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The present study examined whether the ventilatory thresholds during an incremental exhaustive running test could be determined using heart rate variability (HRV) analysis. Beat-to-beat RR interval, V(.-)O (2), V(.-)CO (2) and V(.-) (E) of twelve professional soccer players were collected during an incremental test performed on a track until exhaustion. The "smoothed pseudo Wigner-Ville distribution" (SPWVD) time-frequency analysis method was applied to the RR time series to compute the usual HRV components vs. running speed stages. The ventilatory equivalent method was used to assess the ventilatory thresholds (VT1 and VT2) from respiratory components. In addition, ventilatory thresholds were assessed from the instantaneous components of respiratory sinus arrhythmia (RSA) by two different methods: 1) from the high frequency peak of HRV ( FHF), and 2) from the product of the spectral power contained within the high frequency band (0.15 Hz to fmax) by FHF (HF x FHF) giving two thresholds: HFT1 and HFT2. Since the relationship between FHF and running speed was linear for all subjects, the VTs could not be determined from FHF. No significant differences were found between respective running speeds at VT1 vs. HFT1 (9.83 +/- 1.12 vs. 10.08 +/- 1.29 km x h (-1), n.s.) nor between the respective running speeds at VT2 vs. HFT2 (12.55 +/- 1.31 vs. 12.58 +/- 1.33 km x h (-1), n.s.). Linear regression analysis showed a strong correlation between VT1 vs. HFT1 (R (2) = 0.94, p < 0.001) and VT2 vs. HFT2 (R (2) = 0.96, p < 0.001). The Bland-Altman plot analysis reveals that the assessment from RSA gives an accurate estimation of the VTs, with HF x FHF providing a reliable index for the ventilatory thresholds detection. This study has shown that VTs could be assessed during an incremental running test performed on a track using a simple beat-to-beat heart rate monitor, which is less expensive and complex than the classical respiratory measurement devices.

International audience; A differential model of a cardiac pacemaker cell with only ten state variables is proposed. It is intended for 0D or 3D simulation of the heart under the vagal control of the autonomous nervous system. Three variables are used to describe the membrane (membrane potential and two gate variables of ionic channels), taking into account the dynamics of the main ionic currents (inward sodium, L-type calcium and outward potassium), Na+/Ca2+ exchangers and Na+/K+ pumps. The remaining seven variables are associated with the fluid compartment model that includes Ca2+ binding by myoplasmic proteins, and the intracellular concentrations of free Calcium, Sodium and Potassium. Despite its moderate number of state variables, this model includes the main processes thought to be important in pacemaking on the cell scale and predicts the experimentally observed ionic concentration of calcium, sodium and potassium, action potential and membrane currents. The control by the calcium of the pacemaking activity is also considered.

This article presents a new method for analyzing arterial blood pressure waves. The technique is based on the scattering transform and consists in solving the spectral problem associated to a one-dimensional Schrödinger operator with a potential depending linearly upon the pressure. This potential is then expressed with the discrete spectrum which includes negative eigenvalues and corresponds to the interacting components of an N-soliton. The approach is analogous to the Fourier transform where the solitons play the role of sinus and cosinus components. The proposed method seems to have interesting clinical applications. It can be used for example to separate the fast and slow parts of the blood pressure that correspond to the systolic (pulse transit time) and diastolic phases (low velocity flow) respectively.

International audience; In this paper, a bifurcation analysis of a recently proposed reduced order cardiac cell model is performed to obtain insights into the mechanisms of control of the sinoatrial node pacemaker activity. The objective is to improve the understanding of cardiac arrhythmias caused by abnormal automaticity. The bifurcation structure of the model is studied as a function of the maximal conductances of six sarcolemmal currents: the sodium, calcium, background calcium and potassium currents, the sodium potassium pump and the sodium calcium exchanger. All these parameters, except for the sodium current, allow when varied the annihilation of the physiological rhythmic activity through Hopf bifurcation points. The background calcium current seems to be the current responsible for cycle length sensitivity in the physiological zone and then it appears as the main control input of the pacemaker activity.

"Arterial blood pressure analysis based on scattering transform I" introduces a new method based on the scattering transform for a one dimensional Schrödinger equation to reconstruct the arterial blood pressure waves and separate its systolic and diastolic parts. In this article, we propose to analyse the parameters computed from this technique in different clinical and physiological conditions. Two cases are considered: moderate chronic heart failure and high fit triathletes. The variability of these new parameters is compared to the variability of classical blood pressure parameters. Promising results are obtained.

This article presents a new travelling waves analysis and identification method based on scattering theory. This inverse scattering technique consists in solving the spectral problem associated to a one-dimensional Schrodinger operator perturbed by a potential depending upon the wave to analyze, and optimized in order to approximate this wave by an isospectral flow in the sense of Lax. In this method, the interacting components of an N-soliton are the elementary travelling waves for the approximation. These N solitons play an analogous role to linear superpositions of sinus and cosinus in the Fourier analysis of standing waves. In the proposed analysis of travelling waves, low and high frequency components are replaced by low and high velocity components. Two applications of the method are presented. The first one concerns the identification of an N-soliton and is illustrated with N = 3. The second one consists in the analysis of the arterial blood pressure waves during the systolic phase (pulse transit time) and the diastolic phase (low velocity flow).

A new method for analyzing arterial blood pressure is presented in this article. The technique is based on the scattering transform and consists in solving the spectral problem associated to a one-dimensional Schrödinger operator with a potential depending linearly upon the pressure. This potential is then expressed with the discrete spectrum which includes negative eigenvalues and corresponds to the interacting components of an N-soliton. The approach is similar to a nonlinear Fourier transform where the solitons play the role of sine and cosine components. The method provides new cardiovascular indices that seem to have meaningful physiological information, especially about the stroke volume and the ventricular contractility. We first show how to reconstruct the arterial blood pressure waves and separate its systolic and diastolic phases using this approach. Then we analyse the parameters computed from this technique in two physiological conditions, the head-up 60 degrees tilt test and the isometric handgrip test, widely used for studying short term cardiovascular control. Promising results are obtained.

International audience; A simplified model of arterial blood pressure intended for use in model-based signal processing applications is presented. The main idea is to decompose the pressure into two components: a travelling wave describes the fast propagation phenomena predominating during the systolic phase and a windkessel flow represents the slow phenomena during the diastolic phase. Instead of decomposing the blood pressure pulse into a linear superposition of forward and backward harmonic waves, as in the linear wave theory, a nonlinear superposition of travelling waves matched to a reduced physical model of the pressure, is proposed. Very satisfactory experimental results are obtained by using forward waves, the N- soliton solutions of a Korteweg-de Vries equation in conjunction with a two-element windkessel model. The parameter identifiability in the practically important 3- soliton case is also studied. The proposed approach is briefly compared with the linear one and its possible clinical relevance is discussed.

A reduced order differential model of cardiac Purkinje fibres action potential, with only eight state variables, is presented. Its structure, derived from basic physical principles can be used for the main other cardiac cell types, a useful property for some model-based signal or image processing applications. The electrical activity of cardiac Purkinje fibres is reconstructed using particular values of the parameters. This model of the membrane excitation mechanism and intracellular calcium dynamics describes the principal ionic current underlying autorhythmicity; calcium uptake and release from the sarcoplasmic reticulum; effects of the binding of calcium on myoplasmic proteins which affect the Nernst potential of calcium, and then the membrane potential. The model allows realistic modelling of cardiac Purkinje fibres action potential, total ionic current, CICR dependence on intracellular calcium concentrations. Simulations illustrate the role of the inward sodium current as the dominant mechanism underlying pacemaker depolarization during spontaneous activity.

In this work, we propose to use parametric models for the estimation of arterial tree input impedance. The results of this new method are compared with those of the standard method based on the Fast Fourier Transform (FFT). The comparison is first made with pressure and flow measurements on a calf, then with human blood pressure measurements completed by blood flow data simulated from a soliton+windkessel model. The input impedance is calculated both at aorta and finger. As illustrated by the numerical results, the advantage of the proposed parametric method is its smooth impedance estimations, whereas the standard FFT method yields more disturbed results.

International audience; Future generations of mobile phones, including advanced video and digital communication layers, represent a great challenge in terms of real-time embedded systems. Programmable multicomponent architectures can provide suitable target solutions combining flexibility and computation power. The aim of our work is to develop a fast and automatic prototyping methodology dedicated to signal processing application implementation on parallel heterogeneous architectures, two major features required by future systems. This paper presents the whole methodology based on the SynDEx CAD tool, that directly generates a distributed implementation onto various platforms from a high level application description, taking real-time aspects into account. It illustrates the methodology in the context of real-time distributed executives for multi-layer applications based on an MPEG-4 video codec and a UMTS telecommunication link. FPGA - UMTS - MPEG-4

During each ovarian cycle, only a definite number of follicles ovulate, while the others undergo a degeneration process called atresia. We have designed a multi-scale mathematical model where ovulation and atresia result from a hormonal controlled selection process. A 2D-conservation law describes the age and maturity structuration of the follicular cell population. In this paper, we focus on the operating mode of the control, through the study of the characteristics of the conservation law. We describe in particular the set of microscopic initial conditions leading to the macroscopic phenomenon of either ovulation or atresia, in the framework of backwards reachable sets theory.

http://dx.doi.org/10.1007/11730637_16; Recent advances of experimental techniques in biology have led to the production of enormous amounts of data on the dynamics of genetic regulatory networks. In this paper, we present an approach for the identification of PieceWise-Affine (PWA) models of genetic regulatory networks from experimental data, focusing on the reconstruction of switching thresholds associated with regulatory interactions. In particular, our method takes into account geometric constraints specific to models of genetic regulatory networks. We show the feasibility of our approach by the reconstruction of switching thresholds in a PWA model of the carbon starvation response in the bacterium Escherichia coli.

{\it Computers \& Structures}, in press; We describe an approach that we propose to model the electromechanical behavior of the heart, and to use the model in a data assimilation procedure in order to perform an identification of the parameters and state. The modeling of the heart tissue is based on an electrically-activated contraction law formulated via multiscale considerations and is consistent with various physiological and thermomechanical key requirements. The global heart system also incorporates a simplified lumped modeling of the blood compartments. We report on numerical simulations and on validations of our model in reference and pathological conditions. Furthermore, the data assimilation procedure is intended to give access to quantities of interest for diagnosis purposes, and we present some promising results in this direction.

Recent advances of experimental techniques in biology have led to the production of enormous amounts of data on the dynamics of genetic regulatory networks. In this paper, we present an approach for the identification of PieceWise-Affine (PWA) models of genetic regulatory networks from experimental data, focusing on the reconstruction of switching thresholds associated with regulatory interactions. In particular, our method takes into account geometric constraints specific to models of genetic regulatory networks. We show the feasibility of our approach by the reconstruction of switching thresholds in a PWA model of the carbon starvation response in the bacterium Escherichia coli.

International audience; A particle filter based method for nonlinear system fault detection and isolation is proposed in this paper. It is applicable to quite general stochastic nonlinear dynamic systems in discrete time. The main result consists of a new particle filter algorithm, derived from the basic bootstrap particle filter, and capable of rejecting a subset of the faults possibly affecting the considered system. Fault isolation is then achieved by the evaluation of the estimated likelihoods related to the designed filters.

De nos jours, le concept de tension artérielle, qui fait référence à la pression artérielle (PA), devient de plus en plus familier et intègre le langage courant. Ceci est dû à l'incidence de la mortalité due aux maladies cardio-vasculaires et en raison du rôle fondamental que joue la PA dans l'appareil circulatoire. L'intérêt porté à la PA a mobilisé depuis des décennies la communauté scientifique qui tente d'élaborer un modèle mathématique permettant de comprendre le fonctionnement du système cardio-vasculaire (SCV), aussi bien dans le cas sain que pathologique. Ce type de modélisation rentre dans le cadre de la modélisation des systèmes vivants qui constitue l'un des plus grands défis de la science du 21ième siècle et fait partie des principaux objectifs de l'INRIA (Institut National de Recherche en Informatique et en Automatique) pour les quatre prochaines années. En plus des spécialistes du domaine, celle-ci nécessite l'implication de chercheurs en automatique, en traitement de l'information et en mathématiques appliquées. Le SCV constitue l'un des systèmes vivants les plus fascinants, mais aussi l'un des plus complexes, rendant sa modélisation très difficile. Bien que la littérature abonde de travaux sur la modélisation de la circulation sanguine, il est possible de distinguer deux approches : les modèles différentiels et les modèles à paramètres distribués. Les premiers, incluant les célèbres modèles Windkessel, reposent sur une analogie avec les circuits électriques. Ils ne comportent pas de dimension spatiale. Ils permettent une bonne compréhension du comportement global du SCV, mais n'expliquent pas tous les phénomènes mis en jeu. Les modèles à paramètres distribués, quant à eux, font appel aux principes de l'écoulement des fluides. Ils sont plus précis mais bien plus complexes, particulièrement en dimension 3. La variabilité de la PA est un phénomène déterminé par de nombreux facteurs physiologiques, physiopathologiques et environnementaux . On distingue principalement la variabilité à long terme qui décrit les variations sur 24 heures et plus (variation saisonnière), et celle à court terme englobant des fluctuations à périodicité brève allant de quelques secondes à quelques minutes. Cette dernière ne peut être étudiée que par des enregistrements continus de la PA, battement par battement, qui font appel à des techniques invasives, intra-artérielles, potentiellement dangereuses pour le patient, qui ne sont utilisables que dans des cas très particuliers et pas en clinique de routine. Il existe cependant un type d'appareil qui permet la mesure non invasive de la PA continue, au niveau du doigt. Le FINAPRES en est un exemple. Il serait alors intéressant de songer à élaborer des méthodes qui permettraient de reconstruire la pression au niveau central à partir de la pression périphérique. Dans cette perspective, différents travaux ont été effectués : les méthodes proposées utilisent généralement la notion de fonction de transfert entre la pression proximale et la pression distale, mais sont délicates à mettre en oeuvre. Le travail présenté, dans le cadre de ce stage de Master-2 Recherche, consiste à étudier un modèle de PA qui prenne en compte aussi bien la phase systolique que la phase diastolique. Ce modèle devrait permettre de remonter au coeur à l'aide d'une mesure non invasive et présenterait des caractéristiques intéressantes permettant d'envisager des applications en clinique, notamment pour le diagnostic. Nous nous intéresserons particulièrement au problème de l'identifiabilité des paramètres de ce modèle et de sa validation.

This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure of these measures becomes discernible. The value of this scale is obtained through what we call the growth speed in H\"older singularity sets of a Borel measure. This growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically self-similar measures. Our results are useful to understand the multifractal nature of various heterogeneous jump processes.

Let $\{x\_n\}\_{n\geq 0}$ be a sequence of $[0,1]^d$, $\{\lambda\_n\} \_{n\geq 0}$ a sequence of positive real numbers converging to 0, and $\delta>1$. Let $\mu$ be a positive Borel measure on $[0,1]^d$, $\rho\in (0,1]$ and $\alpha>0$. Consider the limsup-set \[S\_{\mu}(\rho,\delta,\alpha)= \bigcap\_{N\in \mathbb{N}} \bigcup \_{n\geq N: \mu(B(x\_n,\lambda^\rho\_n)) \sim \lambda\_n^{\rho\alpha}} B(x\_n,\lambda\_n^\delta).\] We show that, under suitable assumptions on the measure $\mu$, the Hausdorff dimension of the sets $S\_{\mu}(\rho,\delta,\alpha)$ can be computed. When $\rho

We evaluate the scale at which the multifractal structure of some random Gibbs measures becomes discernible. The value of this scale is obtained through what we call the growth speed in H\"older singularity sets of a Borel measure. This growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically self-similar Gibbs measures. Our results are useful to understand the multifractal nature of various heterogeneous jump processes.

We study in this report the $H_\infty$-stabilizing properties of PI controllers for particular SISO delay systems of three classes : dead-time systems as well as retarded or neutral systems. For a subclass of neutral systems, this enables us to deduce a parametrization of all $H_\infty$-stabilizing controllers.

An extension to the LuGre dynamic friction model from longitudinal to longitudinal/lateral motion is developed in this paper. Application of this model to a tire yields a pair of partial differential equations that model the tire-road contact forces and aligning moment. A comparison of the steady-state behavior of the dynamic model with existing static tire friction models is presented. This comparison allows one to determine realistic values of the parameters for the new dynamic model. By the introduction of a set of mean states we reduce the partial differential equation to a lumped model governed by a set of three ordinary differential equations. Such a lumped form describes the aggregate effect of the friction forces and moments and it can be useful for control design and on-line estimation. A method to incorporate wheel rim rotation is also discussed. The proposed model is evaluated by comparing both its steady-state as well as its dynamic characteristics via a series of numerical simulations. The results of the simulations corroborate steady-state and dynamic/transient tire characteristics found in the literature.

Computer-aided analysis of electrocardiogram (ECG) is widely used in cardiac disease diagnosis. The purpose of this paper is to propose a new algorithm for T-wave end location, which is known to be the most difficult one among ECG wave form detection and location problems. The proposed algorithm mainly consists of the computation of an indicator related to the area covered by the T-wave curve and delimited in a special manner. Based on simple assumptions, essentially on the concavity of the T-wave form, it is formally proved that the maximum of the computed indicator inside each cardiac cycle coincides with the T-wave end. Moreover, the algorithm is robust to measurement noise, to wave form morphological variations and to baseline wander. It is also computationally very simple: the main computation can be implemented as a simple finite impulse response (FIR) filter. When evaluated with the PhysioNet QT database in terms of the mean and the standard deviation of the \mbox{T-wave} end location errors, the proposed algorithm outperforms the other algorithms evaluated with the same data base, according to the most recent available publications up to our knowledge. \\ L'analyse de l'électrocardiogramme (ECG) assistée par l'ordinateur est largement utilisée en diagnostic de maladies cardiaques. Le but de cet article est de proposer un nouveau algorithme pour la localisation de fins d'ondes T, connu d'être le plus difficile des problèmes concernant la détection et localisation d'ondes dans l'ECG. L'algorithme proposé consiste principalement à calculer un indicateur lié à la surface couverte par l'onde T délimitée d'une manière spéciale. Sous des hypothèses simples, principalement sur la concavité de l'onde T, il est démontré que le maximum de l'indicateur calculé dans chaque cycle cardiaque coïncide avec la fin de l'onde T. En plus, l'algorithme est robuste au bruit de mesure, aux variations morphologiques et à la dérive de la ligne de base. Le calcul numérique est très simple : le calcul principal peut être implémenté sous forme d'un filtre à réponse impulsionnelle finie. Quand cet algorithme est évalué sur la base de données QT de PhysioNet en termes de la moyenne et l'écart type des erreurs de localisation de l'onde T, il obtient de meilleurs résultats par rapport à d'autres algorithmes évalués avec la même base de données, d'après les publications les plus récentes à notre connaissance.

The paper presents a result which relates connectedness of the interaction graphs in a multi-agent systems with the capability for global convergence to a common equilibrium of the system. In particular we extend a previously known result by Moreau by including the possibility of arbitrary bounded time-delays in the communication channels and relaxing the convexity of the allowed regions for the state transition map of each agent., Comment: 18 pages; 7 figures

This study aims at assessing the short term control of the Cardio Vascular system (CV), through a physiological test which involves strictly autonomic response: the handgrip isometric exercise, under vagal influence during the first minute. CVS parameters are extracted from RR and the arterial blood pressure (ABP) signals, respectively giving frequency and amplitude information on the CVS. Mean time series, spectral values and baroreflex sensitivity (BRS), seen as the spectral controller gain between RR and ABP, help to approach the underlying mechanisms of the autonomic control. Results give evidence of two major effects: - The relation between heart rate and contractility (positive staircase or Treppe effect). - The drop of BRS, due to the decrease of heart variability.

Embedded systems account for a major part of crit- ical applications (space, aeronautics, nuclear. . . ) as well Our goal is to automatically obtain a distributed and as public domain applications (automotive, consumer fault-tolerant embedded system: distributed because the electronics. . . ). Their main features are: system must run on a distributed architecture; fault-tolerant because the system is critical. Our starting point is a source algorithm, a target distributed architecture, some distribu- tion constraints, some indications on the execution times of the algorithm operations on the processors of the target ar- chitecture, some indications on the communication times of the data-dependencies on the communication links of the target architecture, a number Npf of fail-silent processor failures that the obtained system must tolerate, and finally some real-time constraints that the obtained system must satisfy. In this article, we present a scheduling heuristic which, given all these inputs, produces a fault-tolerant, dis- tributed, and static scheduling of the algorithm on the ar- chitecture, with an indication whether or not the real-time constraints are satisfied. The algorithm we propose consist of a list scheduling heuristic based active replication strat- egy, that allows at least Npf +1 replicas of an operation to be scheduled on different processors, which are run in parallel to tolerate at most Npf failures. Due to the strat- egy used to schedule operations, simulation results show that the proposed heuristic improve the performance of our method, both in the absence and in the presence of failures.

We present recent advances on a 3D numerical modeling of the myocardium which couples electrical and biomechanical models. The long-term objective is to simulate a realistic contraction of the heart from both electrical measurements (typically the ECG) and geometrical measurements (typically provided by medical imaging). This realistic contraction should provide useful quantitative parameters for the diagnosis and also for guiding some new forms of therapy. Our modeling is based on a multi- scale analysis ranging from microscopic to macroscopic scales, and integrates a priori information on the overall geometry and on the fiber directions extracted from specific medical imaging techniques (e.g. dtMRI). The FitzHugh-Nagumo equations are solved along with a constitutive law based on the Hill-Maxwell Rheological model, on which a data assimilation analysis is done. In medical image analysis, we believe that this new generation of physics-based deformable models will be useful to provide a more robust quantitative interpretation of temporal series of cardiac images. Resume. Nous presentons ici nos avancees sur la modelisation du myocarde couplant des modeles ´ et biomecaniques. L'objectiflong terme est de simuler la contraction du cœurpartir de mesures ECG et d'images medicales, afin de fournir des outils d'aide au diagnostic. Notre modele se base sur unemultiechelle des phenomenes et des donnees anatomiques extraites d'images medicales. La partierepose sur le modele de FitzHugh-Nagumo et la partie mecanique reprend le formalisme de Hill-Maxwell avec une nouvelle loi de comportement, sur laquelle de l'assimilation de donnees est realisee. En imagerie medicale, nous pensons que ce nouveau type de modeles devrait permettre une interpretation plus robuste des sequences temporelles.

We present a 3D numerical representation of the heart which couples the electrical and biomechanical models. To achieve this, the FitzHugh-Nagumo equations are solved along with a constitutive law based on the Hill-Maxwell rheological law. Ultimately, the parameters of this generic model will be adjusted by comparing the actual patient's ECG with computational results and the deformation of the biomechanical model with the geometric information extracted from the ultrasound images of the patient's heart.