Pascal Lafourcade
email: pascal.lafourcade@limos.fr

Marius Lombard-Platet
email: marius.lombard-platet@ens.fr

About Blockchain Interoperability

Keywords:

A blockchain is designed to be a self-sufficient decentralised ledger: a peer verifying the validity of past transactions only needs to download the blockchain (the ledger) and nothing else. However, it might be of interest to make two different blockchains interoperable, i.e., to allow one to transmit information from one blockchain to another blockchain. In this paper, we give a formalisation of this problem, and we prove that blockchain interoperability is impossible according to the classical definition of a blockchain. Under a weaker definition of blockchain, we demonstrate that two blockchains are interoperable is equivalent to creating a '2-in-1' blockchain containing both ledgers, thus limiting the theoretical interest of making interoperable blockchains in the first place. We also observe that all practical existing interoperable blockchain frameworks work indeed by exchanging already created tokens between two blockchains and not by offering the possibility to transfer tokens from one blockchain to another one, which implies a modification of the balance of total created tokens on both blockchains. It confirms that having interoperability is only possible by creating a '2-in-1' blockchain containing both ledgers.

Introduction

Blockchain was first introduced in 2008 by Nakamoto in [START_REF] Nakamoto | Bitcoin: A peer-to-peer electronic cash system[END_REF]. In their paper, the anonymous author(s) described the first decentralised ledger: a database in which anyone can write, and that is not controlled by a single or a conglomerate of identities. Since then, many other blockchains have been described: Ethereum [START_REF] Buterin | Ethereum: A next-generation smart contract and decentralized application platform[END_REF], Ripple [START_REF] Schwartz | The ripple protocol consensus algorithm[END_REF] and many others. In May 2019, 248 active blockchains were listed on [START_REF]CryptoID, Crypto-currency blockchain explorers[END_REF].

While many different blockchains exist, there is no direct way of reaching interoperability, at least without a trusted third party. Consider for instance a client willing to convert their Bitcoins to Ether: they would need to consume the amount of Bitcoins they wants to convert and to generate the equivalent amount of Ether. While Bitcoin consumption may be reachable (by sending coins to a non-existing address, such as the address 0), it is impossible to spontaneously generate Ether (or any other kind of cryptocurrency). For now, the problem is solved with the help of trusted brokers (also called escrows), even though other solutions are on their way [START_REF] Johnson | Sidechains and interoperability[END_REF][START_REF] Thomas | A protocol for interledger payments[END_REF].

The issue of interoperability is solved in some cases, like "atomic exchanges" and hash-locking [START_REF] Buterin | Chain interoperability[END_REF], in which game theory ensures that a broker only benefits when following the protocol. However the question of trustless interoperability in the general context remains open.

Contributions. We introduce a theoretical background to blockchain interoperability, providing a formal definition of a blockchain and of interoperability. We then prove that, by definition, interoperability between two public blockchains is impossible. However, we contend that there may be special conditions under which two blockchains can be interoperable. This leads us to prove the equivalence between two interoperable public blockchains and a ledger emulating both blockchains on two separate registries.

Related Work. The concept of sidechains (a sidechain is a blockchain attached to another blockchain, with exchanges possible between the two blockchains) has been explored in [START_REF] Back | Enabling blockchain innovations with pegged sidechains[END_REF]. The authors describe a two-way peg in which a sidechain is fed with an SPV proof, a short proof of the transaction allowing for lightweight clients. The sidechain plays the role of a lightweight client, and can thus allow subsequent operations following the SPV proof. However, this pegging system requires a contest period, during which it is assumed that people will verify that the SPV proof does not come from a fork. Hence, additional trust is required in this model. In a paper from 2016 [START_REF] Buterin | Chain interoperability[END_REF], Buterin lists ways of reaching interoperability, and focuses on trusted inter-chains exchanges, where one sends money on blockchain A and receives some in blockchain B.

Similarly, the Interledger protocol [START_REF] Thomas | A protocol for interledger payments[END_REF] (ILP) allows one to automatize money transfers while leveraging the risk of fraud, thanks to micro-transactions. Yet, ILP is more about escrow synchronization than interoperability as we define it later on. In an ILP transaction from blockchain A to blockchain B, one must find an escrow having enough money on B (or several escrows having in total enough money), so the transfer can occur. More generally, we consider that interoperability can for instance allow money to 'disappear' from A and to 'reappear' on B, without the need for trusted escrows.

Interoperability has been notably implemented in the blockchain network Kadena [START_REF] Martino | Chainweb whitepaper[END_REF], in which transfers from one blockchain of the network to another is possible. The money is destroyed on one side and generated on the other. Kadena also uses smart contracts for securing escrow transfer. However, there is no indication that Kadena can operate with chains outside of their specific network. So in our terminology, we say that Kadena is a "N-in-1 blockchain", which is to say one blockchain, with several ledgers.

To the best of our knowledge, no theoretical work on interoperability has been done to date. Our work, rather than giving a practical implementation of an interoperable blockchain, gives a theoretical background to the topic, and explores the conceptual meaning of having interoperable blockchains.

Outline. In the next section, we formally define a blockchain and interoperability. In Section 3, we prove that it is impossible by design to have interoperability between blockchains. In Section 4, we show that interoperability is possible with a weaker definition of the blockchain. Before concluding, in Section 5, we prove that interoperability is equivalent to having a blockchain with two ledgers.

Preliminaries

Sets and tuples are noted in calligraphic font: A, algorithms in serif: Mine. When a deterministic algorithm, say Algorithm, returns some value x from some input i, we use the notation x←Algorithm(i). If Algorithm is randomised, we use the notation x $ ← -Algorithm(i). A list of elements e 1 ,...,e n (in this order) is represented by [e 1 ,...,e n ]. We denote concatenation of two lists a and b with a b. The set of elements belonging to A but not to B is noted A\B (this set is also called the difference of A and B.)

Blockchain Definition

Various definitions of blockchain have already been given [START_REF] Garay | The bitcoin backbone protocol: Analysis and applications[END_REF][START_REF] Anta | Formalizing and implementing distributed ledger objects[END_REF]. In this work, we rather give a formalization of blockchains, which we believe is easier to use for proving theoretical results such as the one in this paper.

Intuitively, a blockchain is a chain of transactions. More precisely, each element of the chain (each block) contains several transactions (or one or none), as well a proof needed for consensus to take place. For instance in Bitcoin [START_REF] Nakamoto | Bitcoin: A peer-to-peer electronic cash system[END_REF] or similar Proof of Work blockchains, the proof is a nonce (a random number such that the hash of the block is below a threshold value); in a Proof-of-Stake such as the Casper version for Ethereum [START_REF] Buterin | Ethereum: A next-generation smart contract and decentralized application platform[END_REF] the proof consists of the successive bets on what the next block will be; in a Proof-of-Elapsed-Time as designed by Intel [START_REF]Hyperledger sawtooth[END_REF], the proof is instead a certificate obtained from the SGX (a trusted enclave). Note that it exists blockchains not requiring proofs (for instance, one can argue that PBFT consensus does not require proof), in which case we consider the proof is empty.

Definition 1 (Blockchain). Let T be a set of transactions and P be a set of proofs. A blockchain is a tuple of elements B =(L,W, Emit,Mine), where:

• A ledger L is a list of transactions with their proofs defined by: L

= [([t 1,1 ,t
$ ← -Mine(L,W), we have that L is of the form L [(transacs,p)],
where transacs is a list containing all elements from W\W , and p∈P a proof. Furthermore, after a call to Emit or Mine, the ledger L and the waiting pool W of B are updated with the values returned by said algorithms. In other words, Mine and Emit are not pure functions [START_REF] Milewski | Pure functions, laziness, i/o, and monads[END_REF], as they have side effects on the blockchain. At this point, transactions are appended (or not) to the blockchain after a call to Mine. We hereby give a formal definition of what a valid transaction is.

Definition 2 (Valid Transaction). Let B = (L,W,Emit,Mine) be a blockchain, and let t be a transaction (t∈W), t is a valid transaction for B (currently in state L) if and only if there exists a block in the ledger returned by Mine containing t.

As we can see, the validity of a transaction depends on the state of the ledger; if a transaction is valid at one point, it may not be valid forever, and reciprocally. For instance, a transaction from user U to user V is valid only as long as U has enough funds. Yet, after the emission and the insertion of the transaction in the blockchain, U may issue other transactions, emptying their wallet. This is the classical issue of double spending.

The same is true for smart contracts: here, they are seen as a special subset of transactions, and they affect the state of the ledger. Because Mine has access to the whole ledger, it can take into account the smart contract's side effects.

Note that Mine is a randomized algorithm, and as such, there is no guarantee that all users will agree on the same ledger. Because blockchain is a decentralised ledger, state synchronisation must be ensured. For this, we introduce a synchronisation algorithm, called Consensus.

Definition 3 (Decentralised Blockchain).

A decentralised blockchain is a tuple B =(L,W,Emit,Mine,Consensus) where: The idea of Consensus is that when a peer updates their local version of the blockchain, they first receive possibly more than one new version (i.e., new blocks) from peers. However only one of these new blocks will be accepted, and all the network must agree on this block. Definition 4 (Secure Blockchain). We say that a decentralised blockchain (L,W, Emit, Mine, Consensus) is secure if it is computationally hard for a user to craft a new ledger L and a new transaction pool W such that for all S such that (L ,W )∈S, we have both that Consensus(B,S)=(L ,W ) and L is not a prefix of L . This definition makes a blockchain immune against history rewriting (and double spending), as it is computationally hard to rewrite old blocks.

• B =(L,W,Emit,Mine) is a blockchain, • Consensus is a deterministic algorithm, taking as input B, a set S of tuples (L i ,W i ) such that ∀(L i ,W i )∈S, we have that (L i ,W i ,Emit,

Interoperability Definition

The concept of interoperability is to enable two blockchains to work together. A classic blockchain A accepts transactions because given the current state of A's ledger, the transaction does not violate A's rules. Similarly, we say that a blockchain A that is interoperable with blockchain B accepts transactions because, given the current state of A and B's ledgers, the transaction does not violate A's rules. Furthermore, if the rules for said transaction only imply conditions on A's ledger, then the transaction does not require B to be valid, and as such does not make use of the interoperability. So an interoperable transaction on A must be dependent on B's ledger: if B's ledger is equal to some values, then the transaction is valid; otherwise it is invalid.

