Mathilde Le Boudic-Jamin
email: mathilde.le_boudic-jamin@irisa.fr

Antonio Mucherino
email: antonio.mucherino@irisa.fr

Rumen Andonov
email: rumen.andonov@irisa.fr

Modeling protein flexibility by distance geometry

Keywords: protein conformation, protein flexibility, distance geometry, combinatorial optimization, protein docking

Introduction

The Molecular Distance Geometry Problem (MDGP) is the problem of finding the possible three-dimensional conformations of a molecule for which a certain subset of its atoms satisfies some distance constraints. A great interest is given to this problem because experimental techniques such as the Nuclear Magnetic Resonance (NMR) are able to estimate some distances between pairs of atoms of the molecule, which can then be exploited for reconstructing the possible conformations associated to a given molecule. Much attention is given to proteins, because they are biological molecules that are able to perform several important functions in the cells of living beings.

Due to the great interest given to the MDGP, many approaches for the solution of this problem have been proposed over the last years. By its definition, the MDGP is a constraint satisfation problem, but it is usually reformulated as a global optimization problem in a continuous space, where a penalty function is used for measuring the satisfation of the constraints. The interested reader is referred to a recent survey for a wide discussion on the different approaches to the MDGP [START_REF] Lavor | Recent Advances on the Discretizable Molecular Distance Geometry Problem[END_REF].

In this context, we are particularly interested in the approach to the MDGP recently proposed in [START_REF] Lavor | The Discretizable Molecular Distance Geometry Problem[END_REF], the Discretizable MDGP (DMDGP). The search space of the optimization problem is here transformed in a discrete space, so that the problem becomes combinatorial. Even if the NP-hardness of the problem is not lost while performing the reformulation, the combinatorial structure of the new search domain makes it possible to use an efficient Branch & Prune (BP) algorithm for the solution of MDGPs that can be discretized. The BP algorithm is the first algorithm potentially able to identify all possible solutions to the problem. As explained in the following, we can exploit this property of BP for modeling the natural flexibility of proteins.

Protein flexibility

Even if the BP algorithm was initially tested on artificially generated instances, where the assumptions needed for the discretization were always satisfied, it was recently proved in [START_REF] Lavor | The interval Branch-and-Prune Algorithm for the Discretizable Molecular Distance Geometry Problem with Inexact Distances[END_REF] that its extension iBP (interval BP) can be used for solving DMDGPs containing real NMR data. This is possible because of a special ordering that have been identified for the atoms forming protein backbones. In this special ordering, atoms are re-arranged so that the distance between each atom and its three immediate predecessors in the ordering is always known. Moreover, the ordering ensures that only one of these three distances may be imprecise, while all others are exact (distances between chemically bonded atoms, or between pairs of atoms bound to a common atom). In this situation, a finite set of possible coordinates can be computed for each atom of the molecule.

We artificially generated some instances of the DMDGP with the technique detailed in [START_REF] Lavor | The interval Branch-and-Prune Algorithm for the Discretizable Molecular Distance Geometry Problem with Inexact Distances[END_REF]. These instances simulate NMR data for short peptides containing 3 amino acids, and use intervals to define distances between hydrogen atoms (which are likely to be estimated by NMR). We defined different instances with different lengths ℓ ∈ {1.0Å, 0.8Å, 0.5Å} for the intervals corresponding to distances between hydrogens. As expected, when we tried to solve these instances with the iBP algorithm, the total number of solutions we found was different for each instance, and it increased with the length ℓ of the intervals. For a peptide formed by 3 amino acids, we obtained 8 solutions when ℓ was 0.5, 155 solutions when ℓ was 0.8, and 2368 solutions when ℓ was 1.0.

This simple experiment shows that modifying the lengths of the intervals allows to model the flexibility of the molecule. When iBP is invoked for solving the problem, the flexibility is reflected by the increased total number of solutions, while the solutions corresponding to shorter intervals keep being contained in the final solution set. Naturally, for longer peptides, the number of solutions should not increase exponentially with ℓ, because of the presence of short range distances between pairs of amino acids which are far in the sequence. Nevertheless, we believe that DMDGPs can be used as a valid model for the flexibility of compact molecules such as proteins.

We are starting to work in order to exploit this property of the iBP algorithm in the context of protein docking. Given a protein A and a protein B with known conformations, the conformation of the two proteins A + B, during their interaction, is searched [5]. During the interaction, it is evident that the surfaces of the two molecules may slightly modify their conformations. We will attempt the generation of all suitable three-dimensional conformations for A+B by finding all solutions to a DMDGP where the flexibility of the two molecules is regulated by the intervals used to replace computed distances. This is one of our main research directions.

Conclusions

We discussed about the possibility of modeling the natural protein flexibility by an MDGP where known exact distances between atoms are substituted by suitable intervals. Among the approaches to the MDGP proposed over the years, we considered a recent combinatorial approach, where the search domain of the formulated optimization problem is discrete. Differently from other methods for the MDGP which are based on other approaches, this combinatorial approach allows for enumerating all possible conformations for a given instance of the problem. As a consequence, when intervals representing distances are enlarged for modeling flexibility, the total number of solutions for the instance increases, because the molecule is actually free to assume a larger range of conformations. One possible application of this idea is to protein docking, where the interacting surfaces of the two molecules are in fact flexible.


Julien Fayolle

Murat Saraclar
email: murat.saraclar@boun.edu.tr

Fabienne Moreau

Christian Raymond

Guillaume Gravier

Murat Sarac ¸lar

Lexical-phonetic automata for spoken utterance indexing and retrieval

Keywords: information retrieval, speech indexing, lexical-phonetic automata, confidence measures, edit distances, supervised learning

come

Introduction

Spoken content retrieval [START_REF] Chelba | Retrieval and browsing of spoken content[END_REF] relies on the fields of automatic speech recognition (ASR) and information retrieval (IR). However, IR tools made for text are not adapted to automatic transcripts which are particularly incomplete and uncertain. Even if in-vocabulary words (IV) are usually well-recognized, these transcripts contain many recognition errors affecting notably out-of-vocabulary words (OOV) and named entities (NE) that convey important discourse information (e.g., person names, localisations, organisations) necessary for IR. Two kinds of approaches can be used to attenuate these drawbacks by either improving the recall or the precision. First, the recall can be improved by using a lower level of representation consisting in sub-words (e.g., syllables, phonemes) to represent OOV words and, more generally, all types of lexical errors. Representations denser than a simple transcript can also be used, such as graphs, confusion networks and N-best lists. Second, the precision can be improved by filtering out noisy parts of the recognition thanks to meaningful features (e.g., confidence measures). We are interested in combining the two approaches for a task of spoken utterance retrieval.

Spoken utterance retrieval consists in retrieving, in a spoken content set, all the segments (called utterances) containing a given textual query. Two strategies are used in state-of-the-art systems to combine efficiently both lexical and phonetic levels for searching. The first one considers two separated indexes used in "cascade", i.e., the search is, by default, based on the lexical index and can fall back on the phonetic one if necessary [START_REF] Saraclar | Lattice-based search for spoken utterance retrieval[END_REF]. This limits the usage of the phonetic index, rather noisy, only to mis-recognized queries. The second approach models the two levels in one hybrid index [START_REF] Hori | Openvocabulary spoken utterance retrieval using confusion neworks[END_REF][START_REF] Yu | A hybrid-word/phoneme-based approach for improved vocabulary-independent search in spontaneous speech[END_REF], offering the advantage of a hybrid matching between the query and the index.

