Jodi Schneider
email: jodi.schneider@inria.fr

Automated argumentation mining to the rescue? Envisioning argumentation and decision-making support for debates in open online collaboration communities

Argumentation mining, a relatively new area of discourse analysis, involves automatically identifying and structuring arguments. Following a basic introduction to argumentation, we describe a new possible domain for argumentation mining: debates in open online collaboration communities. Based on our experience with manual annotation of arguments in debates, we envision argumentation mining as the basis for three kinds of support tools, for authoring more persuasive arguments, finding weaknesses in others' arguments, and summarizing a debate's overall conclusions.

Introduction

Argumentation mining, a relatively new area of discourse analysis, involves automatically identifying and structuring arguments. Following a basic introduction to argumentation, we describe online debates as a future application area for argumentation mining, describing how we have manually identified and structured argumentation, and how we envision argumentation mining being applied to support these debates in the future.

What is an argument

Informally, an argument is a communication presenting reasons for accepting a conclusion. Unlike proofs that lead step-by-step from premises with logical justifications for a conclusion, arguments are non-monotonic and can be disproven. Arguments may use various approaches including generalization, analogy, inference, and prediction.

More complex arguments

Far more complex arguments can be formed. Arbitrary numbers of arguments can be joined into a larger and more complex argument. Useful terminology is introduced by [START_REF] Adam Z Wyner | Three senses of "Argument[END_REF], who reserve the term argument to refer to the simplest kind: non-decomposable arguments. They distinguish cases which support a single conclusion (see Figure 2) from debates which argue for and against a single conclusion. Figure 3 shows a simple debate, where two arguments attack one another. There are three ways of attacking an argument: attacking a premise (known as undermining), attacking a conclusion (known as rebutting), and attacking an inference (known as undercutting), following [START_REF] Prakken | An abstract framework for argumentation with structured arguments[END_REF]). 1

Inference Rules

Argumentation schemes, e.g. [START_REF] Walton | Argumentation Schemes[END_REF] are one way of expressing Inference Rules. These are patterns for arguing which are stated abstractly: to use an argumentation scheme, it must be instantiated with details. To indicate possible flaws in reasoning, associated with each scheme there are critical questions pointing to the possible counterarguments.

We next introduce an example from our own work, where automated argumentation mining could be used.

Rationale-based debate in open online communities

One place where argumentation mining could be applied is in rationale-based debate in open online communities. The Web has enabled large-scale collaboration, even among people who may never meet face-to-face. A large number of participants present their views and reasoning to make decisions for open, online collaborative software and knowledge development in Mozilla, Wikipedia, OpenStreetMap, etc. In these groups, asynchronous textual debates are the basis for decision making. Participants argue for decisions based on rationales, since the reasons for opinions, rather than majority votes or aggregate sentiment, justify decisions. Thus large-scale decision support in these communities should make evident not just the overall tendency of the group (as in opinion mining) but rather the arguments made, focusing

1 Rebut and undercut are drawn from the well-known work of [START_REF] John | Justification and defeat[END_REF]; Prakken credits undermining to [START_REF] Vreeswijk | Studies in Defeasible Argumentation[END_REF] and [START_REF] Elvang-Gøransson | Acceptability of arguments as 'logical uncertainty[END_REF].

especially on the rationales, or reasons given for a preferred outcome.

In our work, we have analyzed a corpus of debates, to understand how the English-language version of Wikipedia makes decisions about which articles to include and exclude from the encyclopedia. We used two approaches to argumentation theory to annotate asynchronous messages in each debate, in iterative multiparty annotation experiments [START_REF] Schneider | Identifying, Annotating, and Filtering Arguments and Opinions in Open Collaboration Systems[END_REF].

Analysis using argumentation schemes

First, we used Walton's argumentation schemes (outlined in Ch. 9 of [START_REF] Walton | Argumentation Schemes[END_REF]) in order to annotate the arguments, focusing on the internal reasoning of each message. First one person (this author) annotated all the arguments found in the corpus against Walton's 60 schemes, finding 1213 arguments in 741 messages [START_REF] Schneider | Arguments about deletion: How experience improves the acceptability of arguments in ad-hoc online task groups[END_REF]. Then, we focused on the subset of 14 argumentation schemes that appeared more than 2% of the time, with iterative, multiparty annotation. There was a sharp divide between the two most prevalent argument types-Argument from Evidence to Hypothesis (19%) and Argument from Rules (17%)-and the remaining 12 types that appeared from 2-4% of the time.

Besides these patterns, we found statistically significant differences between how experts and novices in the community argued in our corpus of debates. Experts were more likely to use Argument from Precedent, while novices (who had little experience in the debates and in the wider Wikipedia community) were more likely to use several argumentation schemes that the community viewed as less sound bases for decision making.2 These included Argumentation from Values, Argumentation from Cause to Effect, and Argument from Analogy.

Analysis using factors analysis

Second, we used a very different approach, based on factors analysis [START_REF] Ashley | Modeling Legal Arguments: Reasoning with Cases and Hypotheticals[END_REF] and dimensions theory [START_REF] Trevor | Back to the future: Dimensions revisited[END_REF], which have most commonly been used in case-based reasoning. We iteratively derived four factors important in the discussions: Notability, Sources, Maintenance, and Bias [START_REF] Schneider | Deletion discussions in Wikipedia: Decision factors and outcomes[END_REF]. This was an easier annotation task, with stronger inter-annotator agreement than for Walton's argumentation schemes: factors analysis had Cohen's kappa [START_REF] Cohen | A coefficient of agreement for nominal scales[END_REF] of .64-.82 depending on the factor [START_REF] Schneider | Deletion discussions in Wikipedia: Decision factors and outcomes[END_REF], versus .48 for Walton's argumentation schemes [START_REF] Schneider | Arguments about deletion: How experience improves the acceptability of arguments in ad-hoc online task groups[END_REF]). Factors provide a good way to organize the debate; filtering discussions based on each factor can show the rationale topic by topic, which supported decision making in a pilot user-based evaluation [START_REF] Schneider | Identifying, Annotating, and Filtering Arguments and Opinions in Open Collaboration Systems[END_REF].

We can also identify the misunderstandings that newcomers have about which factors are important, and about what kind of support is necessary to justify claims about whether a factor holds. When an article is unacceptable because it lacks reliable sources, it is not enough to counter that someone will publish about this website when it gets out of beta testing.3 This newcomer's argument fails to convincingly establish that there are reliable sources (because for Wikipedia, a reliable source should be published, independent, and subject to full editorial control), and may make things worse because it suggests that the sources are not independent. Rather, a convincing counterargument would explicitly address how the most relevant criteria are met.

Envisioned applications of argumentation mining

The manual annotations described above, of argumentation schemes and of factors, suggest several possibilities for automation. Scalable processes for analyzing messages are needed since Wikipedia has roughly 500 debates each week about deleting borderline articles. Argumentation mining could be the basis for several support tools, helping participants write more persuasive arguments, find weaknesses in others' arguments, and summarize the overall conclusions of the debate.

First consider how we might give participants feedback about their arguments. From our research, we know which argumentation schemes are viewed as acceptable and persuasive within the community. If real-time algorithms could identify the argumentation schemes used in the main argument, authors could be given personalized feedback even before their message is posted to the discussion. When the argumentation scheme used in a draft message is not generally accepted, the author could be warned that their message might not be persuasive, and given personalized suggestions. Thus debate participants might be nudged into writing more persuasive arguments.

Next consider how we could help participants find weaknesses in others' arguments. Automatically listing critical questions might benefit the discussion. Critical questions point out the possible weaknesses of an argument, based on the argumentation scheme pattern it uses. Listing these questions in concrete and contextualized form (drawing on the premises, inference rules, and conclusions to instantiate and contextualize them) would encourage participants to consider the possible flaws in reasoning and might prompt participants to request answers within the debate. In the authoring process, supplying the critical questions associated with argumentation schemes might also help the author (who could consider elaborating before submitting a message).

Finally, we could envision argumentation mining being used to summarize the debate. Macroargumentation, such as the factors analysis described above, would be a natural choice for summarization, as it has already proven useful for filtering discussions. A more reasoning-intensive approach would be to calculate consistent outcomes [START_REF] Wyner | Towards web-based mass argumentation in natural language[END_REF], if debates can be easily formalized.

Challenges for argumentation mining

In previous work, argumentation schemes have been classified in constrained domains, especially in legal argumentation [START_REF] Mochales | Argumentation mining[END_REF] and by using [START_REF] Wei | Classifying arguments by scheme[END_REF][START_REF] Wei | Classifying arguments by scheme[END_REF] the Araucaria corpus [START_REF] Katzav | Argument Research Corpus[END_REF]. 4Each of our envisioned applications of argumentation has certain requirements. Automatically detecting the argumentation schemes used in a message could be used for supporting authoring and finding weaknesses of arguments, which focus on the interior of each message. In order to ask the appropriate critical questions, the premises, conclusions, and inference rules would first need to be detected. To get at the point of each message, the macro-level argumentation (for instance using factors and dimensions) would be useful for summarizing the debate, especially if we record rationales.

Another challenge is to create scaleable architectures for real-time or batch reprocessing of argumentation mining on the Web. In our scenarios above, support for authoring arguments would require real-time feedback (i.e. within minutes). Slower batch processing would be useful for the two other scenarios (support in challenging arguments with critical questions; support for summarizing debates) since Wikipedia's debates are generally open for 7 days.

Related scenarios

This is a single use case, but it represents a wide array of related ones. Open source and open knowledge projects are full of decision making discussions available widely in textual form. Rhetorical studies of them so far take place on qualitative, discursive level. Examples include dissent and rhetorical devices in bug reporting (Ko and Chilana, 2011) and how Python listservs select enhancement proposals [START_REF] Barcellini | A study of online discussions in an open-source software community[END_REF]. Interestingly, the role of a participant in the Python community is related to the kinds of message they quote (Syntheses, Disagreements, Proposals, or Agreements), and Syntheses and Disagreements are the most quoted. The organizational relevance of these open decision making discussions in collaborative communities makes them a promising target for support, and argumentation mining technology is an appropriate tool to deploy towards that end.

Conclusions

This paper detailed how automated argumentation mining could be leveraged to support open online communities in making decisions through online debates about rationale. We first gave a basic overview of argumentation structures, describing arguments as consisting of Statements, Inference Rules, and (possibly) Attacks. Then we described our own work on manual identification of argumentation schemes in Wikipedia information quality debates. We envisioned three kinds support tools that could be developed from auto-mated argumentation mining in the future, for authoring more persuasive arguments, finding weaknesses in others' arguments, and summarizing a debate's overall conclusions. Open online communities are a wide area of application where argumentation mining could help participants reason collectively.

Figure 1 :

 1 Figure 1: The simplest possible argument.

Figure 2 :

 2 Figure 2: Cases support a single conclusion. Cases may (a) use multiple, independent premises to support a single conclusion; (b) draw an intermediate conclusion, and use it as an additional premise in order to support a final conclusion; or (c) require two linked premises (both required as input to the inference rule) to support a conclusion.

Figure 3 :

 3 Figure 3: Debates argue for and against a single conclusion. This kind of attack is called a rebuttal.

Our analysis of acceptability of arguments drew from community documentation and took community responses to messages into account. For instance, Argumentation from Values might be countered by a messages saying "Whether you personally like an article or its subject, is totally irrelevant." (This exchange appeared in our corpus in fact http://en.wikipedia.org/wiki/Wikipedia: Articles_for_deletion/Log/2011_January_ 29.)

This is a real argument from a newcomer from our corpus, slightly reworded for clarity.

Further work is needed on argument scheme prevalence, which seems to vary by domain. Only 3 of Feng's

'most common argumentation schemes' appear in the top 14 most common schemes in our corpus, excluding Argument from Example and Argument from Cause to Effect.

This work was carried out during the tenure of an ERCIM "Alain Bensoussan" Fellowship Programme. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n o 246016.


Jodi Schneider

Carol Collins

Lisa E Hines

John R Horn

Richard Boyce

Modeling Arguments in Scientific Papers to Support Pharmacists

come   L'archive ouverte pluridisciplinaire

The scientific literature is a well-known source of arguments, which are embedded in natural language publications. Ontologies and knowledge bases have become increasingly valuable sources of knowledge synthesized from an ever-increasing body of scientific publications [Renear and Palmer2009]. We present a motivating scenario for using argumentation within a scientific knowledge base.

The Drug Interaction Knowledge Base (DIKB) [Boyce et al.2009] is a handconstructed evidence-base of safety issues that may occur when two drugs are coprescribed and taken together. It collects evidence about pharmacokinetic drug interactions for over 60 drugs. This sort of evidence can be used to make clinical decisions on whether it is safe to prescribe two drugs together. This is a complex decision-making environment: decisions are made under uncertainty and reasonable people may come to different conclusions, in effect disagreeing with each others' decisions [Boyce et al.2009]. Using formal argumentation structures could make the assumptions and logical steps of reasoning open to examination, making the resulting knowledge base more robust and trustworthy.

Currently, the DIKB (Version 1.2) has no way to explicitly model the data and methods in papers, which may need to be reviewed as new knowledge comes to light.

The SWAN Discourse ontology it uses only models evidence in the form of citations to an entire paper, with swanco:citesAsSupportingEvidence and swanco:citesAsRefutingEvidence1 [Ciccarese et al.2008]. Fortunately, a new model is now available for explicitly modeling data and methods.

Recently, [Clark et al.2014] proposed a new semantic model for claims, evidence, arguments and annotation in biomedical communications. This model, the Micropublications ontology,2 is inspired by the Toulmin model of argumentation (and Verheij's formalization thereof [Verheij2009]) in order to organize citable claims from scientific papers into networks of agreement and disagreement. A minimal micropublication is a claim with attribution-as in earlier models such as nanopublications [Groth et al.2010]. Unlike those models, Micropublications enable explicitly representing the warrant, i.e. the materials and methods that were used to collect the data. The data collected is considered meaningful due to a subfield's approval of the materials and methods. This approval is the backing of claims made in everyday science (e.g. 'paradigm' science in the terms of [Kuhn2012]). With this model, truth-bearing Statements (possibly with Qualifier s) from biomedical communications are explicitly connected to the Data, Material, and Method s. Attribution also has a place (for instance justifying use of a method by citing it in the literature). A subargument can be represented as a micropublication for a related claim, however far back we wish to extend the network.

In ongoing work, we are focusing on creating micropublications through manual annotation. Currently we are engaging with pharmaceutical curators to envision the most appropriate way to record evidence for the next generation of the DIKB knowledge base. Argumentation will play a key part in this model, especially for auditing the available evidence as the state of knowledge changes. In particular, with the Micropublications model, "methods and materials later found to be flawed might be easily traced to claims based upon them" [Clark et al.2014]. This motivates us to experiment with Micropublications as the underlying model, using a Web-based annotation tool (Domeo3 ) to help a panel of three drug interaction experts create the formal markup of a Micropublication. To determine what evidence should be modeled, we are drawing on new guidelines for systematically evaluating drug-drug interaction evidence [Scheife et al.2014]. The knowledge representations that result from this work will enable people to audit the evidence from scientific papers.

Subsequent automation in constructing such knowledge representations is also conceivable. Previous work has automatically categorized scientific discourse, often using rhetorical zoning approaches [Teufel1999], and a human annotated corpus can be used as the basis for predicting patterns on new examples, with supervised machine learning. Machine learning systems such as SAPIENTA [Liakata et al.2012] have achieved reasonable accuracy in recognizing Hypothesis, Motivation, Goal, Object, Background, Method, Experiment, Model, Observation, Result and Conclusion in highly-structured texts from chemistry and biochemistry. Previous work studied the Conclusion category and found that SAPIENTA's automatically mined efficacy/effectiveness claims compared favorably to manual annotation from the same abstracts [Boyce et al.2013]. Systematically evaluating drug-drug interaction evidence is a difficult problem, requiring human oversight. For identifying and recording complex evidence, mixed-initiative systems (e.g. [De Liddo et al.2012]) have been suggested: machine annotation can draw the attention of human curators to the zones most likely to contain the data and methods that provide evidence about a harmful drug-drug interaction. Our goal is to transform natural language papers, with the manual work of expert curators, into elaborated claim-argument networks.

In the future we plan to test what sort of machine annotation can aid human curators in extracting the evidence recorded in papers and whether expressing the current evidence on pharmacokinetic drug interactions as micropublications facilitates searching and updating knowledge bases.

Schneider, Boyce, & Horn, Modeling Arguments in Scientific Papers

http://swan-ontology.googlecode.com/svn/tags/1.2/swan.owl

http://purl.org/mp/

http://swan.mindinformatics.org/ Schneider, Boyce, & Horn, Modeling Arguments in Scientific Papers

Acknowledgements

Thanks to the reviewers for helpful comments. This work was carried out during the tenure of an ERCIM "Alain Bensoussan" Fellowship Programme. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n o 246016.

Funding is also provided by a grant from the United States National Library of Medicine: "Addressing gaps in clinically useful evidence on drug-drug interactions" (1R01LM011838-01).


Amira Zaylaa

Sébastien Ménigot

Jamal Charara

Jean-Marc Girault

Automatic Optimization of Chirp Setting Parameters In Medical Ultrasound Contrast Imaging

Keywords: Medical Ultrasound Contrast Imaging, Chirp Inversion, Chirp Setting Parameters, Automatic Technique, Optimal Command. !

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Introduction



Ultrasound contrast imaging is an inevitable modality in medicine. It has significantly improved medical diagnosis by ameliorating the contrast after injecting a contrast agent into the patient's vascular system [START_REF] Frinking | Ultrasound contrast imaging: current and new potential methods[END_REF]. Several methods have been proposed in literature to improve the contrast-to-tissue ratio (CTR). These methods were classified into two major groups. The first group (i) was based on continuous encoding such as harmonic chirp imaging (HCI) [START_REF] Borsboom | Nonlinear coded excitation method for ultrasound contrast imaging[END_REF][START_REF] Borsboom | Harmonic chirp imaging method for ultrasound contrast agent[END_REF]. HCI has improved resolution and increased the signal-to-noise ratio (SNR) of images. It was also capable of solving the trade-off between resolution and penetration [START_REF] Misaridis | U se of modulated excitation signals in medical ultrasound. Part I: Basic concepts and expected benefits[END_REF][START_REF] Chiao | Coded excitation for diagnostic ultrasound: a system developer's perspective[END_REF]. The second group (ii) was based on discrete encoding imaging methods such as pulse inversion [START_REF] Simpson | Pulse inversion Doppler: a new method for detecting nonlinear echoes from microbubble contrast agents[END_REF], contrast pulse sequence [START_REF] Brock-Fisher | Means for increasing sensitivity in non-linear ultrasound imaging systems[END_REF] and pulse subtraction [START_REF] Brosboom | Pulse Subtraction time delay imaging method for ultrasound contrast agent detection[END_REF]. These methods were capable of efficiently extracting the harmonic frequency components out of the spectrum of backscattered signals even if any overlap existed in this Corresponding authors: Amira Zaylaa, Ph.D. Student, research fields: Signal Processing and Ultrasound Imaging. E-mail: amira.zaylaa@inserm.fr. Jean-Marc Girault, Ph.D., H.D.R., research fields: Signal and Image processing and Medical Instrumentation. E-mail: jmgrault@univ-tours.fr.

spectrum.

Few years later, in order to benefit from the two aforementioned groups that contributed to the enhancement of the CTR, several scientists have proposed to merge some techniques together. For instance, chirp reversal has been proposed in harmonic contrast imaging [START_REF] Bouakaz | chirp reversal ultrasound contrast imaging[END_REF] and chirp inversion in tissue harmonic imaging [START_REF] Song | Coded tissue harmonic imaging with nonlinear chirp signals[END_REF].

In this paper, we have proposed for the first time to merge chirp inversion with harmonic ultrasound contrast imaging. The reason behind this was to benefit from the advantage of not only each approach alone but also their fusion. However, our contribution was not limited to this combination. Indeed, as it has been shown recently the necessity of setting the chirp frequency parameters in an optimal way through a theoretical approach [START_REF] Barlow | A theoretical investigation of chirp insonification of ultrasound contrast agents[END_REF] and more recently, the possibility of automatically optimizing the transmitted pulse parameters, without using apriori information of the medium perfused with microbubbles [START_REF] Menigot | Optimization of contrast to tissue ratio by frequency adaptation in pulse inversion imaging[END_REF], we proposed to set automatically and in an optimal way the chirp setting parameters in chirp inversion.

Besides, by automatically seeking the best power backscattered by microbubbles, we hope to increase the quality of harmonic ultrasound images and thus improve the medical diagnosis.

To advocate the feasibility and powerfulness of the novel proposed approach, we will compare, through simulations, the performances of our method to wellknown pulse inversion imaging chosen as a reference method.

Materials

In this section the coded ultrasound contrast imaging system is presented (see the flowchart in Fig. 1). Such system is used to image the perfused medium (the liver for instance). To achieve this task, physicians inject microbubbles, the constituents of ultrasound contrast agent (subsection 2.3). At the same time, ultrasound chirp excitation (see subsection 2.1), which is transmitted by a transducer to the explored medium, is encoded and simulated (see subsection 2.2). When the ultrasound waves interact with the medium perfused with microbubbles, echoes are reflected and backscattered towards the receiver (see subsection 2.4). At the receiver, the electrical signals are decoded and used to construct the image.

Transmitter, Transmitting Transducer and Chirp Excitations

As already mentioned, a transducer was used to transmit chirp excitations. During transmission these chirps were filtered by the pass band filters of the transmitting transducer Tx (see Fig. 1). The bandwidth of the simulated transmitting transducer was 74 % at -3 dB and central frequency 2.25 MHz. Chirp excitations are signals possessing a dynamic (instantaneous) frequency. A chirp 𝐶 𝑗 𝑡 is said to be linear when its dynamic frequency is linear (Eq.( 1)) [START_REF] Song | Coded tissue harmonic imaging with nonlinear chirp signals[END_REF]:

𝐶 𝑗 𝑡 = 𝐴 0 𝑒𝑥𝑝 - 𝑡-𝑡 0 2 2𝜍 2 . cos 𝜃 𝑖 𝑡 , 𝜃 𝑖 𝑡 = 2𝜋 𝑓 𝑖 𝑡 𝑡 + 𝜑 𝑗 , 𝑓 𝑖 𝑡 = 𝑓 + 𝛽𝑡 , (1)
where A 0 is the normalized driving pressure of the chirp, t 0 time delay, t time, f starting frequency or first setting parameter of chirp, 𝛽 frequency modulation index or second setting parameter, f i instantaneous frequency, 𝜑 angular phase, θ i the instantaneous phase of the chirp and σ width of the Gaussian's envelope chosen through our simulation as proposed by [START_REF] Wilhjelm | Bandwidth expressions of Gaussian weighted chirp[END_REF] to be 3. Note that the well-known pulse definition can be obtained from (Eq. 1) by setting 𝛽 =0. Chirp excitations were then encoded.

Chirp Inversion Encoding

Chirp inversion encoding simulated with Matlab (Mathworks, Natick, MA, USA) is the process of transmitting two 180 o out of phase chirps sequentially into the medium perfused with microbubbles. Chirp echoes reflected by the contrast agent are then summed up such that echoes at the starting frequency f cancel out while those at the harmonic frequencies show up [START_REF] Simpson | Pulse inversion Doppler: a new method for detecting nonlinear echoes from microbubble contrast agents[END_REF][START_REF] Song | Coded tissue harmonic imaging with nonlinear chirp signals[END_REF]. Chirp inversion encoding was illustrated by the two branches following transmission in Fig. 1. The first emitted chirp 𝐶 1 𝑡 was fed into a time-delay block and then a phase inverse block to get 𝐶 1 𝑡 -𝑡 0 with 𝜑 1 = 𝜋. The second chirp was 𝐶 2 𝑡 with 𝜑 2 = 0. Then 𝐶 1 𝑡 -𝑡 0 and 𝐶 2 𝑡 were filtered and fed into the medium of microbubbles.

Microbubble Model

!! Transmission) Chirp) Inversion) Encoding) Reception) Chirp) Inversion) Decoding) ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
Simulated medium consisted of micrometer-sized bubbles. For simplicity, and without loss of generality, in order to simulate the mean behavior of a microbubble cloud, we assumed that the response (nonlinear vibration) of a cloud of N microbubbles was N times the response of a single microbubble possessing the mean properties.

Bubblesim software [START_REF] Hoff | Acoustic Characterization of Contrast agents for Medical Ultrasound Imaging[END_REF] was used in this work, in order to account for the microbubble's response when exposed to a megahertz-frequency ultrasound chirp. It is based on simulating the response by digitally solving modified Rayleigh-Plesset model (Eq. 2).

𝑅 𝑡 𝑅 𝑡 + 3 2 𝑅 (𝑡) 2 + 𝑝 0 +𝑝 𝑖 (𝑡)+𝑝 𝐿 (𝑡) 𝜌 𝐿 - 𝑝 𝐿 𝑡 𝑝 𝐿 𝑐 𝐿 𝑅 𝑡 = 0, ( 2
)
where R is the instantaneous radius of microbubbles, 𝑅 and 𝑅 first and second derivative respectively, p 0 static pressure, p i instantaneous acoustic pressure, p L liquid pressure on the surface of the micro-bubbles, ρ L liquid density and c L velocity of sound in the liquid. Eq. ( 2) was based on modeling microbubbles by air-filled particles where the surface layer resembles that of an elastic solid.

SonoVue [START_REF] Greis | Technology Overview: SonoVue (Bracco[END_REF] contrast agent was simulated according to experiments in literature. The mean diameter of simulated SonoVue (Bracco Research SpA, Geneva, Switzerland) microbubbles was 5 μm [START_REF] Greis | Technology Overview: SonoVue (Bracco[END_REF] and the shell thickness d Se 1 nm [START_REF] Chetty | P1F-4 High speed Optical observations and Simulation Results of Lipid Based Microbubbles at Low Insonation Pressures[END_REF]. The shell shear modulus Gs was 46 MPa [START_REF] Hoff | Acoustic Characterization of Contrast agents for Medical Ultrasound Imaging[END_REF] and the shear viscosity 1 Pa•s.

Receiving Transducer, Chirp Inversion Decoding and Receiver

The first element of the reception stage (Fig. 1) was the transducer Rx, the bandwidth of Rx was 63 % at -3 dB and central frequency 3.5 MHz. For illustration, the transducer's effect was taken into consideration in transmission and reception, such that, its bandwidth was 160 % at -3 dB and central frequency 3 MHz. The same transducer received the echoes used for constructing the ultrasound image. The backscattered signals were decoded (Eq. 3) and a time delay was imposed on the second backscattered chirp (Fig. 1).

𝑟 1 𝑡 = 𝑒𝑐𝑜 𝐶 1 𝑡 -𝑡 0 , 𝑟 2 𝑡 -𝑡 0 = 𝑒𝑐𝑜 𝐶 2 𝑡 . (3)
Then the backscattered chirp y(t) was computed (Eq. 4).

𝑦 𝑡 = 𝑟 1 𝑡 + 𝑟 2 𝑡 -𝑡 0 , (4)
The former phase is called feed forward phase.

Method

In this section, the automatic optimization of the chirp setting parameters that enabled to optimize the power in the ultrasound image was presented, thanks to the feedback line (dashed line in Fig. 1).

Automatic Optimization Technique

Automatic optimization was based on gradient ascent technique inspired from adaptive filtering. It is an iterative process that tracks the maximum of a cost function J [START_REF] Fletcher | Conjugate Direction Methods[END_REF] being the backscattered power:

𝐽 𝜙 𝑘 = 𝑦 𝑡, 𝜙 𝑘 2 𝑑𝑡, (5)
where 𝜙 𝑘 = 𝑓 𝑘 , 𝛽 𝑘 𝑇 is the vector of the setting parameters to be optimized at the k th iteration, T the transpose, 𝑓 𝑘 the starting frequency, 𝛽 𝑘 the modulation index and 𝑦(𝑡, 𝜙 𝑘 ) the backscattered chirp of inversion decoding. The automatic algorithm was implemented to find the maximum of 𝐽 𝜙 𝑘 at 𝑓 * and 𝛽 * according to the following equation:

𝜙 𝑘 * = 𝑎𝑟𝑔𝑚𝑎𝑥 𝜙 𝐽 𝜙 𝑘 , (6)
The automatic algorithm iteratively generates the optimum value 𝑓 * and 𝛽 * from 𝐽 𝜙 𝑘 . The algorithm was summarized in the following points:

 Three initial values of (f,β) parameters thus far have been predefined. The algorithm launched in the forward stage for the first three iterations k=1,2,3;  The output of chirp inversion processing (i.e. forward process) was fed into the optimization feedback after the third iteration i.e. {k≥ 4};  The cost function was measured as in Eq. ( 5);  The iterative equation (Eq. ( 6)) was then implemented to compute steps proportional to the positive of the gradient of J at the current point. This step was responsible of setting the maximum power that could have been attained. It is equivalent to:

𝜙 𝑘+1 = 𝜙 𝑘 + 𝜇. ∇ 𝜙 𝑘 𝐽 𝜙 𝑘 , (7)
where μ is the speed of convergence of 𝑓 * and 𝛽 * to the optimum value, it was initialized absolutely to 2. The choice of 2 was settled on after testing 0.1 ≤μ≤ 3;

 The gradient was approximated by the discrete gradient (Eq. ( 8)) as there is no analytical expression that describes the variation of the power as a function of the frequency parameters given below:

∇ 𝜙 𝑘 𝐽 𝜙 𝑘 = 𝐽 𝜙 𝑘 -𝐽 𝜙 𝑘-1 𝜙 𝑘 -𝜙 𝑘-1 ; (8)
 The power of 𝑦(𝑡, 𝜙 𝑘 ) converged and (𝑓 * , 𝛽 * ) were automatically obtained.

Gain

The power gain G dB was defined as the ratio of the automatically optimized chirp inversion system (i.e. the block diagram with the feedback stage Fig. 1) to the pulse inversion imaging [START_REF] Simpson | Pulse inversion Doppler: a new method for detecting nonlinear echoes from microbubble contrast agents[END_REF] i.e. for 𝛽 = 0 (as mentioned in subsection 2.1). In pulse inversion the frequency parameters were set to f ref =2.25 MHz and β=0 MHz/s [START_REF] Zaylaa | Empirical Optimization of frequency parameters in chirp inversion imaging[END_REF]. Therefore, the gain G dB was obtained by the following equation:

𝐺 𝑑𝐵 = 10 • 𝑙𝑜𝑔 10 𝐽 𝑓 * ,𝛽 * 𝐽 𝑓 𝑟𝑒𝑓 ,0 . (9)

Simulation Results and Discussion

Simulations were carried out on an ultrasound contrast agent composed of 5 μm-diameter bubbles. A linear chirp of driving pressure 100 kPa with three initial predefined central transmitted frequency 1.5, 3 and 3.5 MHz as proposed in [START_REF] Menigot | Optimization of contrast to tissue ratio by frequency adaptation in pulse inversion imaging[END_REF] and initial second frequency parameter assigned the values 0.2, 0.4 and 0.6 MHz/s were tested using the automatic algorithm. Fig. 2 represented the power image of the backscattered chirp y(t), coded in colors, as a function of f and 𝛽. The chirp parameters f and 𝛽 were ranging between 0.5 and 6.5 MHz and -2 and 2 MHz/s, respectively. The power was computed empirically i.e. point-by-point by (Eq. ( 5)) in logarithmic unit. The power values were associated with colormap jet such that points exhibiting high power were associated a dark red color and those exhibiting lowest power outcomes were associated dark blue color. This power was considered as our cost function.

From Fig. 2, it was obvious that the maximum of the cost function was obtained for 𝛽 different from zero and for f different from f ref . This empirically demonstrated the necessity of using chirp excitations and thus to seeking the optimal value of the two setting parameters 𝛽 and f that maximizes the cost function. Nevertheless, instead of empirically testing all the (f, 𝛽) couples, we desired to achieve this optimally and automatically using a gradient ascent method.

Since the image seemed to be symmetric with respect to the line 𝛽 =0, it was sufficient to merely study the cost function for 𝛽 > 0. So, we have superimposed on Fig. 2 the trajectory of the automatic technique that led to the optimal values. The bold black line elaborated the novel automatic optimization path and the circles indicated the number of iterations that was 7, after which the algorithm converged to the optimum setting parameters. Note that f ref denotes the frequency value of the reference method, which is pulse inversion as mentioned in section 1.

Fig. 3 represented the variation of the power of the backscattered chirp y(t) as a function of the number of iterations for chirps of driving pressure 100 kPa. In the first iteration, the power of chirp was -32.1 logarithmic power units, then as the number of iterations increased the power increased gradually, then decreased at the fourth iteration. Afterwards it increased until it reached its maximum of -30.8 logarithmic power units at the seventh iteration and attained a plateau until the fiftieth iteration. This variation in the power values proves the sensitivity of the cost function J to the choice of (f, 𝛽) couples. Note that the power obtained by pulse inversion was illustrated by the horizontal dashed line (Fig. 3) and the power difference was approximately 5 dB. Fig. 4 manifested the automatic optimization of f as a function of the number of iterations. The optimum value of the first setting parameter was attained at the point of convergence of the power i.e. at the seventh iteration. The algorithm converged to 3.1 MHz. This implied that the optimal transmitted frequency was 3.1 MHz and was different from the reference frequency f ref =2.25 MHz in pulse inversion. The optimal frequency was 0.1 MHz above the central frequency of the transducer and 0.85 MHz above the reference frequency 2.25 MHz in pulse inversion, [START_REF] Menigot | Optimization of contrast to tissue ratio by frequency adaptation in pulse inversion imaging[END_REF], regardless of the initial driving pressure level A 0 . Fig. 5 exhibited the variation of the second frequency chirp setting parameter 𝛽 as a function of the number of iterations. The optimum value was 0.1 MHz/s, selected after the seventh iteration where the power converged to its maximum value. Table 1 represented the optimal setting parameters in automatic chirp inversion in addition to the gain (Eq.( 9)). The novel automatic technique of chirp inversion achieved a gain of 5 dB as compared to the existing pulse inversion technique.

To sum up, chirp's frequency setting parameters, transmitted frequency f and frequency modulation index β, were optimized and thought to improve the backscattered power. Results showed that the proposed

Setting Parameters

Gain (dB)

𝑓 * (MHz) 𝛽 * (MHz/s) 5

3.1 0.1 -optimization method does not require apriori knowledge of the microbubble, since it requires merely the cost-function. Simulations revealed that optimization feedback in chirp inversion was crucial. A 5 dB gain was achieved by the automatic feedback as compared to pulse inversion where (𝛽 = 0). The speed of convergence of the algorithm was appreciated such that it was attained in 7 iterations knowing that there were 3 measurements required per iteration. If the cost function was neither convex nor concave, the initial conditions of the frequency parameters should be carefully chosen. This could be fulfilled by testing various points to meet the demand. Otherwise, additional optimization technique capable of selecting the proper initial conditions should be considered.

The major practical advantage of the proposed technique is that, neither the technician nor clinician is required to tune his transducer to any frequency value. Indeed, the technique will automatically adapt itself and select the optimum setting parameters that maximize the backscattered power from the patient. The enhancement of the resolution and SNR guaranteed by the use of chirp excitations was associated with iterative power increase; this might improve the CTR of contrast ultrasound images during the whole examination even if different kinds of variations occurred.

Conclusion

Chirp Inversion in ultrasound contrast imaging accompanied by automatic optimization technique enhances the backscattered power. Since the technique is not limited to linear chirps, other chirp types could be investigated. However, experimental verification of the simulation is needed.

Fig. 1

 1 Fig. 1 Block diagram of chirp inversion in ultrasound contrast imaging.

Fig. 2

 2 Fig. 2 The backscattered power (coded in colors) of the linear chirp y(t) of driving pressure 100 kPa as a function of f and 𝜷 with the automatic optimization trace.

Fig. 3

 3 Fig. 3 Automatic optimization of the backscattered power of chirp y(t) with initial driving pressure 100 kPa.

Fig. 4 Fig. 5

 45 Fig. 4 Automatic optimization of the first chirp parameter f for initial driving pressure 100 kPa.

Table . 1 Automatic optimization setting parameters and gain.

 .

Acknowledgements

The authors are grateful to the National Council for Scientific Research in Lebanon, Lebanese University and Imaging and Brain Laboratory INSERM U930, Université François Rabelais de Tours in France for supporting this work.


Abstract-In utero, Monitoring of fetal wellbeing or suffering is today an open challenge, due to the high number of clinical parameters to be considered. An automatic monitoring of fetal activity, dedicated for quantifying fetal wellbeing, becomes necessary. For this purpose and in a view to supply an alternative for the Manning test, we used an ultrasound multitransducer muligate Doppler system. One important issue (and first step in our investigation) is the accurate estimation of fetal heart rate (FHR). An estimation of the FHR is obtained by evaluating the autocorrelation function of the Doppler signals for ills and healthiness foetus. However, this estimator is not enough robust since about 20% of FHR are not detected in comparison to a reference system. These non detections are principally due to the fact that the Doppler signal generated by the fetal moving is strongly disturbed by the presence of others several Doppler sources (mother' s moving, pseudo breathing, etc.). By modifying the existing method (autocorrelation method) and by proposing new time and frequency estimators used in the audio' s domain, we reduce to 5% the probability of non-detection of the fetal heart rate. These results are really encouraging and they enable us to plan the use of automatic classification techniques in order to discriminate between healthy and in suffering foetus.

Keywords-fetal monitoring, fetal heart rate, Doppler

I. INTRODUCTION

T HE present paper proposes two algorithms for com- puting the fetal heart rate. Section II shortly presents our system developed in a view of realizing this task. Having multiple Doppler signals, the problem of estimating the fetal heart rate reduces to two separate problems. Section III.A proposes an algorithm for solving the first problem that is to find correctly the FHR on each Doppler signal, which is not always easy because of the complex nature of signals. For the second problem, two algorithms for fusioning multiple estimates are presented in section III.B. The experimental results together with our conclusion are reported in section IV. Finaly, in the last section we shortly discuss some future trends in our project.

II. EQUIPEMENT

As we can see in figure 1, our Doppler system (the Actifoetus system) contains three groups of four ultrasound transducers each, with sensors working at five depths between 1.88 cm and 15 cm. One group is used for lower members, another one for upper members while the third group is for detecting the FHR. The caracteristics of transducers used in detection of FHR are: bandpass 2.2 MHz -

The authors work at 1 Université François Rabelais de Tours, Inserm U930 -CNRS FRE 2448, Tours, France. E-mail: jeanmarc.girault@univ-tours.fr, iulian.voicu@etu.univ-tours.fr.

III. FETAL HEART RATE ESTIMATION A. SLIDING WINDOW ALGORITHM

The first problem that we solve is to estimate the FHR for a given Doppler signal at some depth. For this, we split up the Doppler signal in two directional signals. This task consists in distinguish between the positives and negatives frequencies. We achieve this separation operation by filtering the Doppler signal with an analytic passband filter and it conjugate. An analytic filter eliminates the negative frequencies while the conjugate filter do the same thing for the positives frequencies. It remains only to take the absolute value of filtered signals to obtain the "positives amplitudes" for the signals that get close to the sensor, respective "negative amplitudes" for the signals that move away. Next step is to filter the "positives amplitudes" and "negatives amplitudes" at 4 Hz. This frequency is set to respect the maximum physiological heart rate (as is reported in [START_REF] Jezewski | Horoba -Extraction of Fetal Heart-Rate Signal as the Time Event Series From Evenly Sam-Fig. 6. Autocorrelation I 1 : 19-SAB-CA: Sensor 2, Depth 3: a) W=4s, no overlapping; b) W=2s, overlapping of 250ms Fig. 7. Patient 19-SAB-CA: a) Reference SONICAID; b) Algorithm 1, W=4s with no overlapping; c) Algorithm 1, W=2s with overlapping step of 250ms; d) Algorithm 2, W=2s with overlapping step of 250ms pled Data Acquired Using Doppler Ultrasound Technique[END_REF] of a foetus it's 240 beats/minute).

The cardiac rhythm will be estimated from peaks of functions which enhance some patterns in the signal. These functions, autocorrelation (1), crosscorrelation (2), correlation coefficient (3) and YIN estimator (4) [START_REF] Cheveigne | a Fundamental Frequency Estimator for Speech and Music[END_REF] are widely used in voice signal processing domain. We mention that in case of YIN estimator we look for minimums of the function and not for the maximums. Below we note these functions with I i , i=1,...,4 and we present their expressions:

I 1 (t, k) = 1 W W -|k|-1 n=1 x(t, n) • x(t, n + k) (1)
I 2 (t, k) = 1 W W n=1 x(t, n) • x(t, n + k) (2)
I 3 (t, k) = W n=1 x(t, n) • x(t, n + k) W n=1 x(t, n) • x(t, n) (3)
I 4 (t, k) =    1, if k = 0 d(t, k)/ 1 k k j=1 d(t, j) d(t, k) = W n=1 (x(t, n) -x(t, n + k)) 2 (4)
Here, we noted with W the size of slidding window, t the time at witch we compute the function and k the lag. First step is to find the positions of maximums or minimums M n , n = 0, ..., N -1, of the used function I i , with N the number of extrema. Having M n , we compute the time distances D n = M n -M n-1 between positions of two consecutives maximums where n = 1, ..., N -1. Further, we will label with

∆ n = |D n -D n-1 |, n = 1, .
.., N -1 the absolute difference of two consecutives distances and with ∆={∆ 1 , ..., ∆ n } the vector of differences. For a true fetal cardiac rhythm it is necessary that ∆ vector be lower than a threshold value. We note the threshold value (in beats/minute). The threshold establishs the time interval where we expect a new maximum value of the function. If all the ∆ vector's values are lower than , the fetal cardiac rhythm is considered as the average value of D, while in the other case is decided a non-detection decision of the fetal cardiac rhythm. Figure 2 illustrates the calcul of vector ∆. For the autocorrelation function of a synthetic signal of 2048 samples we have found position's maximums M 0 ,...,M 5 and the distances D 1 ,...,D 5 . If the threshold condition is satisfied then the cardiac rhythm is the average of D 1 ,...,D 5 , else we decide that there is no cardiac fetal rhythm. We tested the same algorithm for each defition ( 1)-( 4) and for several patients. An example of FHR computed for a patient coded 19-SAB-CA and for all techniques is presented in the figure 3. Autocorrelation in the upper left corner of the figure, crosscorrelation in the lower left corner, correlation coefficient in the upper right corner and YIN estimator in the lower left corner are presented. Our calculus show that the technique which gives the best trade-off in terms of precision and computation is the autocorrelation function. It performs better than the other techniques I 2 , I 3 , I 4 , and it gives more estimations of FHR on the Doppler signal at a given depth and a given sensor. This is a major advantage comparing with the others techniques. Also, another advantage of the autocorrelation technique is the fewer number of operations used. We also point out that the inconvenience for the same autocorrelation technique

B. FUSION FETAL HEART RATES ALGORITHM

Applying the algorithm described in previous section to all received Doppler signals leads to multiple estimates of the same physiological parameter, the FHR. The questions that we adresse at this point is how to choose the best estimate through all estimates? For solving this problem, we propose two algorithms. First of them is based on the maximum of the autocorrelation function and on the detection probability, while the second is based on the statistical properties of the FHR on each channel and on the final fusioned FHR.

B.1 ALGORITHM 1

The first algorithm that we tested takes into account the value of autocorrelation function utilized in the analyse of Doppler signals. The reasons of choosing this function have been ennumerated in the previous section. As we can see in the figure 4 the algorithm supposes a temporal window during the analyze is made. We note this window with t 0 ,...,t n . Also, the Doppler signals are labeled S i D j , with S from sensor, D for depth, i=1,...,4 and j=2,...,5. The fact that j is starting from 2 means that we ignored the first depth of exploration where a high probability of untrusted value of fetal cardiac rhythm was observed. Assume now that for a given instant t n+1 we apply the algorithm described in previous section. This leads to 16 estimations of the fetal heart rate if we consider only the "positives amplitudes" or 32 estimates if we analyse the "positive" and "negatives amplitudes" in the same time. We selected the second posibility. A vector with all estimations is formed. It is clear that through the 32 cases we might be decided that for some Doppler signals S i D j no cardiac rhythm exists, and thus the first step in our algorithm is to search the Doppler signals where we have found a cardiac FHR estimation. For sensors and depths where an estimation is available, we sorted in descending order of the values of I 1 (t n+1 , S i , D j ). If an equal value of I 1 (t n+1 , S i , D j ) is detected on several signals, then the final FHR is chosen as the heart rate estimated on the signal with the highest detection probability in the analysing window, F HR(t n+1 ) = argmax(I 1 (t n+1 , S i , D j ), Ω(t n , S i , D j )).

The detection probability is computed at each instant time, for every Doppler signal, as the ratio between the number of the valid estimation heart rates and the total number of intervals analysed inside the time window. For example, suppose that for signal S 1 D 2 we found 5 valid estimation in our time window t 0 ,. . . ,t n . The total number of estimations is n+1. The detection probability for the Doppler signal S 1 D 2 is 5/n+1, with n obviously bigger than 4. After we chosen fetal heart rate at time t n+1 , F HR(t n+1 ), the last step in our algorithm consists in updating the detection probabilities. The updating procedure of detection probability is performed in the time window t 1 ,. . . ,t n+1 . We will compute the detection probability after validation of heart rates detected on each signal at time t n+1 . The validation step consists in eliminating those heart rates that are outside of the interval |FHR(t n+1 ) -FHR(t n+1 ,S i ,D j )| < . The procedure is expressed by:

         if |F HR(t n+1 ) -F HR(t n+1 , S i , D j )| > F HR(t n+1 , S i , D j ) = N aN else F HR(t n+1 , S i , D j ) = F HR(t n+1 , S i , D j ) B.2 ALGORITHM 2
As we have mentioned, the second algorithm is based on the statistics properties of the FHR on each Doppler signal and on the statistics of fusioned final FHR. In figure 5 we present the principle of this algorithm. Suppose that our analyse is made in the same temporal in- terval t 0 ,. . . ,t n . We made the same notation S i D j regarding the Doppler signals and FHR for the final fusioned FHR. With the values of FHR computed at moments t 0 ,. . . ,t n , we make a statistic for every Doppler signal. This statistic is available at time instant t n+1 . Thus, for every Doppler signal S i D j we have at t n+1 a mean µ(t n , S i , D j ) and a variance σ 2 (t n , S i , D j ), that depend on the values at t 0 ,. . . ,t n . Also, at t n+1 we have a mean µ F HR (t n , S i , D j ) and a variance σ 2 F HR (t n , S i , D j ) corresponding to final fusioned FHR. The first step in our algorithm is to find the number P (t n+1 ) of the Doppler signals where the FHR estimation verifies their statistic in the same time with the statistic of final cardiac rhythm. For example the value of FHR at time instant

t n+1 on S 1 D 2 , which is F HR(t n+1 , S 1 , D 2 ), should be inside of the two intervals [µ(t n , S 1 , D 2 ) -3σ 2 (t n , S 1 , D 2 ), µ(t n , S 1 , D 2 ) + 3σ 2 (t n , S 1 , D 2 )], and [µ F HR (t n ) -3σ 2 F HR (t n ), µ F HR (t n ) + 3σ 2 F HR (t n )].
If this is true then we increase P (t n+1 ), if not, we simply ignore this Doppler signal and its estimate. After we identified the signals, the step two of the algorithm consists in finding the weigths used in the linear combination [START_REF] Gelb | Applied Optimal Estimation[END_REF], that gives the fusion FHR at time t n+1 . The weights k p (t n+1 , S i , D j ) satisfy the folowing relation:

         P (tn+1) p=1 k p (t n+1 , S i , D j ) = 1 k p (t n+1 , S i , D j ) = 1 σ 2
p (tn,Si,Dj )

P (t n+1 ) p=1 1 σ 2 p (tn,S i ,D j ) F HR(t n+1 ) = P (tn+1) p=1 k p (t n+1 , S i , D j )F HR(t n+1 , S i , D j )
(5) The third step is to find the fusioned FHR at time t n+1 . This is done by the equation just above. Having the value of the fusioned FHR at t n+1 , we must only update the time interval analyse and the statistics. For doing this, we drop out the value of FHR at t 0 and we count the value of FHR at t n+1 . Thus, we compute a new mean and variance with the values for time interval t 1 ,. . . ,t n+1 . This is true both for Doppler signals and for final fusioned FHR.

IV. EXPERIMENTAL RESULTS

In a first time we point out the influence of size W, and the overlapping step, in detection of FHR. Figure 6 presents the results obtained using I 1 for W=4s with no overlapping and W=2s with an overlapping step of 250ms for the same Doppler signal. The overlapping value was chosen to detect the heart rates of 60 beats/min [START_REF] Jezewski | Horoba -Extraction of Fetal Heart-Rate Signal as the Time Event Series From Evenly Sam-Fig. 6. Autocorrelation I 1 : 19-SAB-CA: Sensor 2, Depth 3: a) W=4s, no overlapping; b) W=2s, overlapping of 250ms Fig. 7. Patient 19-SAB-CA: a) Reference SONICAID; b) Algorithm 1, W=4s with no overlapping; c) Algorithm 1, W=2s with overlapping step of 250ms; d) Algorithm 2, W=2s with overlapping step of 250ms pled Data Acquired Using Doppler Ultrasound Technique[END_REF]. We found that an optimum value for W, is around of 2 seconds. In [START_REF] Jezewski | Horoba -Extraction of Fetal Heart-Rate Signal as the Time Event Series From Evenly Sam-Fig. 6. Autocorrelation I 1 : 19-SAB-CA: Sensor 2, Depth 3: a) W=4s, no overlapping; b) W=2s, overlapping of 250ms Fig. 7. Patient 19-SAB-CA: a) Reference SONICAID; b) Algorithm 1, W=4s with no overlapping; c) Algorithm 1, W=2s with overlapping step of 250ms; d) Algorithm 2, W=2s with overlapping step of 250ms pled Data Acquired Using Doppler Ultrasound Technique[END_REF] an adaptive method of selecting W is proposed as being 3-4 times the value of last beat to beat interval. Knowing that for normal foetus the heart rate is between 110 beats/min. -160 beats/min, which corresponds in time domain to the interval 545ms -375ms, our choise is closely to what we have found in the literature. Because the adaptive method of setting W value seems to be unclear when the rhythm is lost, we decided to keep W constant.

Another interesting point was to test which method (1)-( 4) estime better the FHR on a given signal. This discusion was made in section A.1, where the results for all methods were shown in figure 3. We remarked the superiority of autocorrelation technique, both from a detection and real time computation point of view. Autocorrelation, is the best trade-off in terms of probability detection, false detection and speed computation.

Further investigation was to determine precisely how the algorithms work. We found that in case of high W values (like 4 seconds), generaly we have a poor detection probability, specifically in accelerations and decelerations moments. This is true even when we are using or not an overlapping step. In this case our monitoring is not a sure one, and for some examens, the time for which we lost the rhythm is important. We reduced the time of non detections to a smaller period than the period of a reference system, using a smaller value for W in the same time with an overlapping step. We can observe this in figure 7.c, d comparing with figure 7.b, where we used the first algorithm based on amplitude of autocorrelation function. By comparing the two algorithms between them, we found that for the same parameters W and overlapping step, see figures 7.c and 7.d, the second algorithm estime better the fetal heart rate. The comparation was made in a subjective way, because it is impossible to access to numerical values of our reference.

V. PERSPECTIVES

Future investigations will be made in estimating the FHR using the algorithms that implies a prediction for the next time t n+1 of FHR. Algorithms which use Kalman filtering [START_REF] Ebrahim | Bar-Kana -A Robust Sensor Fuion Method for Heart Rate Estimation[END_REF]- [START_REF] Tarassenko | Combining Measurements from Different Sensors[END_REF], are reported. The problem of interest in these algorithms is to see until which point we are able to make such a prediction of FHR in terms of overlapping. Another point of interest is to develop fusion algorithms that find the final heart rate starting from groups of signals. The reason for doing this, is to eliminate the corrupted signals or the false estimates of the FHR. A final task, will be to use the information given by the others sensors focalized on lower and upper members, helping in this way to decide if the lost of FHR is caused by a foetus moving.

Robust

  Estimation of Fetal Heart Rate from US Doppler Signals I. Voicu 1 , J.-M. Girault 1 , C. Roussel 2 , A. Decock 2 , D. Kouamé 3 ,

Fig. 1 .

 1 Fig. 1. The Actifoetus System

Fig. 2 .

 2 Fig. 2. Exemple of FHR computation

Fig. 3 .

 3 Fig. 3. Patient 19-SAB-CA. Fetal heart rate detection on the Doppler signal acquired with Sensor 2 at Depth 3 with: a) upperright corner: Autocorrelation function I 1 ; b) lower-right corner: Crosscorrelation I 2 ; c) upper-left corner: Correlation coefficient, I 3 ; d) lower-left corner: YIN estimator

Fig. 4 .

 4 Fig. 4. Principle of algorithm 1: The fetal heart rate at time instant t n+1 is function of the value of the autocorrelation function I 1 (t n+1 , S i , D j ) and of detection probability Ω(tn, S i , D j )

Fig. 5 .

 5 Fig. 5. Principle of algorithm 2: The fetal heart rate at time instant t n+1 is function of the statistics properties on each Doppler signal µ(tn, S i , D j ), σ 2 (tn, S i , D j ) and of statistic properties of final fusioned fetal heart rate µ F HR (tn, S i , D j ), σ 2 F HR (tn, S i , D j )