers reactions that are efficient, stereospecific, modular, requiring simple conditions (not sensible to oxygen and water), and results quickly in very high yields while involved reagents must be readily available [START_REF] Kolb | Click Chemistry: Diverse Chemical Function from a Few Good Reactions[END_REF]. Click chemistry was seldom used to modify cellulose nanofibrils. CuAAC and thiol-ene click chemistry were applied to CNF films in order to immobilize fluorescent compounds [START_REF] Navarro | Multicolor Fluorescent Labeling of Cellulose Nanofibrils by Click Chemistry[END_REF][START_REF] Pahimanolis | Surface functionalization of nanofibrillated cellulose using click-chemistry approach in aqueous media[END_REF]. So far, only two publications mention the use of thiol-yne click chemistry with CNF. These researcher's aim was to tailor the wettability of CNF films surface to develop fluidic channels for biosensing [START_REF] Guo | Micro-patterns on nanocellulose films and paper by photo-induced thiol-yne click coupling: A facile method toward wetting with spatial resolution[END_REF][START_REF] Solin | Two-Dimensional Antifouling Fluidic Channels on Nanopapers for Biosensing[END_REF]. In the present work, CNF was modified with a two-step chemical strategy: in the first part an alkyne group was introduced through amidation, while in the second step, the thiol-yne chemistry was used to bind the prodrug to the intermediate alkyne-CNF, as described in Figure 1.

To the best of our knowledge, this work constitutes the first example of such a sophisticated strategy towards active CNF based materials in situ release. Furthermore, the use of dynamic nuclear polarization NMR (DNP-NMR), a recent hyperpolarization technique that allows enhancing the NMR signal sensitivity by several orders of magnitude, was the ultimate tool, for the second time for our team [START_REF] Kumar | The surface chemistry of a nanocellulose drug carrier unravelled by MAS-DNP[END_REF], to confirm the success of the chemical functionalization applied to cellulose nanofibrils. Its unique sensitivity allows the identification and quantification of any trace of compound, thus overcoming the challenging modified CNF characterization.

Experimental procedure

Materials

The cellulose nanofibrils (CNF) suspensions were provided by the Centre Technique du Papier (CTP, Grenoble, France). A first suspension referred as CNF-e was produced by a 2h enzymatic pre-treatment of a pre-refined (40°SR) bleached birch pulp followed by homogenization: 3 passes at 1500 bars in an Ariete homogenizer from GEA. The second suspension, which is referred as CNF-t, was also produced by the Centre Technique du Papier (CTP, Grenoble, France). The TEMPO mediated oxidation was performed on a pre-refined (40°SR) bleached bisulfite pulp provided by TEMBEC following classical procedure developed by A. Isogai's team in the end of 2000s [START_REF] Isogai | TEMPO-oxidized cellulose nanofibers[END_REF][START_REF] Saito | Homogeneous Suspensions of Individualized Microfibrils from TEMPO-Catalyzed Oxidation of Native Cellulose[END_REF].

The cellulose fiber pulp concentration was set at 1.5 wt% and the pre-treatment was done at pH 10 for 2h and involved NaBr, NaClO and the TEMPO reagent. The oxidized pulp was then subjected to the high pressure homogenizer (GEA Niro Soavi) to produce the CNF-t suspension. (7-oxyl-3,11-dioxa-7-azadispiro[5.1.5.3] (2,5,8,11-tetraoxatridecan-13-ylamino)}-[3,11-dioxa-7-azadispiro[5.1.5.3]hexadec-7-yl])oxidanyl (AMUpol) was obtained from ICR (Aix-Marseille University, UMR7273, France). Deionized water was used for every experiment. Carboxylesterase 2 human (expressed in baculovirus infected BTI insect cells) was purchased from Sigma Aldrich and used as received. Tris(hydroxymethyl) aminomethane (TRIS, >99.8% CAS: 77-86-1) was purchased from Euromedex.

hexadec-15-yl)carbamoyl][2-

Alkynation of CNF-t through amidation

The CNF-t suspension concentration was decreased from 1.5wt% to 0.4wt% in order to be easily stirrable. Deionized water was added before homogenization with an IKA Ultra-Turrax high shear mixer (China) for 1 minute at 10 000 rpm. The pH of the suspension was then adjusted to 4 under magnetic stirring using a 0.5 M HCl solution.

dissolution the solution was added to the suspension of CNF-t. A molar ratio of 4 equivalents of EDC and NHS for 1 equivalent of carboxyl group of CNF-t was used. The mixture was magnetically stirred for 30 min at room temperature in order to activate the carboxyl groups of the CNF-t. The pH was maintained at 4 during the reaction with 0.5M HCl or NaOH solution droplets addition. This pH favors the EDC carbocation availability and acid form of the carboxyl groups that are both required for a better reaction.