The proposed method takes up the idea of a hybrid index because it can tolerate lexical-phonetic matchings that are impossible with two separate indexes. The index structure is based on automata as they can represent all types of ASR outputs. The originality of the method consists in the weighting of automaton transitions with a vector of different features that can be used to estimate the relevance of the candidate utterances for a given query. The features used include : edit distance scores (counts of correct symbols, deletions, insertions, substitutions) indicating the imperfection of the matching between the query and the index; and a lexical-phonetic confidence measure indicating the reliability of the recognized symbols. The experiments conducted compare the performances between the cascaded and hybrid searches to retrieve named entity queries. We present first the proposed method (section 2), then the results of the experiments (section 3) and finally conclude the paper (section 4).

Method

The proposed method is based on the general indexing of weighted automata presented by Allauzen et al. [START_REF] Allauzen | General indexation of weighted automata -application to spoken utterance retrieval[END_REF] and adapted for the case of lexical-phonetic automata (see figure 1 for an overview of the method). From the ASR outputs, we build the lexical-phonetic automata to be indexed (section 2.1). The textual query is phonetized and converted into a lexical-phonetic automaton as well. A more or less imperfect matching is possible by composing successively the query, an edit transducer and the in-Figure 1: Overview of the proposed method. dex (section 2.2). This process returns a list of candidate utterances that can be filtered thanks to the feature vector weighting each utterance (section 2.3).

Lexical-phonetic automata

In this paper, a lexical-phonetic automaton simply denotes a weighted finite-state automaton whose symbols are either from a lexical alphabet Σ lex or a phonetic alphabet Σ ph , and whose weights are multi-dimensional. Thus, a lexical-phonetic automaton can have concurrent lexical and phonetic paths weighted by a vector of various features (e.g., see figure 2). If defined over the tropical semi-ring, then the weight of a path is the sum of its transition weights and the shortest path is the one with the minimum weight. This minimum weight can always be found only if the weights are always comparable, i.e., if they are totally ordered. This is precisely the case when the lexicographic order (also known as the alphabetical order) is considered as in [START_REF] Can | Lattice indexing for spoken term detection[END_REF]. Each transition corresponds to a symbol (either lexical or phonetic) recognized between the start time t s and the end time t e with an associated confidence measure c. The weight of the transition is the following :

v = (0, 0, 0, 0, 0, w lex+ph conf = -(t e -t s ).log(c))
where w lex+ph conf is the lexical-phonetic confidence score because it is common to both lexical and phonetic levels. The confidence score is proportional to the duration of the symbol so that concurrent lexical-phonetic paths of different numbers of symbols can be comparable.

Once built, the automaton is turned into a corresponding factor transducer that accepts all the sub-sequences of the automaton in input and gives the utterance identifier in output. The index consists in the union of all the factor transducers (as presented in [START_REF] Allauzen | General indexation of weighted automata -application to spoken utterance retrieval[END_REF]).

Lexical-phonetic matching

The matching between the query Q and the index I can be realised by the simple automaton-transducer composition Q • I. It is however possible to get a more flexible matching using an edit transducer E by the successive composition Q • E • I [START_REF] Mohri | Edit-distance of weighted automata[END_REF]. We present three types of lexical-phonetic edit transducers corresponding to perfect, imperfect and semi-imperfect matchings. Their aim is to compute the edit distance scores in the vector v = (w lex cor , w ph cor , w ph del , w ph ins , w ph sub , 0)

consisting in the counts of correct words, correct phonemes, and phonetic deletions, insertions and substitutions.

The perfect matching transducer only counts correct words and phonemes. The count of correct words is chosen to be the first dimension of the vector in order to favour the lexical matching rather than the phonetic matching when both are possible. No imperfections are allowed, which makes this transducer particularly restrictive.

The imperfect matching transducer is able to count, besides correct words and phonemes, also phonetic deletions, insertions and substitutions. Its problem is that the matching is done without any constraints and, thus, all imperfections are tolerated (even paths with no correct symbols), which makes this transducer quite greedy.

A good trade-off between the two previous extreme approaches can be to count the imperfections under certain constraints. The proposed semi-imperfect matching transducer takes into account the a priori phonetic variability to limit the imperfection possibilities : "in a sliding window of α phonemes, the rate of correct phonemes must be greater than ρ". In this paper, the parameters are arbitrarily set to α = 2 and ρ = 1/2 for preliminary experiments. Figure 3 illustrates these three types of transducers for a small lexical-phonetic alphabet.

Filtering of candidate utterances

After matching and projection on the output label, we obtain a list of weighted utterances ranked according to the lexicographic order. Thus, each candidate utterance is associated to a vector of 7 features : f = (rank, w lex cor , w ph cor , w ph del , w ph ins , w ph sub , w lex+ph conf )

Determining if an utterance contains (or not) the query from these features can be posed as a binary classification problem solvable by any learning method (e.g., decision trees). Then, the estimated probability of an utterance to contain the query is turned into a binary decision with a threshold set according to the desired recall-precision trade-off.

Figure 2: Example of a lexical-phonetic automaton : accepting the lexical path "l' ena", the phonetic path " l E n a", and the lexical-phonetic paths "l' E n a" and " l ena"; and weighted by a vector of 6 different features.

Experiments

In this section, we present the necessary experimental setup (section 3.1) to implement the proposed method and carry out two experiments, one on the complementarity of the lexical and phonetic levels (section 3.2) and a second one on spoken utterance retrieval (section 3.3).

Setup

The audio data used for the experiments consists of 6 hours of French radio broadcast news material extracted from the ESTER2 corpus [START_REF] Galliano | The ESTER 2 evaluation campaign for the rich transcription of French radio broadcasts[END_REF] containing reference transcripts with manually annotated named entities. The ASR system is a large vocabulary (65k words) transcription system for which the word error rates on this corpus vary between 16.0% and 42.2%. The data are automatically segmented into 3447 utterances. The N-best hypotheses are then re-scored using a morpho-syntactic tagger [START_REF] Huet | Morpho-syntactic postprocessing of n-best lists for improved french automatic speech recognition[END_REF]. The lexical level is made only of the 1-best hypothesis. The phonetic level is obtained by forced alignment between the audio signal and the pronunciation of the lexical level. Lexical and phonetic confidence measures are calculated from the a posteriori probabilities and the entropy between the different hypotheses [START_REF] Chen | On using entropy information to improve posterior probability-based confidence measures[END_REF]. The au-tomata are implemented based on OpenFST2 and the size of the lexical, phonetic and hybrid indexes are 9.9, 32.8 and 47.6 MB respectively. To avoid matching problems that might appear due to morphological variations, words are turned into lemmas with TreeTagger3 . To estimate the probability of an utterance to contain the query, we used a bagging over 20 decision trees (Bonzaiboost4 ). The evaluation is done according to a 5-fold cross-validation using 80% of the candidate set for training and 20% for testing. The queries are all named entities extracted from the transcripts of reference. The pronunciation of the query is given by the phonetic lexicon ILPho5 . If a certain word doesn't belong to the lexicon, multiple pronunciations of it are generated by the phonetizer Lia phon 6 . In addition to the usual sets of IV and OOV queries, we propose a third set of queries made of both IV and OOV words (e.g., an IV first name followed by an OOV family name). These mixed IV/OOV queries are interesting because they represent an intermediate level of difficulty (a priori more difficult than IV queries but less difficult than OOV ones) and they are more frequent than the OOV queries. Table 1 shows the query distribution. To evaluate the performance of spoken utterance retrieval, we use the mean average precision (MAP) and the precision at N (P@N) where N is the number of the expected relevant utterances for a given query.

