Pierre Dauby

Bénard–Marangoni instability in rigid rectangular containers

Thermocapillary convection in three-dimensional rectangular finite containers with rigid lateral walls is studied. The upper surface of the fluid layer is assumed to be flat and non-deformable but is submitted to a temperature-dependent surface tension. The realistic ‘no-slip’ condition at the sidewalls makes the method of separation of variables inapplicable for the linear problem. A spectral Tau method is used to determine the critical Marangoni number and the convective pattern at the threshold as functions of the aspect ratios of the container. The influence on the critical parameters of a non-vanishing gravity and a non-zero Biot number at the upper surface is also examined. The nonlinear regime for pure Marangoni convection ( Ra = 0 ) and for Pr = 10 4 , Bi = 0 is studied by reducing the dynamics of the system to the dynamics of the most unstable modes of convection. Owing to the presence of rigid walls, it is shown that the convective pattern above the threshold may be quite different from that predicted by the linear approach. The theoretical predictions of the present study are in very good agreement with the experiments of Koschmieder & Prahl (1990) and agree also with most of Dijkstras (1995 a, b ) numerical results. Important differences with the analysis of Rosenblat, Homsy & Davis (1982 b ) on slippery walls containers are emphasized.

Model-based identification and diagnosis of a porcine model of induced endotoxic shock with hemofiltration

A previously validated cardiovascular system (CVS) model and parameter identification method for cardiac and circulatory disease states are extended and further validated in a porcine model (N=6) of induced endotoxic shock with hemofiltration. Errors for the identified model are within 10% when the model is re-simulated and compared to the clinical data. All identified parameter trends over time in the experiments match clinically expected changes both individually and over the cohort. This work represents a further clinical validation of these model-based cardiovascular diagnosis and therapy guidance methods for use with monitoring endotoxic disease states.

Linear and nonlinear Rayleigh–Bénard–Marangoni instability with surface deformations

Thermoconvective instabilities in a bilayer liquid–gas system with a deformed interface are investigated. In the first part of the work which is devoted to a linear approach, emphasis is put on the role of the upper gas layer on the instability phenomenon. The condition to be satisfied by the gas to remain purely conductive is established. The so-called Oberbeck–Boussinesq approximation is discussed and its range of validity is carefully defined. Instead of the classical Rayleigh, Marangoni, crispation, and Galileo numbers, new dimensionless groups are introduced. A critical comparison with several previous works is made. The nonlinear analysis consists in studying the different convective patterns which can appear above the threshold. Particular attention is devoted to the shape of the interface and the so-called “hybrid” relief. The amplitude of the deformation is also determined and comparison with experimental data is discussed.

Cardiovascular Modelling and Identification in Septic Shock - Experimental validation

Abstract Cardiovascular disturbances are difficult to diagnose and treat because of the large range of possible underlying dysfunctions combined with regulatory reflex mechanisms that can result in conflicting clinical data. A cardiovascular system (CVS) model and patient specific parameter identification method could better aggregate the clinical data into a more direct and simpler form for clinicians. A previously developed model and parameter identification method is improved to accurately capture physiological response to septic shock under continuous hemofiltration, further confirming the potential for using this model-based approach in critical care. Clinical data is matched with mean absolute errors less than 8% and the optimized parameters closely follow a previous study using significantly more invasive procedures and measurements.

A multi-scale cardiovascular system model can account for the load-dependence of the end-systolic pressure-volume relationship

BackgroundThe end-systolic pressure-volume relationship is often considered as a load-independent property of the heart and, for this reason, is widely used as an index of ventricular contractility. However, many criticisms have been expressed against this index and the underlying time-varying elastance theory: first, it does not consider the phenomena underlying contraction and second, the end-systolic pressure volume relationship has been experimentally shown to be load-dependent.MethodsIn place of the time-varying elastance theory, a microscopic model of sarcomere contraction is used to infer the pressure generated by the contraction of the left ventricle, considered as a spherical assembling of sarcomere units. The left ventricle model is inserted into a closed-loop model of the cardiovascular system. Finally, parameters of the modified cardiovascular system model are identified to reproduce the hemodynamics of a normal dog.ResultsExperiments that have proven the limitations of the time-varying elastance theory are reproduced with our model: (1) preload reductions, (2) afterload increases, (3) the same experiments with increased ventricular contractility, (4) isovolumic contractions and (5) flow-clamps. All experiments simulated with the model generate different end-systolic pressure-volume relationships, showing that this relationship is actually load-dependent. Furthermore, we show that the results of our simulations are in good agreement with experiments.ConclusionsWe implemented a multi-scale model of the cardiovascular system, in which ventricular contraction is described by a detailed sarcomere model. Using this model, we successfully reproduced a number of experiments that have shown the failing points of the time-varying elastance theory. In particular, the developed multi-scale model of the cardiovascular system can capture the load-dependence of the end-systolic pressure-volume relationship.

