Nicolas Nadisic

Arnaud Vandaele

Nicolas Gillis

Jeremy E Cohen

EXACT SPARSE NONNEGATIVE LEAST SQUARES

Keywords: nonnegative least squares, sparse coding, branch-and-bound

We propose a novel approach to solve exactly the sparse nonnegative least squares problem, under hard 0 sparsity constraints. This approach is based on a dedicated branch-and-bound algorithm. This simple strategy is able to compute the optimal solution even in complicated cases such as noisy or ill-conditioned data, where traditional approaches fail. We also show that our algorithm scales well, despite the combinatorial nature of the problem. We illustrate the advantages of the proposed technique on synthetic data sets, as well as a real-world hyperspectral image.

INTRODUCTION

Nonnegative least squares (NNLS) problems of the form min ||Ax -b|| 2 2 such that x ≥ 0,

where x ∈ R n , A ∈ R m×n , and b ∈ R m , are a variant of least squares (LS) problems where the solution is required to be entrywise nonnegative. Nonnegativity is useful for models where data are additive combinations of meaningful components [START_REF] Lee | Unsupervised learning by convex and conic coding[END_REF]. For example, in hyperspectral images, the spectra of pixels are nonnegative linear combinations of the pure components they contain [START_REF] José | Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches[END_REF]. NNLS is also one of the principal tools used in the so-called "alternating approaches" to solve nonnegative matrix factorization [START_REF] Gillis | The why and how of nonnegative matrix factorization[END_REF]. As a constraint, nonnegativity is known to naturally induce sparsity, that is, produce solutions with few non-zero components; see for example [START_REF] Foucart | Sparse recovery by means of nonnegative least squares[END_REF] and the references therein. Sparse solutions express data points as combinations of only a few atoms, thus improving the interpretability of the decomposition. For instance, in the task of identifying the materials present in the pixels of a hyperspectral image, sparsity means a pixel will be composed of only a few materials. However, there is no guarantee on the sparsity of the solution to a general NNLS problem, while controlling the sparsity level of solutions is important in many applications, such as hyperspectral imaging [START_REF] Wing-Kin | A signal processing perspective on hyperspectral unmixing: Insights from remote sensing[END_REF] and sparse NMF [START_REF] Hoyer | Non-negative matrix factorization with sparseness constraints[END_REF]. Hence comes the need to design sparsity-enhancing techniques. The sparsity of a vector x is typically measured by its 0-"norm", x 0 = |{i : xi = 0}|. It is equal to the number of nonzero components in x. However, as this "norm" is non-convex and non-smooth, it is hard to enforce 0 constraints. One way to overcome this issue is to use the 1-norm as a convex surrogate, via the well-known NN and NG acknowledge the support by the European Research Council (ERC starting grant No 679515), and by the Fonds de la Recherche Scientifique -FNRS and the Fonds Wetenschappelijk Onderzoek -Vlanderen (FWO) under EOS project O005318F-RG47.

LASSO approach [START_REF] Tibshirani | Regression shrinkage and selection via the lasso[END_REF]. This approach implies a regularization parameter (usually denoted λ) that can be hard to tune, especially if one requires a specific level of sparsity. This regularization also introduces a bias: the optimized problem is different, therefore the solution and its support may change. Thus, in some cases, it is preferable to directly solve an optimization problem with 0 constraints, without the use of a convex surrogate. In this setting, we propose a technique for solving the sparse NNLS problem with an explicit level of sparsity via a hard constraint on the 0-"norm" of the solution.

Problem: Given A ∈ R m×n , b ∈ R m and k ∈ N, we wish to solve exactly the following sparse NNLS problem

x * = argmin Ax -b 2 2 such that x 0 ≤ k and x ≥ 0. (2)
This problem is also referred to as nonnegative sparse coding [START_REF] Hoyer | Non-negative sparse coding[END_REF].

Because of the discrete nature of the 0-"norm", Problem (2) is combinatorial, with n k possible supports for x. A brute-force algorithm would solve a NNLS subproblem for each possible support and select the solution with minimal error. This is the approach used by [START_REF] Cohen | Nonnegative Lowrank Sparse Component Analysis[END_REF] in the context of sparse NMF. However, the number of possible supports grows exponentially with n and k. To avoid computing all of them, the solution we propose can prune the search space using a branch-and-bound strategy. With this technique, the problem is still solved exactly, but far fewer NNLS subproblems are solved, leading to reasonable computing times even for large n and k.

In Section 2, we discuss competing algorithmic approaches to the nonnegative sparse coding problem. In Section 3, we present a novel branch-and-bound algorithm. Finally, in Section 4, we illustrate the effectiveness of the approach on synthetic data sets and on a practical application of hyperspectral unmixing.

RELATED WORK

Sparse coding is a well-studied problem, with many heuristic approaches available for solving large-scale problems [START_REF] Foucart | A Mathematical Introduction to Compressive Sensing, Applied and Numerical Harmonic Analysis[END_REF]. One of the most popular, the 1-regularized LASSO, solves the problem min x≥0 ||Ax -b|| 2 2 + λ||x||1 for some λ > 0. In this method, sparsity is encouraged through the regularization parameter λ. Selecting a value for this parameter that achieves a given level of sparsity is not straightforward. Moreover, existing theoretical guarantees for support recovery such as the Exact Recovery Condition [START_REF] Gribonval | Sparse representations in unions of bases[END_REF] are quite restrictive for some uses of sparse NNLS, in particular when used as a routine for solving sparse NMF [START_REF] Cohen | Nonnegative Lowrank Sparse Component Analysis[END_REF]. However, it benefits from the powerful properties of convex optimization, and efficient convex optimization algorithms exist that make use of optimality conditions to perform screening or design a stopping criterion [START_REF] Ghaoui | Safe feature elimination in sparse supervised learning[END_REF].

Greedy algorithms are another popular approach. Techniques of this type start with an empty support, and then select the atoms one by one to enrich the support, until the desired sparsity, k, is reached. The atom selection is done in a greedy way, selecting at each iteration the atom that maximizes the decrease of the residual error.

Orthogonal variants of these algorithms ensure an atom will not be selected more than once. Popular examples are orthogonal matching pursuit (OMP) [START_REF] Chandra Pati | Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition[END_REF] and orthogonal least squares (OLS) [START_REF] Chen | Orthogonal least squares methods and their application to non-linear system identification[END_REF]. Nonnegative variants of these algorithms have been proposed; see [START_REF] Nguyen | Non-Negative Orthogonal Greedy Algorithms[END_REF] and the references therein. They aim to solve (2) heuristically, but theoretical recovery guarantees are similarly limited.

Bienstock proposed a branch-and-cut algorithm to solve a cardinality-constrained quadratic program (CCQP), a problem similar to (2) with different constraints, using continuous relaxation at every iteration [START_REF] Bienstock | Computational study of a family of mixedinteger quadratic programming problems[END_REF]. Bertsimas and Shioda extended it by proposing a new way to solve the continuous relaxation problems [START_REF] Bertsimas | Algorithm for cardinality-constrained quadratic optimization[END_REF]. Mhenni et. al generalized this CCQP and proposed a novel branch-and-bound algorithm to solve exactly the continuous relaxation problems using dedicated optimization methods [START_REF] Bourguignon | Exact sparse approximation problems via mixed-integer programming: Formulations and computational performance[END_REF][START_REF] Mhenni | Global optimization for sparse solution of least squares problems[END_REF].

THE ARBORESCENT ALGORITHM

We propose a novel technique to solve the sparse NNLS problem exactly via a branch-and-bound algorithm called arborescent1 . In this algorithm, the possible patterns of zeros (that is, the possible supports) in the solution vector are enumerated on a tree, as shown in Figure 1. Each node represents an over-support K of x. The entries of x indexed by K are those that are not constrained to be 0. The cardinality of K is equal to the current tree depth. Exploring a node means solving the following NNLS subproblem

f * (K) = min ||A(:, K)x(K) -b|| 2 2 such that x(K) ≥ 0, (3)
where x(K) is the subvector of x whose entries are specified by the subset K ⊆ {1, 2, . . . , n}. The value f * (K) is the error associated with the node corresponding to K. In arborescent, an activeset algorithm [START_REF] Luís | A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables[END_REF] is used as the NNLS solver. The key property of active-set methods is that they solve the NNLS problem exactly, without a need for parameter tuning. Note that active-set methods allow for a warm start, that is, the algorithm can be initialized at the current node with the solution from a previous node. This significantly speeds up the iterative process since it starts close to the optimal solution. Branch. The root of the tree represents the unconstrained problem. No component of x is constrained to zero, that is, K = {1, 2, . . . , n}. At this root node, the support of x is required to have cardinality at most k = n (unconstrained). From this root we generate one child node for each component of x, where the respective component is not in the support (and thus constrained to zero). The cardinality of the support of x in these children nodes is therefore at most k = n -1. The tree is constructed recursively, by constraining one additional component to be equal to zero per node. When the tree has reached the depth were the cardinality of the support set is k = k, the desired sparsity is obtained and the leaf nodes at this depth represent feasible solutions to (2). As described above, several nodes of the arborescent tree would correspond to the same over-support K. For example, in Figure 1 there would be a redundant node {0, 0, x3, x4, x5} as the child of both {0, x2, x3, x4, x5} and {x1, 0, x3, x4, x5}. To avoid this redundant computations, we first order the nodes in the root node in order of increasing magnitude of the entries of the unconstrained solution. Let x * be the optimal solution of (1), we reorder the entries of x * so that the