Complementarity of lexical and phonetic levels

This preliminary experiment consists in measuring the quality of the lexical and phonetic representations and their complementarity. For each utterance, we align the lexical-phonetic automata of reference and hypothesis with an imperfect edit transducer to obtain Table 2, which gives the correct symbol rate on named entities. On the one hand, the lexical level is used on areas correctly recognized. On the other hand, the phonetic level is only used on mis-recognized areas. We note that 73.89% of the lemmas are well recognized. For the mis-recognized lemmas, we can fortunately fall back on the phonetic level for which 67.73% of the phonemes are correct. This justifies the combination of lexical and phonetic levels to search for named entities. Table 3: Spoken utterance retrieval results : baseline, better than the baseline, best result(s).

Spoken utterance retrieval

The goal of this experiment is to compare the spoken utterance retrieval for different settings. We perform the search using either a lexical index, a phonetic index, both indexes in cascade or a hybrid index. The queries are IV, OOV or IV/OOV while the matching is perfect or semiimperfect. The imperfect matching has been discarded because it is too greedy. Two filtering methods are considered using a simple threshold either over the lexicalphonetic confidence score (th-conf) or over the probability estimated by the decision trees using all the features (dt-all). The baseline corresponds to the cascade search using a perfect matching and a th-conf filtering. Table 3 reports the obtained performances. Generally, we first notice that the baseline can easily be improved for all types of queries using a semiimperfect matching with the dt-all filtering (the th-conf filtering is not sufficient). Second, the hybrid search using the dt-all filtering always performs better or equally than both lexical and phonetic searches. This proves that the hybrid combination is justified.

More specifically, the hybrid search obtains the best results for IV queries. For OOV queries, the hybrid, cascaded and phonetic search are equivalent as they can only use the phonetic level. For mixed IV/OOV queries, it is surprising that the phonetic and cascaded searches are better than the hybrid one. This is due to the fact that the ranking gives too much importance to lexical match even if this one is not really relevant (mis-recognized or very frequent words). We think that adding a tf*idf score in the feature vector will help to deal with these cases.

Finally, the hybrid search (with the semi-imperfect matching and the dt-all filtering) offers the best overall performances.

Conclusion

We have presented a method to index lexical-phonetic automata for spoken utterance retrieval. The results demonstrates the complementarity of the lexical and phonetic levels (extracted from the 1-best speech recognition hypothesis) and the advantage of using a hybrid index, a semi-imperfect matching and a supervised filtering (combining edit distance scores and a confidence measure).

Figure 3 :

 3 Figure 3: Edit transducers for a lexical-phonetic matching that is perfect (a), imperfect (b) or semi-imperfect (c) where Σ lex = {ab, ba} and Σ ph = { a, b}.

Table 1 :

 1 Query distribution in function of the type and the length in number of words.

	#words IV OOV IV/OOV	1 209 276 125 73 29 24 2 3 4 5 6 76 43 1 . . . . 120 73 29 11 8	7+ 34 . 6	total 770 (68%) 120 (10%) 247 (22%)	NE terms IV OOV Overall	% lemmas in reference 93.57 6.43 100.00	%correct lemmas %correct phonemes in erroneous areas 78.97 67.34 0.00 68.54 73.89 67.73

Table 2 :

 2 Complementarity of lexical and phonetic representations for named entities.

	Evaluation				MAP							P@N
	Matching		Perfect			Semi-Imperfect			Perfect			Semi-Imperfect
	Index		lex	ph	cas	hyb	lex	ph	cas	hyb	lex	ph	cas	hyb	lex	ph	cas	hyb
	IV	th-conf	.634 .577	.673	.577	.634	.015	.047	.013	63.2 64.3 65.5	64.1	63.3 29.3	67.1	27.6
		dt-all	.631 .646	.677	.681	.629	.693	.713	.729	63.6 64.9	65.9 65.9	63.2	74.5 73.7	74.8
	OOV	th-conf	.000 .036	.036	.036	.000	.001	.001	.001	6.6	12.6 12.6	12.6	6.6	8.1	8.1	8.1
		dt-all	.000	.053	.053	.053	.000	.139	.139	.139	6.6	12.0 12.0 12.0	6.6	27.2	27.2	27.2
	IV/OOV	th-conf	.000 .024	.024	.029	.000	.001	.001	.001	16.5 19.5 19.5	19.5	16.5	25.0	25.0	24.5
		dt-all	.000	.024	.024	.024	.000	.256	.256	.250	16.5 19.5 19.5 19.5	16.5	41.2	41.2	40.2
	OVERALL th-conf	.523 .479	.556	.478	.523	.009	.015	.008	47.1 49.1 49.8	48.9	47.1 26.3	52.0	25.4
		dt-all	.520 .540	.568	.570	.519	.610	.637	.650	47.4 49.2	50.0 50.1	47.3	62.8	62.6	63.5

This work was partly achieved as part of the Quaero Programme, funded by OSEO, French State agency for innovation.

http://www.openfst.org/

http://www.ims.uni-stuttgart.de/projekte/corplex/TreeTagger/

http://bonzaiboost.gforge.inria.fr/

http://catalog.elra.info/product info.php?products id=760

http://www.atala.org/LIA-PHON


Boris Vidolov
email: bvidolov@utc.fr

A Discrete-Time Design of Time Delay Control Focus on Control Experimentations of coordinated motion control of hydraulic excavator

Keywords: discrete-time control, tuning parameter, coordinated motion control, hydraulic excavator 

In this paper a discrete-time design of continuous-time delay (TDC) is presented. The main goals are: (i) to eliminate the TDC assumption of accessibility to all the delayed derivative of the plant state variables, and (ii) to design discrete-time controllers based on approximate discrete-time models. Simulations results are given, for an articulated arm actuated with linear hydraulic motors with variable payloads, to illustrate the robustness of the proposed control design. The new proposed controller has similar results as that obtained by TDC without the use of a delay element which has become a time constant. Moreover, there is no need of measuring the joints jerk. The controller robustness is guaranteed despite the uncertainties in dynamic model caused by payload variation, imprecise modeling, etc. Other uncertainties such as friction and external disturbances are rejected in the controller automatically. Real time experimentations, with a small scale Liebherr excavator, of coordinated motion control of implements are presented.

INTRODUCTION

In 1987, Youcef-Toumi and Ito [START_REF] Youcef-Toumi | Controller Design for Systems with Unknown Dynamics[END_REF]) proposed a robust control method for a class of nonlinear continuous-time systems with unknown dynamics and unexpected disturbances, i.e.

     

t x h u x B x f x ,    
where   t x h , represents both unknown dynamics and unexpected disturbances, which is called Time Delay Control (TDC). Under the assumption of accessibility to all the state variables and estimates of their delayed derivative, TDC is characterized by a direct estimation of the function   t x h , . This estimation is accomplished using time delay. This delayed observation of uncertainties is used to modify the control action directly, rather than to adjust the controller parameters like in gain scheduling or adaptive control techniques. Although TDC has been recognized as an efficient technique, see e.g. Youcef-Toumi et al. (1992[START_REF] Hun | On Improving Time Delay Control under Certain Hard Nonlinearities[END_REF], it requires a good estimate of the system state derivative, and it is also inherently a continuous-timebased design introducing a delay in the control loop.

