Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Aeroelastic stability of structures: flutter analysis using Computational Fluid Dynamics

Thanks to the increasing slenderness and lightness allowed by new construction techniques and materials, the effects of wind on structures became in the last decades a research field of great importance in Civil Engineering. Thanks to the advances in computers power, the numerical simulation of wind tunnel tests has became a valid complementary activity and an attractive alternative for the future. Due to its flexibility, during the last years, the computational approach gained importance with respect to the traditional experimental investigation. However, still today, the computational approach to fluid-structure interaction problems is not as widely adopted as it could be expected. The main reason for this lies in the difficulties encountered in the numerical simulation of the turbulent, unsteady flow conditions generally encountered around bluff bodies. This thesis aims at providing a guide to the numerical simulation of bridge deck aerodynamic and aeroelastic behaviour describing in detail the simulation strategies and setting guidelines useful for the interpretation of the results.

Numerical modelling of fluid-structure interaction with application in hemodynamics

The thesis deals with numerical algorithms for fluid-structure interaction problems with application in blood flow modelling. It starts with a short introduction on the mathematical description of incompressible viscous flow with non-Newtonian viscosity and a moving linear viscoelastic structure. The mathematical model consists of the generalized Navier-Stokes equation used for the description of fluid flow and the generalized string model for structure movement. The arbitrary Lagrangian-Eulerian approach is used in order to take into account moving computational domain. A part of the thesis is devoted to the discussion on the non-Newtonian behaviour of shear-thinning fluids, which is in our case blood, and derivation of two non-Newtonian models frequently used in the blood flow modelling. Further we give a brief overview on recent fluid-structure interaction schemes with discussion about the difficulties arising in numerical modelling of blood flow. Our main contribution lies in numerical and experimental study of a new loosely-coupled partitioned scheme called the kinematic splitting fluid-structure interaction algorithm. We present stability analysis for a coupled problem of non-Newtonian shear-dependent fluids in moving domains with viscoelastic boundaries. Here, we assume both, the nonlinearity in convective as well is diffusive term. We analyse the convergence of proposed numerical scheme for a simplified fluid model of the Oseen type. Moreover, we present series of experiments including numerical error analysis, comparison of hemodynamic parameters for the Newtonian and non-Newtonian fluids and comparison of several physiologically relevant computational geometries in terms of wall displacement and wall shear stress. Numerical analysis and extensive experimental study for several standard geometries confirm reliability and accuracy of the proposed kinematic splitting scheme in order to approximate fluid-structure interaction problems.

Numerical analysis of the relation between interactions and structure in a molecular fluid

Coarse graining is a popular technique used in physics to speed up the computer simulation of molecular fluids. An essential part of this technique is a method that solves the inverse problem of determining the interaction potential or its parameters from the given structural data. Due to discrepancies between model and reality, the potential is not unique, such that stability of such method and its convergence to a meaningful solution are issues.rnrnIn this work, we investigate empirically whether coarse graining can be improved by applying the theory of inverse problems from applied mathematics. In particular, we use the singular value analysis to reveal the weak interaction parameters, that have a negligible influence on the structure of the fluid and which cause non-uniqueness of the solution. Further, we apply a regularizing Levenberg-Marquardt method, which is stable against the mentioned discrepancies. Then, we compare it to the existing physical methods - the Iterative Boltzmann Inversion and the Inverse Monte Carlo method, which are fast and well adapted to the problem, but sometimes have convergence problems.rnrnFrom analysis of the Iterative Boltzmann Inversion, we elaborate a meaningful approximation of the structure and use it to derive a modification of the Levenberg-Marquardt method. We engage the latter for reconstruction of the interaction parameters from experimental data for liquid argon and nitrogen. We show that the modified method is stable, convergent and fast. Further, the singular value analysis of the structure and its approximation allows to determine the crucial interaction parameters, that is, to simplify the modeling of interactions. Therefore, our results build a rigorous bridge between the inverse problem from physics and the powerful solution tools from mathematics. rn