X = [x1 x2 x3 x4 x5] root node, unconstrained k ≤ n = 5 X = [0 x2 x3 x4 x5] X = [0 0 x3 x4 x5] X = [0 0 0 x4 x5] X = [0 0 x3 0 x5] X = [0 0 x3 x4 0] k ≤ 2 = k → stop X = [0 x2 0 x4 x5] X = [0 x2 x3 0 x5] ... k ≤ 3 X = [x1 0 x3 x4 x5] ... k ≤ 4
x * 1 ≤ x * 2 ≤ • • • ≤ x * n .
With this information, we can deduce if the node has already been explored. Bound. As an additional entry of x is constrained to be zero for each child node, the error of a given node will always be greater than or equal to the error of its parent, by construction. As soon as we reached a leaf of the tree, we obtain a feasible solution whose error is therefore an upper bound for [START_REF] José | Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches[END_REF]. Hence if a given node has an error greater than this upper bound, all the children of this node will also have a higher error, and it can be safely pruned. A key element of a branch-and-bound algorithm is the strategy used to explore the tree. A relevant exploration can quickly lead to a good admissible solution, and thus to a bound allowing the pruning of large parts of the search space. As described above, in arborescent, the solution x * to the unconstrained problem is computed in the root node and the components of x * are sorted in ascending order. Thereafter, the exploration is done depth-first, and "left-first". Among all children of a node, the node furthest left is explored first, that is, the components that are closest to zero in the unconstrained solution are constrained first. This is based on the hypothesis that if a component is close to zero in the solution of the unconstrained problem, it is more likely to be zero in the optimal solution of the constrained problem. We have observed empirically that this approach outperforms more complex strategies, including greedy node selection (that is, selecting the node with the lowest error). Pseudocode. arborescent is detailed in Algorithm 1. The set P is the pool of nodes. On line 5, it is initialized with the root node, that has a full support (no component is constrained). On line 6, a node is selected in P , following the strategy described above, and removed from P on line 8. On line 9, the NNLS subproblem defined by A and b limited to the corresponding over-support K is solved using the initialization x. If the error is larger that the current lowest error, no child node can be optimal, and the node is pruned (line 11). Otherwise, the exploration continues. If the desired sparsity level k is not reached, a new node is generated for every component of the over-support (lines 14 and 15). If the value of k is reached, the error of the current node is compared to the lowest error found so far (line 17), and if it is lower, it replaces it (line 18). Computational complexity. In the worst case, arborescent has to build and explore the whole tree, that is, to solve a number of NNLS subproblems equal to r l=k r l . In the best case, all nodes except the leftmost ones are pruned, so the number of NNLS subproblems to solve is r l=k l. In practice, the number or nodes explored is far from the worst case; see section 4.2.

EXPERIMENTS

The code of arborescent, along with test scripts, is provided on gitlab.com/nnadisic/sparse-nmf. All experiments were performed on a personal computer with an i5 processor, with a clock frequency of 2.30GHz. arborescent is implemented in C++ with a MEX interface, and its competitors are implemented in Matlab. All algorithms are monothreaded.

Algorithm 1: arborescent

Input: A ∈ R m×n + , b ∈ R m + , k ∈ {1,

Comparison on Synthetic Datasets

We compare arborescent to four algorithms:

• A 1-penalized coordinate descent, implemented by modifying the Matlab code from [START_REF] Gillis | Sparse and unique nonnegative matrix factorization through data preprocessing[END_REF]. This method uses a dynamic tuning of the regularization parameter λ to reach the desired sparsity. After a first run, the support of the solution is restricted to the k highest values, and a NNLS solver is run only for the values within the support so that the solution is guaranteed to be k-sparse while the bias of the 1 approximation is removed. We refer to this method as L1-CD.

• The interior-point method SDPT3 (version 4.0) [START_REF] Toh | Sdpt3a matlab software package for semidefinite programming, version 1.3[END_REF][START_REF] Reha | Solving semidefinite-quadratic-linear programs using SDPT3[END_REF] with CVX as a modeling system [START_REF] Inc | CVX: Matlab software for disciplined convex programming, version 2.0[END_REF][START_REF] Michael | Graph implementations for nonsmooth convex programs[END_REF] that solves the 1-penalized problem.

The regularization parameter λ is chosen as the final value of λ obtained by the previous method presented above, and the same postprocessing is used. We refer to this method as CVX.

• Nonnegative OMP (NNOMP) and Nonnegative OLS (NNOLS) [START_REF] Nguyen | Non-Negative Orthogonal Greedy Algorithms[END_REF] for which the Matlab codes are provided by the authors. Synthetic test cases are built by generating a random matrix A ∈ R m×n + and a random k-sparse vector xtrue ∈ R n + , computing b = Axtrue, and trying to find again xtrue with A, b and k as parameters of the sparse NNLS algorithm. We consider four cases: well-conditioned A and noiseless b, well-conditioned A and noisy b, ill-conditioned A and noiseless b, ill-conditioned A and noisy b. For well-conditioned A, each entry of A is generated using the uniform distribution in [0,1] (rand(m,n) in Matlab). For ill-conditioned A, we proceed in the same way, then compute the SVD of A = U ΣV T , replace Σ by values between 10 -6 and 1 equally spaced in a logscale (logspace(-6,0,n) in Matlab), and finally take A = U ΣV T . For b, we also use the uniform distribution in [0,1]. For the noise e added to b, we generate a vector where each entry is generated using the normal distribution of mean 0 and variance 1 (randn(m,1) in Matlab), then rescale e ← 0.05 e ||e|| 2 ||b||2 so that ||e||2 = 0.05||b||2 (the noise level is 5%). We generate such data sets for three values of m: 1000, 100, and 20, with fixed n = 20 and k = 10, for a total of 12 test settings. For each setting, 100 data sets are randomly generated, and processed by the 5 algorithms. For each algorithm, we measure the relative error ||Ax-b|| 2 ||b|| 2 averaged over these 100 runs, as well as the average computational time, and the number of successes (meaning the number of times the support of xtrue is recovered).

Tables 1 to 3 present the results of the experiments. As expected, arborescent always has an error of zero for noiseless data as it solves the problem exactly. This is particularly interesting when A is ill-conditioned, because then the competitors generally fail to identify the support. For noisy data, it always outperforms the competitors in terms of error, and of number of successes. It has a large majority of successes in all but the most difficult cases, when m = 20 and b is noisy. However, the superior performance of arborescent comes at the cost of an increase in running time.

Scalability of arborescent

To test the scalability of our solution, we run it with the same data model as in Section 4.1, in the well-conditioned and noiseless case, with the following parameters: m = 1000, n = {10, 12, ..., 60} and k = n 2 . Again 100 datasets are generated for each pair {n, k}, and processed by arborescent. The results are presented in table 4. We see that, despite the exponentially increasing size of the combinatorial problem (in the worst case scenario, arborescent would have to explore n l=k n l nodes; note that 60 30 > 10 17 ), most of the search space is pruned, and only a few nodes are explored. The running times does not increase exponentially, allowing the use of our solution in medium-scale problems. Note the computational time is not always monotonic as n increases (for example, n = 52). The reason is that the NNLS is sometimes significantly more difficult to solve (hence more nodes need to be explored) which increases the computational time. This happens very rarely.

Application on a Hyperspectral Image

In this section, arborescent is used to identify the materials present in the pixels of a hyperspectral image. The input data is the well-known Cuprite image [START_REF]USGS spectroscopy lab[END_REF]. It features 250 × 191 = 47750 pixels in m = 188 denoised spectral bands. We refer to this 188 × 47750 matrix as M . For the dictionary D, we use the output of the successive projection algorithm algorithm [START_REF] Gillis | Fast and robust recursive algorithms for separable nonnegative matrix factorization[END_REF] that selects a subset of the columns of M . The number of materials is n = 12, so D is a 188 × 12 matrix, and we want to find a 12 × 47750 matrix, V , representing the abundances of materials in each pixel such that M ≈ DV . Every column of this matrix represents a pixel, and an independent NNLS subproblem: V is computed by solving 47750 NNLS problems. As an additional constraint, we require the solution to be column-wise k-sparse with k = 5. We solve the problem first with a NNLS algorithm with no sparsity constraints (we refer to it as NNLS), then with arborescent and with L1-CD, using the same post-processing and settings as section 4.1. For each algorithm we report the running time, the relative reconstruction error ||M -DV || F ||M || F , and the average column-wise sparsity. Table 5 shows the results of the three considered algorithms. Although NNLS naturally produces a relatively sparse solution, it is higher than the sparsity target. L1-CD, on the contrary, produces a solution sparser than required (showing the difficulty to tune the parameter), at the cost of a high error (from 1.74% for NNLS to 4.21% for L1-CD). arborescent produces a solution with the required sparsity, and at the same time a low error, very close to the NNLS one (1.78%). Figure 2 shows the resulting material abundances for arborescent.

CONCLUSION

We proposed arborescent, a dedicated branch-and-bound algorithm to tackle the k-sparse nonnegative least squares problem exactly. It works in very general settings, where existing approaches such as LASSO or greedy algorithms fail to identify the support of the optimal solution. The branch-and-bound technique allows for substantial pruning of the search space, so this combinatorial problem can be solved exactly with a drastic reduction of computation time over brute-force methods. The combination of relative speed, scalability, and an exact solution provide a broadly applicable technique for medium-scale sparse nonnegative least squares problems.

Fig. 2. Material abundances in the Cuprite image. These correspond to true materials; for example the first row corresponds to Muscovite, Dumortierite, Alunite and Montmorillonite; see [START_REF] Ambikapathi | Chance-constrained robust minimumvolume enclosing simplex algorithm for hyperspectral unmixing[END_REF]. (Note that spatial coherence is strong while this is not explicitly enforced as the sparse NNLS are solved independently for each pixel. This indicates that the solution is meaningful.)

Fig. 1 .

 1 Fig. 1. Ex. of the arborescent search tree, for = 5 and k = 2.

  Well-cond A, Noiseless b Well-cond A, Noisy b Ill-cond A, Noiseless b Ill-cond A, Noisy b

  2, . . . , n} Output: x best = arg min

		x≥0	||Ax -b|| 2 2 s.t. ||x||0 ≤ k
	1 Init x0 ← NNLS(A, b)
	2 Sort the elements in x0 in increasing order
	3 Init K0 ← {1, ..., n}
	4 Init best error ← +∞
	5 Init P ← {(K0, x0)}
	6 while P = ∅ do
	7	(K, xparent) = P .select()
	8	P ← P \ {(K, xparent)}
	9	(error, x) ← NNLS(A(:, K), b, xparent(K))
	10	if error > best error then
	11	prune (do nothing)
	12	else
	13	if size(K) > k then
	14	foreach i ∈ K do
	16	else
	17	if error < best error then
	18	best error ← error

15

P ← P ∪ {(K \ {i}, x) } 19 x best ← x 20 return x best

Table 1 .

 1 Results for m = 1000. Relative error is in percent. Time is in milliseconds. Succ. is the number of successes, that is, the number of times the algorithm recovered the support of xtrue.

		Rel. Err. Time	Succ. Rel. Err. Time	Succ. Rel. Err. Time	Succ. Rel. Err. Time	Succ.
	L1-CD	0	6.83	100	5.01	3.13	97	3.50	8.61	16	6.28	4.12	9
	CVX	0	796.90 100	4.96	634.62	100	0.08	609.45 96	4.98	571.72	98
	NNOMP 0	5.60	100	4.96	3.73	100	2.79	4.14	3	5.83	3.63	3
	NNOLS	0	4.67	100	4.96	3.36	100	1.95	4.21	23	5.50	3.13	22
	arbo.	0	43.09	100	4.96	1369.30 100	0	29.80	100	4.96	1223.20 100
		Well-cond A, Noiseless b	Well-cond A, Noisy b		Ill-cond A, Noiseless b	Ill-cond A, Noisy b
		Rel. Err. Time	Succ. Rel. Err. Time	Succ. Rel. Err. Time	Succ. Rel. Err. Time	Succ.
	L1-CD	0.27	1.93	93	4.97	2.48	84	3.65	2.22	11	6.02	1.97	7
	CVX	0	536.95 100	4.73	502.00	100	0.02	508.60 98	4.84	489.68	58
	NNOMP 0.48	2.83	89	4.98	2.79	83	3.09	2.83	3	5.50	2.80	2
	NNOLS	0.20	2.52	95	4.88	2.62	91	2.15	2.55	14	5.11	2.55	18
	arbo.	0	46.32	100	4.73	1145.10 100	0	29.39	100	4.71	1304.40 63

Table 2 .

 2 Results for m = 100. Measures are defined as in table1.

		Well-cond A, Noiseless b	Well-cond A, Noisy b		Ill-cond A, Noiseless b	Ill-cond A, Noisy b
		Rel. Err. Time	Succ. Rel. Err. Time	Succ. Rel. Err. Time	Succ. Rel. Err. Time	Succ.
	L1-CD	2.88	1.39	23	4.29	1.31	15	3.41	1.44	5	4.66	1.53	1
	CVX	0.00	532.23 100	3.26	495.62	23	0.95	548.41 39	3.07	509.10	7
	NNOMP 3.02	2.85	12	3.85	2.74	6	2.07	2.96	2	3.57	2.88	0
	NNOLS	2.57	2.59	18	3.73	2.54	10	1.48	3.02	12	3.26	3.08	1
	arbo.	0	46.84	100	3.09	1472.20 30	0	34.20	100	2.83	1283.70 11

Table 3 .

 3 Results for m = 20. Measures are defined as in table1.

	n	Time (ms.) NNE	n	Time (ms.) NNE
	10 3.6504	9.24	36 678.09	60.62
	12 6.3706	11.02	38 667.68	48.9
	14 9.3337	15.41	40 1034.3	63.56
	16 16.386	18.16	42 3134.9	166.41
	18 24.837	23.15	44 2070.5	97.17
	20 42.344	29.37	46 2610.7	97.94
	22 83.267	41.06	48 8236.9	249.19
	24 97.774	35.82	50 1936.8	52.14
	26 137.17	38.1	52 39119	900.74
	28 277.33	59.06	54 6209.8	132.3
	30 268.09	48.33	56 9173.5	161.73
	32 392.77	54.57	58 8752.4	146.14
	34 601.7	67.74	60 14149	182.91

Table 4 .

 4 Results of the scalability test of arborescent. Time is the average over 100 instances (for k = n/2, m = 1000). NNE is the average number of nodes explored in the tree.

		NNLS L1-CD arbo
	Time (s.)	15.81	22.35	1053
	Rel. Error (%) 1.74	4.21	1.78
	Sparsity	6.61	4.34	4.77

Table 5 .

 5 Results of the regression on Cuprite image.

arborescent Realizes a Branch-and-bound Optimization to Require Explicit Sparsity Constraints to be Enforced in NNLS Tasks.


domain: sdv info shs

text:
Claudia Terlouw
email: claudia.terlouw@clermont.inra.fr

Cécile Bourguet

Véronique Deiss

Consciousness, unconsciousness and death in the context of slaughter. Part II. Evaluation methods

Keywords:

This second review describes indicators of consciousness and unconsciousness that can be used in the abattoir. These indicators evaluate different aspects of cerebral functioning, but only indirectly. It is therefore necessary to monitor several indicators. Animals are considered unconscious if signs of consciousness are absent, and signs of unconsciousness are present. Given that the unconscious state may be reversible it is further necessary to monitor these indicators until the end of bleeding. The techniques used to diagnose brain death in humans cannot be used in the slaughterhouse. Under field conditions, at the end of bleeding, the absence of breathing and of brainstem reflexes and the adequacy of the exsanguination are verified. If these three aspects are confirmed, in the context of the slaughterhouse and at this stage of the slaughter process the loss of vital functions is irreversible and the animal can be considered dead.

Introduction

Our first review presented the current state of scientific knowledge on brain functioning in the context of unconsciousness and the process of death at slaughter [START_REF] Terlouw | Consciousness, unconsciousness and death in the context of slaughter. Part I. Neurobiological mechanisms underlying stunning and killing[END_REF]. Loss of consciousness is the result of a reversible or irreversible dysfunction of certain brain structures: the reticular formation, the ascending reticular activating system or the cerebral hemispheres globally. The death of an individual is defined in terms of brain death. This implies the irreversible cessation of brain structures responsible for vital functions like breathing and thermal and cardiovascular regulation that are in the brainstem [START_REF] Laureys | Science and society: Death, unconsciousness and the brain[END_REF]. This second review aims to contribute to the reflection on the use and interpretation of indicators of consciousness and unconsciousness. The difficulty of assessing brain death in the context of slaughter is also addressed. The synthesis concerns the major food species consumed in Europe, with the exception of fish.

Indicators of consciousness and unconsciousness

Following stunning, to avoid unnecessary stress or pain, the unconscious state should be ensured before shackling and hoisting of cattle, pigs and sheep [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. A number of indicators are used to assess the state of consciousness or unconsciousness of the animal [START_REF] Efsa | Welfare aspects of the main systems of stunning and killing the main commercial species of animals[END_REF][START_REF] Efsa | Scientific opinion on monitoring procedures at slaughterhouses for bovines[END_REF]. These clinical signs are indirectly associated with brain functions involved in consciousness, particularly the reticular formation and/or the cerebral cortex. Some of these indicators indicate almost certainly a conscious and others an unconscious state (Table 1). To ensure unconsciousness, indicators of consciousness must be absent and indicators of unconsciousness must be present. The absence or presence of these indicators must be checked after stunning and during bleeding, for both conventional and religious slaughter. Other indicators have a lower discriminating power and can be used as complementary information [START_REF] Gregory | Depth of concussion in cattle shot by penetrating captive bolt[END_REF]. The relationships between the different indicators and brain functioning, including consciousness and unconsciousness, are discussed below.

Indicators of consciousness

Standing posture

In the slaughter context, the standing posture is an indicator of consciousness (Table 1). Therefore, the immediate and permanent loss of the standing posture is used as an indicator of the potential loss of consciousness. Immediate collapse following application of the stun is a main indicator because it is relatively visible; it allows assessing the quality of the stun or of bleeding in non-stunned animals that are bled in the standing posture. This indicator should be interpreted with caution, however, because collapse can be caused by an inability to stand, for example, when the stun gun is placed in the neck and severs the upper spinal cord only paralysing the animal without damaging the brain. Moreover, the collapse cannot be evaluated in animals maintained in a box which restrains the head or body, in a V-shaped restrainer, or animals suspended on a rail (poultry).

Following an effective mechanical stunning the animal collapses immediately. This collapse can be explained by damage to the reticular formation, involved in the control of the standing posture [START_REF] Purves | Motor control centers in the brainstem: Upper motor neurons thatmaintain balance and posture[END_REF][START_REF] Schepens | Independent and convergent signals from the pontomedullary reticular formation contribute to the control of posture and movement during reaching in the cat[END_REF]. Electrical stunning also causes immediate collapse, due to the seizure spreading through the cerebral hemispheres and subcortical structures, particularly the reticular formation [START_REF] Tatum | Atypical absence seizures, myoclonic, tonic and atonic seizures[END_REF]. Gas stunning and bleeding without stunning gradually induce a loss of capacity to maintain the standing posture probably due to a global progressive dysfunction of cortical and subcortical structures including the reticular formation.

Widespread anoxia in the brain following bleeding of non-stunned animals results also in a global progressive dysfunction of cortical and subcortical structures explaining the progressive loss of the capacity to stand upright. It was suggested that the first loss of posture may be only a sign of the early stages of onset of unconsciousness [START_REF] Gibson | Effect of neck cut position on time to collapse in halal slaughtered cattle without stunning[END_REF][START_REF] Gregory | Time to collapse following slaughter without stunning in cattle[END_REF]. This may explain why in some cases, during religious slaughter some cattle can regain the standing posture briefly, probably due to transient physiological adjustments partly restoring neurological function, before the final collapse [START_REF] Bourguet | Behavioural and physiological reactions of cattle in a commercial abattoir: Relationships with organisational aspects of the abattoir and animal characteristics[END_REF][START_REF] Gregory | Time to collapse following slaughter without stunning in cattle[END_REF].