TDC implementations are thus carried out as time discretized functions of continuous-time functions, and this can lead to unstable closed-loop behavior as illustrated in the following example. Consider the first-order nonlinear plant proposed in [START_REF] Youcef-Toumi | A Time Delay Controller for Systems with Unknown Dynamics[END_REF]. This plant is exactly represented by

  d u x x    cos  ,

 

x cos is treated to be the unknown dynamics, and

    5 . 0 5 . 0    t t d
is the unexpected disturbance acting at t = 0.5s. Note that   t  represents a unit step function. As expressed in [START_REF] Youcef-Toumi | A Time Delay Controller for Systems with Unknown Dynamics[END_REF], the TDC is given by:

          t t x L t x L t u t u        
Let the sampling period be equal to the time delay L, then the discretized TDC is 1 shows simulation results where the plant output converges to the desired set-point under continuous-time control with L set to 0.05 s., and diverges under discretized control.

          L k x k x k x k u k u 2 1 1 1         Fig.
In this paper, in opposition to the standard TDC, we first focus on the fact that the design model has to be a discretetime model, which is necessarily, an approximate model of the real system.

Performance of the control system was evaluated through simulations. Through simulations for a first order nonlinear plant, good model following and disturbance rejection property were obtained within a large range of sampling periods. The good model following and disturbance rejection property was confirmed through simulations for a more complicated non-linear systema two-link manipulator carrying an unknown payload.

Real time experimentations, with a small scale Liebherr excavator, of coordinated motion control are presented. Proposed discrete-time TDC law is applied for the tracking control. Only the hydraulic cylinders positions are measured and only two tuning parameters are used, i.e. the sampling period T, and the dynamic of the desired state trajectory.

The required motion will be achieved via a two-stage sampled data system: the first one solves the inverse kinematics problem and send joint velocity set points to a tracking control system.

PRELIMINARIES AND PROBLEM STATEMENT

The design of any feedback control law requires some a priori knowledge about the dynamics of the plant to be controlled. In this paper, we consider the designer's a priori knowledge is a continuous-time plant model:

         u x B x f x  (1)
where the term  is completely unknown and represents both unmodeled plant dynamics and external unexpected perturbations. This plant model satisfies the matching condition that the unknown term  enters the plant through the same input distribution matrix  

x B as the control input u . As usual, we use the following notations:

    p T p n T n U u u u X x x x         ,..., , ,..., 1 1         x b x b x B p ,..., 1  ,
and assume the nonlinear functions, i b f , for p i ... 1  are known and are, at least continuous. Given this a priori knowledge, and under the assumption of accessibility to all the state variables and estimates of their delayed derivative, TDC is characterized by a simple estimation of the unknown vector:

      t x B t x h   , , i.e.       L t L t x h t x h    , , ˆ which is directly derived from (1) at L t  .
In opposition to TDC, we first require that the design model to be used is a discrete-time model. However, even though the unknown term  in (1) is ignored, an exact discrete-time model of ( 1) is impossible to obtain in general. Hence, it is realistic to use approximate discrete-time models in the control design. In the sequel, only the Euler forward integration scheme will be considered. This simple approximation scheme is consistent, and moreover, the 1

 p known functions p b b f ,...,
, 1 are evaluated once only at each sampling instant.

Assuming,       k x k u k x , 1 , 1   are known at kT t 
, then the consistency error due to the Euler-forward integration scheme is given by:

          1 1 ~1 1          k k u B f T x k e k k k  ,
where short-hand notations such as

    k x k x x k     1 ,     k x f f k 
, and

    k x B B k  are used. Therefore, since   1  k  is unknown at that time, this later equation is rewritten as:       1 1 1        k u B f T x k T k k k  (2) where       1 ~1     k TB k e k T k  
represents both the consistency error due to the approximate numerical integration scheme, and the effects of unmodeled dynamics as well as unexpected disturbances over a sampling period.

Note that,    

    ) ( 1 ˆk u B f T x u k x k k k k k       (3)
In summary, given the a priori known continuous-time model (1), the model that will be used to design a control law is the one-step ahead prediction model (3), where

      T k x u k x k 1 ˆ 
can be viewed as a prediction of the next state derivative under a particular choice of k u .

DERIVATION OF CONTROL LAWS

Assume, the desired n-dimensional trajectory is known one step ahead at each sampling instant, i.e.

 

1  k x d is known at kT t  such that       k Gr k Fx k x d d   1 . Let,       k x k x k e d  
, be the tracking error. After some algebra, this leads to:

            k k u x T k x I F k Gr k Fe u k e 1 ˆ       , where   k u k e 1 ˆ
is the predicted tracking error, and

    k u B f u x k k k k      ~.
Hence, if it is possible to determine a control such that the following equation is always met:

      k k k u x T x I F Gr k Ke      (4) This will lead to,       k e K F u k e k   1 ˆ where K is an   n n 
error feedback matrix. The control k u , that satisfy (4), must then be selected in order to obtain a desired error dynamic. However, equation (4) cannot always be satisfied because the number of state variables is generally greater than the number of control inputs. Thus, the least square solution of ( 4) is adopted to determine the control k u :

    k B u k k k      (5)
where

  T k k T k k B B B B 1   
is the Moore-Penrose pseudo inverse matrix of k B , and:

            T k Ke k x I F k Gr k f k k          (6)
Control laws derived in this manner are based on the assumption of accessibility to all the state variables; they have only two tuning parameters, i.e. the sampling period T, and the dynamic of the desired state trajectory.

Using equations ( 3), ( 5), and ( 6), it is easy to exhibit the general equation governing the dynamics of the tracking error,

      k k e K F k e     1 (7)
where,

        k B B k T B B I k k k k k k            1 (8)
Therefore, the tracking error   k e will be ultimately bounded if it can be proved that k

 is bounded, i.e.    k , provided the matrix (F + K) is a stable matrix, i.e. 1     K F .
The effectiveness of the proposed design method can be briefly illustrated on the example already mentioned in the introduction. The control is now expressed as:

              T k x k x k r a k u k u        1 1
where the desired state trajectory

  1  k x d
has been derived from a continuous-time first-order dynamic system, i.e.

 

      t x t x t e d  
, corresponding respectively to T = 0.04 s., and T = 0.4 s. respectively. In both cases, the closed-loop plant trajectory converges to the desired trajectory.

APPLICATION TO MANIPULATOR CONTROL

The a priori knowledge representation of the dynamics of a nlink robot manipulator is:

      t q q q u q G q q D , , ,          (9)
In this representation, the control vector u is the ndimensional vector of forces/torques applied on the joint axis,

    0   q D q D
T is an approximate inertia matrix (e.g. the inertia matrix derived from the assumption that all the links are point masses),   q G is also an approximation of the gravity terms. Hence, the unknown vector   t q q q , , ,     is a lumped representation of the centrifugal and Coriolis terms, of the friction torques on joints axis, and of the force/torque acting at the end-effector.

The state

    T T T T T x x q q x 2 1 , ,  
 is a 2n-dimensional vector, and the design model is thus characterized by:

                           1 1 1 1 1 2 0 ; x D x B x G x D x x f (10) Fig. 2. Tracking error     t x t x d 
of the nonlinear first-order system under the control (7).