The pH was then increased to 8.5 for the second part of the reaction i.e. the amine addition. A solution of propargyl amine was prepared in deionized water and added to the mixture. Again, a molar ratio of 4 equivalents for 1 equivalent of carboxyl groups of CNF-t was used. The mixture was magnetically stirred for 72h at room temperature and the pH was kept at 8.5 with 0.5M HCl or NaOH solution droplets addition.

After 72h of reaction, the mixture was washed by centrifugation and dialysis. First, the reaction was quenched by decreasing the pH to 2-2.5 with 0.5M HCl solution. Then, centrifugation -re-dispersion cycles were applied to the suspension: centrifugations were operated during 10 minutes at 20 000 g (about 11 100 rpm) and re-dispersions were done in acidic water (pH 2-2.5) in order to remove all the non-covalently bound chemicals (EDC, NHS and free amine). In between each centrifugation cycle, redispersions were done using high shear mixer (Ultra-turrax, IKA) for 1 min. A total of 6 centrifugation -re-dispersion operations were performed to ultimately isolate the alkyne modified CNF-t, referred as CNF-yne. The last dispersion was done in neutral water.

The last step of purification consisted in a dialysis of the CNF-yne suspension against neutral water with 6-8 kDA MWCO membranes (Spectra/Por® 1 Standard RC Tubing, SPECTRUM) for at least 5 days under slow magnetic stirring and renewal of the medium twice a day. The prodrug approach is a new way to investigate drug anchoring strategy to CNF. A specific prodrug need to be designed. S-Trityl-3-mercaptopropionic acid (1) was synthetized according to a procedure designed by Sharma et al [START_REF] Sharma | Glucose-Based Amphiphilic Telomers Designed to Keep Membrane Proteins Soluble in Aqueous Solutions: Synthesis and Physicochemical Characterization[END_REF]. This product 1 (1.05 g, 3 mmol), metronidazole 2 (467 mg, 2.73 mmol) and DMAP (24 mg, 0.2 mmol) were dissolved in 30 ml of CH2Cl2 at 0°C. DCC (618 mg, 3 mmol) was added in the solution after 15 minutes. The reacting mixture was stirred during 3 h at room temperature, then filtered and concentrated under vacuum. The crude product was purified by flash chromatography on silica gel with CH2Cl2 as eluent to give the protected compound as a white solid (1.15 g, 2.3 mmol, 84 %). The tritylated compound was dissolved at 0°C in 30 ml of CH2Cl2 and 15 ml of TFA. After 10 minutes, TiPS (1 ml, 4.87 mmol, 2 equiv.) was added to the solution that was warmed up to room temperature and stirred for 1 h. The solution was concentrated under vacuum and the TFA was co-evaporated twice with methanol. The residue was washed three times with cold

Synthesis of Metro-SH compound

Immobilization of Metro-SH on CNF substrates through thio-yne click chemistry

The prodrug metro-SH 3 (62.5 mg, 0.25 mmol) was dissolved in a 15 g mixture of deionized water and ethanol (50:50 v/v ratio). To this solution, 5 ml of deionized water containing a 5% molar ratio relative to the thiol groups of 3 of tris-(2-carboxyethyl)phosphine (TCEP) (3.1mg, 0.0125 mmol), was added to prevent the air oxidation of the thiol into disulfure, and lithium phenyl(2,4,6trimethylbenzoyl)phosphinate (LAP), a biocompatible photoinitiator required to activate the thiol-yne click reaction, was introduced at a quantity of 0.01wt% relative to the CNF-yne mass (0.02mg, 6.8E -5 mmol). Then the resulting mixture was added to the CNF-yne suspension. The whole mixture was transferred to a UV transparent two necked balloon and put under magnetic stirring. The suspension was exposed to UV radiation with a UV lamp (Fire Edge™ FE300, Phoseon Technology USA, wavelength 345-385nm) and a nitrogen flux was used to remove the dioxygen from the free volume of the balloon.

The UV-exposition and nitrogen flux were maintained for 4 h. The modified CNF (CNF-Metro), was purified by several centrifugation -re-dispersion steps as described before: three steps of washing with water/ethanol mixture (50/50 v/v) and two steps with deionized water only. Washed suspensions were further purified by dialysis against deionized water under slow magnetic stirring for 5 days with daily renewal of dialysis medium in order to completely remove non-covalently bound compounds.

Dialysis membranes were 6-8 kDA MWCO membranes (Spectra/Por® 1 Standard RC Tubing, SPECTRUM). CNF-Metro suspensions were stored in the fridge at 5°C before characterization. The corresponding CNF films were produced by solvent casting in Teflon molds and let dry overnight in an oven at 40°C, these films were used for solid state characterization.