A Unified Extended Thermodynamic Description of Diffusion, Thermo-Diffusion, Suspensions, and Porous Media

It is shown that extended irreversible thermodynamics (EIT) provides a unified description of a great variety of processes, including matter diffusion, thermo-diffusion, suspensions, and fluid flows in porous media. This is achieved by enlarging the set of classical variables, as mass, momentum and temperature by the corresponding fluxes of mass, momentum and heat. For simplicity, we consider only Newtonian fluids and restrict ourselves to a linear analysis: quadratic and higher order terms in the fluxes are neglected. In the case of diffusion in a binary mixture, the extra flux variable is the diffusion flux of one the constituents, say the solute. In thermo-diffusion, one adds the heat flux to the set of variables. The main result of the present approach is that the traditional equations of Fick, Fourier, Soret, and Dufour are replaced by time-evolution equations for the matter and heat fluxes, such generalizations are useful in high-frequency processes. It is also shown that the analysis can be easily extended to the study of particle suspensions in fluids and to flows in porous media, when such systems can be viewed as binary mixtures with a solid and a fluid component.

Time-dependent Marangoni-Bénard instability of an evaporating binary-liquid layer including gas transients

We are here concerned with Benard instabilities in a horizontal layer of a binary liquid, considering as a working example the case of an aqueous solution of ethanol with a mass fraction of 0.1. Both the solvent and the solute evaporate into air (the latter being insoluble in the liquid). The system is externally constrained by imposing fixed “ambient” pressure, humidity, and temperature values at a certain effective transfer distance above the liquid-gas interface, while the ambient temperature is also imposed at the impermeable rigid bottom of the liquid layer. Fully transient and horizontally homogeneous solutions for the reference state, resulting from an instantaneous exposure of the liquid layer to ambient air, are first calculated. Then, the linear stability of these solutions is studied using the frozen-time approach, leading to critical (monotonic marginal stability) curves in the parameter plane spanned by the liquid layer thickness and the elapsed time after initial contact. This is achieved fo...

RHEOLOGICAL PROPERTIES OF DILUTE POLYMER-SOLUTIONS - AN EXTENDED THERMODYNAMIC APPROACH

It is shown that extended irreversible thermodynamics can be used to account for the shear rate and frequency dependences of several material functions like shear viscosity, first and second normal stress coefficients, dynamic viscosity and storage modulus. Comparison with experimental data on steady shearing and small oscillatory shearing flows is performed. A good agreement between the model and experiment is reached in a wide scale of variation of the shear rate and the frequency of oscillations. The relation between the present model which includes quadratic terms in the pressure tensor and the Giesekus model is also examined.

Structural identifiability analysis of a cardiovascular system model

The six-chamber cardiovascular system model of Burkhoff and Tyberg has been used in several theoretical and experimental studies. However, this cardiovascular system model (and others derived from it) are not identifiable from any output set. In this work, two such cases of structural non-identifiability are first presented. These cases occur when the model output set only contains a single type of information (pressure or volume). A specific output set is thus chosen, mixing pressure and volume information and containing only a limited number of clinically available measurements. Then, by manipulating the model equations involving these outputs, it is demonstrated that the six-chamber cardiovascular system model is structurally globally identifiable. A further simplification is made, assuming known cardiac valve resistances. Because of the poor practical identifiability of these four parameters, this assumption is usual. Under this hypothesis, the six-chamber cardiovascular system model is structurally identifiable from an even smaller dataset. As a consequence, parameter values computed from limited but well-chosen datasets are theoretically unique. This means that the parameter identification procedure can safely be performed on the model from such a well-chosen dataset. Thus, the model may be considered suitable for use in diagnosis.

Model-based computation of total stressed blood volume from a preload reduction manoeuvre

Total stressed blood volume is an important parameter for both doctors and engineers. From a medical point of view, it has been associated with the success or failure of fluid therapy, a primary treatment to manage acute circulatory failure. From an engineering point of view, it dictates the cardiovascular systems behavior in changing physiological situations. Current methods to determine this parameter involve repeated phases of circulatory arrests followed by fluid administration. In this work, a more straightforward method is developed using data from a preload reduction manoeuvre. A simple six-chamber cardiovascular system model is used and its parameters are adjusted to pig experimental data. The parameter adjustment process has three steps: (1) compute nominal values for all model parameters; (2) determine the five most sensitive parameters; and (3) adjust only these five parameters. Stressed blood volume was selected by the algorithm, which emphasizes the importance of this parameter. The model was able to track experimental trends with a maximal root mean squared error of 29.2%. Computed stressed blood volume equals 486 ± 117 ml or 15.7 ± 3.6 ml/kg, which matches previous independent experiments on pigs, dogs and humans. The method proposed in this work thus provides a simple way to compute total stressed blood volume from usual hemodynamic data.