It is easy to show

that       1 0 x D x B   
. Hence, using ( 5) and ( 6), only the n-dimensional vector

  k T 2  has to be computed at each sampling instant, i.e.       1 1 1 1 2 2         k k k G u D k x k T (11)
In order to determine the desired joint trajectory, a continuous-time reference model can be selected as a set of second order linear systems described by Br Ax x

d d    , such that: r b x x A A I x x d d d d d n d d                           2 2 1 2 1 2 1 0 0   Then, using the Euler-forward-integration scheme, this leads to       k Gr k Fx k x d   1 ˆ, where: TB G TA I F    ; (12)
Note that, the error feedback matrix K, in (6), can be selected as K = 0, provided F = I + TA is a stable matrix. Thus, under this assumption, substituting (10)-( 12) into (5), the control k u can be expressed as:

      k k D G u k k k 2 2      (13)
where

      T k x G u D k k k k 2 1 1 1 1 2          (14) and         k r B k x A k x A k d d d 2 2 2 1 1 2     (15)
Note that, the second term in the right-hand side of ( 14) represents an approximation of the joint acceleration at t =kT. Practical implementations of this control, ( 13)-( 15), can be carried out using only sampled joint position information

  2 , 1 , 0 , 1   i i k x
, provided each joint sensor output is suitably filtered before sampling.

Simulation was done for a two-link manipulator, for which all the inertia and center of mass parameters were obtained from an industrial company. These technical data correspond to those of a heavy-duty excavator. The Matlab/Simulink toolbox was used to represent this system, where an additional point mass (m) situated at the end of the second link was used to represent an unknown payload.

In the design model the two links were assimilated as point masses. The same second order reference model was chosen for each link, ; 0 0

; 2 0 0 2 ; 0 0 2 2 2 2 2 2 2 2 1                                n n d n n d n n d B z z A A      
The simulation was performed with a sampling period T=0.05 s., with m = 0 kg, and m = 300 kg, respectively, using the same values of natural frequency ( n  = 2.0 rad/s) and damping ration (z = 2.0). The input commands 1 r and 2 r where chosen to be step inputs.

COORDINATED-MOTION CONTROL OF A HYDRAULIC EXCAVATOR

To illustrate the effectiveness of the proposed control law, we have chosen to consider a highly nonlinear system that is the arm of hydraulic excavator. The testbed (Fig. 8.) consists of a small scale hydraulic excavator, xPC targetBox (Matlab/Simulink, Real Time Workshop) and joystick (definition of the Cartesian velocity    , , y x V V

). Each hydraulic cylinder is instrumented with linear displacement sensor SLS 095 Penny&Giles (mounted in parallel to the cylinders). The hydraulic system is driven by one hydraulic pump with output pressure of 10 [bars] and constant flow. The flow from the pump to the cylinders is controlled through variables orificies (Fig. 7.) by micro servo Graupner. The control signal u is a digital PWM signal with a 50 Hz frame rate. (derived from ( 17)), the relationship between Cartesian velocity vector and hydraulic velocities can be presented as:

        1 1     k k u k v   (16) v -
                   y x V V J q B q  1  (18)
thus, joint velocity set points to a tracking control system are defined.

Fig. 1 .

 1 Fig. 1. Response of the first-order nonlinear system under continuous-time TDC versus a time-discretized implementation.

  plant state is expressed as:

  two cases of behaviors of the tracking error

Fig. 3 .

 3 Fig. 3. Response of the first joint variable.

Fig. 5 .

 5 Fig. 5. Torque input on the first joint axis.

Fig. 6 .

 6 Fig. 6. Torque input on the second joint axis.

Fig. 7 .

 7 Fig.7. Flow control5.1 Actuator modelThe aim of this stage of model building was to establish a simplest actuator model. Let a highly simplified model be given as:

  is the linear hydraulic cylinder velocity;  -represents the non-modeled dynamics and all external perturbations and  -is a static caracreristic of hydraulic cylinder. The latter caractericstic is obtained by some open loop experimentationswith zero initial velocity different control values u are applied at time k and v(k+1) -the stabilized velocity at time k+1. Thus the steady states characteristics are obtained (Fig.10.). The control law proposed above is based on this simplest model.

Fig. 8 .

 8 Fig. 8. Experimental testbedThe relationship between joint variables and measured hydraulic (Fig.9) cylinders displacements can be written as:  1 1

Real time experimentations

The experimentation was performed with 0 , 0    However, the design model which is used here is a nonlinear discrete-time model derived from a nonlinear continuoustime model, both being approximate models. In this design model, only the more recent past effects of unmodeled dynamics and unexpected disturbances are estimated at the beginning of each sampling period, together with the last consistency error due to the necessary use of an approximateintegration scheme (in this paper only the Euler-forwardintegration scheme was used). This is accomplished under the assumption of accessibility to all the state variables.

Through simulations for a first order nonlinear plant, good model following and disturbance rejection property were obtained within a large range of sampling periods. The good model following and disturbance rejection property was confirmed through simulations for a more complicated nonlinear systema two-link manipulator carrying an unknown payload. In this case, all the joint velocities involved in the control were estimated using first order difference of joint positions. Performance of the control system was evaluated through simulations and real time experimentations with highly nonlinear system.


François-Clément Bidard
email: fcbidard@curie.fr

Tanja Fehm

Michail Ignatiadis

Jeffrey B Smerage

Catherine Alix-Panabières

Wolfgang Janni

Carlo Messina

Costanza Paoletti

Volkmar Müller

Daniel F Hayes

Martine Piccart

Jean-Yves Pierga

Implementing circulating tumor cells in routine practice of breast cancer management: overview of the interventional trials

In 2004, circulating tumor cells (CTC) enumeration by the CellSearch® technique at baseline and during treatment was reported to be associated with prognosis in metastatic breast cancer patients. In 2008, the first evidence of the impact of CTC detection by this technique on survival of cM0(i+) patients were reported. These findings were confirmed by other noninterventional studies, whereas CTC were also investigated as a surrogate for tumor biology, mainly for HER2 expression/amplification. The aim of this report is to present the current prospective large interventional studies that have been specifically designed to demonstrate that CTC enumeration/characterization may improve the management of breast cancer patients: STIC CTC METABREAST (France) and Endocrine Therapy Index (USA) assess the CTC-guided hormone therapy vs chemotherapy decision in M1 patients; SWOG0500 (USA) and CirCe01 (France) assess the CTC count changes during treatment in metastatic patients; DETECT III (M1 patients, Germany) and Treat-CTC (cM0(i+) patients, EORTC/BIG) assess the use of anti-HER2 treatments in HER2-negative breast cancer patients selected on the basis of CTC detection/characterization. These trials have different designs in various patient populations, but are expected to be the pivotal trials for CTC implementation in the routine management of breast cancer patients.