Characterization methods and tools

Atomic Force Microscopy

AFM images were recorded on a Dimension icon® (Bruker, USA). A 7,5.10 -4 wt% suspension was prepared by several dilution of the gel using high shear mixer Ultra-Turrax (IKA). A drop of this suspension was deposited on freshly cleaved mica plate before drying overnight under fumehood at room temperature. The acquisition was performed in tapping mode using a silica coated cantilever (OTESPA® 300 kHz -42 N/m, Bruker, USA). Zones of 3,3*3,3 µm² were analyzed.

FTIR

FTIR spectra of the films were obtained on a Perkin Elmer Spectrum One spectrometer (Waltham, Massachusetts, USA) in attenuated total reflectance (ATR) mode. At least 5 measurements of 16 scans with a resolution of 2cm -1 between 600 and 4000 cm -1 on each side of the CNF films were performed.

Spectra were normalized at 1110 cm -1 , the approximate wavenumber of C-O-C bonds in cellulosic substrates. The most representative spectra were chosen for discussion.

RAMAN

Raman spectra were recorded on a Renishaw (INVIA, UK) spectrometer equipped with a 1200 lines/mm grating and a CCD detector. Excitation wavelength was 785 nm and the beam power was adjusted to avoid sample degradation. The incident beam was focused on the samples through an x50 ultra-long working distance objective which resulted in a spot size of an approximate diameter of 2 µm. The spectra were recorded between 0 and 3600 cm -1 .

Conductometric titration and DO/DS calculation

The carboxylic content of the CNF-t suspension was measured before and after the first step of The carboxylic group content Xox on CNF-t can be calculated with equation ( 1) and is expressed in micro-mole of carboxylic group per gram of dry CNF (µmol/g).

(1)

X !" = C × (V #$% -V #$& ) m
The (

) DO = 162 × C × (V #$% -V #$& ) m -36 × C × (V #$% -V #$& ) 2
The value of 162 (g/mol) is the molar mass of the AGU. The value 36 (g/mol) is the difference between the molar mass of the carboxylate form of the carboxylic groups including the sodium counter ion (198 g/mol) and the molar mass of the AGU (162 g/mol). This term arises from the partial replacement of primary hydroxyl groups by carboxylate groups during the TEMPO mediated oxidation process.

All titrations were repeated at least three times.

Elemental analysis

CNF films were prepared by solvent casting from CNF suspensions. The suspensions were poured into Teflon molds and evaporated overnight in an oven at 40°C. Elemental Analysis was performed on a vario Micro Cube device from Elementar. Carbon, Hydrogen, Nitrogen, Sulfur and Oxygen mass proportion of CNF films were measured. Films pieces of 4 to 7 mg were weighted on a micro-balance.

An average of four measurements was made for each sample.

Conventional NMR analyses

Liquid 1 H and 13 C NMR analyses of the new prodrug were performed at ICMG (FR2607) Chemistry

Nanobio Platform, Grenoble. The results are detailed in SI.

Solid state 13 C nuclear magnetic resonance ( 13 C ssNMR) analyses were performed at the « Institute for Nanoscience and Cryogenics (INAC) » in the «French Alternative Energies and Atomic Energy Commission (CEA) » at Grenoble, on a Bruker AVANCE400 spectrometer. Acquisition, data treatment and peaks deconvolution were done using the LINUX TopSpin 3.2 software. Samples were placed in 4 mm ZrO2 rotors. All spectra were recorded using a combination of cross-polarization (CP), high power proton decoupling and magic angle spinning (CP/MAS). 13 C NMR spectra were acquired at 298 K, with a 4 mm probe operating at 100.13 MHz. The chemical shift values were measured with respect to TMS via glycine as a secondary reference with the carbonyl signal set to 176.03 ppm. MAS was performed at 14 kHz. The number of scans was 15 000 with a recycle delay of 2 s and CP time of 1.5 ms.

Dynamic Nuclear Polarization -NMR (DNP-NMR)

DNP experiments were performed on a 263 GHz/400 MHz AVANCE III Bruker DNP system at the « École Polytechnique Fédérale de Lausanne (EPFL) ». The spectrometer is equipped with a low temperature MAS probe and a 263 GHz gyrotron capable of outputting ca. 5-10 W of CW microwaves. The probe was configured in double mode 1 H/ 13 C. The sweep coil of the main magnetic field was optimized so that microwave irradiation gave the maximum positive proton DNP enhancement for AMUPol (a biradical polarizing agent). Proton and carbon DNP enhancements were determined by comparing the intensity of their respective spectra acquired with and without microwave irradiation. For DNP experiments, 30 mg of sample is impregnated with 16 μl of 10 mM AMUPol in D2O/H2O (9/1 v/v). The DNP sample is then packed in a 3.2 mm sapphire rotor and capped with a Teflon plug and zirconia cap.

