Functional optimization of the arterial network

We build an evolutionary scenario that explains how some crucial physiological constraints in the arterial network of mammals - i.e. hematocrit, vessels diameters and arterial pressure drops - could have been selected by evolution. We propose that the arterial network evolved while being constrained by its function as an organ. To support this hypothesis, we focus our study on one of the main function of blood network: oxygen supply to the organs. We consider an idealized organ with a given oxygen need and we optimize blood network geometry and hematocrit with the constraint that it must fulfill the organ oxygen need. Our model accounts for the non-Newtonian behavior of blood, its maintenance cost and F\aa hr\ae us effects (decrease in average concentration of red blood cells as the vessel diameters decrease). We show that the mean shear rates (relative velocities of fluid layers) in the tree vessels follow a scaling law related to the multi-scale property of the tree network, and we show that this scaling law drives the behavior of the optimal hematocrit in the tree. We apply our scenario to physiological data and reach results fully compatible with the physiology: we found an optimal hematocrit of 0.43 and an optimal ratio for diameter decrease of about 0.79. Moreover our results show that pressure drops in the arterial network should be regulated in order for oxygen supply to remain optimal, suggesting that the amplitude of the arterial pressure drop may have co-evolved with oxygen needs.Comment: Shorter version, misspelling correctio

Murray's law revisited: Qu\'emada's fluid model and fractal trees

In 1926, Murray proposed the first law for the optimal design of blood vessels. He minimized the power dissipation arising from the trade-off between fluid circulation and blood maintenance. The law, based on a constant fluid viscosity, states that in the optimal configuration the fluid flow rate inside the vessel is proportional to the cube of the vessel radius, implying that wall shear stress is not dependent on the vessel radius. Murray's law has been found to be true in blood macrocirculation, but not in microcirculation. In 2005, Alarc\'on et al took into account the non monotonous dependence of viscosity on vessel radius - F{\aa}hr{\ae}us-Lindqvist effect - due to phase separation effect of blood. They were able to predict correctly the behavior of wall shear stresses in microcirculation. One last crucial step remains however: to account for the dependence of blood viscosity on shear rates. In this work, we investigate how viscosity dependence on shear rate affects Murray's law. We extended Murray's optimal design to the whole range of Qu\'emada's fluids, that models pseudo-plastic fluids such as blood. Our study shows that Murray's original law is not restricted to Newtonian fluids, it is actually universal for all Qu\'emada's fluid as long as there is no phase separation effect. When phase separation effect occurs, then we derive an extended version of Murray's law. Our analyses are very general and apply to most of fluids with shear dependent rheology. Finally, we study how these extended laws affect the optimal geometries of fractal trees to mimic an idealized arterial network

Addendum to "Local Controllability of the Two-Link Magneto-Elastic Micro-Swimmer"

In the above mentioned note (, , published in IEEE Trans. Autom. Cont., 2017), the first and fourth authors proved a local controllability result around the straight configuration for a class of magneto-elastic micro-swimmers.That result is weaker than the usual small-time local controllability (STLC), and the authors left the STLC question open. The present addendum closes it by showing that these systems cannot be STLC

Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations

A reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convection-diffusion-reaction equations. The streamline-upwind Petrov--Galerkin (SUPG) stabilization is used in the practically interesting case of dominant convection, both for the full order method (FOM) and the ROM simulations. The asymptotic choice of the stabilization parameter for the SUPG-ROM is done as proposed in the literature. This paper presents a finite element convergence analysis of the SUPG-ROM method for errors in different norms. The constants in the error bounds are uniform with respect to small diffusion coefficients. Numerical studies illustrate the performance of the SUPG-ROM method

Modélisation de l'écoulement polyphasique à l'intérieur et en sortie des injecteurs diesel

Les normes d'émission de polluants concernant les véhicules poussent les constructeurs automobiles à s'intéresser à l'injection Diesel haute pression et au phénomène de cavitation qui y tient un rôle prépondérant. En ce domaine, la simulation numérique est un moyen d'investigation puissant et économique. Un modèle polyphasique homogène a été développé : il considère un mélange de carburant (constitué de liquide et/ou de vapeur) et de gaz. Il est basé sur une équation d'état construite par tabulation entre une loi barotrope pour le carburant et la loi des gaz parfaits pour le gaz. La validité de l'approche est testée sur un cas d'implosion de bulle et sur des cas 2D classiques d'injection. Des calculs 3D d'injecteurs réalistes mettent en évidence l'influence de la cavitation et des écoulements secondaires, à l'intérieur de l'orifice de l'injecteur, sur la déstabilisation du jet et l'atomisation primaire du coeur liquide

Modélisation de l'écoulement polyphasique à l'intérieur et en sortie des injecteurs diesel