We now give a formalization of this definition. • a transaction t∈T ,

• a non-empty subset ω A ⊂Ω A ,

• a non-empty proper subset ω B Ω B such that there exists a block containing t that is accepted by Consensus A if L A ×L B ∈ω A ×ω B , and rejected otherwise.

A and B are interoperable if they are both interoperable with each other.

General Impossibility of Interoperability

Our first result is to show that it is impossible to have interoperability between two blockchains in general.

Theorem 1 Under the definitions 3 and 5, blockchain interoperability is impossible.

Proof. Assume that an interoperable transaction t exists. Then there is a set ω B of possible ledger values of B for which a block containing t is accepted by Consensus A , if L B ∈ω B . Moreover, if L B ∈Ω B \ω B , then Consensus A will refuse any block containing t.

However, Consensus A only takes A,S as arguments, where S is a set of tuples (L i ,W i ) (see Definition 3). As a consequence, Consensus A is independent from B, and especially from L B . Then, if t is accepted by Consensus A when L B ∈ω B , then t is also accepted by Consensus A when L B ∈ Ω B \ω B ; this implies that Ω B \ω B = ∅, i.e., ω B =Ω B , which is a contradiction with the hypothesis of Definition 5, namely that ω B is a proper subset of Ω B . This result is actually quite straightforward if we remember that a blockchain is, by construction, made to be self-sufficient: no blockchain can rely on external data. Especially, no blockchain can rely on another blockchain for asserting the validity of a transaction. Hence, interoperability is a contradiction of one of the intrinsic characteristics of blockchain.

The interpretation of the result is as follows: without additional assumptions, interoperability between two blockchains is impossible. Therefore, to achieve interoperability further assumptions need to be made. For instance, in the two-way pegged blockchain mechanism, a dispute period is required for each interoperabilty operation; as the blockchain cannot know by itself whether the proposed SPV proof is the one of the latest block.

Then, let us construct Mine B : a transaction t is valid for Mine B (L B ,L A ,W B ,W A ) if and only if t is valid for Mine A (L A ,∅,W A ,∅), or if both statements are true:

• t is an interoperability transaction transferring some amount of money m from 0 B to an account on B, • L A contains a transaction sending at least m on the zero-address 0 A . Similarly, Consensus B (B, A, •) is conceived to accept new ledgers that would have been accepted by Consensus A (B,∅,•), as well as ledgers where the new blocks are constituted solely of transactions that are accepted by Consensus A (B,∅,•) and valid interoperability transactions (valid in the meaning that at the time of their incorporation in the ledger, the sender has enough funds to emit the transaction).

With this construction, we immediately get that B is interoperable with A: a user can transfer assets from A to B, which is shown by the fact that some transactions (here denoted t * ) are only valid on B if the sender has enough funds on A.

Equivalence of Interoperable Blockchains with a Single Blockchain

Even though interoperable blockchains can be tweaked into existence, we argue that they are conceptually equivalent to a single blockchain. More precisely, we argue that they are equivalent to one blockchain, composed of two ledgers. Such a blockchain can be easily implemented: if the first bit of the transaction is 0, then apply the transaction to the first ledger, and if 1 to the second.

We say that two blockchains are equivalent if any valid transaction on one blockchain corresponds to one valid transaction on the other blockchain. This definition implies that two equivalent blockchains will have very similar evolutions of their ledgers. As Mine is not deterministic, we cannot ensure that the two ledgers will be identical, but the definition we give is enough for practical uses.

Definition 7 (Blockchain equivalence). Let there be two blockchains A=(L A , W A ,Emit A ,Mine A ) and B =(L B ,W B ,Emit B ,Mine B ) accepting transactions from T A and T B , respectively. A and B are said to be equivalent if there exists a bijection ϕ:T A →T B such that, if both ledgers are equivalent, then there is an equivalence of the valid transactions. In mathematical terms, ϕ(L A )=L B ⇒∀t A ∈T A ,t A is a valid transaction for A⇔ϕ(t A ) is a valid transaction for B).

Note that ϕ(L

A ) is the generalization of ϕ to ledgers: if L A = [[t 1,1 ,t 1,2 ,...] , ...,[t n,1 ,t n,2 ,...]], then ϕ(L A )=[[ϕ(t 1,1
),ϕ(t 1,2 ),...],...,[ϕ(t n,1 ), ϕ(t n,2 ),...]], in the case of a ledger without proofs. If the ledger has proofs (see Definition 1), ϕ would need to work on a projection of the ledger: a projection in which every poof is removed. This subtlety has been removed from the definition for the sake of simplicity.

For instance, let us assume that two blockchains are equivalent, and two smart contracts being the reciprocal image of each other. This means that whatever transaction triggers one smart contract, the effects on the state of the blockchain will be equivalent to the effects on the state of the image blockchain: in both cases, the acceptable elements after the transaction are the same (up to a bijection). This definition does not guarantee that the smart contract will behave identically: for instance, one could image a smart contract updating a useless write-only variable, which by definition does not affect the set of future acceptable transactions as it is write-only. However, it ensures that the behaviour of the blockchain is strictly the same in both cases.

Theorem 3 A decentralised blockchain A interoperable with a blockchain B is equivalent to a decentralised blockchain C containing both A and B's ledgers.

Proof. Let A = (L A ,W A ,Emit A ,Mine A ,Consensus A ) and B be two decentralised blockchains, with A being interoperable with B. A being interoperable with B, we have Mine A of the form Mine A (L A , L B , •), and Consensus A of the form Consensus A (A,B,•).

Let T A (resp. T B ) be the set of transactions for A (resp. B). Note that T A contains interoperability transactions. Let C be the tuple C

=(L C ,W C ,Emit C , Mine C , Consensus C ).
We define the set of transactions for C, T C = (T A ×∅)∪(∅×T B ). Let c A (resp. c B ) be the canonical projector of T C on T A (resp. T B ).

For In practice, Theorem 3 means that creating two interoperable blockchains is equivalent to creating one blockchain, with a ledger divided into two separate registries: a '2-in-1' blockchain. So while creating interoperable blockchains (with a lax definition of a blockchain) is possible, we argue that the conceptual interest of doing so is limited. However, it may be interesting to create an interoperable blockchain on top of an already existing blockchain. Doing so allows both blockchains to fully operate, without the older blockchain being affected by anything. Nonetheless the obvious restriction is that only one of the two blockchains will be interoperable with the other, with all the limits implied by this fact.

(L A [(transacs A ,p A )],W A )=Mine A (L A ,L B ,c A (W C )) and (L B [(transacs B ,p B )],W B ) = Mine B (L B ,c B (W C )), we define: Mine C (L C ,W C ) = (L C [(transacs A ×∅ ∅×transacs B ,p A ×p B ), (W A ×∅)∪(∅×W B )]) Simply put, Mine C is

Conclusion

In this paper, we explored the possibility of making two blockchains interoperable. We showed that, under classical definitions, it is impossible to make a blockchain interact with anything other than itself. If we relax the definition, we do get the possibility of interoperable blockchains, but doing so is equivalent to creating a '2-in-1' blockchain, i.e., a blockchain with two ledgers.

  Mine) is a blockchain. Furthermore, for (L * ,W * ) ← Consensus(B,S), then (L * ,W * ) ∈ S ∪(L,W). In other words, from a list of potential new blocks, Consensus chooses (or accepts) one of them, or rejects them all (and returns (L,W)).• After a call to Consensus, B 's ledger and waiting pool components are replaced with the values returned by said algorithms.

  a parallelisation of Mine A and Mine B : a block proposed by Mine C is a block comprised of the transactions accepted by Mine A and Mine B . Similarly, Consensus C is built as a parallelisation of Consensus A and Consensus B . If Consensus A (A,B,c A (S C )) = (L * A ,W * A ) and Consensus B (B,c B (S B )) = (L * B ,W * B ), then we define Consensus C =(L A ×∅ ∅×L B ,W A ×∅∪∅×W B ).By construction, we see that C is a decentralised blockchain. Furthermore, by construction each transaction accepted by Mine C is either accepted by Mine A or Mine B and, conversely, each transaction accepted by Mine A or Mine B is accepted by Mine C , hence the equivalence of the blockchains.

  Definition 5 (Blockchain Interoperability). Let A=(L A ,W A ,Emit A , Mine A , Consensus A ) and B = (L B , W B , Emit B , Mine B , Consensus B ) be two decentralised blockchains. Let Ω A (resp. Ω B ) be the set of all possible values for A's ledger L (resp. L B ). A is interoperable with B if there exists:

Note that for a real cryptocurrency more checks would be needed for any practical use, notably because of the fact that in the current setting, anyone can withdraw m from 0 B as many times as they want. However, for the sake of simplicity, we only describe a simple, naive interoperability operation here, so these checks are omitted.

Interoperability with a Weaker Definition

Even though blockchain is not suited for interoperability stricto sensu, we can generalise our blockchain definition, in order to make a blockchain interoperable.

Hypothesis 1 We assume that for two blockchains A = (L A ,W A ,Emit A ,Mine A , Consensus A ) and B, with A both Mine A and Consensus A have access to both A and B: Consensus A is of the form Consensus A (A,B,S), and Mine A is of the form

We now use the notation Consensus A (A,B,•) to note the new consensus algorithm. Hence, the 'version' of Consensus in the previous definition, is now noted Consensus A (A,∅,•). Similarly, the non-interoperable version of Mine is now noted as

Definition 6 (Interoperable transaction). Under the assumption hypothesis 1, a transaction t on the blockchain A is said to be interoperable with B if t can be accepted by Consensus A (A,B,•) but cannot be accepted by Consensus A (A,∅,•).