The filled DNP rotor was then spun at room temperature in the spinning station up to 12.5 kHz before being inserted into the pre-cooled (ca. 100 K) 3.2 mm low temperature MAS NMR probe, where the sample is frozen within a few seconds.

For 13 C NMR experiments, the recycle delays were 3 or 4 s. The 1 H π /2 pulse length used for the variable amplitude CP experiments was 2.5 μs to afford 100 kHz 1 H decoupling using SPINAL-64 [START_REF] Fung | An Improved Broadband Decoupling Sequence for Liquid Crystals and Solids[END_REF]. The contact time was typically 5 ms. The MAS frequency used is 12.5 kHz. [START_REF] Cadars | The refocused INADEQUATE MAS NMR experiment in multiple spin-systems: Interpreting observed correlation peaks and optimising lineshapes[END_REF][START_REF] Lesage | Through-Bond Carbon-Carbon Connectivities in Disordered Solids by NMR[END_REF]. Tau delay, synchronized with the rotation, was optimized and set to 4 ms. The number of scans was set to 64 and the number of experiments in the indirect dimension to 128 and the recycling delay to 3s leading to an experiment time in the range of 8 h.

Drug release in enzymatic medium

In order to confirm the controlled drug activation, the enzymatic release of metronidazole was assessed from the suspension of CNF-metro. It was induced by the addition of a human carboxylesterase 2 (hCE2), inspiring from a recent work with similar enzymatic release strategy [START_REF] Bliman | Enzymatically Activated Glyco-Prodrugs of Doxorubicin Synthesized by a Catalysis-Free Diels-Alder Reaction[END_REF]. This enzyme favors the cleavage of the ester bond that binds metronidazole to the CNFmetro and prodrug arm. CNF-metro suspension was centrifuged at 20 000 g for 10 min and redispersed in TRIS buffer (pH 7.4, 50 mM). This operation was repeated 2 times. A volume of 10 ml of CNF-metro suspension was poured into a balloon and heated at 37°C. The commercial enzyme solution was diluted to 1 mg/ml with TRIS buffer and 2 ml of this solution was introduced in the CNF-metro suspension. The mixture was maintained under magnetic stirring and at 37°C for 48 h. In parallel, a 10 ml CNF-metro suspension without the enzyme (also re-dispersed in TRIS buffer) was exposed to the same condition, acting as a reference. Aliquots were collected from both balloons in order to assess the influence of the enzyme addition on the release of the metronidazole. 500 μl aliquots were collected at predetermined time intervals and centrifuged at 14 000g for 10 min and filtrated with syringe filter (0.45 μm, polyamide/nylon, CHROMAFIL AO-45/3 MACHEREY NAGEL) before characterization. Reverse-phase high performance liquid chromatography (HPLC) was performed with a micro-bondapak-C18 analytical column (Waters Associates) to track the presence of metronidazole in the aliquot. A Waters chromatographic system was used, with two M-510 pumps and photodiode array detector Waters 996 using Millenium 32 software. A linear gradient from 10 to 100 % methanol in H2O pH 2.5 (phosphoric acid), 1 ml/min flow rate, was used.

Results and discussions

Characterization of CNF-t starting materials

Considering the numerous commercially available CNF types and the wide variety of lab-scale produced CNF, it is of high importance to precisely describe the properties and characteristics of the CNF that are used in this work. Cellulose nanofibrils suspensions are often a mixture of nanoscale particles, microfibrillated fibers, aggregates and residual fibers. The objective is to understand the starting material and be able to draw relevant conclusions from the presented results.

The CNF-t suspension that was produced by the CTP has the appearance of a thick transparent gel at 1.6wt% concentration as depicted on Figure 2 . AFM images of the low concentrated CNF-t suspension were also recorded in order to confirm the nanosize morphology of cellulose nanofibrils, as depicted on Erreur ! Source du renvoi introuvable.b. In order to assess the chemical reactivity of the CNF-t suspension, conductometric titration was performed to measure the degree of oxidation (DO) and initial carboxylic acid group content Xox. A degree of oxidation of 30% and quantity of 1.7 mmol/g ± 0.1 of carboxylic acid group was detected, which confirmed the high surface charge arising from TEMPO-mediated oxidation.

First step: Introduction of alkyne function through amidation

The first reaction of the two-step immobilization procedure involves the CNF-t gel, on which an amidation reaction was performed with propargyl amine to tether pending alkyne groups. After purification steps, characterization of the grafting was made, either by analyzing the resulting CNF-yne suspension or CNF-yne dry films produced by solvent casting. Characterization techniques allowed to confirm the presence of the propargyl amine and/or the covalent nature of the bond between CNF-t and propargyl amine. We will first present the data that indicate the presence of alkyne groups, and then discuss the data confirming the covalent nature of the bond and the success of the amidation.

Spectroscopies

Chemical structure of the resulting CNF-yne dry films was investigated through FTIR spectroscopy in ATR mode. The surface of the films was then analyzed in order to reveal new chemical bonds. Erreur ! Source du renvoi introuvable.a shows FTIR spectra of CNF-t, CNF-yne and CNF-Metro. The three spectra showed classical peaks for cellulose backbone: stretching of O-H and C-H bonds around 3300 cm -1 and 2900 cm -1 , C-O-C glycosidic bond stretching at 1160 cm -1 and C-O bonds at 1100, 1050 and 1030 cm -1 (Johan [START_REF] Foster | Current characterization methods for cellulose nanomaterials[END_REF]. CNF-t IR spectrum also showed two clear peaks at 1602 cm -1 and 1715 cm -1 that were respectively associated with C=O of carboxylate and carboxylic acid groups. The pH of the CNF-t suspension was adjusted to 3 before producing films for analysis thus explaining the presence of carboxylic acid group signal. CNF-yne also showed the same peaks but with a lower intensity. Moreover, another peak arising around 1655 cm -1 was attributed to the C=O bond of amide I function, and a weak signal around 1550 cm -1 was due to to the C-N bond of amide I function [START_REF] Hoeng | Charge density modification of carboxylated cellulose nanocrystals for stable silver nanoparticles suspension preparation[END_REF]. These data qualitatively proved the successful amidation reaction. Recent papers on amidation of CNF-t showed similar behavior in FTIR experiments and based their main conclusions on this characterization tool [START_REF] Lavoine | Optimization of preparation of thermally stable cellulose nanofibrils via heat-induced conversion of ionic bonds to amide bonds[END_REF]. In our case, as the shifts were limited, complementary characterizations were performed. and vice versa, especially when the proportion of the expected bond is low. This is the case of alkyne bonds, which appeared to be more sensitive to Raman spectroscopy than in FTIR [START_REF] Mangiante | Green Nondegrading Approach to Alkyne-Functionalized Cellulose Fibers and Biohybrids Thereof: Synthesis and Mapping of the Derivatization[END_REF]. The Raman spectroscopy spectra are shown on Erreur ! Source du renvoi introuvable.b. Both spectra showed characteristic peaks of cellulosic materials: C-H stretching at 2900 cm -1 and C-O bridges around 1100 cm -1 [START_REF] Agarwal | Raman Spectroscopy of CNC-and CNF-Based Nanocomposites[END_REF]. On CNF-t spectrum, the peak at 1660 cm -1 referred to the C=O of carboxylic acid groups. A clear signal appearing at 2120 cm -1 was attributed to the C≡C bond on the grafted propargyl-amine moiety [START_REF] Mangiante | Green Nondegrading Approach to Alkyne-Functionalized Cellulose Fibers and Biohybrids Thereof: Synthesis and Mapping of the Derivatization[END_REF]. This signal was not detected on the ATR-FTIR spectra. Moreover, the signal of the C=O of the carboxylic acid was slightly flatten indicating its partial conversion to amide group. This Raman spectroscopy analysis further confirmed the success of the amidation.

Conductometric titration results

After the amidation reaction with propargyl amine, the remaining carboxylic group were also quantified by conductometric titration and the residual degree of oxidation DOres was calculated with equation (3) (detailed in SI) by integrating the molecular weight of the propargylamine and the same previous terms as it was done before on cellulosic nanomaterials [START_REF] Hoeng | Charge density modification of carboxylated cellulose nanocrystals for stable silver nanoparticles suspension preparation[END_REF].

A value of 9% of residual carboxylic acid content DOres was obtained. According to equation (4) (detailed in SI), a proportion of 69% of initial carboxylic acid groups converted to amide function. This first quantitative result indicates that more than two-third of the carboxylic acid moieties reacted to become amide function. From the values of Xox and %COOHconv obtained with equations ( 3) and ( 4), it was possible to calculate with equation (5) a degree of substitution based on conductometric titration measurements DScond (detailed in SI). The degree of substitution based on conductometric titration was calculated with equation ( 5) and revealed to be DScond = 0.19, which is in accordance with commonly reported results for this kind of heterogeneous chemical grafting [START_REF] Missoum | Nanofibrillated Cellulose Surface Modification: A Review[END_REF][START_REF] Rol | Recent advances in surface-modified cellulose nanofibrils[END_REF]. This hyperpolarization method can increase sensitivity of solid state NMR by several orders of magnitude [START_REF] Rossini | Dynamic Nuclear Polarization Surface Enhanced NMR Spectroscopy[END_REF]. As a proof of its potential, Figure 5

Solid state 13 C NMR

Second step: thiol-yne click chemistry reaction

The second step of the grafting strategy involved a click reaction to anchor the thiol-modified Metro-SH to the CNF-yne. As depicted in Figure 1, the CNF-metro product displays only one molecule of thiolmodified drug per residue while the alkyne group is supposed to bind up to two thiol containing molecules by thiol-yne click reaction. However, considering the strong steric hindrance and the heterogeneous conditions of the chemistry that happened here, the binding of two molecules on the alkyne group is probably strongly disfavored. We therefore depicted the result of the single addition even if double addition was not completely ruled out.