Righting reflex of the head and/or body

An animal on the floor that is conscious following an unsuccessful stun may attempt to lift the head and/or body, or at least to position them in the usual angle (head/body axis perpendicular to the axis of the earth; [START_REF] Anil | Studies on the return of physical reflexes in pigs following electrical stunning[END_REF]. After an effective stun, as long as the animal is unconscious, it does not attempt to recover its normal posture. Recovery movements are oriented but sometimes difficult to distinguish from other movements which are automatic or reflex movements (see below: paddling and other movements).

Vocalizations

When unrelated to social communication, vocalization expresses most often pain [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. It was found that 99% of the vocalizations of cattle and pigs during slaughter were preceded by aversive situations, such as the use of an electric prod, a fall, a failed stun or excessive pressure during restraint [START_REF] Grandin | The feasibility of using vocalization scoring as an indicator of poor welfare during cattle slaughter[END_REF][START_REF] Warriss | Relationships between subjective and objective assessments of stress at slaughter and meat quality in pigs[END_REF][START_REF] Watts | Vocal behaviour in cattle: The animal's commentary on its biological processes and welfare[END_REF][START_REF] White | Vocalization and physiological response of pigs during castration with or without a local anesthetic[END_REF]. As pain can only be perceived if the animal is conscious, intentional vocalizations occurring after a stun are indicative of consciousness [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. Some guttural sounds are reflex-like that should not be confounded with vocalizations (see below: gasping). According to this memorandum, the clinical signs to check are:-Lack of pupillary reflex;-Absence of corneal reflex;-Absence of spontaneous breathing.

Spontaneous blinking

Spontaneous blinking involves circuits in the brainstem and in the cortex, that are partly the same as those involved in the corneal blink reflex that will be discussed below [START_REF] Bour | Origin of eye and eyelid movements during blinking[END_REF][START_REF] Morcuende | Neuronal premotor networks involved in eyelid responses: Retrograde transneuronal tracing with rabies virus from the orbicularis oculi muscle in the rat[END_REF]. Spontaneous blinking is considered as an indicator of consciousness [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF], but further studies are required to know their exact relationship with the level of consciousness. For example, in a study involving 20 bulls, none showed a corneal reflex after stunning, suggesting a state of unconsciousness, but 3 presented spontaneous blinking [START_REF] Terlouw | Origins of movements following stunning and during bleeding in cattle[END_REF].

Eye pursuit movements

Eye pursuit movements aim to track moving stimuli in the visual field. Following an effective mechanical or gas stun, the eyes are open with eyelids and eyeballs immobile [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. After an effective electrical stun, the eyes are initially closed, then reopened. The eyelids and eyeballs are immobile [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. Eye pursuit movements are considered a sign of consciousness because they involve not only different structures in the brainstem but also in the cortex [START_REF] Enderle | The fast eye movement control system. the biomedical engineering handbook[END_REF][START_REF] Tehovnik | Eye fields in the frontal lobes of primates[END_REF]. While the presence of eye pursuit movements is considered indicative of the presence of consciousness, the absence of eye movements does not necessarily indicate unconsciousness (Table 1). In one study, humans were asked to determine the movements of a pendulum while a neck pressure was exerted to stop the cerebral circulation. The eyeballs remained fixed in the centre of the eyes about 1 s before consciousness was lost as indicated by the presence of delta waves in the EEG. Questioned later, the subjects said they were still conscious but unable to move their eyes [START_REF] Rossen | Acute arrest of cerebral circulation in man[END_REF].

Response to the threat test

To test the response to a threat stimulus, a finger or the hand is moved rapidly towards the eye of the animal and the presence of a blinking response or withdrawal reaction is checked [START_REF] Limon | An evaluation of the humaneness of puntilla in cattle[END_REF][START_REF] Verhoeven | Validation of behavioural indicators used to assess unconsciousness in sheep[END_REF]Verhoeven, Hellebrekers, Gerritzen, & Kemp, in press). To conduct the test properly, it must be ascertained that the animal has adequate vision (e.g. no eyeball rotation or nystagmus, no blood in the eyes). The response involves higher-order brain mechanisms, including cortical functions to integrate the information coming from the environment [START_REF] Liu | Reflex blink to visual threat[END_REF]. The relationship between threat test and consciousness was shown in sheep and calves as the reflex was lost several seconds before unconsciousness was reached [START_REF] Verhoeven | Validation of behavioural indicators used to assess unconsciousness in sheep[END_REF]2016). In a group of more than 300 cattle having undergone puntilla and of which 82% showed rhythmic breathing, 61% showed a response to the threat stimulus [START_REF] Limon | An evaluation of the humaneness of puntilla in cattle[END_REF], suggesting a potential good sensitivity of the test, but also that it needs to be associated with other tests. More research is needed, including different contexts and species.

Indicators of unconsciousness

Absence of rhythmic breathing

Following the stun, an animal that breathes may be unconscious, but an animal that has stopped breathing is unconscious or dead [START_REF] Verhoeven | Indicators used in livestock to assess unconsciousness after stunning: A review[END_REF]. The presence of rhythmic breathing after stunning is an indication to proceed with a second stunning [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. The respiratory muscles are innervated by control centres located in the medulla oblongata, located in the lower part of the brainstem. These centres consist of different groups of neurons controlling either inspiration or expiration. These groups of neurons are activated alternately and thus form a neurological network underlying rhythmic breathing. They are stimulated by the reticular formation that receives information from the periphery and higher brain centres [START_REF] Siegel | The reticular formation, part 23[END_REF][START_REF] Silbernagl | Color atlas of physiology[END_REF].

Gasping corresponds to intermittent, rather forceful inspiratory movements which are not organised in the same manner as normal breathing and can be induced by ischaemia or hypoxia [START_REF] St John | Noeud vital for breathing in the brainstem: Gasping-yes, eupnoea-doubtful[END_REF]. Gasping reflects the dysfunction of brain centres in the pons and recruits medullary mechanisms [START_REF] St John | Noeud vital for breathing in the brainstem: Gasping-yes, eupnoea-doubtful[END_REF]. Gasping precedes death and should not be confused with rhythmic breathing. It is often accompanied by guttural sounds that should not be confused with vocalizations. Gasping has been observed in a captive bolt stunned calf whose EEG had been isoelectric for 60 s (Blackmore & Newhook, 1982).

Following a successful mechanical stun regular breathing movements are absent. Following bleeding of non-stunned animals, rhythmic breathing changes progressively into irregular breathing (alternation of shallow breathing, gasping, rapid shallow breathing, transient apnoeas; [START_REF] Verhoeven | Validation of behavioural indicators used to assess unconsciousness in sheep[END_REF]. Some consider that the presence of gasps is indicative of a bad stun if mechanical stunning was used, but that some gasping may be observed after a successful electrical stun [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. Gasping may also be a first indication of recovery following gas stunning [START_REF] Atkinson | Assessing pig welfare at stunning in Swedish commercial abattoirs using CO 2 group-stun methods[END_REF]. The cessation of breathing due to a mechanical stun can be explained by the dysfunction of the reticular formation or the medulla. The cessation of breathing after gassing (CO 2 overload/lack of O 2 ) is explained by a slowing of neuronal activity of the hemispheres and brainstem. Following electrical stunning, spreading of the epileptic seizure to subcortical regions (thalamus, brainstem), and certain cortical areas can cause respiratory arrest [START_REF] Kaada | Respiratory responses to stimulation of temporal pole, insula, and hippocampal and limbic gyri in man[END_REF][START_REF] Devinsky | Effects of seizures on autonomic and cardiovascular function[END_REF]. Involuntary muscle contractions, including those involved in breathing, contribute to the effects of the epileptic seizure on breathing. In general, the absence of breathing causes anoxia in the brain and thus contributes to the state of unconsciousness.

Absence of eye reflexes

In principle, following the stun, an animal presenting eye reflexes may be unconscious, but an animal that does not present them is unconscious or dead (Table 1). The presence of eye reflexes after stunning is an indication to proceed with a second stun [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. However, as will be indicated below, to carry out the test and interpret the result correctly, several considerations should be taken into account.

The corneal reflex is tested by lightly touching the cornea. 1 The reflex involves the transmission of sensory information to the brainstem eliciting a motor response: if present, the eyeball is slightly retracted and the eyelid closes. The sensory information passes through the trigeminal nerve to reach the trigeminal nucleus next to the reticular formation [START_REF] Cruccu | The clinical use of brainstem reflexes and hand-muscle reflexes[END_REF]. It is connected with the facial nucleus to stimulate the facial motor nerve which allows closing the eyelid. The trigeminal nucleus has a further input to the abducens and accessory abducens nuclei which are involved in the retraction of the eyeball in its socket [START_REF] Delgado-Garcia | Behavior of accessory abducens and abducens motoneurons during eye retraction and rotation in the alert cat[END_REF]. The connections between the trigeminal and facial nuclei pass through the reticular formation (Aramideh & Ongerboer de Visser, 2002;[START_REF] Dauvergne | Projections from the superior colliculus to the trigeminal system and facial nucleus in the rat[END_REF].

In the slaughter context, the corneal reflex is considered the most reliable eye reflex to evaluate the state of unconsciousness. Any interruption of the underlying neural circuit will cause the modification or the absence of the reflex. The neural circuit of the corneal reflex crosses the reticular formation. If the corneal reflex is absent, there is a large probability that the disruption is associated with a wider dysfunction, comprising part of the reticular formation, and thus with a state unconsciousness [START_REF] Cruccu | Corneal reflex responses to mechanical and electrical stimuli in coma and narcotic analgesia in humans[END_REF][START_REF] Kimura | Orbicularis oculi reflex in the Wallenberg syndrome: Alteration of the late reflex by lesions of the spinal tract and nucleus of the trigeminal nerve[END_REF][START_REF] Laureys | Science and society: Death, unconsciousness and the brain[END_REF][START_REF] Sturges | Neuro-ophthalmology: The visible nervous system[END_REF][START_REF] Zerari-Mailly | Localization of trigeminal, spinal, and reticular neurons involved in the rat blink reflex[END_REF]. For this reason, the absence of the corneal reflex is considered a fairly reliable indicator of unconsciousness.

The absence of the corneal reflex should be associated with other indicators of unconsciousness because there are exceptions. For example, very small, focal lesions2 can abolish the corneal reflex, at least unilaterally, without inducing unconsciousness (Ongerboer de [START_REF] Ongerboer De Visser | Late blink reflex changes in lateral medullary lesions. An electrophysiological and neuro-anatomical study of Wallenberg's Syndrome[END_REF]. This situation is, however, unlikely in the context of stunning or bleeding without stunning. On the opposite, dysfunction of the reticular formation at a remote distance from the neural circuit of corneal reflex, or interruption of the ascending reticular activating system can both induce a state of unconsciousness without abolishing the corneal reflex. For this reason an unconscious animal can present a corneal reflex, including at slaughter. For example, in a study on pigs, returns of the corneal reflex were observed on average 37 s after electrical stunning. At this stage, in most slaughterhouses, bleeding is in progress and the animals are unlikely to be conscious [START_REF] Mckinstry | The effect of repeat application of electrical stunning on the welfare of pigs[END_REF][START_REF] Vogel | Head-only followed by cardiac arrest electrical stunning is an effective alternative to head-only electrical stunning in pigs[END_REF]. Accordingly, in these studies, the return of the corneal reflex was not associated with a return of other signs, such as breathing, confirming that the animal was still unconscious [START_REF] Mckinstry | The effect of repeat application of electrical stunning on the welfare of pigs[END_REF][START_REF] Vogel | Head-only followed by cardiac arrest electrical stunning is an effective alternative to head-only electrical stunning in pigs[END_REF].

A temporary return of the corneal reflex is possible in the context of slaughter without stunning [START_REF] Bourguet | Behavioural and physiological reactions of cattle in a commercial abattoir: Relationships with organisational aspects of the abattoir and animal characteristics[END_REF]. These returns can be explained by different phenomena. As mentioned above ("standing posture"), physiological changes may restore sufficiently functionality of neurons to allow a temporary recovery of the reflex [START_REF] Gregory | Time to collapse following slaughter without stunning in cattle[END_REF]. These signs are not necessarily indicative of a partial or total return of consciousness but leave a doubt [START_REF] Bourguet | Behavioural and physiological reactions of cattle in a commercial abattoir: Relationships with organisational aspects of the abattoir and animal characteristics[END_REF][START_REF] Gregory | Time to collapse following slaughter without stunning in cattle[END_REF]. Second, under certain circumstances the reflex cannot be tested correctly and the apparent initial absence of a reflex may simply be due to a misinterpretation of the result. Particularly, in the case of strong eye muscle contraction it is impossible to carry out the test correctly. This may the case in religious slaughter or slaughter by puntilla, where bovine eye muscles may contract after the start of the bleeding. This contraction prevents closing of the lid in response to stimulation of the cornea and the reflex appears absent but the animal may be conscious. Incidentally, this contraction often causes the eyeball to rotate, making it impossible to reach the cornea and therefore to carry out the test [START_REF] Limon | An evaluation of the humaneness of puntilla in cattle[END_REF]Terlouw et al., personal observations). Similarly, to check a classical corneal reflex after electrical stunning, it is necessary to wait because the animal is in a tonic state and the reflex is blocked [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. Subsequently, the animal is in a clonic state characterized by vigorous movements, such as paddling or wing flapping, but the eye muscles may also be involved, again making it difficult to carry out the test correctly [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. Finally, it may be difficult, however, to carry out the corneal reflex when the animal has blood in the eyes, as may occur during bleeding.

The palpebral reflex can be tested by a light touch of the eyelid and the eyelash reflex by lightly brushing the eyelashes. The responses are the same, eyelid closure, and at least for the palpebral reflex the neural circuit is largely similar to that of the corneal reflex. At least under certain conditions, the palpebral reflex appears less resistant than the corneal reflex as in cattle bled without stunning the palpebral reflex was lost before the corneal reflex [START_REF] Bourguet | Behavioural and physiological reactions of cattle in a commercial abattoir: Relationships with organisational aspects of the abattoir and animal characteristics[END_REF][START_REF] Verhoeven | Validation of indicators used to assess unconsciousness in veal calves at slaughter[END_REF]. The eyelash reflex is considered unreliable for the assessment of the effects of certain pharmacological anaesthesia [START_REF] Vuyk | Pharmacodynamics of propofol in female-patients[END_REF]. During slaughter without stunning, the eyelash reflex is generally lost after the loss of corneal reflex (personal observations), suggesting that it is more resistant to the effects of anoxia. Compared to the corneal reflex, it may be more difficult to standardize the palpebral and eyelash test in the slaughter context and the exact interpretation of their presence or absence needs further studies.

The nictitating membrane or third eyelid is a transparent eyelid present in many birds, reptiles, amphibians and fish, but also in some mammals such as rabbits. It moves horizontally below the outer lid. This membrane also closes in response to touching the cornea. The neuronal circuit is partially similar to that described for the corneal reflex [START_REF] Desmond | An HRP study of the brainstem afferents to the accessory abducens region and dorsolateral pons in rabbit: Implications for the conditioned nictitating membrane response[END_REF]. Following electrical stunning, the external eyelids close but the third eyelid remains open. In birds and possibly other species possessing a third eyelid we can test the corneal reflex even if external eyelids are closed: by touching the corner of the eye it is possible to visually observe or to feel underneath the fingers, the closing movement of the third eye lid [START_REF] Erasmus | Measures of insensibility used to determine effective stunning and killing of poultry[END_REF]Bourguet, Deiss & Terlouw, personal observations).

The pupillary reflex corresponds to the contraction of the pupil when exposed to light and is an important evaluation for the prognosis of comatose patients [START_REF] Thomas | The differential diagnosis of fixed dilated pupils: A case report and review[END_REF]. The presence of mydriasis (dilated pupils) may be a useful indicator of a correct electrical stun in pigs [START_REF] Efsa | Welfare aspects of the main systems of stunning and killing the main commercial species of animals[END_REF]. The pupillary reflex necessitates however a functional condition of the retina. The neurological system involves the optic nerve (sensory information) and the oculomotor nerve (motor response). The integration centre is located in the midbrain, near the reticular formation. This reflex may be less adapted after the start of bleeding because the blood loss can reduce the functioning of the retina [START_REF] Blackman | Differences in blood supply to the cerebral cortex between sheep and calves during slaughter[END_REF]. Blood covering the cornea may also reduce the feasibility of the test.

In summary, as indicated above, in the slaughter context, the corneal reflex is considered the most reliable eye reflex to evaluate the state of unconsciousness, but should be associated with other indicators of unconsciousness.

Indicators with low discriminatory power or needing further development

Muscle tone

Following an effective mechanical stun cattle collapse with the legs more or less bent, then after a few seconds, the front legs are stretched [START_REF] Atkinson | Assessment of stun quality at commercial slaughter in cattle shot with captive bolt[END_REF]. After an effective electrical stun, a collapsed sheep or pig is first rigid with the hind legs bent and front legs stretched, due to a general contraction of the muscles lasting 10 to 20 s (tonic phase). Subsequently, the animals show involuntary paddling movements for 15 to 60 s (clonic phase; [START_REF] Velarde | Assessment of return to consciousness after electrical stunning in lambs[END_REF]. In birds the tonic phase is characterized by an extension of the legs, while the wings are pressed against the body and the neck is arched. The clonic phase is characterized by wing flapping. The body of an animal stunned by CO 2 inhalation is relaxed first, but subsequently, muscle contractions can occur, especially in birds [START_REF] Raj | Effect of carbon dioxide stunning on somatosensory evoked potentials in hens[END_REF]. Muscle tone is more difficult to use under field conditions, because physical movements evolve following the stun on the one hand, and incorrectly stunned animals may make movements that can be confounded with them, on the other [START_REF] Terlouw | Consciousness, unconsciousness and death in the context of slaughter. Part I. Neurobiological mechanisms underlying stunning and killing[END_REF].

Eyeball rotation

After captive bolt stunning, cattle that do not breathe and do not show a corneal reflex may present a rotation of the eyeball [START_REF] Gregory | Depth of concussion in cattle shot by penetrating captive bolt[END_REF][START_REF] Terlouw | Consciousness, unconsciousness and death in the context of slaughter. Part I. Neurobiological mechanisms underlying stunning and killing[END_REF]. Even when eyeball rotation is present at the same time as signs of unconsciousness, its presence indicates that there is a risk of a shallower depth of unconsciousness or a return of consciousness [START_REF] Atkinson | Assessment of stun quality at commercial slaughter in cattle shot with captive bolt[END_REF][START_REF] Gregory | Depth of concussion in cattle shot by penetrating captive bolt[END_REF]. Taking into account the degree of the rotation may improve its discriminatory power. One study showed that the presence of a full rotation required a second stun, while a partial rotation required increased monitoring of the animal [START_REF] Atkinson | Assessment of stun quality at commercial slaughter in cattle shot with captive bolt[END_REF]. During bleeding without stunning, eyeball rotation may occur while the animal is still conscious (Terlouw et al., personal observations). However, in the later stages following bleeding without stunning eye rotation may be associated with a state of profound unconsciousness [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF] 3 . This suggestion is consistent with the progressive increase of the proportion of cattle with rotating eyeballs following bleeding without stunning [START_REF] Bourguet | Behavioural and physiological reactions of cattle in a commercial abattoir: Relationships with organisational aspects of the abattoir and animal characteristics[END_REF]. 4 Eyeball movements depend on 6 extraocular muscles that receive information from different lower brain centres including the oculomotor, trochlear and abducens nuclei, located in the pons and midbrain of the brainstem [START_REF] Enderle | The fast eye movement control system. the biomedical engineering handbook[END_REF][START_REF] Tehovnik | Eye fields in the frontal lobes of primates[END_REF]. These lower brain centres are controlled by higher brain centres [START_REF] Enderle | The fast eye movement control system. the biomedical engineering handbook[END_REF][START_REF] Tehovnik | Eye fields in the frontal lobes of primates[END_REF]. The mechanisms underlying the movements of the eyeballs after stunning and after the bleeding without stunning are not yet known.