Introduction -Background

Circulating tumor cells (CTC) designate cancer cells that are detected in the blood of cancer patients. Their detection, quantification and characterization represent a new window on cancer dissemination and have opened major perspectives for both biological and clinical research on the metastatic process. Technically, as most carcinomas do not have specific and recurrent DNA mutation or fusion transcripts, CTC isolation methods rely on the detection of cells that express epithelial-related markers in blood. Since the normal components of human whole blood are mesenchymally derived, they are not identified using this strategy; this principle is similar to the detection of isolated breast tumor cells in axillary lymph node in pN0(i+) breast cancer patients. In 2012, the standard for CTC detection remains the CellSearch® system (Veridex), which is still the only system that has been approved by the FDA for in vitro diagnosis purposes. In 2004, a seminal study with this technique showed that CTC count was an independent prognostic factor for both progression-free (PFS) and overall (OS) survival in metastatic (M1) breast cancer patients [START_REF] Cristofanilli | Circulating tumor cells, disease progression, and survival in metastatic breast cancer[END_REF]. In this report, the threshold of ≥5 CTC/7.5ml to define the poor prognosis group was "learned" from a training group (n=102 patients) and validated in another group of patients (n=75 patients). This prognostic value for PFS and OS has been repeatedly validated in smaller following studies [START_REF] Nole | Variation of circulating tumor cell levels during treatment of metastatic breast cancer: prognostic and therapeutic implications[END_REF][START_REF] Nakamura | Multicenter study evaluating circulating tumor cells as a surrogate for response to treatment and overall survival in metastatic breast cancer[END_REF][START_REF] Dawood | Prognosis of Women With Metastatic Breast Cancer by HER2 Status and Trastuzumab Treatment: An Institutional-Based Review[END_REF]. Unsurprisingly, a pooled analysis confirmed these results in multivariate analysis [START_REF] Liu | Clinical validity of circulating tumor cell (CTC) enumeration in 841 subjects with metastatic breast cancer (MBC)[END_REF]. A prospective study "IC 2006-04", specifically designed and powered to assess the prognostic value of CTC count changes in patients treated by first line chemotherapy (with or without targeted therapy), had the same conclusions in multivariate analysis and supported the use of the ≥5 CTC/7.5ml threshold [START_REF] Pierga | High independent prognostic and predictive value of circulating tumor cells compared with serum tumor markers in a large prospective trial in first-line chemotherapy for metastatic breast cancer patients[END_REF]. Serum markers have been also prospectively assessed [START_REF] Bidard | Assessment of circulating tumor cells and serum markers for progression-free survival prediction in metastatic breast cancer : a prospective observational study[END_REF] and were not prognostic markers in multivariate analysis. The only issue appeared with the use of targeted therapy, namely trastuzumab and bevacizumab, which decrease profoundly the CTC count: some reports suggested that this decrease might impact its prognostic value [START_REF] Bidard | Clinical value of circulating endothelial cells and circulating tumor cells in metastatic breast cancer patients treated first line with bevacizumab and chemotherapy[END_REF][START_REF] Giordano | Artificial neural network analysis of circulating tumor cells in metastatic breast cancer patients[END_REF]. Moreover, recent data has suggested an adverse prognostic value of CTC detection in non metastatic breast cancer [START_REF] Pierga | Circulating tumor cell detection predicts early metastatic relapse after neoadjuvant chemotherapy in large operable and locally advanced breast cancer in a phase II randomized trial[END_REF][START_REF] Bidard | Single circulating tumor cell detection and overall survival in nonmetastatic breast cancer[END_REF][START_REF] Rack | Prognostic Relevance of Circulating Tumor Cells in the Peripheral Blood of Primary Breast Cancer Patients[END_REF]. At the same time, HER2-expression on CTCs using the CellSearch® system was studied in the neoadjuvant setting [START_REF] Riethdorf | Detection and HER2 expression of circulating tumor cells: prospective monitoring in breast cancer patients treated in the neoadjuvant GeparQuattro trial[END_REF], and across all breast cancer stages from preinvasive lesions to overt metastatic disease [START_REF] Ignatiadis | HER2-positive circulating tumor cells in breast cancer[END_REF].

With these numerous non-interventional studies published, interventional controlled "phase III" trials were needed to demonstrate that the use of CTC enumeration and monitoring could improve the outcome of breast cancer patients and/or lower the medical costs paid by the patient or its insurer. The aim of this article is to report and discuss the different interventional trials currently ongoing or on the edge of starting that have been set up by different CTC research groups in the world. Basically, CTCs are investigated as prognostic markers in the STIC CTC METABREAST trial and ETI study, as early surrogate of chemotherapy efficacy in the SWOG0500 and in the CirCe01 trials and finally as an indicator of tumor biology in the Treat CTC, DETECT III and CirCe XXX1 trials.

STIC CTC METABREAST (France)

Rationale: As stated above, baseline CTC count has unambiguously demonstrated its very good performance as an independent prognostic marker. Multivariate analyses performed in both the pooled analysis and in the IC 2006-04 study showed that the other independent prognostic factors were the performance status and hormone-receptor (HR) status.

Oppositely, the other criteria that are frequently used to choose between hormone therapy and chemotherapy for the treatment of first line metastatic HR+ breast cancer patients (e.g. metastatic sites, metastasis-free interval…) were not independent prognostic factors. It has been then proposed that CTC count may be a better criterion for this important choice than the currently used empiric criteria, which have a low level of evidence (expert consensus).

Design:

In the STIC CTC METABREAST trial (NCT awaited), about 1000 HR+ M+ breast cancer patients will be randomized between the clinician choice and CTC count-driven choice (Figure 1). In the CTC arm, patients with ≥5 CTC/7.5ml will receive chemotherapy whereas patients with <5 CTC/7.5ml will receive endocrine therapy as first line treatment.

Within each treatment category (hormone or chemotherapy), the treatment type will be the clinician choice, targeted therapy being allowed. The only difference between CTC and standard arms will be the rates of hormone therapy vs chemotherapy-based treatment. As every patient will receive a treatment, this pivotal trial has been designed to show a noninferiority of the CTC arm for PFS (primary clinical endpoint) and a superiority of the CTC arm for the medico-economics study (co-primary endpoint). This trial began in February 2012. Several secondary endpoints are pre-planned (subgroups analyses).

Funding:

The STIC CTC METABREAST trial has been funded by the French Ministry of Health (STIC program, #50%) and Veridex (#50%). The promoter is the Institut Curie (Paris). Based on the same rationale (standard criteria for treatment decision between hormone therapy or chemotherapy may be weaker than CTC count), another strategy is currently developed, that takes into account not only the number but also the biology of CTC [START_REF] Paoletti | Development of Circulating Tumor Cell-Endocrine Therapy Index in metastatic breast cancer patients[END_REF][START_REF] Paoletti | Multiparameter molecular characterization of circulating tumor cells (CTC): Development of a CTC-Endocrine Therapy Index (CTC-ETI)[END_REF].

STIC CTC METABREAST

CTC-arm

Four biological markers are assessed on isolated CTC by immunocytofluorescence in the CellSearch® system: estrogen receptor, Bcl2, HER2, and Ki67. The global level of expression per isolated CTC of each marker is determined, and a score, called "Endocrine Therapy Index" is assigned for each marker for that blood draw, based on both the staining intensity and the proportion of positive CTC. The relative weights of the criteria (the number of CTC and the expression of each of the 4 biomarkers) are used to derive an "ETI score".

An american pilot study to establish the analytical validity of this assay is near completion and a larger trial to test the clinical validity is now being planned.

SWOG 0500 (USA)

Rationale: As stated above, several observational studies support the fact that CTC changes during the weeks following the first cycle of chemotherapy is associated with PFS and OS (1). This observation is intriguing, since other soluble, protein markers often rise before they declinethe so-called "tumor marker spike." This phenomenon makes assessment of protein biomarkers much less accurate in the early phases of a new treatment, whereas CTC spikes have not been observed. Therefore, CTC levels early in the course of a new therapeutic regimen for metastatic disease appear to reflect response, whereas lack of reduction of CTC levels may reflect futility of the respective treatment, thus making early CTC levels a short-term "predictive" factor. These data opened a whole new vision of the "personalized medicine" in metastatic breast cancer as no predictive factorexcept HR and HER2-have been strongly validated in stage IV breast cancer. In this context, the promise of CTC count was to evaluate the efficacy of any chemotherapy after only one cycle and then to switch non responding patients to another chemotherapy before the disease progression. However, the clinical benefit of such revolutionary managementcompared to the standard radiological evaluation-was unknown. This protocol was the first interventional trial to be designed to demonstrate that CTC-driven management of chemotherapy improves the outcome of metastatic breast cancer patients.