Design and fluid dynamic analysis of a custom drip chamber in a medical disposable device

Negli ultimi anni, parallelamente allo sviluppo di calcolatori elettronici sempre più performanti, la fluidodinamica computazionale è diventata uno strumento di notevole utilità nell’analisi dei flussi e nello sviluppo di dispositivi medici. Quando impiegate nello studio di flussi di fluidi fisiologici, come il sangue, il vantaggio principale delle analisi CFD è che permettono di caratterizzare il comportamento fluidodinamico senza dover eseguire test in-vivo/in-vitro, consentendo quindi notevoli vantaggi in termini di tempo, denaro e rischio derivante da applicazioni mediche. Inoltre, simulazioni CFD offrono una precisa e dettagliata descrizione di ogni parametro di interesse permettendo, già in fase di progettazione, di prevedere quali modifiche al layout garantiranno maggiori vantaggi in termini di funzionalità. Il presente lavoro di tesi si è posto l’obiettivo di valutare, tramite simulazioni CFD, le performances fluidodinamiche del comparto sangue “camera venosa” di un dispositivo medico monouso Bellco impiegato nella realizzazione di trattamenti di emodialisi. Dopo una panoramica del contesto, è presentata una breve descrizione della disfunzione renale e dei trattamenti sostitutivi. Notevole impegno è stato in seguito rivolto allo studio della letteratura scientifica in modo da definire un modello reologico per il fluido non-Newtoniano preso in considerazione e determinarne i parametri caratteristici. Il terzo capitolo presenta lo stato dell’arte delle apparecchiature Bellco, rivolgendosi con particolare attenzione al componente “cassette” del dispositivo monouso. L’analisi fluidodinamica del compartimento “camera venosa” della cassette, che sarà presa in considerazione nei capitoli quinto e sesto, si inserisce nell’ambito della riprogettazione del dispositivo attualmente in commercio: il quarto capitolo si incentra sul suo nuovo design, ponendo specifico interesse sul layout della camera venosa di nuova generazione. Per lo studio dei flussi che si sviluppano internamente ad essa ci si è avvalsi del modulo CFD del software COMSOL multiphysics® (versione 5.0); la definizione del modello implementato e della tipologia di studio effettuato sono presi in considerazione nel quinto capitolo. Le problematiche di maggior impatto nella realizzazione di un trattamento di emodialisi sono l’emolisi e la coagulazione del sangue. Nell'evenienza che si verifichino massivamente occorre infatti interrompere il trattamento con notevoli disagi per il paziente, per questo devono essere evitate. Nel sesto capitolo i risultati ottenuti sono stati esaminati rivolgendo particolare attenzione alla verifica dell’assenza di fenomeni che possano portare alle problematiche suddette.

Acute fluid ingestion in the treatment of orthostatic intolerance - important implications for daily practice

Rapid water ingestion improves orthostatic intolerance (OI) in multiple system atrophy (MSA) and postural tachycardia syndrome (PoTS). We compared haemodynamic changes after water and clear soup intake, the latter being a common treatment strategy for OI in daily practice.

Formation of caries-like lesions in vitro on the root surfaces of human teeth in solutions simulating plaque fluid

