New Cardiovascular Indices Based on a Nonlinear Spectral Analysis of Arterial Blood Pressure Waveforms

A new method for analyzing arterial blood pressure is presented in this report. The technique is based on the scattering transform and consists in solving the spectral problem associated to a one-dimensional Schr\"odinger 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 contain relevant physiological information. We first show how to use this approach to decompose the arterial blood pressure pulse into elementary waves and to reconstruct it or to separate its systolic and diastolic phases. 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

Projections d’habitants face à des données climatiques localisées : Ruse rétrospective pour un territoire apprenant

L’article présente les actions conduites par un Parc naturel régional (PNR) français avec des habitants de son territoire pour les sensibiliser aux changements climatiques. La nature même des enjeux climatiques soulève de délicates questions stratégiques en matière de communication et d’information de la population. Parmi toutes les démarches menées par le PNR pour la diffusion des données scientifiques élaborées sur les effets locaux des changements climatiques, l’analyse porte spécifiquement sur l’animation « d’ateliers de prospective territoriale » conduits avec des groupes d’habitants pour initier une dynamique collective et identifier les enjeux engageant l’avenir de l’espace géographique du PNR. La réflexion est issue du dialogue et d’une co-écriture entre une chargée de mission « éducation » et une chercheuse en observation participante sur trois des ateliers. La philosophie des ateliers se fonde sur la projection sur l’avenir articulant savoirs citoyens expérientiels et connaissances individuelles sur le climat, et les savoirs scientifiques et scénarisations contrastées et hypothétiques de tendances sur le territoire afin de construire une vision débattue voire partagée des actions à mener. Le détour par une projection en 2070, à travers les co-productions des habitants dans ces ateliers, est expérimenté comme « ruse rétrospective » : conscientisant les scénarii de l’inacceptable, pour définir collectivement les enjeux à relever. Il a pour effet pour les participants de se positionner dans le présent comme plus proactif face à l’avenir. L’atelier met en évidence la nécessité de structures institutionnelles propices à la délibération et un territoire « apprenant » permettant durablement aux individus d’aller vers la sphère publique.The article presents the actions carried out by a French Regional Natural Park (PNR) with inhabitants of its territory to make them aware of climate change. The very nature of climate change raises delicate strategic questions in terms of communication and public information. Among all the proceeding taken by the Park for the dissemination of scientific data developed on the local effects of climate change, the analysis relates specifically to the animation of “territorial prospective workshops” conducted with groups of residents to initiate a collective dynamic and identify the issues involving the future of the PNR geographic area. The reflection result of a dialogue between an “education” project manager and an observation researcher participating in three of the workshops. The philosophy of the workshops is based on the projection on the future articulating experiential citizen knowledge and individual knowledge on the climate, and scientific knowledge and contrasting and hypothetical scenarios of trends on the territory, in order to build a discussed, even shared vision of actions to be taken. The detour through a projection in 2070, through this co-productions of the résidents in these workshops, is experienced as a "retrospective ruse": raising awareness of the scenarios of the unacceptable, to collectively define the issues to be addressed. It has the effect for participants of positioning themselves in the present as more proactive in the future. The workshop highlights the need for institutional structures conducive to deliberation and a "learning" territory that allows individuals to move into the public sphere on a lasting basis

Stabilisation avec retard de l'équation de Korteweg-de Vries sur un réseau de type étoile.

International audienceIn this work we deal with the exponential stability of the nonlinear Kortewegde Vries (KdV) equation on a finite star-shaped network in the presence of delayed internal feedback. We start by proving the well-posedness of the system and some regularity results. Then we state an exponential stabilization result using a Lyapunov function by imposing small initial data and a restriction over the lengths. In this part also, we are able to obtain an explicit expression for the rate of decay. Then we prove the exponential stability of the solutions without restriction on the lengths and for small initial data, this result is based on an observability inequality. After that, we obtain a semi-global stabilization result working directly with the nonlinear system. Next we study the case where it may happen that a control domain with delay is outside of the control domain without delay. In that case, we obtain also a local exponential stabilization result. Finally, we present some numerical simulations in order to illustrate the stabilization

Travelling-wave analysis and identification. A scattering theory framework

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 Schrödinger 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)

Signal Analysis by Expansion Over the Squared Eigenfunctions of an Associated Schrödinger Operator

International audienceThis article introduces a new signal analysis method. The main idea consists in interpreting a pulse-shaped signal, after multiplying it by a positive parameter, as a potential of a Schrödinger operator and representing this signal with the discrete spectrum of this operator. We present some results obtained in the analysis of the arterial blood pressure with this method

Arterial blood pressure analysis based on scattering transform I

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

New cardiovascular indices based on nonlinear spectral analysis of arterial blood pressure waveforms

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