In this context, we have the following result.

Theorem 2 Under Hypothesis 1, it is possible to build interoperable blockchains.

Proof. Note that we already know that interoperable blockchains exist, such as Kadena [START_REF] Martino | Chainweb whitepaper[END_REF] or other blockchains listed in [START_REF] Johnson | Sidechains and interoperability[END_REF], but we give an example of interoperable blockchain in our own theoretical framework.

Consider two decentralised blockchains A=(L A ,W A ,Emit A ,Mine A , Consensus A ) and B. On the blockchains we define accounts. An account ownership is defined by the knowledge of a private key, and for simplicity the public key is assimilated to the account itself. A transaction t∈T A (resp. T B ) specifies the sender's public key, the receiver's public key, an amount and a signature of the previous fields by the sender's private key. An account i on blockchain A (resp. B) is designed by i A (resp i B ).

We build blockchain B so that it is interoperable with blockchain A in the following sense: a user can 'create' money on B if and only if at least the same amount of money has been consumed on A, by sending it to a 'bin' account.

We first note that accounts owned by nobody exist. In our scheme, in most cryptosystems the public key 0 (consisting of only zeroes) is not linked to any private key. Thus, while the account 0 A exists and money can be transferred on this account, it cannot be claimed by anyone.

Let us construct B in order to fulfil the previous requirements. First, let us define the interoperability transactions t * (m B ,pk B ), which sends some amount of money m B from 0 B to the account pk B on B. t * (m B ,pk B ) is only valid if 1 there is at least one transaction on L A sending m to the account 0 A , with m>m B .


Mustapha Najib

Eliot Patrick Botosoa

Walid Hallab

Karim Hallab

Zaher Hallab

Monzer Hamze

Guillaume Delaplace

Romdhane Karoui
email: romdhane.karoui@univ-artois.fr

Nour-Eddine Chihib
email: nour-eddine.chihib@univ-lille.fr

Utilization of front-face fluorescence spectroscopy for monitoring lipid oxidation during Lebanese Qishta aging

Keywords: Qishta, Fat Oxidation, Aging, Fluorescence spectroscopy, PCA

Front-face fluorescence spectroscopy technique coupled with chemometric tools was used for predicting the freshness state of a Lebanese dairy product called Qishta, stored up to 20 days.

Acid, peroxide and thiobarbituric acid reactive substances (TBARS) values reached no more than 0.93 mg NaOH g -1 fat, 6.22 meq O2 Kg -1 fat, and 0.0313 mg malonaldehyde (MA) kg -1 sample, respectively, throughout the investigated storage time. In parallel, fluorescence emission spectra of tryptophan and riboflavin, and fluorescence excitation spectra of vitamin A were recorded and showed the highest fluorescence intensity for the Qishta samples aged of 20 days and the lowest intensity for the fresh ones. The primary and secondary indicators of lipid oxidation showed that Qishta can be stored for 20 days without any alteration despite the increase in the TBARS after 16 days of storage. Principal component analysis (PCA) applied on riboflavin emission spectra allowed better discrimination between Qishta samples with a clear distinction of those aged 20 days while some overlapping was noticed between samples aged below 16 days. A high correlation (R 2 = 0.923) was observed between the peroxide value and the intensity of the riboflavin fluorescence recorded at 460 nm.

Introduction

Heat treatment is used as an efficient processing tool to increase the shelf life of food products such as dairy products. However, the heat treatment applied can generate undesirable effects such as fat oxidation and proteolysis [START_REF] Ajmal | Lipid compositional changes and oxidation status of ultra-high temperature treated milk[END_REF][START_REF] Vazquez-Landaverde | Effect of high-pressuremoderate-temperature processing on the volatile profile of milk[END_REF]. Nowadays, consumers are more conscientious and aim a category of fresh food free of artificial additives and being less processed. [START_REF] Jensen | The composition of milk fat[END_REF] define the milk fat as an exceptional medium where different systems exist. Milk fat, which represents around 3 to 5 % in cow milk, is presented as small globules or droplets and dispersed in the aqueous phase of milk. Their diameters vary from 0.1 to 20 µm. Triglycerides are the principal components of milk fat.

Moreover, di-and monoglycerides, fatty acids, sterols, carotenoids are present in milk giving it a yellow color [START_REF] Jensen | The Composition of Bovine Milk Lipids: January 1995 to December 2000[END_REF][START_REF] Jensen | The composition of milk fat[END_REF][START_REF] Jensen | Lipids of Bovine and Human Milks: A Comparison1[END_REF].

In food products, the lipid may undergo autoxidation, photo-oxidation, thermal oxidation and enzymatic oxidation that differ in the type of free radical produced or oxygen species.

Autoxidation is the most common oxidation process leading to oxidative deterioration, which can alter the texture and the flavor, generating some undesirable volatile products such as aldehydes, ketones, alcohols, esters, lactones, and hydrocarbons. The unsaturated aldehydes and ketones formed are mainly responsible for undesirable smells and taste in the dairy products known as rancidity (O'Brien & O'Connor, 2011).

Qishta is a Lebanese heated dairy product consumed as a dessert and used as a filler in some Oriental sweet production such as Knefeh, Mafrouke, etc. It can be defined as a lipoprotein product containing almost an equal amount of fat and protein (≈ 12%), pH quite similar to milk (≈ 6.4), high aw (≈ 0.98) and high moisture content (≈ 70 %). Due to these characteristics, Qishta is considered as highly perishable items and has a shelf life of 5 days when stored at 4 °C [START_REF] Kassaify | Microbiological and chemical profile of Lebanese qishta [heat-coagulated milk[END_REF]. Despite the wide consumption of Qishta in Lebanon and Middle East countries, no bibliography was found investigating the effect of the fat oxidation on its shelf life.

Primary and secondary indicators of fat oxidation have been used as indicators of food quality [START_REF] Barriuso | A review of analytical methods measuring lipid oxidation status in foods: A challenging task[END_REF][START_REF] Botosoa | Use of front face fluorescence for monitoring lipid oxidation during ageing of cakes[END_REF]O'Brien & O'Connor, 2011;[START_REF] Al-Rowaily | Effect of Heating Treatments, Processing Methods and Refrigerated Storage of Milk and Some Dairy Products on Lipids Oxidation[END_REF]. [START_REF] Al-Rowaily | Effect of Heating Treatments, Processing Methods and Refrigerated Storage of Milk and Some Dairy Products on Lipids Oxidation[END_REF] has studied the effect of heat treatment on the chemical variations of lipids in some local dairy products using peroxide, p-anisidine, TBARS, acid and TOTOX values. Even though the physico-chemical analyses had been proved as efficient methods, they are considered as time-consuming and require the use of a lot of chemical products.

Rapid screening techniques are mainly used nowadays to predict the fat oxidation level instead of the laborious and destructive methods mentioned above. Front-face fluorescence spectroscopy (FFFS) is considered today as a rapid, non-destructive, and relatively cheap technique, for measuring quality parameters especially in the dairy field [START_REF] Kamal | Monitoring of mild heat treatment of camel milk by front-face fluorescence spectroscopy[END_REF][START_REF] Botosoa | Use of front face fluorescence for monitoring lipid oxidation during ageing of cakes[END_REF][START_REF] Karoui | Front face fluorescence spectroscopy coupled with chemometric tools for monitoring the oxidation of semi-hard cheeses throughout ripening[END_REF]Karoui et al., 2006a;[START_REF] Karoui | Utilisation of front-face fluorescence spectroscopy for the determination of some selected chemical parameters in soft cheeses[END_REF]Miquel Becker et al., 2003). This technique was used to: i) predict the fat oxidation of semi-hard cheeses during ripening [START_REF] Karoui | Front face fluorescence spectroscopy coupled with chemometric tools for monitoring the oxidation of semi-hard cheeses throughout ripening[END_REF]; ii) monitor the light-induced changes in plain yogurt and the effect of light on the oxidation of cheese products during storage (Miquel Becker et al., 2003;[START_REF] Christensen | Application of fluorescence spectroscopy and chemometrics in the evaluation of processed cheese during storage[END_REF][START_REF] Mortensen | Effect of specific wavelengths on light-induced quality changes in Havarti cheese[END_REF][START_REF] Wold | Nondestructive measurement of light-induced oxidation in dairy products by fluorescence spectroscopy and imaging[END_REF]. Finally, [START_REF] Karoui | Potentiality of front-face fluorescence spectroscopy to determine the geographic origin of milks from the Haute-Loire department (France)[END_REF] have utilized the FFFS technique to discriminate milk samples according to their geographic origins. The high abundance of fluorophores in milk products such as vitamin A, tryptophan, riboflavin and nicotinamide adenine dinucleotide (NADH), among several other fluorescent compounds, gave this technique an added value in the dairy field [START_REF] Karoui | Utilisation of front-face fluorescence spectroscopy for the determination of some selected chemical parameters in soft cheeses[END_REF].

Our study aims to monitor fat oxidation of Qishta during its storage for up to 20 days at 4 °C using: i) primary and secondary indicators of oxidation; and ii) FFFS as a rapid and nondestructive technique to predict the chemical changes, especially lipid oxidation. To the best of our knowledge, this study is the first to aim in investigating the effect of storage on the lipid oxidation of Qishta.

Materials and Methods

2.1.Production of Qishta

According to Hallab 1881 company (Lebanon), the process of Qishta consists of heating whole milk in a large open shallow plate (diameter of 1 m and capacity of 12 L) from one side for 3 hours. Fifteen minutes after the beginning of heating, aggregates appear on top of the milk in the heated zone, where the temperature reaches 100 °C. These aggregates, defined as a mixture of protein and fat globule, are the main components of Qishta. Milk is added continuously in order to readjust its level in the plate due to the evaporation of water. The aggregates and/or the gel formed were gathered at the opposite side of the flame until a precise amount was obtained (usually between 2 and 3 Kg). Qishta was drained at 4 °C for one hour and then distributed in 14 plastic containers with a capacity of 150 g each, and stored at 4 °C during 0, 3, 6, 9, 16 and 20 day(s).

Milk was provided from Lactel (Lactel, France). It is an UHT whole milk having 3.6 % fat and 3.2 % protein. The plate (stainless-steel, 316 L) was provided from Nafco (Nafco, Lebanon) and the burner was provided from AEM (AEM, Chelles, France) equipped with a pressure regulator.

2.2.Physicochemical analysis

Acetic acid glacial 100 %, dichloromethane, n-hexane, Celite ® 545, sodium sulphate anhydrous, ethanol denatured 95 % volume and propan-2-ol were purchased from VWR (France), while Para-anisidine and 2-thiobarbituric acid reagent were provided from MERCK (Germany).

Roquette (France) and VWR (France) provided starch and chloroform respectively. Potassium iodide 99 %, phenolphthalein solution (1 % ethanol) and pure sodium hydroxide (97 %) were purchased from VWR (France) and LABOGROS (France). Finally, Isooctane (UV-IR-HPLC) and sodium thiosulphate were provided from VWR (France) and Panreac Quimica (Spain), respectively.

2.3.Extraction of fat

Fat extraction was held at the same day of the analyses and according to the Association Françoise de Normalisation (AFNOR (1991). A volume of 400 mL of hexane/ethanol (3/1; v/v) was added to 135 g of Qishta. The mixture was stirred at ambient temperature for 90 minutes (10 3 rpm). The extracted fat was filtered by Whatman No. 1 filter paper. It was then eluted and separated from the mixture by passing it through a 2 cm high column of Celite ® and sodium sulphate laid on the bottom of a Büchner filter. The filtrate was dried in a rotary evaporator (Büchi, Rotavap R-3) at speed 4. Bath temperature was previously equilibrated at 40 °C. All the physico-chemical analyses were performed in triplicate.

2.4.Measurement of acid value

Acid value of Qishta was determined according to AOCS (Cd 6d-63, 1997) method with a slight modification since only 2.5 g of the extracted fat were mixed with 15 mL of a solution of ethanol/dichloromethane (1/1; v/v) [START_REF] Botosoa | Use of front face fluorescence for monitoring lipid oxidation during ageing of cakes[END_REF].

2.5.Measurement of peroxide values

Peroxide value of Qishta was analyzed according to AOCS (Cd 8-53, 1997) method with a slight modification, which corresponded to the fact that only 20 mL of a mixture of acetic acid / chloroform (3/2; v/v) and 15 mL of ultrapure water were necessary for 2.5 g of extracted fat. The titration was done using sodium thiosulfate (Na2S4O6) (0.005 mol L -1 ) [START_REF] Botosoa | Use of front face fluorescence for monitoring lipid oxidation during ageing of cakes[END_REF].

2.6.Measurement of thiobarbituric acid

Thiobarbituric acid value of Qishta, during storage was determined using the direct method described by [START_REF] Pokorny | Determination of 2-thiobarbituric acid value : Direct method[END_REF] with a slight modification. 0.05 g of extracted fat was mixed with 5 mL of TBA solution (0.02 mol L -1 ) and 5 ml of butanol and maintained in a heated bath (Büchi, France) equilibrated at 95 °C for 2 hours. The solution was cooled with tap water for 10 minutes before analyzing the absorbance values. TBA reacting with malonaldehyde (MA) forms a pink MA-TBA complex at 530-535 nm, which was measured using a spectrophotometer (UV 2600, Shimadzu, Noisiel, France).

2.7.Fluorescence spectroscopy measurements

Fluoromax-4 spectrofluorimeter (Jobin Yvon, Horiba, NJ, USA) was used in order to record the fluorescence spectra. The incidence angle of the excitation radiation was set at 60° in order to minimize the reflected light, the scattered radiation and the depolarization phenomena. The spectrofluorimeter was supplied with a thermostated cell and Haake A25, AC 200 temperature controller (Thermo-Scientific, France). A quartz cuvette filled with three grams of Qishta was used for the analysis. Spectra of Qishta were recorded in duplicate. The sample was illuminated by the photons of excitation (light beam: ~3 mm wide and ~0.3 mm high) at its center for 3 min, limiting sample dehydration. Emission spectra of tryptophan (305 < λem < 450 nm) and riboflavin (405 < λem < 650 nm) were recorded after excitation at 290 nm and 380 nm respectively. Excitation spectra of vitamin A (252 < λex < 390 nm) were acquired with the emission wavelength set at 410 nm. A rhodamine cell in the reference channel was used in order to correct the recorded spectra.

2.8.Mathematical analyses of data

All spectra recorded were normalized by reducing the area under each spectrum to a value of 1 in order to reduce the scattering effects (Karoui et al., 2007;[START_REF] Al-Rowaily | Effect of Heating Treatments, Processing Methods and Refrigerated Storage of Milk and Some Dairy Products on Lipids Oxidation[END_REF]. Principal component analysis (PCA) was applied on the normalized spectra to visualize the variations between Qishta samples during storage. PCA is a descriptive, representative and exploratory method aiming to reduce the variables into a lower number. It allows the visualization of correlations among the original variables by finding a combination between them that describe the major trends in the data.

Variables are transformed into new orthogonal axes called principal components (PCs). In addition, the eigenvectors are similar to spectra and are nominated spectral patterns. The interpretation of the positive and negative peaks allows a better characterization of the emission and excitation spectra. The correlation between the spectral patterns and the PCs allows the characterization of the potential wavelengths used to discriminate between spectra.

PCA and spectral patterns were performed using MATLAB version R 2013b and 2014a (The MathWorks Natick, MA, USA) and PLS Toolbox 7.9 and 8.0 (Eigenvector Research Inc., Wenatchee, WA, USA).

One-way analysis of variance (ANOVA) was conducted using the SPSS software for Windows (version 13.0, SPSS). A Duncan test was carried out to assess any significant differences between the means. The difference was considered statistically significant when P ≤ 0.05.

Results and discussion

3.1.Evolution of the physico-chemical parameters during aging

Evolution of acid value during Qishta aging

Table 1 showed the variation of acid value during 20 days of Qishta storage at 4°C. Acid value reflects the quantity of acids resulting from the hydrolysis of triacylglycerols. In fact, the term free fatty acid refers to a fatty acid without glycerol [START_REF] Mannion | Free fatty acids quantification in dairy products[END_REF]. Acid values varied between 0.8 and 0.9 mg NaOH g -1 fat. The minimum value (0.8) was obtained for Qishta samples aged 20 days, while the highest one (0.93) was observed for those kept for 16 days at 4 °C. Fresh Qishta (0 day) exhibited an acid value of 0.89 mg NaOH g -1 fat, which is significantly higher compared with values usually reported for UHT milk. This significant increase (P<0.05) may be due to the impact of heat treatment (100 °C) during the production of Qishta related to lactose degradation and formations of acids such as formic acid. In addition, it was reported that half of this increase of acid value is due to the formation of organic acids from lactose; the remainder is due to the precipitation of calcium phosphate and dephosphorylation of casein [START_REF] Fox | Heat-induced changes in milk[END_REF].

The significant increase (P<0.05) of acid value observed between days 9 and 16 could be ascribed to the development of microorganisms presenting lipolytic activity during storage at 4 °C. Thereby, psychrotrophic bacteria, yeasts and molds are usually present in refrigerated products.

Evolution of primary oxidation products during Qishta aging

Hydroperoxides formation, as a result of primary lipid oxidation, is responsible of undesired reactions, giving rise to complexes of saturated and unsaturated ketones and aldehydes. These molecules can negatively alter the flavor and the color of food products [START_REF] Ramis-Ramos | ANTIOXIDANTS | Synthetic Antioxidants[END_REF].

Table 1 showed the variation of primary parameters of oxidation values. Concerning the evolution of peroxide, the average value decreased from 6.22 to 3.47 meq O2 kg -1 fat after 20 days of storage. Fatty products having a peroxide value higher than 20 meq O2 kg -1 fat are considered rancid and non-edible, while a value between 0 and 5 meq O2 kg -1 fat corresponds to a fresh high-quality product (O' Keefe & Pike, 2010). Fresh Qishta has a peroxide value of 6.22 meq O2 kg -1 fat which reflects a medium level of oxidation. The sudden decrease between day 16 and 20 could be explained by the formation of the secondary products of oxidation. [START_REF] Rehman | Effect of synthetic antioxidants on storage stability of Khoa -a semi-solid concentrated milk product[END_REF] found an amount of 0.38 and 17.8 meq O2 kg -1 fat for fresh and aged Khoa stored for 10 days at 25 °C. Khoa is an Indian dairy product obtained by a similar process to that of Qishta. Al-Rowaily ( 2008) noted an amount of 0.155 meq O2 kg -1 fat for raw cow milk. The high peroxide value obtained in fresh Qishta could be due to the use of UHT milk and the process applied which consists of boiling milk for more than 3 hours. affecting the lipid oxidation. These results must be coupled with microbiological and sensory analysis in order to conclude on the shelf life of Qishta.

3.2.Evolution of fluorescence spectra during Qishta aging

The abundance of intrinsic fluorophores in dairy products, such as vitamin A, riboflavin, tryptophan, NADH and so on, has promoted the development of fluorescence spectroscopy methods. These techniques can provide, coupled with the chemometric tools, some chemical and physical properties of food products. FFFS is considered as a cheap, rapid and non-destructive method that could replace the physico-chemical analyses [START_REF] Andersen | Fluorescence Spectroscopy: A Rapid Tool for Analyzing Dairy Products[END_REF]Karoui & De Baerdemaeker, 2007). The fluorescence spectra of vitamin A was reported to provide information related to: i) the interaction between proteins and lipids; and ii) the physical state of the triglycerides [START_REF] Andersen | Fluorescence Spectroscopy: A Rapid Tool for Analyzing Dairy Products[END_REF]; while the fluorescence spectra of riboflavin was linked with protein and fat oxidation [START_REF] Karoui | Common components and specific weights analysis: A tool for monitoring the molecular structure of semi-hard cheese throughout ripening[END_REF][START_REF] Becker | Front-Face Fluorescence Spectroscopy and Chemometrics in Analysis of Yogurt: Rapid Analysis of Riboflavin[END_REF].