Elemental analysis

Carbon, hydrogen, nitrogen and sulfur mass proportion were measured for each sample. Elemental composition is available for the first step amidation reaction. However, the amount of nitrogen arising from the new amide function competes with the amount of nitrogen contained in potential residual adsorbed coupling agents EDC/NHS and reaction by-products such as EDC-urea and NHS-ester, despite thorough washing steps [START_REF] Fujisawa | Formation of N-acylureas on the surface of TEMPO-oxidized cellulose nanofibril with carbodiimide in DMF[END_REF][START_REF] Kumar | The surface chemistry of a nanocellulose drug carrier unravelled by MAS-DNP[END_REF]. The detection of nitrogen on CNFyne, compared to CNF-t, supports the presence of the propargyl amine and its alkyne function at best.

Nevertheless, when it comes to discuss the outcome of the thiol-yne click chemistry, elemental analysis provided more robust information, especially for sulfur atoms since they are introduced for the first time in the chemical sequence. Considering the amount of nitrogen and sulfur atoms that were theoretically introduced at this second step, the confirmation of the presence of the Metro-SH on the CNF-yne was clearly set. In fact on Table 1, a significant increase of nitrogen content in comparison with the CNF-yne was detected, going from 1.15 % ±0.05 to 1.42 % ±0.03. Moreover, in the second step, no nitrogen-containing chemical agents were introduced confirming that the increase of this element is only due to the presence of Metro-SH. In parallel, sulfur was also detected at 0.37% ±0.01 while it was not detectable on CNF-yne. Also, the final ratio between the quantity of nitrogen and sulfur atoms must be close to 4 according to the chemical structure of CNF-Metro. The elemental analysis results gave a ratio of 1.42/0.37 = 3.8, which roughly fits with the expected result. The progressive increase of nitrogen and the detection of sulfur both confirmed the immobilization of the Metro-SH onto the CNF. displayed on Figure 7 perfectly fits with the low signal to noise experimental signal of CNF-metro (blue).

A combination of model carboxylic acid, amide and ester contributions allowed the overlap to reach 98.9%, confirming indirectly the presence of an ester function. The thiol-modified drug is the only compound that contained such a chemical function. This is a complementary proof that the immobilization of the modified metronidazole on the cellulosic substrate was successful. The release of metronidazole under enzymatic stimuli was analyzed. Indeed, infection sites have important enzymatic activity that may be useful for prodrug activation through ester bond cleavage.

Two suspensions of CNF-metro were maintained at 37°C for 48 h under magnetic stirring. Human carboxylesterase 2 was added in one of the two suspensions for releasing the metronidazole grafted on CNF substrate, through the cleavage of the ester function. Aliquots of the suspensions were analyzed by HPLC analysis. After 1 h of agitation, a clear signal with a 3.7 minute retention time (RT)

was obtained with the suspension that contains the enzyme, as illustrated on Figure 9a. By comparison with the HPLC data of metronidazole itself (results not shown), this signal (both RT and UV-Visible maximum at 283.9 nm) can be attributed to the release of the metronidazole. The CNF-metro suspension that was gently stirred in the absence of the enzyme was also analyzed with HPLC.

However, even after 4 h, no trace of the metronidazole was detected as confirmed by both the chromatogram and UV spectrum of Figure 9b. This preliminary studies would deserve more investigation however the main outcome is that CNFmetro suspension, when exposed to hCE2 enzyme, is able to release metronidazole molecule in one hour. This result validates our starting hypothesis of controlled release of metronidazole from CNF under enzymatic activity.

Conclusion

In this work, a multistep immobilization procedure was proposed to graft thiol modified metronidazole prodrug onto TEMPO oxidized cellulose nanofibrils. The first step was an amidation reaction between carboxylic acid groups of CNF-t mainly confirmed by Raman spectroscopy, Solid state NMR and especially DNP enhanced NMR, with 2D analysis. Thus, an alkyne function was introduced at the surface of CNF. This key intermediate alkyne CNF opened the way to a range of chemical functionalization such as the thiol-yne reaction with thiol containing metronidazole prodrug described here, or a Michael-type addition of a suitably thiol-or amine-substituted prodrug. The presence of the prodrug was then confirmed by elemental analysis, conventional solid-state NMR and, more importantly DNP enhanced NMR that appeared as the ultimate tool to confirm the covalent nature of the grafting of the prodrug onto CNF substrates. These results further expand the strength of DNP enhanced NMR in the field of material characterization. Finally, the in situ drug release, arising from the presence of the cleavable ester function, was validated with the human carboxylesterase 2 medium, thus confirming that the presence of the CNF material did not prevent the enzyme activity.

Following this work, the modified CNF system can be implemented in the design of innovative medical devices. Inspiring from commercial collagen-based implantable meshes, a composite of the prodrug modified CNF and collagen has been prepared to obtain an in situ triggered release of the drug (data not shown). The prototypes shows efficient preliminary antibacterial activity against anaerobic bacteria, confirming the particular potential of CNF-based medical devices in implantable applications.

Figure 1 :

 1 Figure 1: General multistep immobilization procedure of thiol modified metronidazole prodrug on CNF-t. Note that thiolyne click reaction can give a double addition of thiol compound. However, due to steric hindrance, the second addition is less likely to happen so that only the "one-addition" product is depicted.

  Propargyl-amine (CAS: 2450-71-7), propargyl-bromide (CAS: 106-96-7), N-(3-dimethylaminopropyl)-Nʹethylcarbodiimide hydrochloride (EDC, CAS: 25952-53-8), N-hydroxysuccinimide (NHS, CAS: 6066-82-6), sodium hydroxide (NaOH, CAS: 1310-73-2), and hydrogen chloride (HCl, CAS: 7647-01-0) 4-(dimethylamino)pyridine (DMAP, CAS: 1122-58-3), N,N-Dicyclohexylcarbodiimide (DCC, CAS: 538-75-0), trifluoroacetic acid (TFA, CAS: 76-05-1), triisopropylsilane (TiPS, CAS: 6485-79-6) were purchased from Sigma Aldrich and used as received. Isopropanol (CAS: 67-63-0) was purchased from ACROS Organics. Tris(2-carboxyethyl)phosphine hydrochloride (TCEP, >98%, CAS: 51805-45-9(LAP, >98%, CAS: 85073-19-4) was purchased from Tokyo Chemical Industry. The biradicals 15-{[

Scheme 1 :

 1 Scheme 1: Synthesis path of metronidazole-thiol (3) from Metronidazole (2) and S-trityl-3(mercaptopropionic acid (1)

  cyclohexane and dried under vacuum. The amorphous solid was purified by flash chromatography on silica gel with CH2Cl2/MeOH : 97/3 as eluent to give the compound 3 (Erreur ! Source du renvoi introuvable.) as a rosy amorphous solid. (568 mg, 95%). The full liquid 1 H and 13 C NMR characterization of the intermediate product and prodrug 3 are available in the supporting information (SI) on Figure S 1 and Figure S 2.

  functionalization by conductometric titration. The amount of CNF-t suspension corresponding to 50 mg of dry material was precisely diluted to 200 ml with de-ionized water. Magnetic stirring and high shear mixer Ultra-Turrax (IKA) were used to produce a homogeneous dispersion. The pH was decreased around 2.5 with 0.1 M HCl to turn every remaining carboxylate moieties of CNF surface into the acid form of the carboxylic acids, and the volume of added HCl solution was recorded. The titration was done with a 0.01 M NaOH solution, which precise concentration was measured with 3 colorimetric titrations before the titration of the CNF suspensions. The conductivity of the suspension was recorded after stabilization all along NaOH addition and added volumes of NaOH were reduced when the curve indicated changes in the slopes to improve the assessment of the transitions. The titration curves typically display three regions, a first slope showing a decrease of the conductivity corresponding to the neutralization of remaining strong acid, a plateau were the weak acid groups are titrated (carboxylic groups of CNFs) and a last part where conductivity increases when all acids are titrated.

  precise concentration of the NaOH solution is C. The CNF dry quantity is m. The two NaOH solution equivalent volumes Veq1 and Veq2 are extracted at the edge of the plateau on the titration curve by calculating the intersections of the first (decreasing slope) and third (increasing slope) part of the curve with the plateau. The degree of oxidation (DO) represent the number of carboxylic groups per anhydroglucose unit (AGU) on oxidized CNF. It can be calculated with equation (2) according to Da Silva Perez et al. (da Silva Perez et al., 2003), and uses common terms C, m and equivalent volumes.

For

  the 1D and 2D INADEQUATE experiments the corresponding sequences are those of TOPSPIN, the NMR software proposed by Bruker Corporation. The 2D 13 C-13 C INADEQUATE is the version proposed by Lesage et al. adding DNP conditions

Figure 2 :

 2 Figure 2: CNF-t starting material characterization: a) picture of the thick 1.6 wt% gel, b) an AFM height sensor image of a 15.10 -5 wt% suspension and c) results of the conductometric titration (DO: degree of oxidation)

Figure 3 :