Design:

The SWOG 0500 (NCT00382018) design is shown Rationale: The CirCe01 study is basically another attempt to demonstrate that patients who received a first cycle of chemotherapy and whose CTC count did not drop should be switched off this chemotherapy. Based on the assumption that CTC count is a test to detect chemoresistance, it was supposed that this test will perform better in a population with chemoresistance prevalence, i.e. in the advanced metastatic setting. Another idea is that, to show a clinical improvement in the CTC-managed arm, the CTC test should be repeated more than once in patients. So the early CTC "go / no go" test will be performed not only once, but at the beginning of every new chemotherapy line in patients randomized in the CTC arm (i.e. to evaluate the 3 rd , 4 th , 5 th … lines). In the CTC arm, it has been hypothesized that many patients with chemoresistant tumor will experience repeated early chemotherapy changes (e.g. 3 chemotherapy regimens tested in 9 weeks), giving support to the discontinuation of inefficient, toxic and costly chemotherapies and the start of palliative care.

It is believed, for this subgroup of patients, that such de-escalating management will benefit both patients and healthcare systems. For some other patients, it is also expected that they will benefit from the early chemotherapy turn-around and find quicker an efficient therapy among all those tested.

Design:

The first step of the CirCe01 (NCT01349842) trial was conducted from March 2010 to October 2011. This non-interventional step was intended to check the clinical relevance of the ≥5 CTC/7.5ml threshold in these heavily pretreated patients or to propose alternate decision criteria. The design of the interventional part of the trial, which started in February 2012, is shown Figure 3: 304 patients with high CTC count before the start of the 3 rd line of chemotherapy will be randomized between the CTC-driven arm and the standard arm. In the CTC-driven arm, CTC counts will be performed after each first cycle of every new chemotherapy drug and will indicate whether or not this regimen is worth to be pursued.

Patients with insufficient CTC decrease will be switched off this chemotherapy line and will be eventually proposed a further line of treatment, which will be, again, evaluated by early CTC changes (and so on). Patients with a significant CTC decrease before the second chemotherapy cycle will continue their treatment, and then managed by standard clinical/radiological tools (the next chemotherapy line being again initially evaluated by CTC, and so on). The medical primary endpoint of the trial is the overall survival, whereas a medico-economic study as a co-primary endpoint. Several secondary endpoints are preplanned, including progression-free survival, quality of life, anxiety/depression and comparison with serum markers. Rationale: "Treat CTC" is the first, multi-center international trial assessing CTC detection as a liquid biopsy to test a new treatment strategy in breast cancer that is the use of trastuzumab in HER2 non amplified disease. Currently trastuzumab, is administered as part of the standard of care only in women with HER2-overexpressing / amplified tumors [START_REF] Ignatiadis | HER-2 as a target for breast cancer therapy[END_REF].

However, data from subset analyses of the NASBP B-31 and the NCCTG N9831 trials [START_REF] Paik | HER2 status and benefit from adjuvant trastuzumab in breast cancer[END_REF][START_REF] Perez | Four-year follow-up of trastuzumab plus adjuvant chemotherapy for operable human epidermal growth factor receptor 2-positive breast cancer: joint analysis of data from NCCTG N9831 and NSABP B-31[END_REF], and results of a single-center phase 2 study [START_REF] Georgoulias | Trastuzumab decreases the incidence of clinical relapses in patients with early breast cancer presenting chemotherapy-resistant CK19 mRNA-positive circulating tumor cells: results of a randomized phase II study[END_REF] suggest that benefit from adjuvant trastuzumab may not be confined to HER2-amplified tumors. These interesting findings could be explained by several hypotheses that are not mutually exclusive: (i) Lower levels of HER2 This is a randomized phase II trial for patients with HER2-non amplified primary breast cancer with ≥1CTC/15 ml of blood after completion of (neo-) adjuvant chemotherapy and surgery. Before randomization, a central review on both the HER2 status of the primary tumor and the Cellsearch ® CTC images will be performed. Eligible patients will be randomized in 1:1 ratio to either the trastuzumab or the observation arm. Patients randomized to the trastuzumab arm will receive a total of 6 injections every 3 weeks (loading dose 8 mg/kg IV and 5 cycles at 6 mg/kg every 3 weeks). Patients randomized to observation shall be observed for 18 weeks. The primary endpoint will compare CTC detection rate at week 18 between the two arms, while the secondary endpoint will compare recurrence free interval.

Treat CTC EORTC 90091

Trastuzumab arm • HER2 overexpression on CTCs will also be studied in all patients, but it is not required to enter the study patients with metastatic breast cancer and with up to three chemotherapy lines for metastatic disease will be tested for HER2-positive CTC. In all patients the HER2 status of the primary tumor and, if analyzed, of metastatic lesions has to be negative. At least one HER2-positive CTC /7.5 ml blood has to be detected in these patients (immunocytofluorescence). 228 patients meeting the inclusion criteria will be randomized between two arms receiving standard therapy or standard therapy plus lapatinib. Standard treatment will consist of chemo-or endocrine therapy that is either approved for the combination with lapatinib or that has been investigated in clinical trials. Patients with bone metastases will be treated with denosumab in both arms. The maximum duration of randomized treatment period is twelve months; the adjacent follow-up period has an estimated maximum duration of 24 months.

Primary endpoint of the DETECT III study is progression-free survival; secondary endpoints are overall survival, overall response rate, clinical benefit rate and the dynamic of CTC.

Funding: DETECT III is funded by GlaxoSmithKline (82.5%), Cephalon (15.5%) and Pierre Fabre Pharma (2%). The promoter is the Heinrich Heine University Düsseldorf.

DETECT III

CTC

Alternate proposal:

Based on the same rationale (HER2 "gain" in CTCs at metastatic stage in HER2-negative primary breast cancers), an interventional phase 2 study is planned to open in winter '12 in France. The "CirCe XXX1" study (provisional name) will use the gold-standard technique for HER2 amplification assessment that is HER2/CEP17 ratio measurement by FISH. In this single arm study, patients with HER2-amplified CTC will receive an anti-HER2 drug without combined chemotherapy; response rate will be the study main endpoint. It has been anticipated that such strategy might be relevant only in patients with high number of HER2-amplified CTCs; an original adaptive design (Figure 6) will allow isolating which patient population will benefit (i.e. the "granularity" of the screening procedure).