Fluorescence spectra of tryptophan acquired after excitation at 290 nm on Qishta samples during aging

In dairy products analysis, tryptophan emission spectra was considered as an indicator of the protein structure [START_REF] Andersen | Fluorescence Spectroscopy: A Rapid Tool for Analyzing Dairy Products[END_REF]. Figure 1a showed the normalized emission spectra acquired after excitation wavelength set at 290 nm. The emission spectra of all samples exhibited a maximum at around 375 nm. Except for the 20 days aged Qishta that had the highest fluorescence intensity and the largest width, all Qishta samples exhibited almost the same emission spectra. The observed shift from the maximum emission wavelength to the larger wavelength range can be explained by exposing more tryptophan residues to the aqueous phase of aged Qishta samples, in agreement with previous findings of [START_REF] Karoui | Monitoring the egg freshness during storage under modified atmosphere by fluorescence spectroscopy[END_REF] who observed a red shift of tryptophan emission spectra acquired on aged egg albumen. Additionally, the exposed tryptophan residues in Qishta could be shielded from the aqueous phase by other protein molecules as a result of protein-protein interactions, the rate of which increases with protein unfolding. The high fluorescence intensity observed for Qishta aged 20 days could be due to protein aggregation that impact significantly the fluorescence intensity compared to the storage time-induced protein unfolding, which causes more tryptophan residues to become exposed to the aqueous phase of Qishta samples.

Fluorescence properties of vitamin A acquired after emission at 410 nm on Qishta samples during aging

Figure 1b showed the excitation fluorescence spectra recorded after emission wavelength set at 410 nm. These excitation spectra exhibited a maximum peak located at ~320 nm and two other minors located at 292 and 305 nm. These observations are in agreement with previous findings of [START_REF] Karoui | Dynamic testing rheology and fluorescence spectroscopy investigations of surface to centre differences in ripened soft cheeses[END_REF] reporting that the maximum fluorescence intensity of vitamin A excitation spectra scanned on different varieties of soft cheese, after emission at 410 nm, was located at 322 and 305 nm. Again, as observed for tryptophan spectra, vitamin A spectra acquired on Qishta samples aged 20 days presented the highest fluorescence intensity. Indeed, Qishta samples aged 0 day had the lowest fluorescence intensity at 320 nm, while those kept up to 20 days had the highest one. It has been reported that the shape of the vitamin A excitation spectrum is correlated with the physical state of the triglycerides in the fat globules (Karoui et al., 2006a). The ratio of fluorescence intensity at 320nm/292 nm increase with the increase of storage time which could be explained by the increase of the viscosity of triglycerides. This could be attributed to cristallization of triglyceride during storage, in agreement with previous findings [START_REF] Andersen | Fluorescence Spectroscopy: A Rapid Tool for Analyzing Dairy Products[END_REF]Karoui et al., 2006a). Similar trend was observed during the ripening of semi-hard cheeses since changes in the fluorescence intensity ratios at 322 nm/295 nm were noted and ascribed to the crystallization of triglycerides between 1 day and 81 days of ripening [START_REF] Dufour | Phase transition of triglycerides during semi-hard cheese ripening[END_REF]. Finally, the changes in the shapes of vitamin A spectra may also result from fluorescence transfer between tryptophan residues of proteins and vitamin A located in the fat globule membrane.

Fluorescence properties of riboflavin acquired after excitation at 380 nm on Qishta samples during aging

Considering the riboflavin fluorescence spectra (Figure 1c), the emission spectra exhibited 2 maxima located at 455 and 530 nm. Except for Qishta spectra acquired on day 0, the fluorescence intensity increased with the storage time. As observed for vitamin A and tryptophan spectra, the 20 days aged Qishta exhibited the highest fluorescence intensity.

An increase in the fluorescence intensity in the region located between 405 and 480 nm was noticed during the storage period of Qishta. This region was reported to reflect the oxidation resulted from the products formed by aldehydes and amino acids. In the same region, lumichrome, a photo breakdown product from riboflavin, exhibits fluorescence between 444-479 nm. In addition, β-carotene absorbs in the region located between 400-500 nm. β-carotene can also undergo photodegradation, which may influence the shape of riboflavin fluorescence spectra. The obtained results are in line with the findings of Karoui et al., (2007;2006a) who observed an increase of the fluorescence intensity of spectra acquired after excitation set at 380

nm for both egg and cheese. Surprisingly, we noticed an increase of the fluorescence intensity at 530 nm, which is in discordance with the findings of [START_REF] Wold | Nondestructive measurement of light-induced oxidation in dairy products by fluorescence spectroscopy and imaging[END_REF]. An explanation could arise from the transfer of energy that occurs between fluorescent compounds allowing an increase of fluorescence intensity at 530 nm and/or from the presence of other fluorophores in Qishta having maximum excitation at 530 nm. Most of the investigated spectra presented similar shapes, therefore it was of high importance to find a mean in order to distinguish between the samples studied. Thus, PCA was used to extract information from the data tables. This multidimensional statistical technique was applied to the 12 spectra collected on Qishta at different storage times (Figure 2). The map defined by PCs 1 and 2 (69.74 and 27.79 % of the total variance, respectively) of the PCA performed on spectra acquired after excitation at 290 nm (corresponding to tryptophan) divided the samples into 2 groups. Group 1 consisted mostly of the samples aged from 0 to 16 days, while group 2 comprised the samples aged 20 days. A clear differentiation was shown between these 2 groups since the former group is located mostly on the negative side of PC1, while the latter one is positioned on the positive side. However, the distinction inside group 1 was not feasible since Qishta samples were overlapped.

3.3.Discrimination based on fluorescence spectra recorded on

Evaluation of the discriminant ability of fluorescence spectra acquired on Qishta excitation during storage after emission wavelength at 410 nm on Qishta

Concerning PCA applied to the excitation spectra recorded after emission at 410 nm (excitation spectra of vitamin A), a better discrimination was obtained than that observed with the emission tryptophan spectra. In fact, the map defined by PCs 1 and 2 (93.42 % and 5.44 % of the total variance, respectively) showed some clear discrimination of Qishta samples according to their storage time (Figure 3a). Qishta samples aged 20 days were always distinguishable from all the other samples. Regarding PC1, all samples had negative score values except those aged 20 days and one sample aged 9 days.

The spectral pattern 2 showed an opposition between a negative peak located at 310 nm and a positive one at 375 nm (Figure 3b) indicating major changes at the molecular level between samples aged 0 and 3 days from the others. [START_REF] Karoui | Dynamic testing rheology and fluorescence spectroscopy investigations of surface to centre differences in ripened soft cheeses[END_REF] have already obtained this spectral pattern while they were comparing the difference between the centers and the surfaces of ripened soft cheeses. They suggested that the shape of the spectral pattern of vitamin A reflects the variation occurred in the triglyceride molecules, as well as the interaction between proteins and fat globules during cheese ripening and storage. [START_REF] Botosoa | Use of front face fluorescence for monitoring lipid oxidation during ageing of cakes[END_REF] have used the spectral pattern of vitamin A in order to discriminate between cake samples during aging. According to the results obtained on the emission and excitation spectra of tryptophan and vitamin A respectively, it can be concluded that Qishta samples aged 20 days can be discriminated from other samples. The distinction between Qishta samples aged 0, 3, 6, 9 and 16 was not so clear due to the overlapping observed. The differences detected could be due to the interaction developed between protein and fat globule during the storage, aggravated by the high moisture content which has been suggested to increase the molecular interactions in the food matrix [START_REF] Botosoa | Use of front face fluorescence for monitoring lipid oxidation during ageing of cakes[END_REF][START_REF] Karoui | Dynamic testing rheology and fluorescence spectroscopy investigations of surface to centre differences in ripened soft cheeses[END_REF].

Evaluation of the discriminant ability Fluorescence spectra of riboflavin acquired after excitation at 380 nm on Qishta samples

The map defined by PC 1 and 2 (97.13 % and 2.57 % of the total variance, respectively) showed always a clear discrimination between samples aged 20 days and other samples (Figure 4a).

Concerning PC1, Qishta samples aged 0, 3 and 6 days had negative values while almost all the other samples (age > 6 days) exhibited positive values. It can be concluded that PC1 divided the samples according to their ages, and contrary to the previous spectra, the discrimination between all Qishta samples was better with less overlapping. These results were in accordance with the TBARS analysis since the map defined by PCs 1 and 2 divided the samples into 3 groups: the first one consists of Qishta aged 0 day, the second one belongs to Qishta aged 3, 6, 9 and 16 days and the last one contains Qishta aged 20 days. The ANOVA test held on the TBARS values has also divided the Qishta samples into 3 groups significantly different and consisting of the same Qishta samples.

The spectral pattern 2 (Figure 4b) showed a positive peak located around 460 nm suggesting the formation of photo break down products from Qishta samples stored for 3, 6, 9 and 16 days.

The correlation between primary indicators of oxidation and high-intensity bands obtained at 460 nm of the spectra scanned after excitation set at 380 nm was investigated. A high correlation (R² = 0.923) was found between peroxide values and the fluorescence intensity. A negative correlation was noticed between peroxide value and normalized fluorescence intensity at 460 nm suggesting probably that this could be used as an indicator of the transformation of primary products to secondary ones.

Conclusion

From fat oxidation point of view, the physico-chemical results have shown that Qishta could be stored for 20 days without any quality deterioration. TBARS value highly increased after 20 days while peroxide value showed a slight decrease. Fluorescence spectra coupled with chemometric tools were able to detect the variation that occurred during Qishta storage. In fact, PCA showed clear discrimination between Qishta samples aged 20 days and all other samples. Tryptophan and vitamin A showed an overlapping between samples aged from 0 to 16 days, while the fluorescence spectra corresponding to riboflavin demonstrated its ability to determine the freshness level of Qishta. A high correlation was observed between the fluorescence intensity at 460 nm and peroxide values. It could be concluded that riboflavin spectra could be used as an effective tool for the evaluation of Qishta freshness.

  Qishta samples 3.3.1. Evaluation of the discriminant ability of fluorescence spectra of tryptophan acquired after excitation wavelength set at 290 nm on Qishta samples during 20 days of storage.

  Means values within a column sharing a common alphabet do not differ significantly (p < 0.05); values presented are mean values for three samples (n = 3).

Figure 1 :

 1 Figure 1: Normalized emission fluorescence spectra recorded after excitation wavelength set at (a) 290 nm, (b) 410 nm and (c) 380 nm on Qishta sample aged 0 (-), 3(-. -), 6(-. . ), 9 (---), 16 (-. -) and 20 days (…).

Figure 2 :

 2 Figure 2: PCA similarity map defined by the principal components 1 and 2 after excitation wavelength set at 290 nm on Qishta samples during 20 days of storage.

Figure 3 :

 3 Figure 3: (a) PCA similarity map defined by the principal components 1 and 2 after emission wavelength set at 410 nm on Qishta samples during 20 days of storage and (b) Spectral pattern corresponding to PC1 and PC2.

Figure 4 :

 4 Figure 4: (a) PCA similarity map defined by the principal components 1 and 2 after excitation wavelength set at 380 nm on Qishta samples during 20 days of storage and (b) Spectral pattern corresponding to PC1 and PC2

Acknowledgments

Mr. Najib is grateful to Hallab 1881 Company Tripoli Lebanon for its financial grant of his Ph.D.

Considering the primary indicators of fat oxidation, a decrease in both acid and peroxide values was observed after 20 days of storage; Qishta samples can be considered acceptable since the values are within the acceptable range.

Evolution of secondary products during Qishta aging

The oxidation level of Qishta was better represented by TBARS than by peroxide value since the noticeable increase in the TBARS of Qishta aged of 20 days was not reflected in peroxide value.

Al-Rowaily ( 2008) reported a similar tendency while measuring the TBA value of microwave heated milk. TBARS measures mainly malonaldehydes (O'Keefe & Pike, 2010) but at those levels of oxidation TBARS could be more representative for oxidation status than peroxide value [START_REF] Al-Rowaily | Effect of Heating Treatments, Processing Methods and Refrigerated Storage of Milk and Some Dairy Products on Lipids Oxidation[END_REF]. During 20 days of storage, the TBARS values increased from 0.0076 to 0.0313 (Table 1). Qishta exhibited the highest value of 0.0313 at 20 days of storage. The most important increase of TBARS (0.0175 to 0.0313) was observed between the 16 th and 20 th day of storage with a difference of 0,0138. Despite this increase, the values obtained reflected an acceptable quality of Qishta even at 20 days of storage at 4 °C. Indeed, these values, particularly TBARS of Qishta aged 16 days (0.0175), are significantly lower when compared to those obtained by [START_REF] Al-Rowaily | Effect of Heating Treatments, Processing Methods and Refrigerated Storage of Milk and Some Dairy Products on Lipids Oxidation[END_REF], who reported TBARS value of 0.086 for yogurt and 0.021 for Labaneh produced by conventional method after 15 days of refrigerated storage. [START_REF] Ishak | Evaluation of the antioxidant potential of some Malaysian herbal aqueous extracts as compared with synthetic antioxidants and ascorbic acid in cakes[END_REF] considered cakes as non-rancid if the TBARS value was less than 0.576 mg MA kg -1 . The TBARS values of raw cow milk and UHT milk were 0.014 and 0.027 mg MA kg -1 respectively [START_REF] Al-Rowaily | Effect of Heating Treatments, Processing Methods and Refrigerated Storage of Milk and Some Dairy Products on Lipids Oxidation[END_REF].

Based on these results (primary and secondary indicators of lipid oxidation), Qishta can be considered as acceptable and non-rancid and can be stored in the same conditions without


Jean-Loup Méreaux
email: jeanloup.mereaux@gmail.com

Vianney Gilard

Floriane Le Goff

Nathalie Chastan

Nicolas Magne

Emmanuel Gerardin

David Maltête

Axel Lebas

Stéphane Derrey

Practice of stereoelectroencephalography (sEEG) in drug-resistant epilepsy: Retrospective series with surgery and thermocoagulation outcomes

Keywords: epileptogenic zone, resective surgery, epilepsy surgery, thermocoagulation Résumé

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

Méreaux

Highlights

• sEEG helped to locate the epileptogenic zone in 92% of cases • sEEG complications were rare (6%) but could be major, with one death due to hematoma • Thermocoagulation reduced the frequency of seizures in 88% of cases

• Three months after surgical resection, 61% of patients were seizure-free

Conclusions

Nos résultats suggèrent que la sEEG est une technique efficace pour localiser la ZE chez les patients atteints d'épilepsie pharmaco-résistante. La sEEG était contributive pour 92 % des patients permettant de proposer une thermocoagulation et/ou une chirurgie de résection de la ZE permettant une disparition des crises épileptiques chez presque deux tiers et une réduction de fréquence pour le tiers restant. Cette étude souligne la nécessité d'une sélection stricte des patients à implanter et d'une hypothèse initiale rigoureuse concernant la localisation de la ZE.

Introduction

Epilepsy is a severe neurological disorder with incidence of 50/100,000/year 1 and prevalence of 5-8/1,000 in Europe [START_REF] Forsgren | The epidemiology of epilepsy in Europe -a systematic review[END_REF][START_REF] Fernández-Suárez | Prevalence, type of epilepsy and use of antiepileptic drugs in primary care[END_REF] . It is associated with increased morbidity and mortality, including sudden unexpected death from epilepsy (SUDEP) [START_REF] Tomson | Sudden unexpected death in epilepsy: current knowledge and future directions[END_REF] . Despite the diversity of anti-epileptic (AE) drugs available, 10% to one-third of epilepsy cases are drug-resistant [START_REF] Jallon | Epidemiology of drug-resistant epilepsies[END_REF][START_REF] Mann | La pharmacorésistance des épilepsies partielles : épidémiologie, mécanismes, pharmacogénétique, perspectives thérapeutiques[END_REF] , defined by the International League Against Epilepsy (ILAE) as "the failure of two tolerated, appropriately chosen and used antiepileptic drug schedules whether as monotherapies or in combination to achieve sustained seizure freedom" [START_REF] Kwan | Definition of drug resistant epilepsy: Consensus proposal by the ad hoc Task Force of the ILAE Commission on Therapeutic Strategies: Definition of Drug Resistant Epilepsy[END_REF] . In this context, surgical resection of the epileptogenic zone (EZ) can be proposed [START_REF] Sheng | Drug-Resistant Epilepsy and Surgery[END_REF] . Locating the EZ may require invasive techniques such as stereoelectroencephalography (sEEG) or sub-dural grids if non-invasive investigations fail. sEEG consists in stereotactic implantation of deep intracerebral electrodes based on a clinical, radiological and electrophysiological hypothesis of EZ location. The usual indications for sEEG are 9,10 : -no visible anatomical lesion on radiological imaging; -radio-electro-clinical discordance; -lesion visible but clinical or electrical evidence suggesting that the EZ is larger than the lesion; -large lesion partly extending in an eloquent cortical area, but with clinical and/or electrical evidence that partial excision could be effective; -clinical or EEG suspicion of involvement of highly functional deep structures.

The objective of the procedure is to obtain an extremely accurate cartography of the EZ and neighboring functional structures and their relations with the EZ, and seizure escape routes. sEEG requires expertise, and has been performed since 2010 in our center. The primary objective of this study was to determine the success rate of sEEG in locating the EZ.

Secondary objectives were to analyze sEEG-related morbidity, and outcome of any thermocoagulation and/or surgical resection based on the Engel and ILAE outcome scales [START_REF] Engel | Outcome with respect to epileptic seizures[END_REF][START_REF]Commission on Neurosurgery of the International League Against Epilepsy[END_REF] .

Material and Methods

Population and Indications

Patients were referred to the neurosurgery department of our tertiary care center for intractable epilepsy. Prior to sEEG, each case was discussed in a national multidisciplinary consultation meeting. Information on the goals and risks of the sEEG procedure was given, with special focus on the possibility of intracranial hematoma. Informed consent was sought and obtained from patients or (for children) legal representatives. The study was approved by the local review board (n° E2019-35). During the study period (November 2010 -June 2018) 49 sEEGs were performed in 46 consecutive patients (mean age, 25 ± 12 years; M/F sex ratio, 0.84), with 585 implanted electrodes. Fourteen (30%) patients were children under 16 years of age. Mean disease duration was 14 ± 7 years, with mean onset age of 14 ± 11 years. Seizure frequency was daily in 22 patients (48%), weekly in 22 (48%), and monthly in 2(4%). The sEEG aimed to explore the temporal lobe (31 of the 49 cases), or the frontal (14), occipital (9), insular (9) or rolandic (4) lobe. Exploration was unilateral in 33 cases and bilateral in 16, with a mean 12 ± 2 electrodes. A lesion was found on MRI-scan in 20 patients (43%).

Technique of sEEG electrode implantation

Under general anesthesia after placement of a Leksell frame, 1.5T or 3T magnetic resonance imaging (MRI) was performed using 3D-T1-weighted gadolinium-enhanced sequences (Avento 1.5 Tesla, Siemens, Erlangen, Germany), stereotactic CT-scan and multislice CT angiography (MCTA) (Optima 660, GE Healthcare, Milwaukee, WI). MRI was acquired in the axial plane with: 256x256 matrix, FOV 256x256 mm, and section thickness of 1 mm, for a spatial resolution of 1x1x1. MCTA was acquired in the axial plane with: 512x512 matrix, FOV 270x270 mm, section thickness of 0.625 mm, and 0.4 reconstruction interval. The injection rate was 3.5 mL/s of 50 ml contrast agent pulsed by 50 mL saline. Bolus tracking by aortic arch enhancement was used as reference. Volumes of interest were displayed as both arterial and venous contrast opacification. At the end of the pipeline, the processed data were loaded in the stereotactic planning software (Framelink R 5.0, Stealth-Station R , Medtronic, MN). For each electrode, using MRI and MCTA data, a trajectory (orthogonal or double obliquity) was planned, avoiding sulci and cortical vessels. The rest of the procedure, with electrode implantation in the operating room, has been previously described [START_REF] Gilard | Usefulness of multidetector-row computerized tomographic angiography for the surgical planning in stereoelectroencephalography[END_REF] . Since December 2016, depth electrode implantation (n=10 patients) has been performed with robotic stereotactic system guidance (ROSA®; Medtech Zimmer Biomet); surgical procedure (Figure 1) remains unchanged by robotic assistance except that frameless imaging acquisition and surgical planning are performed several days before implantation.

Results

sEEG outcomes

sEEG outcomes are summarized in Figure 2. After a mean recording time of 7 ± 3 days (range, 3-13 days), sEEG helped to locate the EZ in 45 of 49 recordings: i.e., success rate of 92%. Multifocal EZs were found in 8 patients. One patient underwent two sEEGs, to better define the EZ before surgical resection, and another patient underwent a second sEEG after surgery for new onset of seizures. There was no difference between children (15 sEEGs, 31%) and adults (34 sEEGs, 69%) in terms of sEEG success.

There was 1 major complication, with death due to subdural and intra-parenchymal hematoma. We reported this unusual observation, with onset of delayed hematoma more than 1 week after lead implantation [START_REF] Derrey | Delayed intracranial hematoma following stereoelectroencephalography for intractable epilepsy: Case report[END_REF] . Two patients showed transient complications: confusion (n=1), and behavioral, visuospatial and language symptoms (n=1). During sEEG recording, electrode dysfunction occurred in 6/585 electrodes (1%), including 1 broken electrode surgically removed under local anesthesia at end of recording.

Thermocoagulation and surgical resection

sEEG recording enabled 8 thermocoagulations (16%) [START_REF] Guenot | SEEG-guided RF Thermocoagulation of Epileptic Foci: Feasibility, Safety, and Preliminary Results[END_REF][START_REF] Guenot | La thermocoagulation multiple de foyers épileptogènes guidée par la SEEG (thermo-SEEG)[END_REF] , which were suggested by the neurophysiologist using the first sEEG results. Thermocoagulation was performed when i) the EZ was located in a functional area (language area, most often), ii) when the EZ was very large, and/or iii) to test the main hypothesis with the aim of predicting the result of the cortectomy. Thermocoagulation reduced seizure frequency in 7 patients (88%), with no seizures at 2 years' follow-up in 3 patients; 3 patients showed a 50% decrease, and 1 patient showed transient 50% reduction only for a few months, with seizure frequency finally unchanged.

There was no morbidity due to thermocoagulation. Thirty-three surgical resections were performed: 24 cortectomies, 3 lesionectomies and 6 associated cortectomies-lesionectomies.

Three surgeries were pending at the time of writing, including 1 not performed due to absence of seizures after thermocoagulation. Postoperative complications comprised 2 (6%) transient diplopias, 1 (3%) permanent paresis of the lower limb with deep sensory disorder (cortectomy of the sensory and motor paracentral lobule) and 1 (3%) scar infection. Pathology results were normal in 18 cases (55%). Pathological diagnoses comprised: 4 dysembryoplastic neuroepithelial tumors (DNET), 3 post-traumatic lesions, 2 hippocampal scleroses, 1 cortical dystrophy, 1 tuberous sclerosis of Bourneville, 1 inflammatory lesion, 1 toxoplasmosis and 2 low-grade gliomas (grades I and II). The grade I astrocytoma was an unexpected anatomopathological result, as the patient's history and the radiological features were very suggestive of a DNET. The grade II patient had previously undergone oncological surgery for low-grade glioma in the right cingulum; during follow-up, the patient showed drug-resistant epilepsy that became very disabling, although tumor size was unchanged; revision therefore consisted in epileptic surgery, with prior sEEG. At a mean follow-up of 34 ± 27 [1-85] months, 25 patients were classified as Engel class I, including 20 (61%) who were seizurefree with Engel class IA or ILAE Outcome Scale 1. Outcomes were favorable (Engel class I to III; ILAE Outcome Scale 1 to 4) in 32 (97%) patients, with significant seizure reduction.

One patient showing transient decrease in daily seizure frequency had no long-term benefit from surgery (Engel class IV; ILAE Outcome Scale 5 to 6); seizure recurrence was due to a contralateral rolandic EZ and was partially improved by vagus nerve stimulation. Antiepileptic treatment was decreased in 20 (61%) patients, with no recurrence at more than 1 year's follow-up. Eight patients had less than 1 year's follow-up, either because their operation was too recent (n=5) or because they were lost to follow-up (n=3).

Palliative surgery with vagus nerve stimulation was performed in 2 patients, 1 for surgery failure and 1 for multifocal epilepsy.

Discussion

The present study reports a high success rate of sEEG in localizing the EZ (92%) in a consecutive series of 49 sEEG recordings in 46 patients. Surgery was possible in 36 (80%) of these patients. Our results are concordant with literature data. A meta-analysis published in 2018 reported that sEEG had a mean success rate of 92% [START_REF] Garcia-Lorenzo | Stereoelectroencephalography for Refractory Epileptic Patients Considered for Surgery: Systematic Review, Meta-Analysis, and Economic Evaluation[END_REF] . Two prospective studies showed that EZ resection was achieved in 79.9-87% of cases [START_REF] Serletis | The stereotactic approach for mapping epileptic networks: a prospective study of 200 patients: Clinical article[END_REF][START_REF] Cardinale | Stereoelectroencephalography: retrospective analysis of 742 procedures in a single centre[END_REF] . Localizing an EZ depends on the cerebral lobes involved, the presence of a lesion visible on MRI and the accuracy of the hypothesis based on prior evaluation and clinical analysis of seizures [START_REF] Iida | Stereoelectroencephalography: Indication and Efficacy[END_REF] . The EZ is more difficult to localize in frontal lobe epilepsy because of its large size, the complexity of neural networks involved in seizures with many escape neural pathways, the diversity of clinical ictal patterns and the poor contribution of ictal and interictal EEG correlates [START_REF] Iida | Stereoelectroencephalography: Indication and Efficacy[END_REF][START_REF] Bartolomei | Seizure symptoms and cerebral localization : frontal and rolandic seizures[END_REF] .

We found a 6% rate of sEEG-related morbidity per procedure, with 1 (2%) major event (death) [START_REF] Derrey | Delayed intracranial hematoma following stereoelectroencephalography for intractable epilepsy: Case report[END_REF] . This result is similar to that reported in a series of 215 procedures 21 but higher than in a larger series of 525 procedures [START_REF] Bourdillon | Stereotactic Electroencephalography Is a Safe Procedure, Including for Insular Implantations[END_REF] . In our series, there was a very low complication rate per electrode (0.51%). A systematic review and meta-analysis published in 2016 reported a slightly higher rate (1.3%) of surgical complications per electrode related to sEEG insertion and monitoring [START_REF] Mullin | Is SEEG safe? A systematic review and metaanalysis of stereo-electroencephalography-related complications[END_REF] . The two main complications described in the literature are hemorrhage, at 1.81/1,000 implanted electrodes (1% per sEEG procedure) and infection (0.8% per sEEG procedure) [START_REF] Mullin | Is SEEG safe? A systematic review and metaanalysis of stereo-electroencephalography-related complications[END_REF] . Permanent neurologic deficit is reported as 0.6% of pooled prevalence [START_REF] Mullin | Is SEEG safe? A systematic review and metaanalysis of stereo-electroencephalography-related complications[END_REF] . It has been shown that sEEG was associated with lower mortality (0.2 vs 0.4%) and morbidity (4.8 vs 15.5%) than subdural grids [START_REF] Yan | Method of invasive monitoring in epilepsy surgery and seizure freedom and morbidity: A systematic review[END_REF] .

Despite its low rate, intracranial hemorrhage is the most feared complication, with risk of death (half of reported deaths). Following previously reported intracranial bleeding, CT angiography was added to our preoperative radiological work-up, to reduce risk of hemorrhage. Although arteriography is the gold standard [START_REF] Gilard | Usefulness of multidetector-row computerized tomographic angiography for the surgical planning in stereoelectroencephalography[END_REF][START_REF] Gilard | Analyse prospective de l'apport de l'angioscanner cérébral pour la planification des trajectoires de stéréo-électro-encéphalographie[END_REF] , CT angiography is an interesting complement to MRI for visualization of blood vessels, including those in the insular lobe, which is frequently targeted in sEEG and known for its dense vascularization [START_REF] Iida | Stereoelectroencephalography: Indication and Efficacy[END_REF] .

Obviously, antiplatelets and anticoagulants may be stopped before surgery to prevent bleeding [START_REF] Dewald | Anticoagulants[END_REF] . Valproic acid has a controversial effect on hemostasis [START_REF] Gidal | Valproate-mediated disturbances of hemostasis: relationship to dose and plasma concentration[END_REF][START_REF] Zighetti | Effects of chronic administration of valproic acid to epileptic patients on coagulation tests and primary hemostasis[END_REF] and there is no evidence for withdrawing this treatment before sEEG or epilepsy surgery [START_REF] Guénot | Surgical technique[END_REF][START_REF] Ward | Preoperative valproate administration does not increase blood loss during temporal lobectomy[END_REF] .

Before performing sEEG, a very comprehensive preoperative work-up, including video EEG, 3T-MRI and PET-scan, is systematically performed, while high-resolution EEG (EEG-HR) and magneto-encephalography (MEG) are discussed on a case-by-case basis. Current perspectives include the development of MEG and EEG-HR and the use of 7T high-field MRI [START_REF] Zijlmans | Changing concepts in presurgical assessment for epilepsy surgery[END_REF] , not performed in our center.

