Large deviations estimates for the multiscale analysis of heart rate variability

International audienceIn the realm of multiscale signal analysis, multifractal analysis provides with a natural and rich framework to measure the roughness of a time series. As such, it has drawn special attention of both mathematicians and practitioners, and led them to characterize relevant physiological factors impacting the heart rate variability. Notwithstanding these considerable progresses, multifractal analysis almost exclusively developed around the concept of Legendre singularity spectrum, for which efficient and elaborate estimators exist, but which are structurally blind to subtle features like non-concavity or, to a certain extent, non scaling of the distributions. Large deviations theory allows bypassing these limitations but it is only very recently that performing estimators were proposed to reliably compute the corresponding large deviations singularity spectrum. In this article, we illustrate the relevance of this approach, on both theoretical objects and on human heart rate signals from the Physionet public database. As conjectured, we verify that large deviations principles reveal significant information that otherwise remains hidden with classical approaches, and which can be reminiscent of some physiological characteristics. In particular we quantify the presence/absence of scale invariance of RR signals

Maths Express au carrefour des cultures

International audienceCette brochure a été réalisée à l'occasion de la quinzième édition du Salon Culture et Jeux mathématiques. Elle a pour objectif de montrer que les mathématiques sont au coeur de toutes les activités humaines qu'elles soient sociales, techniques, scientifiques, artistiques ou ludiques. Elles sont nées et se sont développées au rythme des sociétés humaines

Couplage contraction-relaxation myocardique: etude in vitro et in vivo

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : T 81396 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Pression artérielle pulmonaire moyenne et pulsée ; relations pression débit dans l'hypertension artérielle pulmonaire

LE KREMLIN-B.- PARIS 11-BU Méd (940432101) / SudocPARIS-BIUP (751062107) / SudocSudocFranceF

Towards New Indices of Arterial Stiffness Using Systolic Pulse Contour Analysis: A Theoretical Point of View

International audienceTotal arterial stiffness plays a contributory role throughout aging and in numerous cardiovascular diseases, including hypertension. Aortic stiffening is responsible for an increased characteristic impedance (ie, the impedance to the left ventricular pulsatile flow), thus increasing the forward pressure-wave amplitude that contributes to pulse pressure elevation. Aortic stiffening also increases pulse wave velocity, and this results in anticipated and enhanced wave reflections, further augmenting central pulse pressure. Unfortunately, there is no simple time-domain estimate of characteristic impedance. Furthermore, recent guidelines have reviewed the limitations of diastolic pulse contour analysis to estimate arterial stiffness in the time domain. The present theoretical article proposes that systolic pulse contour analysis may provide new, simple time-domain indices quantifying pulsatile load in resting humans. Our proposal was mainly based on 2 simple, validated assumptions: (1) a linear aortic pressure-flow relationship in early systole and (2) a triangular aortic flow wave during systole. This allowed us to describe new time-domain estimates of characteristic impedance, pulsatile load (waveguide ratio), total arterial compliance, and total arterial stiffness. It is demonstrated that total arterial stiffness may be estimated by the following formula: [(Pi - DAP) × ST] / (SV × Δt), where Pi is the aortic pressure at the inflection point (peak forward pressure wave), DAP is diastolic aortic pressure, ST is systolic ejection time, SV is stroke volume, and Δt is the time-to-Pi. A mathematical relationship among time intervals and indices of pulsatile load is demonstrated, and the clinical implications are discussed in terms of cardiovascular risk and stroke volume prediction