Les normes d'émission de polluants concernant les véhicules poussent les constructeurs automobiles à s'intéresser à l'injection Diesel haute pression et au phénomène de cavitation qui y tient un rôle prépondérant. En ce domaine, la simulation numérique est un moyen d'investigation puissant et économique. Un modèle polyphasique homogène a été développé : il considère un mélange de carburant (constitué de liquide et/ou de vapeur) et de gaz. Il est basé sur une équation d'état construite par tabulation entre une loi barotrope pour le carburant et la loi des gaz parfaits pour le gaz. La validité de l'approche est testée sur un cas d'implosion de bulle et sur des cas 2D classiques d'injection. Des calculs 3D d'injecteurs réalistes mettent en évidence l'influence de la cavitation et des écoulements secondaires, à l'intérieur de l'orifice de l'injecteur, sur la déstabilisation du jet et l'atomisation primaire du coeur liquide. ABSTRACT : Because of pollutant emission requirements for individual vehicles, engine designers are very concerned about high pressure Diesel injection and the related cavitation phenomenon. Computational fluid dynamics is a powerful and cheap tool to investigate such complex systems. A homogeneous multiphase model has been developed : it consists in a mixture of fuel – that may be either liquid or vapor – and gas. It is based on an equation of state that was tabulated between a barotropic law for the fuel and the ideal gas equation for the gas. This model is validated on a bubble collapse test and on classical 2D injection cases. 3D computations on realistic injectors highlight the influence of cavitation and secondary flows, inside the injector nozzle, on jet destabilization and liquid core primary atomization

Feeding ecology of Southern Ocean seastars inferred from stable isotopes ratios

The Southern Ocean is currently subjected to strong and contrasted impacts of climate change. The Western Antarctic Peninsula is one of the most rapidly warming regions of the world, resulting in sea ice cover decreases. Increasing seawater temperature and sea ice cover reduction in Western Antarctic Peninsula and associated regions will likely impact food web functioning through temperature-related changes in consumer physiology, modifications of benthic community structure (e.g. expansion of exogenous species such as predatory crabs), modifications of benthic-pelagic coupling intensity or disruption of benthic production. Asteroids (Echinoderms) are an important group of southern benthos. This group also has a great trophic variability and is potentially more resistant than other organisms to temperature changes (Peck et al. 2008). Consequently, they will be likely impacted by modifications in food webs functioning rather by direct warming and investigating their trophic ecology is necessary to infer how climate change will impact them. In this context, the aim of this study is to use stable isotopes ratios of C, N and S to infer sea stars trophic ecology. 16 species of sea stars spanning 10 different families sampled in multiple and contrasted habitats across Subantarctic (South Georgia, South Sandwich Islands, Falkland Islands) and Antarctic (South Shetland Islands, South Orkney Islands, Western Antarctic Peninsula) locations. In total, tegument samples from 213 specimens was analysed. Diversity and plasticity of asteroid diet along Southern Ocean coasts were explored through isotopic niche parametrisation (e.g. niche width and overlap between species and/or populations; Jackson et al. 2011). The data will also be used in a larger scale research project on the trophic ecology of Antarctic sea stars. This project will notably compare trophic resources supporting asteroid communities in Western Antarctic Peninsula, where sea ice cover is decreasing, and in Terre Adélie, where sea ice cover is increasing (Parkinson & Cavalieri 2012). Ultimately, this project will help understanding which ecological processes determine how an animal group copes with environmental modifications linked to climate change

Non-invasive assessment of human multifidus muscle stiffness using ultrasound shear wave elastography: A feasibility study

INTRODUCTION: There is a lack of numeric data for the mechanical characterization of spine muscles, especially in vivo data. The multifidus muscle is a major muscle for the stabilization of the spine and may be involved in the pathogenesis of chronic low back pain (LBP). Supersonic shear wave elastography (SWE) has not yet been used on back muscles. The purpose of this prospective study is to assess the feasibility of ultrasound SWE to measure the elastic modulus of lumbar multifidus muscle in a passive stretching posture and at rest with a repeatable and reproducible method. METHOD: A total of 10 asymptotic subjects (aged 25.5±2.2 years) participated, 4 females and 6 males. Three operators performed 6 measurements for each of the 2 postures on the right multifidus muscle at vertebral levels L2-L3 and L4-L5. Repeatability and reproducibility have been assessed according to ISO 5725 standard. RESULTS: Intra-class correlation coefficients (ICC) for intra- and inter observer reliability were rated as both excellent [ICC=0.99 and ICC=0.95, respectively]. Reproducibility was 11% at L2-L3 level and 19% at L4-L5. In the passive stretching posture, shear modulus was significantly higher than at rest (u<0.05). DISCUSSION: This preliminary work enabled to validate the feasibility of measuring the shear modulus of the multifidus muscle with SWE. This kind of measurement could be easily introduces into clinical routine like for the medical follow-up of chronic LBP or scoliosis treatments.The authors are grateful to the ParisTech BiomecAM chair program on subject-specific musculoskeletal modelling for funding (with the support of ParisTech and Yves Cotrel Foundations, Société Générale, Proteor and Covea)