Nystagmus

Nystagmus is a vertical or horizontal rapid oscillation of the eyeball due to repeated contractions of extraocular muscles. Nystagmus is indicative of damage to the underlying circuits in the brainstem, but may also result from damage to the cerebellum or the vestibular system [START_REF] Hüfner | Structural and functional MRIs disclose cerebellar pathologies in idiopathic downbeat nystagmus[END_REF]. Nystagmus is considered as an indicator with low discriminatory power. A study by captive bolt stunning in cattle showed that nystagmus was rare (occurring in 3% of the animals) but when present, there was 1 in 3 chance that the quality of the stun was insufficient [START_REF] Gregory | Depth of concussion in cattle shot by penetrating captive bolt[END_REF]. This estimate is consistent with other studies [START_REF] Bourguet | Behavioural and physiological reactions of cattle in a commercial abattoir: Relationships with organisational aspects of the abattoir and animal characteristics[END_REF][START_REF] Terlouw | Consciousness, unconsciousness and death in the context of slaughter. Part I. Neurobiological mechanisms underlying stunning and killing[END_REF].

Response to a painful stimulus

To test the response to a pain stimulus, the withdrawal response following a pinch (of the comb, the ear tips, or the nasal septum for example), a skin prick with a hypodermic needle, or spraying with hot water may be tested [START_REF] Limon | An evaluation of the humaneness of puntilla in cattle[END_REF][START_REF] Mckinstry | The effect of repeat application of electrical stunning on the welfare of pigs[END_REF][START_REF] Parotat | Hot-water spraying is a sensitive test for signs of life before dressing and scalding in pig abattoirs with carbon dioxide (CO 2 ) stunning[END_REF][START_REF] Verhoeven | Validation of behavioural indicators used to assess unconsciousness in sheep[END_REF]. Currently, the pain test needs further research to improve its discriminatory power. Certain responses to painful stimuli require cortical input and are indicative of consciousness. Other responses to painful stimuli may be simple nociceptive arc-reflex responses, based on a circuit involving the spinal cord, but not the brain. For example, in the study of [START_REF] Terlouw | Consciousness, unconsciousness and death in the context of slaughter. Part I. Neurobiological mechanisms underlying stunning and killing[END_REF], some cattle showed a movement of the neck in the ventral direction in response to the cutting of the skin and blood vessels when bleeding the animal. This was weaker in bulls following longer stun-stick intervals. This movement is most likely a nociceptive reflex response based on a neural circuit that passes through the spinal cord, but not the brain. The stronger response in bulls bled sooner after the stun indicates that the nerves involved in the arc-reflex response had still a degree of functionality. The reaction to the cut of skin and tissues can therefore not be used as an indicator of consciousness. Similarly, pharmacologically anaesthetised sheep showing an EEG indicative of unconsciousness responded to an ear pinch [START_REF] Verhoeven | Validation of behavioural indicators used to assess unconsciousness in sheep[END_REF]. Hence, certain pain responses are not necessarily indicative of consciousness.

Other studies show that a pain response may be an indicator of a certain degree of brainstem functioning. For example, in a majority of calves bled without stunning, the pain response was lost several seconds before their EEG indicated unconsciousness [START_REF] Verhoeven | Validation of indicators used to assess unconsciousness in veal calves at slaughter[END_REF]. In another study, after stunning and sticking, certain pigs moved when they received a nociceptive stimulus due to a hot water spray. These same pigs showed also eyelid closure upon touching the cornea or when a light was shone in the eye, suggesting that the response to the hot water spray was indicative of a certain degree of brainstem functioning [START_REF] Parotat | Hot-water spraying is a sensitive test for signs of life before dressing and scalding in pig abattoirs with carbon dioxide (CO 2 ) stunning[END_REF]. The interest of the test is that it can be automatized.

Further studies are needed to evaluate the exact relationships between various nociceptive stimuli and brain functioning. For example, in the above study, the same pigs were also tested using a nasal septum pinch but only one third of the pigs that moved when they received the hot water spray responded to the nasal septum pinch [START_REF] Parotat | Hot-water spraying is a sensitive test for signs of life before dressing and scalding in pig abattoirs with carbon dioxide (CO 2 ) stunning[END_REF]. Similarly, immediately following a neck cut of non-stunned sheep, the withdrawal response to an ear pinch was lost, while breathing and the corneal reflex were still present and the EEG indicated the presence of consciousness [START_REF] Verhoeven | Validation of behavioural indicators used to assess unconsciousness in sheep[END_REF]. These results suggest that in the slaughter context, certain stimuli may not be strong enough to evoke a reaction or possibly, that certain animals or species are physically unable to respond.

In conclusion, a response to a painful stimulus may either involve only the spinal cord and thus represent a nociceptive reflex, or involve higher brain centres and thus be indicative of a certain degree of consciousness. Similarly, the absence of a response is not always indicative of unconsciousness. These recent results are promising but further research is needed to fully explore the relationship between reactions to different pain stimuli and brain functioning, while aiming for tests that aim to cause as little pain as possible [START_REF] Parotat | Hot-water spraying is a sensitive test for signs of life before dressing and scalding in pig abattoirs with carbon dioxide (CO 2 ) stunning[END_REF].

Response to sensory stimuli other than threat or pain

Certain responses to sensory stimuli are expected to require cortical input and to be indicative of consciousness. In addition to the threat and pain test discussed above, other tests involving sensory stimuli include withdrawal responses to an air blow in the nostrils, ear movements in response to a hand clap, or a movement of the nostrils or of the tongue in response to odours or flavours, respectively. In a group of cattle having undergone puntilla and of which 82% showed rhythmic breathing, only 11 and 20% responded to a needle prick and a stick in the nostril, respectively [START_REF] Limon | An evaluation of the humaneness of puntilla in cattle[END_REF]. Between 4 and 39% of these animals responded to odours or flavours of molasses, lemon, vinegar, and salt and 21% to a hand clap near the ear [START_REF] Limon | An evaluation of the humaneness of puntilla in cattle[END_REF]. These low percentages indicate much lower discriminatory power for these tests than for the threat test, but further research is needed including other slaughter procedures and species.

Apparently spontaneous neck or leg movements after stunning

Following stunning or following bleeding without stunning, animals present frequently paddling, neck, back or wing movements that are not associated with the clonic phase following electrical stunning [START_REF] Grandin | Recommended animal handling guidelines and audit guide: A systematic approach to animal welfare[END_REF]. A study shows that paddling in correctly stunned cattle is most likely an involuntary movement linked to rhythm-generating centres of the brainstem structures and the spinal cord [START_REF] Terlouw | Consciousness, unconsciousness and death in the context of slaughter. Part I. Neurobiological mechanisms underlying stunning and killing[END_REF] involved in the production of rhythmic motor movements, such as walking [START_REF] Guertin | The mammalian central pattern generator for locomotion[END_REF][START_REF] Frigon | Central pattern generators of the mammalian spinal cord[END_REF]. The functioning of these generators is independent of consciousness.

Lateral neck movements are difficult to interpret. Profoundly unconscious stunned cows may frequently show neck movements [START_REF] Bourguet | Behavioural and physiological reactions of cattle in a commercial abattoir: Relationships with organisational aspects of the abattoir and animal characteristics[END_REF][START_REF] Terlouw | Consciousness, unconsciousness and death in the context of slaughter. Part I. Neurobiological mechanisms underlying stunning and killing[END_REF]. However, in bulls, only animals showing ocular signs (nystagmus, rotating eyeballs, spontaneous blinking) or breathing, showed neck movements [START_REF] Terlouw | Consciousness, unconsciousness and death in the context of slaughter. Part I. Neurobiological mechanisms underlying stunning and killing[END_REF]. None of the bulls showed a corneal reflex, which would suggest that these animals were unconscious. Results suggest that following the stun, the extent of affected areas or type of structures damaged influences behavioural expression, even if the animals are correctly stunned.

In summary, at slaughter, it is essential to use a multi-criteria approach to verify indicators of consciousness and unconsciousness. Standing posture and voluntary vocalizations are signs of consciousness and must be absent. The absence of reflexes and eye movements, and the absence of rhythmic breathing are key signs of unconsciousness. The corneal reflex is generally regarded as the reference ocular reflex. If it is abolished and there is a permanent loss of the standing posture and no rhythmic breathing, then it is considered that the animal is stunned effectively.

Certain indicators, such as nystagmus, have low discriminatory power and its presence requires the verification of other indicators as well as increased monitoring of the animal until death.

Relationships between the different indicators

The localisation of different brain structures and their resistance to anoxia may explain the order in which different functions are lost. In humans, during the process evolving towards brain death following neurological trauma, loss of functions occurs in the rostrocaudal direction: the medulla of the brainstem is often the last structure to lose its functions [START_REF] Wijdicks | The diagnosis of brain death[END_REF]. In the slaughter context, the order of loss of functions varies depending on the species, the techniques used and the indicators observed (Table 2). There are however some consistencies in the disappearance and appearance of certain indicators. For example, during the gassing of chickens, loss of the standing posture occurs on average 6-10 s before closing the eyes (Raj & Gregory, 1990;Raj et al., 1990;Deiss, personal communication). In calves bled without stunning, the abolition of the corneal reflex preceded on average 10 s permanent abnormal EEG, in a fairly reliable manner and gasping stopped after the EEG had become isoelectric (Table 2; [START_REF] Blackmore | Time of onset of insensibility in four-to six-week-old calves during slaughter[END_REF]Newhook & Blackmore, 1982). In other studies on calves bled without stunning, the corneal reflex was abolished between 55 and 126 s after the EEG indicated unconsciousness [START_REF] Lambooij | Restraining and neck cutting or stunning and neck cutting of veal calves[END_REF][START_REF] Verhoeven | Validation of indicators used to assess unconsciousness in veal calves at slaughter[END_REF]. In sheep bled without stunning, loss of the threat reflex occurred on average 8 s before, irregular breathing 28 s after, and absence of the palpebral reflex 59 s after the EEG indicated a state of unconsciousness [START_REF] Verhoeven | Validation of behavioural indicators used to assess unconsciousness in sheep[END_REF]. Hence, when sheep or cattle are bled without stunning, average delays indicate that events occur in the order: loss of response to threat, abnormal EEG indicative of unconsciousness, loss of rhythmic breathing, loss of palpebral reflex and loss of corneal reflex. After mechanical stunning of cattle, rotation of the eyeballs or rhythmic breathing is more frequently present than the corneal reflex [START_REF] Gregory | Depth of concussion in cattle shot by penetrating captive bolt[END_REF][START_REF] Terlouw | Consciousness, unconsciousness and death in the context of slaughter. Part I. Neurobiological mechanisms underlying stunning and killing[END_REF]. These results may indicate that the corneal reflex is often According to data of Newhook & Blackmore (1982).

lost before abolishment of breathing or rotation of the eyeballs. In a study on gas stunning in pigs, it was found that the presence of spontaneous blinking was an indicator of a high risk of an inadequate stun and in the absence of spontaneous blinking, the presence of a corneal reflex an indicator of a high risk of recovery. Pigs presenting spontaneous blinking, regular or difficult breathing presented always at least one other indicator, whether considered discriminatory or not [START_REF] Atkinson | Assessing pig welfare at stunning in Swedish commercial abattoirs using CO 2 group-stun methods[END_REF]Fig. 2).

Data exist also on the order of re-appearance of indicators during recovery. In pigs, during the return of consciousness after reversible electrical stunning, recovery of corneal reflex occurs before resumption of breathing [START_REF] Mckinstry | The effect of repeat application of electrical stunning on the welfare of pigs[END_REF][START_REF] Vogel | Head-only followed by cardiac arrest electrical stunning is an effective alternative to head-only electrical stunning in pigs[END_REF]. However, in calves, the opposite was observed [START_REF] Gregory | Prevalence and duration of insensibility following electrical stunning in calves[END_REF].

Thus, abolition of the corneal reflex and respiratory arrest are considered important indicators of the unconsciousness of the animal because in principle they occur after the loss of consciousness. Moreover, the cessation of breathing induces or contributes to the anoxia of the brain. Despite the importance of these indicators, in the context of slaughter, their precise relationships with the brain state or with other indicators of consciousness or unconsciousness are insufficiently known. They appear to depend on the species and/or type of stunning or slaughter technique used.

The study of relationships between different indicators of unconsciousness and consciousness may benefit from analyses by correlation. The data of [START_REF] Newhook | Electroencephalographic studies of stunning and slaughter of sheep and calves -Part 2: The onset of permanent insensibility in calves during slaughter[END_REF] show that the delays of appearance of various indicators were generally correlated (Table 3; Fig. 1). Similarly, analysis of data produced by [START_REF] Wotton | Electrical stunning of cattle[END_REF] on electrical stunning of adult cattle shows that the duration of the tonic phase depends on the amount of current received. The delays to recover a standing posture were correlated with the duration of the clonic phase and the delay until the resumption of breathing. For half of the animals, the return of respiration took place before the end of the clonic phase (Table 4). This type of analyses may help to increase our understanding of the relationships between indicators of unconsciousness and consciousness and the functional status of different parts of the brain.

Under field conditions, given the variability of the results in terms of delay until induction of unconsciousness, operators must assess indicators of consciousness and unconsciousness of each animal until the end of bleeding. It is necessary to combine a maximum of indicators to achieve a diagnosis as reliable as possible. When in doubt, the operator must proceed as quickly to a second stun, and verify the stunning equipment.

Estimated delay until brain death in the slaughter context

It is difficult to know when exactly death occurs after bleeding. In humans, the exact criteria of the establishment of death vary by country Table 4 Correlations between different indicators relative to epileptic seizure and return of consciousness. According to data on adult cattle by [START_REF] Wotton | Electrical stunning of cattle[END_REF]. -Pupillary light: pupils reactive to light.

Duration of tonic phase

Duration of clonic phase

-Corneal: movement of the eyelid when the cornea is lightly touched. -Oculo-cephalic: eyeball movement in the direction opposite to that of the head when it is suddenly rotated. -Oculo-vestibular: eye movement after injection of the ear canals with ice water when the patient's head is placed at 30°in the horizontal plane. -Oro-pharyngeal: vomiting reflex when stimulating the posterior pharyngeal wall cough reflex when stimulating the endotracheal tube.

but involve the absence of signs of life5 : persistent cardiac and respiratory arrest, the total absence of consciousness and spontaneous motor activity (excluding spinal reflexes), the abolition of all brainstem reflexes (Box 1) and the absence of spontaneous breathing (French Public Health Code, Article R1232-1). The absence of confounding factors (drugs, hypothermia, etc.) must be ensured [START_REF] Wijdicks | The diagnosis of brain death[END_REF]. Confirmatory testing (EEG, angiography, brain tomography) showing the absence of electrical activity, blood flow, metabolic activity [START_REF] Laureys | Science and society: Death, unconsciousness and the brain[END_REF] and of a ventilatory reflex (hypercapnic test, 6 Wijdicks, 2001) may be necessary. 7 It should be noted that the signs of life are at different levels: while cardiac arrest and respiratory arrest are likely to induce death, lack of awareness and lack of brainstem reflexes are the consequences. The diagnosis of death as performed in humans cannot be carried out in the slaughter context for technical and practical reasons. When death is not caused by brain damage due to the stun, it is induced by a lack of oxygen supply to the brain, often associated with a lack of nutrient supply, due to cardiac and/or respiratory arrest, or exsanguination. Cardiac and/or respiratory arrest can be difficult to diagnose with certainty in the abattoir. It is however possible to estimate the average delay until death, relative to the end of bleeding. In humans, after cardiac arrest, the chances of survival depend on the delay until cardiopulmonary resuscitation. When this occurs in less than 4 to 5 min, the chances of survival are two times greater than when it takes place between 5 and 8 min [START_REF] Cole | Four-minute limit for cardiac resuscitation[END_REF][START_REF] Hornby | A systematic review of autoresuscitation after cardiac arrest[END_REF][START_REF] Larsen | Predicting survival from out-of-hospital cardiac arrest: A graphic model[END_REF][START_REF] Waalewijn | Survival models for outof-hospital cardiopulmonary resuscitation from the perspectives of the bystander, the first responder, and the paramedic[END_REF][START_REF] Weston | Outcome of out-of-hospital cardiorespiratory arrest in south Glamorgan[END_REF]. In addition, humans who were not resuscitated within 5 min following cardiac arrest suffer almost always serious heart and brain damage [START_REF] Cole | Four-minute limit for cardiac resuscitation[END_REF][START_REF] Hornby | A systematic review of autoresuscitation after cardiac arrest[END_REF]. In pigs resuscitated after cardiac arrest of up to 4.5 min, electrical brain activity reappeared. If resuscitation took place after 5 min or more electrical brain activity remained absent. Brain stem reflexes were present up to 5 min of cardiac arrest [START_REF] Stiegler | A 10 min "no-touch" time -Is it enough in DCD? A DCD animal study[END_REF]. If we transpose this information to livestock, disregarding the possible consequences of the stun, it is likely that 4 to 5 min after the end of bleeding the animal is deeply unconscious or dead, even when the bleeding was carried out on a non-stunned animal [START_REF] Hornby | A systematic review of autoresuscitation after cardiac arrest[END_REF][START_REF] Stiegler | A 10 min "no-touch" time -Is it enough in DCD? A DCD animal study[END_REF]; but see Box 2).

Conclusion

This second review aims to contribute to the reflection on the use and interpretation of indicators of consciousness and unconsciousness. Indicators of consciousness and unconsciousness are tools to assess indirectly the state of brain function. Their diversity allows evaluating different aspects of the state of consciousness, related to its contents (e.g. the presence of eye pursuit indicates that the animal integrates information from the environment) and level (e.g. the absence of the corneal reflex indicates a priori that the level of wakefulness is zero). As the indicators are only indirectly related to the state of consciousness, it is necessary to check several. A state of unconsciousness is diagnosed when the signs of consciousness are absent and those of unconsciousness are present. When after a stun, all indicators do not concur to establish that the animal is unconscious it is necessary to proceed to a second stun. In abattoirs, since a state of unconsciousness may be reversible, monitoring of the animal must be continued until the end of bleeding.

The death certification procedures used for humans are not applicable in the slaughter context. The European Regulation requires, however, that dressing or scalding is carried out only after verification of the absence of signs of life (council regulation (EC) No 1099/2009). Under field conditions, this rule is adapted to the slaughter context: after bleeding, it is verified that the animal is not breathing, shows no brainstem reflexes and is bled properly. If these three points are confirmed in the context of the abattoir and at this stage of slaughter, the loss of vital functions is irreversible because the animal is completely bled and it can therefore be considered dead.