Conclusion

Beyond the future of CTC analysis as a biological tool for the understanding of the metastatic process, the CTC count is clinically a very promising tool. This new dynamic quantitative and qualitative test deserves an appropriate scientific development in order to be efficient and to further improve the life expectancy and/or the quality of life of breast cancer patients. Each of the interventional trials presented above has been designed using the CellSearch® system, as system has the largest background of non-interventional studies published in the past years. This background allowed the accumulation of clinical data and hypotheses, of which statistical hypotheses used for such large studies. Interestingly, these studies are not part of pre-planned development program and are addressing different but complementary aspects of the CTC clinical utility in different parts of the world. For example, a similar test result with stable intrinsic statistical properties (lack of early CTC changes during chemotherapy) can be used to reach different objectives: in SWOG0500 the underlying concept is to intensify the frontline treatment for the few metastatic patients who are not responding; In contrast, in CirCe01, the underlying concept is to objectively justify the early discontinuation of useless chemotherapies for the vast majority of patients who are in a very palliative setting. It is also expected that the global accuracy of the CTC changes, used as a test for early chemoresistance detection, will vary between these two trials, as chemoresistance rates are different between the first and the latest chemotherapy lines.

Another interesting aspect is the different trials proposed to assess the relevance of CTC detection and characterization as a "liquid biopsy" to test new treatment strategy using anti-HER2 drugs: the DETECT III trial uses a classical randomized phase III trial design, and will answer in a large population whether or not lapatinib should be added in a HER2-breast cancer patients population that has been predefined before the start of the study: metastatic patients with any HER2+ CTC by immunocytofluorescence. A very different approach is lead by the Treat CTC trial, which combines the prognostic information of CTC in the adjuvant setting (cM0(i+) patients( 25)) and the promise of adjuvant trastuzumab given to HER2 negative patients in past studies. Interestingly, the adjuvant setting is characterized by low CTC detection rates and by long follow-up, explaining why this trial is the only one not using survival as first endpoint. Also, the HER2 status of CTC is not used as inclusion criteria, but will be registered, leading to possible subgroups analysis of trastuzumab efficacy in this high risk population.

Finally, these trials represent the first attempts to demonstrate that CTC testing improve the clinical outcome of metastatic breast cancer. Each of them proposes a different original design which may guide the setup of further studies based on dynamic blood markers.

Box 1 Clinical settings and endpoints

The different trials presented above are using commonly accepted endpoints to judge whether a treatment or a strategy is clinically relevant. Two settings must be clearly separated; First, patients diagnosed with a breast cancer and with no overt metastasis (M0) reported by a clinical and radiological screening. In this non-metastatic setting, treatments are intended to cure the patients, and include surgery, followed by loco-regional radiotherapy and systemic treatments (hormone therapy, chemotherapy, targeted therapy). These adjuvant treatments are made to lower the frequency of later metastatic relapse. The most clinically relevant endpoints are therefore the time from breast cancer surgery to any relapse (local or distant), called "disease-free survival", and to patient death, called "overall survival" (OS). As the relapse and/or death generally occur many years after the primary tumor treatment, it is commonly accepted to use surrogate endpoints. The TREAT CTC trial, presented above, will include only M0 patients, and is using as a primary endpoint the rate of CTC disappearance after adjuvant treatments, this data being available quickly. Disease-free and overall survival will be also studied as secondary endpoints, when they will be available (i.e. probably 5 to 10 years later).

The second setting is metastatic (M1) breast cancer. For these patients diagnosed with breast cancer metastases, treatments are generally palliative, and aim at extending the patient life without deteriorating the patient quality of life. Patients are receiving successive "lines" of treatment. Chemotherapy, hormone-therapy and targeted therapy are all assessed similarly, with radiological measurement of the diameter of the different metastases. The radiological measurement is standardized, following the RECIST guidelines [START_REF] Eisenhauer | New response evaluation criteria in solid tumours: revised RECIST guideline (version 1.1)[END_REF]. The sum of the diameters is measured before treatment start, and is used for comparison with new radiological exams made at regular intervals, every 2 to 3 months. The disappearance (100% diameter shrinkage) of the metastases is called a "complete response", a decrease of more than 30% is called a "partial response", variations between -30% and +20% is a "stable disease", whereas an increase of more than 20% of the metastases diameters or the appearance of a new metastasis is a "progressive disease"which signs the end of treatment efficacy, and the start -if possible-of a new line with another treatment. In M1 patients, assessing a treatment or strategy efficacy relies therefore mostly on progressionfree survival (PFS, i.e. time from treatment start to tumor progression), tumor response rate (rate of patients experiencing a complete and or partial response of their tumor) and overall survival (OS, i.e time from treatment start to patient death). Most of the trials presented here aim at improving metastatic patients care, and used response rate, PFS and /or OS as endpoints.

Figure 1 :

 1 Figure 1: STIC CTC METABREAST

Figure 2 :•<5•

 2 in the screening part of the trial, metastatic patients treated by first line chemotherapy (combined or not with targeted therapy) had their CTC count determined before cycles 1 and 2. Patients with persistently elevated CTC (≥5 CTC/7.5ml) after one cycle (i.e. around day 21-28) are at higher risk of early cancer progression and were randomized between continuation of the first line chemotherapy (until classic evidence of clinical or radiological progression) or to early switch to another chemotherapy regimen, before any radiological progression. The "early second line" and further treatment lines were managed by the usual clinicalradiological parameters. Accrual started in 2006 and has been completed in March 2012: about 610 patients were screened and 120 patients randomized (source: www.swogstat.org). The primary endpoint of the trial is to demonstrate an improvement in OS in the CTC-driven arm. Funding: The SWOG 0500 trial has been funded by the National Cancer Institute of the United States through the South-West Oncology Group (SWOG) and Veridex supported the study. The promoter is the SWOG. Primary endpoint: OS (superiority; hypotheses HR=0.59, P=81%) • 2nd endpoints: PFS, toxicities, … Stratified on HER2 status & measurable/bone only disease Inclusion • M+ patient starting a 1st line of chemotherapy (L1) •PS 0-3 Screening • ≥5 CTC / 7.5ML AT BASELINE BEFORE L1 • To avoid early treatment discontinuation in the standard arm, patients and clinicians are blinded to the second CTC test Bidard et al, Cancer Met Rev, 2012

Figure 2

 2 Figure 2: SWOG 0500

Funding:

  Figure 3: CirCe01

•

  on center, estrogen receptor status, chemotherapy (adjuvant vs neoadjuvant)• M0 HER2-patients having completed (neo)adjuvant chemotherapy and surgery• ≥1 CTC / 15ML (2 tubes)Observation• Primary endpoint:CTC detection at week 18

Figure 4 5 .

 45 Figure 4: Treat CTC

•

  on hormone receptor status, lines of chemotherapy, type of palliative treatment, number of metastases, presence of bone metastases • M+ HER2-patients before 1 st -3 rd line • Planned treatment that have been tested in association with lapatinib: aromatase inhibitors, taxanes, capecitabine, vinorelbine, non pegylated liposomal doxorubicin • ≥1 CTC WITH HER2+ IMMUNOCYTOFLUORESCENCE Planned treatment • Primary endpoint: PFS (superiority) • 2 nd endpoints: OS, overall response rate, clinical benefit rate, QoL, CTC dynamics, safety & tolerability of lapatinib compliance to the study protocol, assessment of pain intensity Patients with bone metastasis will also receive denosumab in both arms Bidard et al, Cancer Met Rev, 2012

Figure 5 :

 5 Figure 5: DETECT III

Figure 6 :

 6 Figure 6: CirCe XXX1 (provisional name)

The Treat CTC trial has been at the ECCO-AACR-EORTC-ESMO

Funding:

The Treat CTC trial is sponsored by the European Organization for Research and Treatment of Cancer (EORTC) and has been funded/supported by Roche and Veridex. This trial will be conducted under the Breast International Group (BIG) umbrella.

Conflicts of interest: