Imad Rida
email: imad.rida@insa-rouen.fr

Romain Herault

Gian Luca Marcialis

Gilles Gasso

Palmprint recognition with an efficient data driven ensemble classifier

Palmprint recognition is an important and widely used modality in biometric systems. It has a high reliability, stability and user acceptability. This paper proposes a new and effective ensemble classifier for palmprint recognition based on Random Subspace Method (RSM). The method relies on 2DPCA to build nearly incoherent random subspaces. As 2DPCA is an unsurpevised technique, features are extracted in each subspace using 2DLDA. A simple 1-Nearest Neighbor classifier is associated to each subspace, the final decision rule being obtained by a majority voting rule. Extensive experiments on three public palmprint datasets have been conducted to compare the proposed approach to existing methods. The experimental results demonstrate that our method improves on the state-of-the-art. It turns out that for this kind of data, the use of weak classifiers learned over nearly incoherent features is very efficient. Besides these findings, we provide an empirical analysis of the parameters involved in the random subspace technique to guide the user in the choice of the appropriate hyper-parameters.

Introduction

Over the past two decades, biometric security is increasingly becoming an important tool to enhance security and brings greater convenience. Nowadays, biometric systems are widely used by government agencies and private industries. A large variety of biometric modalities including face, iris, gait, fingerprint and palmprint, have been studied providing different rates of robustness, accuracy and user acceptability [START_REF] Rida | Human body part selection by group lasso of motion for model-free gait recognition[END_REF]. Among these modalities, palmprint-based recognition has gained a growing interest because of its reliability, stability and high user tolerance.

Palmprint refers to the inner surface of hand. This contains an abundant variety of salient features, such as principal lines, wrinkle, ridges, minutiae and textural features [START_REF] Fei | Enhanced minutiae extraction for 527 high-resolution palmprint recognition[END_REF].

Most palmprint identification systems leverage on the extraction of these discriminative features to attain valuable recognition/matching performances. For instance the principal lines are detected using classical edge detectors or dedicated Radon transforms which project the palmprint image intensity along lines oriented at specific angles [START_REF] Huang | Palmprint verification based on principal 568 lines[END_REF]. Other systems consider the orientations of the lines as the most distinctive Label Fig. 1. The flowchart of our proposed method. Each small arrow represents a subspace over which a classifier is learned.

ing from uncontrolled acquisition conditions [START_REF] Lu | Multispectral image fusion for illumination-invariant palmprint recognition[END_REF][START_REF] Yang | 3d palmprint recogni-649 tion using shape index representation and fragile bits[END_REF][START_REF] Ni | 3d palmprint recognition using dempster-shafer fusion theory[END_REF]Zhang et al., 2010b;[START_REF] Pan | Palmprint recognition using gabor feature-based (2d) 2pca[END_REF]. In these adversarial situations, the performances of subspace-based approaches may be severely impacted. To overcome these limitations, we investigate an effective ensemble learning technique for robust palmprint recognition.

In this paper, we introduce a novel subspace learning method directly applied to image pixels for palmprint recognition. Conventional subspace methods mainly seek to determine a relevant low-dimensional subspace in a high-dimensional input space in order to learn a suitable representation. Hence their performances are sensitive to the selected dimensionality. A smalldimensional subspace might loose discriminative information while a large dimensionality could lead to overfitting [START_REF] Nguyen | Random subspace two-dimensional pca for face recognition[END_REF]. To tackle this problem we explore an ensemble learning approach based on Random Subspace Method (RSM) [START_REF] Ho | The random subspace method for constructing decision forests. 557[END_REF][START_REF] Guan | On reducing the effect of covariate factors in 544 gait recognition: a classifier ensemble method[END_REF][START_REF] Li | Random subspace method for source camera identification[END_REF][START_REF] Guan | A robust speed-invariant gait recognition system for 541 walker and runner identification[END_REF]. The RSM builts multiple subspaces by using a random procedure. A simple classifier is associated to each subspace.

The final decision rule is achieved by aggregating the outcomes of the learned classifiers. Indeed, the RSM builds many weak classifiers which may not provide individually good recognition performances but their combination may achieve high recognition accuracy. The main contributions brought by the paper are as follows:

• We propose a new and effective palmprint recognition method based on RSM. This ensemble learning technique proves more efficiency than individual classifiers [START_REF] Kuncheva | Combining pattern classifiers: methods and algorithms[END_REF][START_REF] Rokach | Pattern classification using ensemble methods[END_REF] and was recently applied with success to gait recognition [START_REF] Guan | On reducing the effect of covariate factors in 544 gait recognition: a classifier ensemble method[END_REF] .

• To achieve a simple method, we rely on 2DPCA to build random subspaces. 2DPCA is a linear dimensionality reduction technique for dealing with 2D images as it works on matrices rather than vectors. Contrary to conventional one-dimensional PCA, it has the advantage to preserve the spatial structure of the palmprint images and requires less computational cost [START_REF] Yang | Two-dimensional pca: 652 a new approach to appearance-based face representation and recognition[END_REF]. The subspaces are randomly selected such as they are nearly incoherent [START_REF] Zhang | Discriminative k-svd for dictionary learning in face 673 recognition[END_REF]. The incoherence indicates the degree of dissimilarity between subspaces and is desirable in order to promote different subspaces, hence diverse classifiers.

• As 2DPCA is unsupervised, discriminative features are extracted in each subspace using 2D Linear Discriminant Analysis (2DLDA). A Nearest Neighbor (NN) with Eulidean distance is implemented for each subspace. Finally, the non-linear decision function is obtained and consists in 93 a majority voting of the individual classifiers.

94

The flowchart of the proposed method is depicted in Figure 1. ciple Component Analysis (PCA) [START_REF] Lu | Palmprint recognition using eigenpalms features[END_REF] and its 121 2D variant [START_REF] Sang | Research of palmprint recognition based on 2dpca[END_REF] used in order to preserve 122 spatial structure information of palmprint images. In addi-123 tion to PCA, Independent Component Analysis (ICA) has 124 been also used [START_REF] Connie | An automated palm-522 print recognition system[END_REF]. While PCA seeks to 125 find uncorrelated features, the ICA attempts to find statis- [START_REF] Tamrakar | Kernel discriminant analysis of block-wise gaussian derivative phase pattern histogram for palmprint recognition[END_REF]) 2D Discrete Cosine [START_REF] Leng | Dual-source discrimination power analysis for multi-instance contactless palmprint recognition[END_REF] The holistic approaches mainly act at the pixel level and 135 are subject to poor performances in the presence of degra-136 dations caused by noise and blur [START_REF] Laadjel | Combining fisher locality preserving projections and passband dct for efficient palmprint recognition[END_REF]. To [START_REF] Zhang | 3d palmprint identification using 670 block-wise features and collaborative representation[END_REF][START_REF] Xu | Combining left and right palmprint images 646 for more accurate personal identification[END_REF]. With 146 this assumption, the query image is expected to be well

Texture extractors Works

Local Binary Pattern (LBP) [START_REF] Michael | Touch-less palm print biometrics: Novel design and implementation[END_REF]) Block-based Histogram of Oriented Gradient [START_REF] Hong | A novel hierarchical ap-559 proach for multispectral palmprint recognition[END_REF] Weighted Histogram of Oriented Gradient [START_REF] Hong | Robust palmprint recognition 562 based on the fast variation vese-osher model[END_REF]) Hierarchical multi-scale LBP histogram [START_REF] Guo | Collaborative representation with hm-lbp 547 features for palmprint recognition[END_REF] Table 4 summarizes the different techniques as well as their 176 strengths and limitations. 189

One popular ensemble method is the Random Subspace 190 Method (RSM) [START_REF] Ho | The random subspace method for constructing decision forests. 557[END_REF][START_REF] Guan | On reducing the effect of covariate factors in 544 gait recognition: a classifier ensemble method[END_REF][START_REF] Li | Random subspace method for source camera identification[END_REF] 191 [START_REF] Guan | A robust speed-invariant gait recognition system for 541 walker and runner identification[END_REF]. The idea behind RSM is to use differ- Majority Voting [START_REF] Kittler | On combining classifiers[END_REF]

2D Principal Component Analysis

Given the set of palmprint images

P i ∈ R N 1 ×N 2 n i=1 2DPCA,
used as a first step of our RSM, seeks to reduce the dimensionality of the data. Contrary to conventional one-dimensional PCA, 2DPCA preserves the matrix structure of P instead of working on its vectorized representation (which can be potentially of high dimension when N 1 and N 2 take high values leading to tedious eigenvalue decomposition problem). Formally, 2DPCA

aims at finding a transformation matrix R ∈ R N 2 ×d to project each image P i onto a matrix

Z i = (P i -P) R ∈ R N 1 ×d of re- duced dimension i.e. d ≤ N 2 . P = 1 n n i=1 P i is
Z i = P i -P R * ∈ R N 1 ×d ∀ i = 1, • • • , n (2)

2D Linear Discriminant Analysis

To extract discriminative representation of the data, 2DLDA is applied to the features Z i . It intends to determine a projection matrix W ∈ R N 1 ×m , for fixed m ≤ N 1 , in order to maximize class separability. 2DLDA seeks to maximize the between-class variance relatively to within-class variance leading to the optimization problem [START_REF] Ye | Two-dimensional linear discriminant analy-659 sis[END_REF] max w S b . To sum up, starting from the raw palmprint images P i , the application of 2DPCA followed by 2DLDA brings to the representation

W∈R N 1 ×m Trace W S w W -1 W S b W (3) under column orthogonality of W. The matrix S b = C k=1 n k Zk -Z Zk -Z is the between-class covariance ma- trix whereas S w = C k=1 n i=1 I 1 y i =k Z i -Zk Z i -Zk
X i = W * Z i = W * P i -P R * ∈ R m×d ∀ i = 1, • • • , n (4)
The classification stage of our proposed approach relies on 240 these learned features.

243

We may randomly sample the features related to each subspace 244 directly form the raw palmprint images. However this is not 245 practical as the sampling procedure may loose local spatial rela-246 tionships among the pixels within the image [START_REF] Zhu | Semi-random subspace method for face recog-677 nition[END_REF].

247

In order to preserve these spatial information and build nearly 248 incoherent subspaces, we adopt 2DPCA to generate the random 249 subspaces. Indeed, following [START_REF] Guan | On reducing the effect of covariate factors in 544 gait recognition: a classifier ensemble method[END_REF] we consider

, 2 = R T 1 R 2 2
F is 256 enough small, leading to nearly incoherent subspaces [START_REF] Ramirez | Classification and clustering via dictionary learning with structured incoherence and shared features[END_REF]. Indeed, because of the orthogonality of the eigenvectors, the term ϕ 1 , 2 provides a measure of the mutual coherence of subspaces 1 and 2 .

After sampling each matrix R , we proceed as follows:

the whole training images are projected onto the subspace spanned by the corresponding eigenvectors giving D =

Z i = P i -P R n i=1
. These new data Z i are further used to learn 2DLDA matrix W by solving problem 3 in order to extract discriminative features. Finally, we attain the representation of the data in the th random subspace as

X i = W * Z i , y i n i=1
. It shall be noticed that our random subspace generation procedure transforms each initial palmprint Algorithm 1 Random Subspace Method (RSM) Input:

image P i ∈ R N 1 ×N 2 into representations X i ∈ R m×N (with m ≤ N 1 and N ≤ d ≤ N 2 ) for all = 1, • • • , L
• Training set: (Pi, y i ) ∈ R N 1 ×N 2 × Y n i=1
• Hyper-parameters: N, size of random subspaces; L number of subspaces and m, number of 2DLDA projection directions.

Output:

• {R } L =1 random

Experiments

In this section, we perform several experiments to evaluate the effectiveness of the proposed approach on three popular palmprint datasets: left and right palmprint database [START_REF] Zhang | Online palmprint identifica-666 tion[END_REF], multi spectral palmprint database (Zhang et al., 2010a) and 2D palmprint database [START_REF] Li | Efficient joint 2d and 3d palmprint matching with alignment refinement[END_REF]. The ob- In our experiments we have used the provided palmprint re-309 gion of interest of 32 × 32 (see Figure 2). The proposed method involves three tuning parameters: the 312 dimension of the random subspace N, the number of projection 313 directions of the 2DLDA m and the number of subspaces L.

314

The parameters N and m can be easily optimized using a cross- Code [START_REF] Kong | Competitive coding scheme for palmprint verification[END_REF], Ordinal Code [START_REF] Sun | Ordinal palmprint represention for personal identification [represention read representation[END_REF],

335
Fusion Code [START_REF] Kong | Palmprint identification using featurelevel fusion[END_REF], Robust Orientation Line Code

336

(RLOC) [START_REF] Jia | Palmprint verification based on robust 570 line orientation code[END_REF], Binary Orientation Co-occurrence 337 Vector (BOCV) [START_REF] Guo | Palmprint verification using 549 binary orientation co-occurrence vector[END_REF]), E-BOCV Zhang et al.

338

(2012), Half Orientation Code (HOC) (Fei et al., 2016b) and 339 Double Orientation Code (DOC) (Fei et al., 2016a).

340

For comparison sake, we have performed the same experi-341 ments using the same data splits and protocols in (Fei et gerprints, faces and iris [START_REF] Marcel | Handbook of Biometric Anti-Spoofing: Trusted Biometrics Under Spoofing Attacks[END_REF].

393

Finally we shall state that coding methods remain very at-394 tractive but they heavily rely on priori knowledge to choose 395

Gabor filter parameters and the number of orientations. More-396 over their computation cost is high at testing stage (Zhang et al., 397 2015). This is confirmed by Table 9 which compares the exe- ual classifiers leads to performing ensembles [START_REF] Kuncheva | Combining pattern classifiers: methods and algorithms[END_REF].

413

The feature subspaces on which these individual classifiers are 414 learned represent the key indicator in order to build classifiers 415 with some desired characteristics. [START_REF] Kuncheva | Random subspace ensembles for fmri classification[END_REF] • Coverage: represents the ability to learn a large number of non-identical classifiers.

• Usability: when a classifier is learned on only spurious features its performance may be totally random. A classifier is considered usable when it is learned on subspaces containing discriminative features.

In order to build a performing ensemble classifier, these criteria should be fulfilled as far as possible, i.e. learning a large number of classifiers on incoherent and discriminative subspaces.

95

  Its effectiveness and efficiency are assessed by extensive exper-96 iments on three public palmprint datasets in order to: (i) com-97 pare RSM to conventional palmprint recognition methods and, 98 (ii) analyze the influence of hyper-parameters involved in RSM 99 (as the number of subspaces or their dimensionality) on recog-100 nition accuracy. 101 The paper is organized as follows. Section 2 summarizes re-102 lated work. Section 3 describes the proposed random subspace 103 method. Section 4 reports the experimental results and discus-104 sions. Finally, Section 5 concludes the paper. 105 2. Related work 106 We provide a brief overview of palmprint recognition meth-107 ods. Existing methods in the literature essentially differ by the 108 type of discrimination features they use and can be broadly or-109 ganized in two main categories (Li and Kim, 2017)global methods attempt to process palmprint 113 image as a whole. They can be divided into two main sub-114 categories: i) subspace-based and ii) representation-based. 115 Subspace-based approaches 116 These techniques aim to find a transformation mapping the 117 original data residing in a high-dimensional space onto a 118 lower one using statistical learning techniques. Among 119 them, the most representative unsupervised ones are Prin-120

137

  address this problem, several transformation shown in Ta-138 ble 1 have been applied as pre-processing step. The resultof techniques, the query image is considered 143 as a linear combination of all training samples. It is com-144 mon that the palmprint of a specific subject lies in a lin-145 ear subspace