 3 Figure 3: Spectroscopy results for a) FTIR-ATR and b) Raman spectra of CNF-t and CNF-yne samples While FTIR spectroscopy relies on the study of absorption or transmission of light on a wide range of wavelength, Raman spectroscopy relies on the study of the inelastic scattering of a specific wavelength light beam. This technique is complementary to the FTIR spectroscopy because some chemical bonds are much more active in Raman spectroscopy and could hardly be detected with FTIR spectroscopy

  It was also used to further identify the composition of CNF-t and CNF-yne. The full signals of solid state 13 C NMR are available in SI and display the expected peaks for cellulose based material. The discussion here will focus on the 165-180 ppm region where carboxyl signals are usually detected. Deconvolutions of the 13 C NMR signals for CNF-t and CNF-yne are showed on Figure4. The peak at 174 ppm was associated with the carbon of the carboxylic acid groups of CNF-t[START_REF] Montanari | Topochemistry of Carboxylated Cellulose Nanocrystals Resulting from TEMPO-Mediated Oxidation[END_REF]. This peak was slightly shifted on CNF-yne signal, indicating a change of chemical environment due to the amidation reaction. A deconvolution technique was applied to unveil the contributions that explain this shift. After deconvolution, the experimental CNF-yne signal displayed on Figure4dcan be simulated by a combination of carboxylic acid and amide model contributions. The overlap obtained

Figure 4 :

 4 Figure 4: Deconvolution of solid state 13 C NMR signal for CNF-yne, a) the experimental signal, b) and c) the model carboxyl and amide signals respectively and d) the calculated signal after deconvolution based on b) and c)

  compares the spectra of CNF-t without and with the microwave (MW) irradiation that allows the dynamic nuclear polarization transfer. The acquisition time of such signals is also very fast in comparison with conventional solid state NMR. When several hours are necessary to increase signal to noise ratio in conventional solidstate NMR, only minutes-long acquisition of DNP enhanced NMR result in sharp and fine signals. As a matter of fact, in this example we could reach a 55 fold enhancement of signal to noise ratio. On a practical point of view in order to reach similar signal to noise ratio without DNP technique it would have been necessary to multiply the number of accumulated transients by 3000. This is the reason why 2D 13 C INADEQUATE experiments in the solid phase become possible in natural abundance.

Figure 5 :

 5 Figure 5: 13 C DNP-NMR spectra for CNF-t, with (red) and without(blue) microwave irradiation(μwave)

Figure 6 :

 6 Figure 6: a) 13 C DNP-NMR spectra of CNF-t and CNF-yne. Aliphatic -CH2-carbons arises from CNF-yne signal anb b) 2D 13 C-13 C inadequate DNP-NMR analysis of CNF-t and CNF-yne. The shift indicates the apparition of a carbon involved in an amide function.

Figure 7 :

 7 Figure 7: Deconvolution of solid state 13 C NMR signal for CNF-metro, a) the experimental signal, b), c) and d) the model carboxyl, ester and amide signals respectively and e) the reconstructed model signal based on b), c) and d)

Figure 8 :

 8 Figure 8: a) DNP enhanced 13 C NMR of CNF-yne and CNF-metro samples and b) the same signals completed with the liquid 13 C NMR spectrum of the prodrug Metro-SH containing the metronidazole molecule, a JMOD sequence was used to give negative -CH-and -CH3-signals

Figure 9 :

 9 Figure 9: HPLC chromatograms (diode-array detector) (top) and associated UV spectra (bottom) of CNF-metro suspensions reacted a) with, and b) without the presence of carboxylesterase human 2 (hCE2)

Table 1 : Elemental analysis results for carbon, hydrogen, nitrogen and sulfur mass proportion of the various CNF samples

 1 Solid state 13 C NMR13 C NMR was used to further identify the composition of CNF-metro sample. On Erreur ! Source du renvoi introuvable.4, in the region corresponding to carbons involved in C=O around 170 ppm, we noticed a difference of the shape of the CNF-yne signal suggesting a new chemical environment. The deconvolution technique was used again to clarify this result. The CNF-metro model signal(red)

Acknowledgements

The authors thanks Univ. Grenoble Alpes, CNRS, Grenoble INP, LGP2, F-38000 Grenoble, France, and the French National Research Agency (ANR) (CELLICAL, ANR-15-CE08-0033, Arcane ANR-11-LABX-0003-01 and Glyco@Alps ANR-15-IDEX-02) for financial and technical supports.

We also thank A. Crisci from SIMAP, Grenoble who performed RAMAN spectroscopy measurements and ICR, Aix-Marseille University, UMR 7273, for the AMUPol biradical compound used in DNP-NMR Fot the DNP-ssNMR analysis, M. Bardet was supported by an Outgoing CEA fellowship from the CEA-Enhanced Eurotalents program, co-funded by FP7 Marie-Skłodowska-Curie COFUND program (Grant Agreement 600382) and financial support ERC Advanced Grant No. 320860

Supporting information

The following data may be found in the Supporting Information file