The implementation of Council Regulation No. 1099/2009 significantly improves procedures that aim to assess routinely the state of consciousness/unconsciousness of animals during the slaughter process. However, progress is still necessary and today's needs seem to be of two kinds. First, a clarification of certain terms and concepts related to the regulation is required. For example, it is important to distinguish clearly the concepts of death, cardiac arrest and absence of signs of life. Similarly, in this review we used the two terms, absence of signs of consciousness and presence of signs of unconsciousness, depending on their relationship to consciousness and unconsciousness. Both terms are used in various texts, including Council Regulation No. 1099/2009(see EFSA, 2013;;[START_REF] Gregory | Time to collapse following slaughter without stunning in cattle[END_REF][START_REF] Verhoeven | Indicators used in livestock to assess unconsciousness after stunning: A review[END_REF][START_REF] Von Holleben | Report on good and adverse practices -Animal welfare concerns in relation to slaughter practices from the viewpoint of veterinary sciences[END_REF]. Their exact meaning is not always made explicit, and a more harmonized and consensual use of such terms would facilitate exchanges of ideas. Second, it is necessary to continue research efforts on the interpretation of indicators related to consciousness and unconsciousness, their relationships with different types of brain damage and the reliability of their interpretation in terms of consciousness. Such knowledge would help to confirm or refine the methods of assessment of the state of consciousness of animals and reduce risks of misdiagnosis.

Box 2 New technologies push away the threshold of death.

The transition from life to death is not necessarily immediate; it is not an all-or-nothing phenomenon but a process that progressively leads to death [START_REF] Laureys | Science and society: Death, unconsciousness and the brain[END_REF]. Until recently it was believed that more than 4 or 5 min of global and complete brain ischemia caused death or survival with severe negative consequences because the brain damage was irreversible (Allen & Buckberg, 2012;[START_REF] Cole | Four-minute limit for cardiac resuscitation[END_REF][START_REF] Madl | Brain function after resuscitation from cardiac arrest[END_REF]. However, new techniques are developed, such as cardiopulmonary bypass and controlled perfusion of organs including the brain before the restoration of normal blood flow and before the resumption of normal cardiac activity. Under experimental conditions, in pigs, the use of these techniques allowed cerebral resuscitation without sequelae after 10-15 min of cardiac arrest and after 30 min of complete global brain ischemia [START_REF] Allen | Studies of isolated global brain ischaemia: II. Controlled reperfusion provides complete neurologic recovery following 30 min of warm ischaemiathe importance of perfusion pressure[END_REF][START_REF] Liakopoulos | Resuscitation after prolonged cardiac arrest: Role of cardiopulmonary bypass and systemic hyperkalemia[END_REF][START_REF] Nichol | Systematic review of percutaneous cardiopulmonary bypass for cardiac arrest or cardiogenic shock states[END_REF][START_REF] Trummer | Successful resuscitation after prolonged periods of cardiac arrest: A new field in cardiac surgery[END_REF]. These results do not change the definition of brain death, in many countries defined as the irreversible and permanent cessation of the functioning of brain structures responsible for vital functions like breathing and thermal and cardiovascular regulation located in the brainstem [START_REF] Laureys | Science and society: Death, unconsciousness and the brain[END_REF]. They ask, however, the question of the definition of "irreversibility".

partie_2.pdf). The authors thank the referees for their relevant and helpful comments that allowed us to improve the review.

Fig. 1 .

 1 Fig. 1. Correlation between the delay until abolition of the corneal reflex and the appearance of EEG incompatible with consciousness.According to data ofNewhook & Blackmore (1982).

Fig. 2 .

 2 Fig. 2. Venn diagram of numbers of pigs presenting different indicators, following gas stunning in commercial abattoirs. Blinking: spontaneous eyelid closure; corneal reflex: eyelid closure in response to lightly touching the cornea; difficult or rhythmic breathing: opening the mouth apparently taking short gasps of air while flexing the head forwards more than 3 times within 10 s intervals or rhythmic air inhalation as shown by movements of the chest or flank. Pigs showing blinking were at a high risk of inadequate stunning. Pigs showing a corneal reflex were at a high risk of recovery. If regular kicking and convulsions are also taken into account as indicators (not shown), results showed that presence of spontaneous blinking or breathing was always associated with at least one other positive indicator. After Atkinson et al. (2012).

  Brainstem reflexes tested as a contribution to the diagnosis of unconsciousness or death in humans.

Table 1

 1 Indicators of consciousness and unconsciousness a . Other indicators may be used but their discriminatory power is lower. As the indicators are only indirectly related to the state of consciousness, it is necessary to check several. The animal is unconscious when the signs of consciousness are absent and signs of unconsciousness are present. Some indicators are explicitly mentioned in the memorandum of the French Ministry of Agriculture DGAL/SDSSA/N2012-8250 of 05 December 2012, based on Council Regulation No. 1099/2009: Operators must carry out systematic checks to ensure that animals do not show any sign of life before undergoing dressing or scalding.

	Indicator	Sign of
	Standing posture
	Head or body righting reflex
	Voluntary vocalizations	Consciousness
	Spontaneous blinking
	Eye pursuit
	Response to the threat test
	Absence of corneal reflex
	Absence of eyelash reflex	Unconsciousness or death
	Absence of rhythmic breathing

a

Table 2

 2 Examples of delays of loss of appearance of indicators of the state of unconsciousness and behavioural signs after direct bleeding or stunning.

	Studies on the loss of consciousness: calves (delays in s)
	Ref. a First sign of abnormal	Loss of corneal reflex	Permanent abnormal EEG Isoelectric EEG	End of gasps
		EEG
	1	70 ± 6	187 ± 25	197 ± 22	225 ± 27	311 ± 26
	2	75 ± 46	-	164 ± 17	183 ± 17	193 ± 56
	Studies on the loss of consciousness: poultry (delays in s)
	Ref. Permanent eye closure Start and end of intensive	Respiratory arrest	Start and end of weak	Loss of corneal reflex	Loss of muscle tone in the
			wing flapping		wing flapping		neck
	3	8 ± 3	10 ± 1; 29 ± 5	22 ± 10	29 ± 4; 78 ± 10	36 ± 8	81 ± 4
	Ref. Reduction of EEG	Loss of evoked potentials Permanent eye closure	Start and end of clonic	Start and end of tonic phase	Isoelectric EEG
		power			phase	(extension of the wings and
					(wing flapping)	legs)
	4	21 ± 4	30 ± 2	34 ± 5	45 ± 4; 60 ± 5	68 ± 10; 85 ± 7	101 ± 18
	Studies on the return of consciousness: pigs and calves (ref. 5: % of pigs, refs. 6 and 7: delays in s)
	Ref. Corneal reflex	Spontaneous blinking	Eye pursuit	Nose twitch	Righting reflex	Rhythmic breathing
	5	93.8	40.8	32.7	32.7	14.3	12.2
	Ref. End of tonic phase	End of epileptiform EEG	End of clonic phase	Return of corneal reflex	Return of rhythmic breathing Head righting reflex
	6	9 ± 0.8	36 ± 4.9	34 ± 3.3	37 ± 3.0	44 ± 2.0	59 ± 3.8
	Ref. End of tonic phase	End of clonic phase	Return of rhythmic	Return of corneal reflex	Head righting reflex
				breathing
	7	11 ± 0.1	22 ± 1	25 ± 1	67 ± 8	67 ± 7

a References: Ref. 1:

[START_REF] Newhook | Electroencephalographic studies of stunning and slaughter of sheep and calves -Part 2: The onset of permanent insensibility in calves during slaughter[END_REF] 8 calves, slaughter without stunning; Ref. 2: Blackmore et al., 1983; 3

calves, bleeding without stunning; Ref. 3: Bourguet et al., 2012 (personal observations): 20 broilers, bleeding without stunning; Ref. 4: Raj et al., 1990: 9 broilers, 45% of CO 2 (delays in s); Ref. 5: Vogel et al., 2011: 45 pigs, electrically stunned (head only): return of signs of consciousness during bleeding starting 30 s post-stun, observations lasted 4 min; Ref. 6: McKinstry and Anil, 2004: 16 pigs, electrically stunned (head only; 200 V, 3 s); Ref. 7. Gregory et al., 1996: 10 calves, electrically stunned (head only; 200 V, 3 s).

When eliciting the corneal reflex, care should be taken that the response was elicited by touch rather than by the sudden movement towards the eye, i.e. the threat test (cf below; Blumenfeld

, 2002).

Please cite this article as: Terlouw, C., et al., Consciousness, unconsciousness and death in the context of slaughter. Part II. Evaluation methods, Meat Science (2016), http://dx.doi.org/10.1016/j.meatsci.2016.03.010

Following a local haemorrhage or tumour for example.

http://www.grandin.com/ritual/kosher.box.variables.time.lose.sensibility.html.

The small proportion of animals with a rotation of the eyeballs in this study can be explained by the observation method using scan sampling, which is less adapted to shortlasting behavioural expressions than the continuous observation method.

C. Terlouw et al. / Meat Science xxx (2016) xxx-xxx Please cite this article as: Terlouw, C., et al., Consciousness, unconsciousness and death in the context of slaughter. Part II. Evaluation methods, Meat Science (2016), http://dx.doi.org/10.1016/j.meatsci.2016.03.010

The signs of death can only be recognized at a later stage: lowered body temperature, rigor mortis (stiffness), livor mortis (purple-red skin discoloration), dehydration (clouding of the cornea, for example), putrefaction.

Induction of blood pCO 2 of 60 mm Hg, or 20 mm Hg above the normal values

According to the French public health code, if the person whose death is recognized clinically, is assisted by mechanical ventilation and maintains haemodynamic functioning, the absence of spontaneous breathing is verified by a hypercapnia test (absence of breathing in response to a given amount of CO 2 in the blood) and confirmatory tests (2 EEGs at a 4 hour interval or angiography; the public Health Code Article R1232-2).

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 Acknowledgements An earlier version of this review was published in French, in "Viande et Produits Carnés" in March 2015 (http://www.viandesetproduitscarnes.fr/ phocadownload/vpc_vol_31/3123_terlouw_aspects_neurobio_abattage_ C. Terlouw et al. / Meat Science xxx (2016) xxx-xxx Please cite this article as: Terlouw, C., et al., Consciousness, unconsciousness and death in the context of slaughter. Part II. Evaluation methods, Meat Science (2016), http://dx.doi.org/10.1016/j.meatsci.2016.03.010