  147 represented by the training samples of the same subject, 148 which may lead to a sparse representation over all training 149 data. Sparse Representation-Based Classification (SRC) 150 method (Wright et al., 2009; Raghavendra and Busch, 151 2014) and Linear Recognition Classification (LRC) (Cui 152 et al., 2015) are two representative techniques.

  local approaches rely on the extraction of 155 the lines and texture features from the palmprint image. The 156 structural methods can be organized in two sub-categories: i) 157 line-based, ii) coding-based and iii) texture-based described bemost influential and state-of-the-art 161 palmprint recognition techniques. They encode the re-162 sponses of a bank of filters into bitwise codes. PalmCode 163 introduced by (Zhang et al., 2003) represents the basis of 164 other coding-based methods. It essentially encodes the re-165 sponse of one Gabor filter with an orientation equals to π/ 166 4. Motivated by the success of PalmCode, a large variety 167 of coding methods have been proposed and are summa-168 rized in

  {(P i , y i )} n i=1 be a set of n samples where P i ∈ R N 1 ×N 2 180 is a palmprint image and y i ∈ Y the associated label. Y is a 181 discrete set of cardinality |Y| = C representing the identities 182 to whom palmprints to be recognized belong to. The pursued 183 objective is to find a decision function f (P) able to assign to 184 a given image P its correct label y. An interesting strategy for 185 providing an efficient model f is ensemble learning which com-186 bines the strengths of diverse weak classifiers and proves ef-187 fective in different application fields (Fernández-Delgado et al., 188 2014; Guan et al., 2015).

192((

  ent subsets of features, randomly selected from an initial set, 193 to learn the individual classifiers. Effectiveness of such an ap-194 proach relies on one side in building a set of relevant and diverse 195 simple classifiers and on the other side in aggregating the results 196 of these classifiers. In the present work, we focus in the first 197 issue. Specifically we intend to extract, from the raw images 198 P i , discriminative features well suited to palmprint classifica-199 tion. The images P i are customary high-dimensional and only 200 a few training samples are available for a given subject, lead-201 ing to numerical issues (Ye et al., 2005) when linear subspace 202 learning techniques (see section 2.1) are applied. Inspiring from 203 Guan et al., 2015), we adopt 2DPCA (Yang et al., 2004) to 204 build an initial feature space (a space spanned by the eigenvec-205 tors associated to leading eigenvalues of the covariance matrix 206 of the data) from which the subspaces are randomly sampled. 207 Under this 2DPCA model, each palmprint image is projected 208 onto a new matrix in each subspace. However, as 2DPCA acts 209 in an unsupervised manner, resulting images in each subspace 210 are further projected onto new features using a 2DLDA method 211 Ye et al., 2005) to ensure class separability. Finally a Near-212 est Neighbor classification (NN) rule, which has shown good 213 ability to deal with such discrimination problems, is applied to 214 each subspace. The final classification decision is obtained by 215

P

  the mean of the training images. The original image can be reconstructed back as Pi = Z i R . Mathematically, 2DPCA minimizes the reconstruction error by addressing the following optimization problem min . R R = I where • F represents the Frobenius norm and I the identity matrix. The equality constraint R R = I ensures columns' orthogonality of R. Using the property Trace(AA ) = A 2 F and after some algebra the previous problem becomes max R∈R N 2 ×d Trace R SR s.t. R R = I i -P P i -P is the covariance matrix. Solution R * of problem 1 can be shown to correspond to the d-dominant eigenvectors of S (Yang et al., 2004). Any training image can therefore be projected onto the space spanned by the columns of R * giving

  represents the within-class covariance matrix. In these expressions n k is the cardinality of the k th class while Zk stands for the mean matrix of class k and is calculated based on the projected samples Z i issued from 2DPCA. Z is the global mean of the training samples. Solution W * of problem 3 corresponds to the m leading eigenvectors of S -1

  241 3.4. Random Subspace construction 242 RSM is a very simple and popular ensemble learning method.

250L

  subspaces, each spanned by N d randomly selected eigen-251 vectors from R * . Hence, starting from the solution of 2DPCA 252 problem, we generate L projection matrices R ∈ R N 2 ×N L =1 253 where R = R * (:, I ) with I a set of N indexes sampled in the 254 range [1, d]. During the procedure we promote the sampling 255 of subspaces 1 and 2 such that the term ϕ 1

  corresponding to a given subspace. The representations X i differ by the selected eigenvectors (of number N) in R * and the related LDA projection matrix W . It should be noticed that in addition to getting more discrimination ability, 2DLDA also performs dimensionality reduction of the data along rows while 2DPCA has already reduced dimensionality along columns. The processing flow is summarized in algorithm 1.

  subspace matrices and related LDA projection matrices {W } L =1 Solve problem 1 for 2DPCA projection matrix R * ∈ R N 2 ×d ; for = 1 to L do Generate a subspace spanned by R ∈ R N 2 ×N by randomly selecting N (N d) eigenvectors from R * ; Determine unsupervised representation of the data and form D = Z i = P i -P R n i=1 using equation 2; Calculate accordingly the 2DLDA projection matrix W ∈ R N 1 ×m . end for Once the parameters of the subspaces are learned, we associate for simplicity sake a simple 1-Nearest Neighbor classification function to each subspace. The decision rule is the majority vote over the outcomes of these weak classifiers.

288

  served performances (recognition rate) are compared to those of 289 the state-of-the-art holistic and structural approaches. In addi-290 tion, the influence of hyper-parameters involved in RSM on the 291 performances and the computation cost of our proposed RSM 292 are investigated.

  right database was provided by the Hong Kong 295 Polytechnic University (PolyU) 1 . 187 subjects have been asked 296 to provide 10 palmprint images per each hand. In the following 297 this dataset is referred to as PolyU. 298 The multispectral dataset contains four independent spectral 299 palmprint databases, including Red, Green , Blue and Near In-300 frared (NIR) spectrums databases 2 . 12 palmprint images have 301 been recorded per each hand and illumination from 250 volun-302 teers. This dataset will be termed in the sequel as the multispec-303 tral dataset. 304 In the 2D database, 20 palmprint images have been collected 305 per each hand from 200 subjects 3 .The characteristics of the em-306 ployed datasets are summarized inTable 5.Note that the two 307 palms of the same subject are considered as two distinct classes. 308 Table 5. Content of palmprint recognition datasets.

Fig. 2 .

 2 Fig. 2. Example of palmprint region of Interest in different databases.

398

  cution time of our method to coding-based techniques. On the 399 other side, our method proposes a fully integrated pipeline and 400 does not require any expertise on the structure or morphology of 401 human palm hand to extract discriminative features. It should 402 be noticed that RSM also involves hyper-parameters which can 403 be selected using a cross-validation strategy. We provide here-404 after an analysis to guide the user in the choice of these hyperthe influence of RSM hyper-parameters on ac-407 curacy 408 Here we are interested in the impact of the number of sub-409 spaces L, the size of subspaces N and the number of 2DLDA 410 projection directions m on the accuracy. It has been shown 411 that aggregating a large number of accurate and diverse individ-

  412

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig. 3. Impact of the size of subspaces N.

  Core i5 (3.2 GHz) and 8 GB RAM. The execution 468 time to classify a new test palmprint image increases linearly 469 with the increasing dimensionality for either N, m and L as 470 shown in Figure 6. 471 For N = 8, L = 500 and m = 10 our algorithm takes ap-472 proximately 0.06 seconds to classify one test palmprint image, 473 which shows that the speed of proposed method is quite good 474 for real time applications. The speed can further be increased 475 by parallel processing.

487

  Extensive experiments on three public palmprint datasets, 488 with different illumination conditions, have been conducted to 489 compare proposed approach to conventional palmprint recogni-490 tion methods. The experimental results establish that our ran-491 dom subspace strategy improves on the state-of-the art tech-492 niques, such as coding-based methods over all the environ-493 mental conditions under investigation. We provide an analy-494 sis to give insights on the tuning of hyper-parameters involved 495 in RSM. It appears that, on the studied palmprint datasets, the 496 combination of several weak classifiers (a simple 1-NN clas-497 sification method) learned over nearly incoherent or different 498 subspaces leads to consistent performances over various acqui-499 sition conditions. Hence we believe that RSM can partially 500 contribute to the development of robust biometric recognition 501 systems. Finally the paper demonstrates that the computation 502 burden of RSM at testing stage is very competitive as its com-503 putation time is lower than the one of current influential meth-504 ods for palmprint recognition.

  505

Table 1 .

 1 Example of pre-processing transforms for palmprint recognition.

	126
	127	tically independent ones. Supervised projection methods
		including Linear Discriminant Analysis (LDA) (Wu et al.,
	132
	133	its 2D (Hu et al., 2007) and non-linear kernel (Feng et al.,
		2006) variants.

128 2003) and 2DLDA

[START_REF] Wang | Palmprint recognition based on two-dimensional methods[END_REF]

have been also 129 explored. Another interesting approach Locality Preserv-130 ing Projection (LPP) which seeks to preserve the neigh-131 borhood structure of the data (He and Niyogi, 2004) and 134

Table 2 . 169 Table 2 .

 21692 Non exhaustive coding-based methods for palmprint recognition.

		Codes	Remarks	Works
		PalmCode	1 Gabor orientation	(Zhang et al., 2003)
		Competitive	6 Gabor orientations	(Kong and Zhang, 2004)
		Ordinal	3 2-D Gaussian	(Sun et al., 2005)
		Fusion	4 Elliptical Gabor orientations	(Kong et al., 2006)
		Robust Line Orientation 6 MFRAT directions	(Jia et al., 2008)
		Binary Orientation	6 Gabor orientations	(Guo et al., 2009)
		E-Binary Orientation	Masking out the fragile bits	Zhang et al. (2012)
		Half Orientation	6 banks of half-Gabor directions	(Fei et al., 2016b)
		Double Orientation	2 maximum of 6 Gabor responses (Fei et al., 2016a)
	170	Texture feature extraction

175

Table 3 .

 3 Example of texture extractors for palmprint recognition.

Table 4 .

 4 Summary of the most representative techniques for palmprint recognition.

	Approach	Summarize	Advantages & Limitations
			(+) Good description ability
	Subspace	Find subspace with intrinsic features (+) Low computational cost
			(-) Sensitivity to the size of subspace
			(+) Ability to learn data-driven representations
	Representation Learn discriminative features	(+) Good discrimination ability
			(-) Classes should be well represented by training data
			(+) High discrimination ability
	Coding	Extract direction features	(+) Stable characteristics
			(-) High computational cost
			(+) Captured from low resolution images
	Texture	Extract texture features	(+) Stable characteristic
			(-) Sensitive to noise

among the individual NN 216 classifiers. In the following, after a brief description of 2DPCA 217 and 2DLDA, we develop our random subspace methodology.

218

Table 6 .

 6 Palmprint recognition accuracy (%) using 2 training samples. Best two results are highlighted by bold and underline. The first column represents the datasets and the remaining ones report the accuracy of proposed RSM and the competitors. The last row depicts the mean accuracy over the first five datasets. The details of compared methods are provided in the text.

				Subspace-based		Representation-based			Coding-based
		PCA 2D-PCA LDA 2D-LDA 2D-LPP	LRC	SRC	Comp Ordi	Fusn Palm BOCV EBOCV RLOC HOC DOC	RSM
	Red	85.72	85.72	91.54	96.52	86.94	95.54 95.78 98.18 97.80 97.62 96.12 97.76	97.72	96.26 98.40 98.70 98.94 ± 0.06
	Green 56.88	56.92	88.24	91.70	41.58	93.02 94.26 97.86 97.02 96.64 91.58 97.12	97.52	95.60 98.16 98.16 98.21 ± 0.04
	Blue	92.44	92.68	93.72	96.38	91.96	95.50 95.94 97.76 97.08 96.82 93.50 97.42	97.98	96.53 98.06 98.18 98.30 ± 0.02
	NIR	88.48	88.70	97.60	96.38	92.02	95.46 93.98 98.54 97.96 97.28 95.88 96.56	96.30	96.50 98.54 98.94 98.71 ± 0.10
	PolyU 96.46	96.52	94.79	98.00	95.12	96.79 95.52 97.00 96.79 94.89 86.48 94.64	95.76	94.66 98.01 98.43 99.18 ± 0.02
	2D	53.81	53.92	77.72	75.42	70.90	91.21 90.22	-	-	-	-	-	-	-	-	-	92.25 ± 0.21
	Mean 84.00	84.11	93.18	95.80	81.52	95.26 95.10 97.87 97.33 96.65 92.71 96.70	97.06	95.91 98.23 98.48	98.67

intro-416 duced three notions diversity, coverage and usability that may 417 be helpful in order to interpret the results: 418 • Diversity: in an ensemble classifier, two classifiers are 419 considered non-identical or different if they are learned on 420 two incoherent or different subspaces.

421

Table 7 .

 7 Palmprint recognition accuracy (%) using 4 training samples. Best two results are highlighted by bold and underline.

				Subspace-based		Representation-based			Coding-based
		PCA 2DPCA LDA 2DLDA 2DLPP	LRC	SRC	Comp Ordi	Fusn Palm BOCV EBOCV RLOC HOC DOC	RSM
	Red	91.05	91.05	95.63	97.48	93.97	97.38 95.68 98.95 98.82 98.27 97.85 98.52	98.55	98.11 99.08 99.17 99.22 ± 0.04
	Green 64.23	64.25	92.45	95.55	52.90	95.60 94.40 98.78 98.17 97.80 93.85 98.05	98.35	97.24 98.68 98.85 98.90 ± 0.11
	Blue	94.33	94.53	97.45	97.63	95.17	96.93 96.18 98.70 98.20 97.85 95.92 98.07	98.70	97.87 98.75 98.82 99.10 ± 0.04
	NIR	90.55	91.38	98.73	97.53	94.65	97.80 93.95 99.15 99.00 98.47 97.67 98.05	98.00	97.99 99.10 99.35 99.37 ± 0.06
	PolyU 98.66	98.71	99.05	99.07	98.71	99.02 97.01 98.27 97.86 96.47 88.60 96.10	96.76	96.28 99.08 99.23 99.96 ± 0.01
	2D	60.14	60.17	86.23	75.81	76.28	94.25 91.08	-	-	-	-	-	-	-	-	-	94.50 ± 0.14
	Mean 87.76	87.98	96.66	97.45	87.08	97.35 95.44 98.77 98.41 97.77 94.78 97.76	98.07	97.50 98.94 99.08	99.31

Table 8 .

 8 Palmprint recognition accuracy (%) using 6 training samples. Best two results are highlighted by bold and underline.

				Subspace-based		Representation-based			Coding-based
		PCA 2DPCA LDA 2DLDA 2DLPP	LRC	SRC	Comp Ordi	Fusn Palm BOCV EBOCV RLOC HOC DOC	RSM
	Red	91.60	91.67	96.83	97.60	95.27	98.00 95.13 99.20 98.93 98.53 97.93 98.37	98.50	98.35 99.07 99.23 99.23 ± 0.03
	Green 62.10	62.40	94.80	94.60	49.07	96.27 93.60 98.93 98.37 97.87 94.03 98.20	98.43	97.78 98.97 99.10 98.95 ± 0.07
	Blue	94.10	94.37	95.00	97.50	95.07	97.10 95.30 98.93 98.43 97.97 96.57 98.17	98.77	98.68 98.97 99.10 99.02 ± 0.02
	NIR	90.60	90.60	95.60	97.93	94.37	98.10 93.33 99.13 98.90 98.47 97.57 98.20	98.10	98.13 99.14 99.40 99.54 ± 0.04
	PolyU 99.33	99.33	99.60	99.67	99.33	99.47 97.86 99.92 99.87 99.92 99.80 99.92	99.87	99.80 98.99 99.23 99.94 ± 0.01
	2D	59.77	59.75	87.00	74.45	74.58	94.30 90.41	-	-	-	-	-	-	-	-	-	94.64 ± 0.16
	Mean 87.55	87.67	96.37	97.46	86.62	97.79 95.04 99.22 98.90 98.55 97.18 98.57	98.73	98.55 99.03 99.21	99.34

Table 9 .

 9 Table 9 compares the execution time of 476 our method to other state-of-the-art coding-based techniques.It can be seen that the speed of our algorithm compares very Computational cost (at test time) in seconds of the most performing methods tested in our experiments.

	478
	favorably.
	Methods	Execution Time (s)
	Competitive Code	0.08
	Palm Code	0.20
	Fusion Code	0.20
	Ordinal Code	0.90
	RLOC	3.70
	BOCV	0.90
	E-BOCV	2.10
	HOC	0.15
	DOC	3.50
	RSM	0.06
	5. Conclusion

477 479 480 In this paper we have proposed a new and effective palm-481 print recognition method based on Random Subspace Method 482 (RSM). L nearly incoherent subspaces are randomly generated 483 from the eigenvectors of a 2DPCA. The resulting L projections 484 are refined through 2DLDA. Then, on each subspace, subject is 485 identified with a 1-Nearest Neighbor (1-NN) classifier. Eventu-486 ally, the L decisions are aggregated with Majority Voting (MV).

Acknowledgements 506


Dr Anne Lejay
email: anne.lejay@chru-strasbourg.fr

Anne-Laure Charles

Isabelle Georg

Fabienne Goupilleau

Charline Delay

Samy Talha

Fabien Thaveau

Nabil Chakfé

Bernard Geny

Nabil Chakfe

Critical Limb Ischaemia Exacerbates Mitochondrial Dysfunction in ApoE-/-Mice Compared with ApoE+/+ Mice, but N-acetyl Cysteine still Confers Protection

Keywords: MeSh terms): ischemia, atherosclerosis, mitochondria, oxidative stress, muscle, 60 peripheral arterial disease 61

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

-2 -

What does this study add to the existing literature?

Our study shows that critical limb ischemia (CLI) exacerbates mitochondrial dysfunction and that anti-oxidant therapies such as N-acetyl cysteine (NAC) still confers protection, even if comorbidities are known to reduce protective effects of many drugs. Clinical studies using antioxidant strategies have been mostly disappointing and antioxidant therapies are still far from being integrated into treatment algorithms for peripheral arterial disease, but these results suggest that oxidative stress needs to be considered as a target for protective strategies in the setting of CLI.

Materials and methods: ApoE-/-mice (n=9, 29 weeks-old) and their genetic controls ApoE+/+ mice (n=9, 29 weeks-old) were submitted to sequential right femoral and iliac ligations; the left limb served as control. ApoE+/+ mice were divided into 2 groups: Group 1 (n=4) and Group 2 (n=5); as well as ApoE-/-mice: Group 3 (n=3) and Group 4 (n=6). NAC treatment was administered in Group 2 and 4 in drinking water. Mice were sacrificed at day 40 and gastrocnemius muscles were harvested to study mitochondrial respiration by oxygraphy, calcium retention capacity by spectrofluorometry and production of reactive oxygen species by electron paramagnetic resonance.

Results: CLI associated with ApoE deficiency resulted in more severe mitochondrial dysfunction: maximal oxidative capacity and calcium retention capacity were decreased (-42.9% vs -25.1%, p=0.010; and -73.1% vs -40.3%, p=0.003 respectively) and production of reactive oxygen species was enhanced (+63.6% vs +41.4%, p=0.03) in ApoE-/-mice compared to ApoE+/+ mice respectively. Anti-oxidant treatment restored oxidative capacity, calcium retention capacity and decreased production of reactive oxygen species in both mice strands.

Conclusions:

In this small murine study, hypercholesterolemia exacerbated mitochondrial dysfunction, as clinically expected; but anti-oxidant therapy appeared protective, which is counter to clinical experience. Further work is clearly needed.

INTRODUCTION

Critical limb ischemia (CLI) is associated with poor outcomes in terms of survival or limb salvage [START_REF] Aboyans | The 2017 ESC Guidelines on the Diagnosis and Treatment of Peripheral Arterial Diseases, in Collaboration with the European Society for Vascular Surgery (ESVS)[END_REF] . In order to better understand CLI pathophysiology, we developed a stable-over-time murine model based on sequential arterial ligations [START_REF] Lejay | A new murine model of sustainable and durable critical limb ischemia fairly mimicking human pathology[END_REF][START_REF] Lejay | Mitochondria: Mitochondrial participation to ischemia-reperfusion injury in skeletal muscle[END_REF] . This murine model, well mimicking human pathology, allowed the assessment of the key pathophysiological mechanisms of CLI, such as mitochondrial dysfunction and oxidative stress [START_REF] Lejay | A new murine model of sustainable and durable critical limb ischemia fairly mimicking human pathology[END_REF][START_REF] Paradis | Chronology of mitochondrial and cellular events during skeletal muscle ischemia-reperfusion[END_REF] . Indeed, suboptimal energy production from defective mitochondria in addition to reduced oxygen supply enhanced the production of reactive oxygen species (ROS) [START_REF] Lejay | Mitochondria: Mitochondrial participation to ischemia-reperfusion injury in skeletal muscle[END_REF] . Increased ROS production and impaired mitochondrial antioxidant defence system led to high oxidative stress [START_REF] Lejay | Mitochondria: Mitochondrial participation to ischemia-reperfusion injury in skeletal muscle[END_REF] .

The understanding of CLI pathophysiology allowed the development of alternative therapeutic approaches, especially for the 'no option' patients, since up to a third of CLI patients are not amenable to conventional interventions and will ultimately require major amputation [START_REF] Aboyans | The 2017 ESC Guidelines on the Diagnosis and Treatment of Peripheral Arterial Diseases, in Collaboration with the European Society for Vascular Surgery (ESVS)[END_REF] . Indeed, increased ROS production occurs before mitochondrial dysfunction, suggesting that strategies aiming to reduce ROS production might be successful [START_REF] Lejay | A new murine model of sustainable and durable critical limb ischemia fairly mimicking human pathology[END_REF][START_REF] Lejay | Mitochondria: Mitochondrial participation to ischemia-reperfusion injury in skeletal muscle[END_REF] . Such antioxidant strategies have thus been considered as promising therapeutic target, but clinical results have been mostly disappointing and antioxidant therapies are still far from being integrated into treatment algorithms for peripheral arterial disease, despite promising preclinical efficacy [START_REF] Aboyans | The 2017 ESC Guidelines on the Diagnosis and Treatment of Peripheral Arterial Diseases, in Collaboration with the European Society for Vascular Surgery (ESVS)[END_REF][START_REF] Giannopoulos | Antioxidant treatment in peripheral arterial disease: the rationale is there, but what about clinical results?[END_REF][START_REF] Koutakis | Oxidative stress and antioxidant treatment in patients with peripheral arterial disease[END_REF] . This discrepancy has put into question the relevance of the preclinical hind limb ischemia models that were used for efficacy testing [START_REF] Lofti | Towards a more relevant hind limb model of muscle ischaemia[END_REF] .

Thus, although our CLI model can be considered to be relevant to CLI, it does not entirely reproduce the complex human condition and there are important limitations that should be taken into account [START_REF] Lofti | Towards a more relevant hind limb model of muscle ischaemia[END_REF] . Particularly, the surgical protocol was performed on healthy young wildtype mice, constituting a main limitation. Indeed, CLI generally occurs in old patients presenting with cardiovascular risk factors leading to the build-up of atherosclerotic plaque.

Targeting oxidative stress through N-acetyl cysteine (NAC) administration has been shown to confer muscle protection in the setting of CLI [START_REF] Lejay | N-acetyl cysteine restores limb function, improves mitochondrial respiration, and reduces oxidative stress in a murine model of critical limb ischemia[END_REF][START_REF] Medeiros | N-acetylcysteine effects on a murine model of chronic critical limb ischemia[END_REF] . The antioxidant effect of NAC is due to its ability to act as a reduced glutathione precursor, which is a well-known direct antioxidant and a substrate of several antioxidant enzymes. Moreover, NAC can act as a direct antioxidant for some oxidant species such as nitrogen dioxide. The antioxidant activity of NAC is also due to the breaking of thiolated proteins, thus releasing free thiols as well as reduced proteins, which have important antioxidant activity [START_REF] Gonzalez-Montero | Myocardial reperfusion injury and oxidative stress: therapeutic opportunities[END_REF] . However, comorbidities, particularly hypercholesterolemia, has been shown to reduce cardioprotection related to antioxidants during cardiac ischemia-reperfusion [START_REF] Ferdinandy | Interaction of risk factors, comorbidities, and comedications with ischemia/reperfusion injury and cardioprotection by preconditioning, postconditioning, and remote conditioning[END_REF] . Consequently, efficacy of antioxidant therapy deserved to be questioned in the setting of CLI, due to associated comorbidities.

The aim of the present study was therefore to investigate first whether CLI would lead to a more severe mitochondrial dysfunction ApoE-knockout (ApoE-/-) mice, commonly used to simulate the effects of atherosclerosis and dyslipidemia [START_REF] Getz | ApoE knockout and knocking mice: the history of their contribution to the understanding of atherogenesis[END_REF][START_REF] Peck | A functional murine model of hindlimb demand ischemia[END_REF] , and second whether targeting oxidative stress through NAC administration in such mice would still confer muscle protection as previously observed in healthy mice [START_REF] Lejay | N-acetyl cysteine restores limb function, improves mitochondrial respiration, and reduces oxidative stress in a murine model of critical limb ischemia[END_REF][START_REF] Medeiros | N-acetylcysteine effects on a murine model of chronic critical limb ischemia[END_REF] .

MATERIALS AND METHODS

Animals

The protocol was approved by the Ethics Committee for Animal Research of our university (reference number AL/70/77/02/13). ApoE-/-mice (n=9, 29 weeks-old) and their genetic controls ApoE+/+ mice (n=9, 29 weeks-old) were fed a diet consisting of high fat and handled while observing the French criteria for the care and use of laboratory animals in research.

CLI model

Surgery was performed in all animals under general anaesthesia, according to our established model [START_REF] Lejay | A new murine model of sustainable and durable critical limb ischemia fairly mimicking human pathology[END_REF] . In rodents, ligation of the femoral artery just distal to the origin of the profundal femoris is most commonly used, but this method leaves most of the collateral circulation to the lower limb intact and blood flow to the lower limb is restored within 7 days. Our model is thereby based on a two-step procedure performed under microscope. The first step consists of a ligation of the right femoral artery, performed midway between the superficial epigastric artery and bifurcation of the popliteal and saphenous arteries, and of three collateral vessels.

The second step consists of the ligation of the right common iliac artery 0.5 cm distal to its origin, since collateral vessels in the mice arise mostly from the internal iliac artery. By performing sequential ligations, a sustainable ischemia was thereby obtained. The left limb can be considered as control [START_REF] Lejay | A new murine model of sustainable and durable critical limb ischemia fairly mimicking human pathology[END_REF][START_REF] Thaveau | Contralateral leg as control during skeletal muscle ischemia reperfusion[END_REF] (Supplemental data).

Subcutaneous buprenorphine (1.5 mg/kg) was daily administered to all animals until day 7.

During follow-up once CLI was established, clinical evaluation of all animals was conducted twice a day, to ensure their well-being and health status. Indicators of pain such as no grooming, vocalizations, isolation of an animal from the rest of the group, changes in posture were searched, according to the French criteria for the care and use of laboratory animals in research. Buprenorphine was administered accordingly.

Anti-oxidant treatment

NAC was administered by dissolution in drinking water for 4 weeks, starting on day 7 [START_REF] Mokhtari | A review on various uses of N-acetyl cysteine[END_REF][START_REF] Roseguini | Effects of Nacetyl cysteine on skeletal muscle structure and function in a mouse model of peripheral arterial insufficiency[END_REF] . A dose of 1.5 g/kg/day was chosen since we previously showed that this dose reduced oxidative stress and triggered mitochondrial biogenesis [START_REF] Lejay | N-acetyl cysteine restores limb function, improves mitochondrial respiration, and reduces oxidative stress in a murine model of critical limb ischemia[END_REF] .

Mitochondrial respiratory chain complex activities

The study of mitochondrial complex activity was measured by oxygraphy through oxygen consumption in skinned fibres, assessing the functional oxidative capacity of the skeletal muscle in its cellular environment. Substrates were added in order to activate or inhibit the different complexes of the respiratory chain. Adenosine diphosphate (2 mM) was added in order to study complex I, III and IV activity. Succinate (25 mM) was then added to study complex I, II, III and IV activity, which determined the maximal oxidative capacity (Vmax).

The addition of amytal (0.02 mM) subsequently inhibited complex I; and the addition of N,N,N', N'-tetramethyl-p-phenylenediamine dihydrochloride (0.5 mM) and ascorbate (0.5 mM) specifically activated complex IV.

Calcium retention capacity

Calcium retention capacity was measured by spectrofluorometry. It represents the high cut-off amount of calcium that determines the opening of the mitochondrial transition pore, which allows the release of calcium that will in turn lead to apoptosis. Calcium pulses (20 µM) were applied to skinned fibers of gastrocnemius muscle. The mitochondrial calcium uptake was thereafter assessed after the addition of a single calcium pulse (20 µM), by measuring the descrease of the extramitochondrial calcium concentration. The measure was monitored using a fluorescence probe (Calcium Green-5N, Invitrogen). When mitochondrial calcium release started, when the calcium uptake showed an inflection point, it was considered that the mitochondrial transition pore opening was observed. Mitochondrial calcium retention capacity, which is a reliable index of mitochondrial transition pore sensitivity, was calculated as the total amount of calcium taken up by mitochondria before calcium release.

Production of ROS

Production of ROS was assessed by electron paramagnetic resonance. Muscles (1 mm 3 fragments) were incubated with a 200 µM molecular probe (1-hydroxy-3-methoxycarbonyl-2,2,5,5-tetramethylpyrrolidine HCl), which is oxidised in the presence of unpaired electrons of ROS. The amount of oxidised probe was measured through the intensity of the resonance signal.

Study design and group assignment

Eighteen 29 weeks of age mice were allocated to our experiment: ApoE-/-(n=9) and their genetic control ApoE+/+ (n=9). Our model showed a good reproducibility over time and an important aim being to determine the potential protective effects of NAC, it was thereby decided in accordance with the statistician to assign more mice in the NAC groups.

Surgery was performed in all animals. ApoE+/+ mice were then divided into 2 groups: Group 1 (n=4) and Group 2 (n=5); as well as ApoE-/-mice: Group 3 (n=3) and Group 4 (n=6). NAC treatment was administered in Group 2 and 4. All animals were sacrificed at day 40.

Gastrocnemius muscles were collected in order to investigate mitochondrial respiratory chain complex activities, calcium retention capacity and ROS production.

Statistical analysis

Number of animals was approved by the Ethics Committee for Animal Research of our university. Statistical analysis was performed with GraphPad Prism 5 (GraphPad Software, La Jolla, CA, USA). Normal distribution of the variables was confirmed by Shapiro-Wilk test.

Inter-individual comparison was assessed using the paired t test. inter-individual comparison

was assessed with a one-way ANOVA test. Results are expressed as means and standard deviation. A p value < .05 was considered to be statistically significant.

RESULTS

Critical limb ischemia in Apoe-/-mice

Maximal oxidative capacity was impaired in ischemic muscles as compared to control muscles in ApoE+/+ mice: 6.95 ± 0.81 vs 9.27 ± 1.01 mmol O2/min/g dw (p=0.001) as well as in ApoE-/-mice: 4.76 ± 0.55 vs 8.43 ± 0.77 mmol O2/min/g dw (p=0.011) (Figure 1a andb).

Such decrease was higher in ApoE-/-mice than in ApoE+/+ mice (-42.9% vs -25.1%, p=0.021) (Figure 1c).

Calcium retention capacity was impaired in ischemic muscles as compared to control muscles in ApoE+/+ mice: 7.28 ± 0.56 vs 12.23 ± 0.70 µM/mg dw (p=0.001) as well as in ApoE-/-mice: 4.86 ± 1.46 vs 11.07 ± 1.33 µM/mg dw (p=0.001) (Figure 2a andb). The decrease was also higher in ApoE-/-mice than in aAoE+/+ mice (-73.1% vs -56.7%, p=0.03) (Figure 2c).

Production of ROS was increased in ischemic muscles as compared to control muscles in ApoE+/+ mice: 0.105 ± 0.019 vs 0.074 ± 0.009 mmol/min/mg dw (p=0.011) as well as in ApoE-/-mice: 0.139 ± 0.011 vs 0.087 ± 0.013 mmol/min/mg dw (p=0.039) (Figure 3a andb).

ROS increase was higher in ApoE-/-mice than in ApoE+/+ mice (+63.6% vs +41.4%, p=0.031) (Figure 3c).

NAC treatment in Apoe-/-mice

Maximal oxidative capacity was restored in ischemic muscles compared to control muscles in ApoE+/+ mice: 9.13 ± 1.75 vs 10.02 ± 1.26 mmol O2/min/g dw (p=NS) as well as in ApoE-/mice: 7.51 ± 1.77 vs 7.91 ± 1.94 mmol O2/min/g dw (p=NS) (Figure 1a andb).

Calcium retention capacity was restored in ischemic muscles compared to control muscles in ApoE+/+ mice: 10.56 ± 1.89 vs 10.90 ± 1.39 µM/mg dw (p=NS) as well as in ApoE-/-mice:

9.07 ± 1.79 vs 9.58 ± 2.16 µM/mg dw (p=NS) (Figure 2a andb).

Production of ROS was comparable in ischemic muscles compared to control muscles in ApoE+/+ mice: 0.048 ± 0.015 vs 0.046 ± 0.017 mmol/min/mg dw (p=NS) as well as in ApoE-/-mice: 0.069 ± 0.018 vs 0.061 ± 0.011 mmol/min/mg dw (p=NS) (Figure 3a andb).

DISCUSSION

The main finding of this study is that CLI leads to a more severe mitochondrial dysfunction under hypercholesterolemic conditions in ApoE-/-mice, since maximal oxidative and calcium retention capacities decreases and production of ROS increases were enhanced as compared to ApoE+/+ mice. Further, targeting oxidative stress through antioxidant therapy such as NAC in such mice still conferred muscle protection, not only in ApoE+/+ but also in ApoE-/-mice.

Intensive research was performed to understand the pathophysiology of ischemia/reperfusion, but surprisingly little effort has been made to uncover the cellular mechanisms by which major cardiovascular risk factors may interfere with ischemia/reperfusion. Moreover, many studies investigated the myocardium and little is known concerning skeletal muscle in the setting of CLI. In epidemiological studies, there is a well-recognized relationship between serum total cholesterol concentrations and the morbidity and mortality due to myocardial infarction [START_REF] Ferdinandy | Interaction of risk factors, comorbidities, and comedications with ischemia/reperfusion injury and cardioprotection by preconditioning, postconditioning, and remote conditioning[END_REF] . Previously, this was attributed solely to the development of coronary atherosclerosis as a result of hypercholesterolemia. However, the majority of preclinical studies, together with some small-scale clinical studies, have shown that hypercholesterolemia per se, and not atherosclerosis, leads to a significant aggravation of myocardial ischemia/reperfusion injury [START_REF] Ferdinandy | Interaction of risk factors, comorbidities, and comedications with ischemia/reperfusion injury and cardioprotection by preconditioning, postconditioning, and remote conditioning[END_REF] . The mechanisms by which hypercholesterolemia may influence the severity of ischemia/reperfusion injury is however not fully understood, but increased oxidative stress, inactivation of protein kinase G, and enhanced apoptotic cell death have been demonstrated as consequences of hypercholesterolemia in the myocardium [START_REF] Ferdinandy | Interaction of risk factors, comorbidities, and comedications with ischemia/reperfusion injury and cardioprotection by preconditioning, postconditioning, and remote conditioning[END_REF] . Our study confirms that hypercholesterolemia further potentiates the deleterious effects of CLI on skeletal muscle. The mechanisms involved combine enhanced mitochondrial dysfunction with reduced oxidative capacity and premature opening of the mitochondrial permeability pore, favouring thereby apoptosis, together with increased oxidative stress.

Whether NAC administration might loss its protective effects in CLI, as previously observed in cardiac ischemia reperfusion, deserved to be investigated. Indeed, hypercholesterolemia attenuates the protective effect of pharmacologic conditioning via changes in protective signalling pathways [START_REF] Ferdinandy | Interaction of risk factors, comorbidities, and comedications with ischemia/reperfusion injury and cardioprotection by preconditioning, postconditioning, and remote conditioning[END_REF] . Again, studies investigated mainly the myocardium. It has thus been demonstrated that pharmacologic activation of the NO-cGMP-PKG pathway significantly reduced infarct size in normal rat hearts, but was ineffective in hearts of rats fed a cholesterolenriched diet [START_REF] Andreadou | The role of gasotransmitters NO, H2S, CO in myocardial ischemia/reperfusion injury and cardioprotection by preconditioning, postconditioning and remote conditioning[END_REF][START_REF] Bice | Novel approaches and opportunities for cardioprotective signaling through 3',5'-cyclic guanosine monophosphate manipulation[END_REF] . The loss of cardioprotection was possibly due to inactivation of PKG by oxidative dimerization of the kinase under dyslipidemic conditions. These results indicated that drug targets upstream of PKG might not provide cardioprotection under hypercholesterolemic conditions [START_REF] Giricz | Hyperlipidaemia induced by a high-cholesteral diet leads to the deterioration of guanosine-3',5'-cyclic monophosphate/protein kinase G-dependent cardioprotection in rats[END_REF] . Similarly concerning ATP-sensitive potassium (KATP) channel activation, it was shown that the infarct size limiting effect of either the nonselective KATP activator cromakalim or the selective mitochondrial KATP activator diazoxide was abrogated in dyslipidemic cholesterol-fed rats [START_REF] Csonka | Cholesterol-enriched diet inhibits cardioprotection by ATP-sensitive K+ channel activators cromakalim and diazoxide[END_REF] . Moreover, in dyslipidemic Zucker obese rats, the mPTP inhibitor cyclosporine A could not exert cardioprotection [START_REF] Huhn | Cyclosporine A administered during reperfusion fails to restore cardioprotection in prediabetic Zucker obese rats in vivo[END_REF] . These results indicated that either activation of the NO-cGMP-PKG pathway or KATP channels, or the inhibition of the mPTP may not be ideal cardioprotective drug targets, because they were ineffective in the presence of dyslipidemia. Consequently, knowing that the beneficial effects of NAC observed in both acute lower-limb ischemia reperfusion and CLI were obtained in healthy animals, such results could not preclude efficacy in case of hypercholesterolemia [START_REF] Giannopoulos | Antioxidant treatment in peripheral arterial disease: the rationale is there, but what about clinical results?[END_REF][START_REF] Lejay | N-acetyl cysteine restores limb function, improves mitochondrial respiration, and reduces oxidative stress in a murine model of critical limb ischemia[END_REF][START_REF] Medeiros | N-acetylcysteine effects on a murine model of chronic critical limb ischemia[END_REF][START_REF] Ferdinandy | Interaction of risk factors, comorbidities, and comedications with ischemia/reperfusion injury and cardioprotection by preconditioning, postconditioning, and remote conditioning[END_REF] .