In the present series, thermocoagulation was performed in 8 patients between 2015 and 2018, with good seizure control in 7 (88%). However, interpretation of these results is limited by short follow-up and the small sample. In larger series [START_REF] Cossu | Stereoelectroencephalography-guided radiofrequency thermocoagulation in the epileptogenic zone: a retrospective study on 89 cases[END_REF][START_REF] Guénot | SEEG-guided RF-thermocoagulation of epileptic foci: A therapeutic alternative for drug-resistant non-operable partial epilepsies[END_REF] , 18% to 25% of patients were initially seizure-free. Others found significant seizure improvement in 28.1% to 48.7% of patients [START_REF] Cossu | Stereoelectroencephalography-guided radiofrequency thermocoagulation in the epileptogenic zone: a retrospective study on 89 cases[END_REF][START_REF] Guénot | SEEG-guided RF-thermocoagulation of epileptic foci: A therapeutic alternative for drug-resistant non-operable partial epilepsies[END_REF] . A 2018 meta-analysis of 296 patients from 6 retrospective studies showed a pooled seizure-free rate of 23% (95% CI, 8-50%) and a responder rate of 58% (95% CI, 36-77%), but with large heterogeneity [START_REF] Bourdillon | Stereo-electroencephalography-guided radiofrequency thermocoagulation in patients with focal epilepsy: A systematic review and meta-analysis[END_REF] . Efficacy was greater in the occipital region, in periventricular nodular heterotopies, and in case of lesions versus normal MRI [START_REF] Cossu | Stereoelectroencephalography-guided radiofrequency thermocoagulation in the epileptogenic zone: a retrospective study on 89 cases[END_REF][START_REF] Bourdillon | Stereo-electroencephalography-guided radiofrequency thermocoagulation in patients with focal epilepsy: A systematic review and meta-analysis[END_REF][START_REF] Bourdillon | SEEG-guided radiofrequency thermocoagulation[END_REF] .

Complications related to thermocoagulation are rare, with reported rates of 2.2-7.3% [START_REF] Cossu | Stereoelectroencephalography-guided radiofrequency thermocoagulation in the epileptogenic zone: a retrospective study on 89 cases[END_REF][START_REF] Guénot | SEEG-guided RF-thermocoagulation of epileptic foci: A therapeutic alternative for drug-resistant non-operable partial epilepsies[END_REF] . In a recent meta-analysis, the main complication was permanent neurologic deficit, in 2.5% of cases (95% CI 1.2-5.3%) [START_REF] Bourdillon | Stereo-electroencephalography-guided radiofrequency thermocoagulation in patients with focal epilepsy: A systematic review and meta-analysis[END_REF] . However, neurologic deficit can be predicted from sEEG and electrical stimulation ahead of thermocoagulation [START_REF] Bourdillon | Stereo-electroencephalography-guided radiofrequency thermocoagulation in patients with focal epilepsy: A systematic review and meta-analysis[END_REF] . A recent systematic review and metaanalysis found no hemorrhagic complications attributed to thermocoagulation [START_REF] Bourdillon | Stereo-electroencephalography-guided radiofrequency thermocoagulation in patients with focal epilepsy: A systematic review and meta-analysis[END_REF] . Others reported use of thermocoagulation to predict the efficacy of epilepsy surgery, with positive predictive value of 93% [START_REF] Bourdillon | Stereo electroencephalography-guided radiofrequency thermocoagulation (SEEG-guided RF-TC) in drug-resistant focal epilepsy: Results from a 10-year experience[END_REF] . These data suggest that stereo-electroencephalography-guided radiofrequency thermocoagulation could be an effective option in drug-resistant epilepsy, above all when surgery is risky or impossible.

Resective surgery is a validated treatment for drug-resistant epilepsy [START_REF] Wiebe | A randomized, controlled trial of surgery for temporal-lobe epilepsy[END_REF][START_REF] Engel | Practice parameter: temporal lobe and localized neocortical resections for epilepsy: report of the Quality Standards Subcommittee of the American Academy of Neurology, in association with the American Epilepsy Society and the American Association of Neurological Surgeons[END_REF] . In our 8-year experience, 80% of contributive sEEGs to locate the EZ enabled resective surgery, representing 74% of all 49 sEEGs. Surgery provided a 61% rate of seizure-freedom and 97% rate of benefit on the Engel classification. In a 2015 literature review on resective epilepsy surgery, between 34% and 74% (median, 62.5%) of patients were reported as being seizurefree [START_REF] Jobst | Resective Epilepsy Surgery for Drug-Resistant Focal Epilepsy: A Review[END_REF] . According to a meta-analysis, 47% of all sEEG patients who underwent resective surgery remained seizure-free [START_REF] Garcia-Lorenzo | Stereoelectroencephalography for Refractory Epileptic Patients Considered for Surgery: Systematic Review, Meta-Analysis, and Economic Evaluation[END_REF] . Outcomes were similar in children and in adults [START_REF] Jobst | Resective Epilepsy Surgery for Drug-Resistant Focal Epilepsy: A Review[END_REF] . In the literature, efficacy depends on resection region, with better results in temporal lobes (66% seizure free) and poor results in frontal lobes (27%) [START_REF] Téllez-Zenteno | Long-term seizure outcomes following epilepsy surgery: a systematic review and meta-analysis[END_REF] . Other factors for better outcome comprise presence of structural lesions, particularly hippocampal sclerosis and benign tumors, seizure without loss of consciousness, complete or extensive lesion resection, prolonged febrile seizures, and long-term postoperative seizure freedom [START_REF] Jobst | Resective Epilepsy Surgery for Drug-Resistant Focal Epilepsy: A Review[END_REF] . Factors for negative outcome comprise preoperative generalized tonic-clonic seizures, infantile spasms or tonic seizures, and intracranial electroencephalographic monitoring. Gender, age and side of resection were not associated with seizure outcome [START_REF] Jobst | Resective Epilepsy Surgery for Drug-Resistant Focal Epilepsy: A Review[END_REF] . Discontinuation of antiepileptic medication was reported in 25-28% of patients [START_REF] Jobst | Resective Epilepsy Surgery for Drug-Resistant Focal Epilepsy: A Review[END_REF] . Surgical complications may occur (12%) but decrease with time, as shown in Tebo's literature review [START_REF] Tebo | Evolution of cranial epilepsy surgery complication rates: a 32-year systematic review and meta-analysis: A review[END_REF] . Perioperative mortality is low (0.1% to 0.5%) [START_REF] Jobst | Resective Epilepsy Surgery for Drug-Resistant Focal Epilepsy: A Review[END_REF] , and higher in extratemporal surgery (1.2%) [START_REF] Hader | Complications of epilepsy surgery-A systematic review of focal surgical resections and invasive EEG monitoring[END_REF] . Medical complications, such as cerebrospinal fluid leakage, aseptic meningitis, infection, hemorrhage and hydrocephalus, have been reported [START_REF] Jobst | Resective Epilepsy Surgery for Drug-Resistant Focal Epilepsy: A Review[END_REF][START_REF] Hader | Complications of epilepsy surgery-A systematic review of focal surgical resections and invasive EEG monitoring[END_REF] . Minor and major neurologic complications occur in 10.9% and 4.7% of patients, respectively. The most common complication is visual field defect, occurring mainly in temporal lobe resection and classified as minor in 12.9% and major in 2.1% of cases [START_REF] Hader | Complications of epilepsy surgery-A systematic review of focal surgical resections and invasive EEG monitoring[END_REF] . The majority of complications are minor or temporary.

The present study was limited by retrospective data collection, a relatively low number of patients with more than 1 year's follow-up after surgery, and the heterogeneous population including both children and adults. Nevertheless, it allowed us to analyze and report our 8 years' experience in sEEG and epilepsy surgery, with outcomes concordant with the data in the literature.

Conclusions

sEEG is an effective technique to localize the epileptogenic zone in patients with drugresistant epilepsy when first-line non-invasive techniques have failed. sEEG helped to localize the epileptogenic zone in nearly all of our patients on the basis of a hypothesis based on the clinical-radio-electroencephalographic data of phase I assessment. sEEG enabled thermocoagulation and/or surgical resection in up to 92% of patients, resulting in seizurefreedom in two-thirds and seizure-reduction in one-third. This study highlights the need for strict patient selection and a rigorous initial hypothesis as to the epileptogenic zone, in order to optimize sEEG success rate.

  Abbreviations:

FiguresFigure 1 :

 1 Figures

Figure 2 :

 2 Figure 2: Flowchart of sEEG outcomes.

Acknowledgments

The authors are grateful to Nikki Sabourin-Gibbs, Rouen University Hospital, for her help in editing the manuscript.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or non-profit sectors.

Disclosure of Conflicts of Interest

We have no conflicts of interest.

Ethical Publication Statement

We confirm that we have read the Journal's position on issues involved in ethical publication and affirm that this report is consistent with those guidelines.


Professor Daniel Wendling
email: dwendling@chu-besancon.fr

Mickael Chouk

Frank Verhoeven

Clément Prati

Unilateral "sacro iliitis"?

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

condensation of the iliac part and geodes of the cancellous bone (horizontal arrow). Sacro iliac joint space is normal, without joint erosion. Transitional abnormality with non-fusion of the hemi first right sacral piece (vertical arrow), resulting in Bertolotti's syndrome [START_REF] Jancuska | A Review of Symptomatic Lumbosacral Transitional Vertebrae: Bertolotti's Syndrome[END_REF]. The latter, causing an asymmetrical change in the mechanical stresses of the pelvic frame, may have favoured degenerative-type lesions of the right sacroiliac joint, which had been wrongly considered as sacroilitis in a 30 years old woman, having had a single pregnancy, with normal CRP and without any personal or familial medical history. Degenerative changes of the sacroiliac joint and lumbosacral transition vertebrae are frequent in patients with low back pain [START_REF] Shea | Inflammatory and degenerative sacroiliac joint disease in a primary back pain cohort[END_REF] and may mimic sacro ileitis.