Importantly, NAC still conferred muscle protection in hypercholesterolemic mice. Indeed, in the present study, targeting oxidative stress by anti-oxidant administration restored mitochondrial function, in both ApoE+/+ and ApoE-/-mice, supporting the hypothesis that antioxidant interventions would be beneficial in terms of vascular disease prevention [START_REF] Giannopoulos | Antioxidant treatment in peripheral arterial disease: the rationale is there, but what about clinical results?[END_REF] .

However, results of clinical studies regarding potential effects of antioxidant administration are disappointing, questioning the relevance of the preclinical hind limb ischemia models in other situations [START_REF] Giannopoulos | Antioxidant treatment in peripheral arterial disease: the rationale is there, but what about clinical results?[END_REF][START_REF] Koutakis | Oxidative stress and antioxidant treatment in patients with peripheral arterial disease[END_REF] . A contrario, recent studies revealed that some pharmacologic targets remain effective even in the presence of hypercholesterolemia [START_REF] Giricz | Hyperlipidaemia induced by a high-cholesteral diet leads to the deterioration of guanosine-3',5'-cyclic monophosphate/protein kinase G-dependent cardioprotection in rats[END_REF] . Thus, pharmacologic inhibition of GSK3β allowed muscle protection in both normal and hypercholesterolemic rats [START_REF] Yadav | Pharmacological inhibition of GSK3β produces late phase of cardioprotection in hyperlipidemic rat: possible involbement of HSP 72[END_REF] . Consequently, even if the majority of clinical studies show that antioxidant strategies are ineffective, it seems mandatory to clearly define drug targets. By identifying the ideal drug target, the increased susceptibility of skeletal muscle to CLI could be reversed, even in hypercholesterolemic situations.

Our study suffers from several limitations. We investigated the role of hypercholesterolemia on 7 months-old ApoE-/-mice, commonly used to simulate the effects of atherosclerosis and dyslipidemia, but other risk factors and comorbidities, including hypertension, diabetes and aging should also be investigated. Another limitation is the small sample size. However, normally distributed continuous data results with small variance between animals in the same groups coupled with valid within-animal data pairing statistics provided very high probabilities of rejecting the null hypothesis. Consequently, significant conclusions may be drawn from our data despite small sample size. Another important point is that we specifically investigated fast glycolytic muscles. This choice was based on the fact that muscles susceptibility to ischemia-reperfusion injury depends on fiber type specific antioxidant level, explaining the greater injuries observed in glycolytic as compared to oxidative muscles [START_REF] Charles | Muscles susceptibility to ischemia-reperfusion injuries depends on fiber type specific antioxidant level[END_REF] . We needed to observe muscle impairment in order to determine an eventual protection by NAC.

Thus, our data apply only to glycolytic muscles, but this is pertinent since they are key targets to protect. Finally, further study will be useful to determine the molecular mechanisms and the signalling pathways involved in both the hypercholesterolemia-related exacerbation of CLI mitochondrial dysfunction and in muscle protection afforded by NAC.

In conclusion, the current study highlights that hypercholesterolemia exacerbates CLI mitochondrial dysfunction. Interestingly, NAC kept its protective properties despite hypercholesterolemia known to reduce efficacy of protective pathways. Complementary studies will be useful to further identify the underlying mechanisms at a molecular level allowing to precise the 'ideal' antioxidant target. 2a and2b).

LEGENDS FOR ILLUSTRATION

Calcium retention capacity decrease was higher in ApoE-/-mice than in ApoE+/+ mice (Figure 2c).

Results are expressed as mean ± standard deviation. * p < .05; ** p < .01.

CTL: control limb; ISC: ischemic limb; NAC: N-acetyl cysteine

Figure 3 .Figure 1 .Figure 2 .Figure 3 .

 3123 Figure 3. Production of ROS was increased in ischemic muscles compared to control muscles in

  Results are expressed as mean ± standard deviation. * p < .05; ** p < .01.Results are expressed as mean ± standard deviation. * p < .05; ** p < .01. Production of ROS was increased in ischemic muscles compared to control muscles in ApoE+/+ mice and in ApoE-/-mice, but comparable in ischemic muscles and in control muscles in

	treatment (Figure 1a and 1b). Maximal oxidative capacity decrease was higher in ApoE-/-mice LEGENDS FOR ILLUSTRATION
	than in ApoE+/+ mice (Figure 1c). Figure 1. Maximal oxidative capacity was impaired in ischemic muscles compared to control
	muscles in ApoE+/+ mice (n=4) and in ApoE-/-mice (n=3), but restored in ischemic muscles
	CTL: control limb; ISC: ischemic limb; NAC: N-acetyl cysteine compared to control muscles in ApoE+/+ mice (n=5) and in ApoE-/-mice (n=6) after NAC
	Figure 2. Calcium retention capacity was impaired in ischemic muscles compared to control muscles treatment (Figure 1a and 1b). Maximal oxidative capacity decrease was higher in ApoE-/-mice
	in ApoE+/+ mice (n=4) and in ApoE-/-mice (n=3), but restored in ischemic muscles compared to than in ApoE+/+ mice (Figure 1c).
	control muscles in ApoE+/+ mice (n=5) and in ApoE-/-mice (n=6) after NAC treatment (Figure 2a Results are expressed as mean ± standard deviation. * p < .05; ** p < .01.
	and 2b). Calcium retention capacity decrease was higher in ApoE-/-mice than in ApoE+/+ mice CTL: control limb; ISC: ischemic limb; NAC: N-acetyl cysteine
	(Figure 2c). Figure 2. Calcium retention capacity was impaired in ischemic muscles compared to control muscles in
	ApoE+/+ mice (n=4) and in ApoE-/-mice (n=3), but restored in ischemic muscles compared to control
	CTL: control limb; ISC: ischemic limb; NAC: N-acetyl cysteine muscles in ApoE+/+ mice (n=5) and in ApoE-/-mice (n=6) after NAC treatment (Figure
	Figure 3. ApoE+/+ mice (n=5) and in ApoE-/-mice (n=6) after NAC treatment (Figure 3a and 3b). Reactive
	oxygen species was higher in ApoE-/-mice than in ApoE+/+ mice (Figure 3c).
	Results are expressed as mean ± standard deviation. * p < .05.
	CTL: control limb; ISC: ischemic limb; NAC: N-acetyl cysteine
	Supplemental Data. Left limbs were compared to sham-operated limbs. Maximal oxidative
	capacity showed no difference in sham-operated muscles (n=4) compared to control muscles
	in ApoE+/+ mice (n=4) (a). Calcium retention capacity showed no difference in sham-
	operated muscles (n=4) compared to control muscles in ApoE+/+ mice (n=4) (b). Production
	of ROS showed no difference in sham-operated muscles (n=4) compared to control muscles
	1. Maximal oxidative capacity was impaired in ischemic muscles compared to control in ApoE+/+ mice (n=4) (c).
	muscles in ApoE+/+ mice (n=4) and in ApoE-/-mice (n=3), but restored in ischemic muscles Results are expressed as mean ± standard deviation. * p < .05; ** p < .01.
	compared to control muscles in ApoE+/+ mice (n=5) and in ApoE-/-mice (n=6) after NAC CTL: control limb
	-17 -

ACKNOWLEDGMENTS

The authors thank Jean Etienne Fabre for his assistance for providing mice.

Conflict of Interest/Funding: None