Lesion formation on root surfaces of human posterior teeth was studied in acetate/lactate buffers with a background electrolyte composition based on plaque fluid analyses. Lesion depth after 28 days at 37 degrees C was measured in relation to: the presence or absence of cementum; the concentration of undissociated buffer; the presence or absence of magnesium ions at plaque fluid concentration. Each factor was evaluated at several values of -log(ion activity product for hydroxyapatite): pI(HA). Solutions were formulated to minimize variation in pH, which varied by < or =0.03 for a given comparison (individual pI(HA)) and by 0.42-0.82 over the range of pI(HA) within experiments. Lesions on surfaces from which cementum had been ground were significantly deeper than on intact surfaces, but this is considered to be due to subsurface mechanical damage and not to a solubility difference. Neither the concentration of undissociated buffer nor the presence of magnesium ions significantly affected lesion depth. Lesion depth was strongly influenced by the correlated variations in pI(HA) and pH. At pI(HA) 54 and 55, only extremely shallow lesions formed. From pI(HA) 56, lesion depth increased with increasing pI(HA). The results confirm that the solubility of the mineral of root tissues is higher than that of hydroxyapatite, but indicate that it is probably lower than suggested by Hoppenbrouwers et al. [Arch Oral Biol 1987;32:319-322]. For calcium concentrations of 3-12 mM, the critical pH for root tissue mineral was calculated as 5.22-5.66 assuming solubility equivalent to pI(HA) 54 and 5.08-5.51 assuming pI(HA) 55.

Is detection of bacterial DNA in ascitic fluid of clinical relevance?

In patients with cirrhosis, bacterial DNA has been found in ascites reflecting bacterial translocation. However, the clinical relevance of this finding is ill-defined especially compared with the standard diagnostics for detection of spontaneous bacterial peritonitis (SBP). Furthermore, other DNA tests have not been sufficiently evaluated.

Immunomodulatory therapy to achieve maximum efficacy: doses, monitoring, compliance, and self-infusion at home

The Oxford Programme for Immunomodulatory Immunoglobulin Therapy has been operating since 1992 at Oxford Radcliffe Hospitals in the UK. Initially, this program was set up for patients with multifocal motor neuropathy or chronic inflammatory demyelinating poly-neuropathy to receive reduced doses of intravenous immunoglobulin (IVIG) in clinic on a regular basis (usually every 3 weeks). The program then rapidly expanded to include self-infusion at home, which monitoring showed to be safe and effective. It has been since extended to the treatment of other autoimmune diseases in which IVIG has been shown to be efficacious.

Effect of site of lactate infusion on regional lactate exchange in pigs

The rate of extra-hepatic lactate production and the route of influx of lactate to the liver may influence both hepatic and extra-hepatic lactate exchange. We assessed the dose-response of hepatic and extra-hepatic lactate exchange during portal and central venous lactate infusion.

Plasma copeptin levels before and during exogenous arginine vasopressin infusion in patients with advanced vasodilatory shock

Plasma copeptin levels before and during exogenous arginine vasopressin infusion (AVP) were evaluated, and the value of copeptin levels before AVP therapy to predict complications during AVP therapy and outcome in vasodilatory shock patients was determined.

Role of selective V2-receptor-antagonism in septic shock: a randomized, controlled, experimental study

ABSTRACT : INTRODUCTION : V2-receptor (V2R) stimulation potentially aggravates sepsis-induced vasodilation, fluid accumulation and microvascular thrombosis. Therefore, the present study was performed to determine the effects of a first-line therapy with the selective V2R-antagonist (Propionyl1-D-Tyr(Et)2-Val4-Abu6-Arg8,9)-Vasopressin on cardiopulmonary hemodynamics and organ function vs. the mixed V1aR/V2R-agonist arginine vasopressin (AVP) or placebo in an established ovine model of septic shock. METHODS : After the onset of septic shock, chronically instrumented sheep were randomly assigned to receive first-line treatment with the selective V2R-antagonist (1 g/kg per hour), AVP (0.05 g/kg per hour), or normal saline (placebo, each n = 7). In all groups, open-label norepinephrine was additionally titrated up to 1 g/kg per minute to maintain mean arterial pressure at 70 ± 5 mmHg, if necessary. RESULTS : Compared to AVP- and placebo-treated animals, the selective V2R-antagonist stabilized cardiopulmonary hemodynamics (mean arterial and pulmonary artery pressure, cardiac index) as effectively and increased intravascular volume as suggested by higher cardiac filling pressures. Furthermore, left ventricular stroke work index was higher in the V2R-antagonist group than in the AVP group. Notably, metabolic (pH, base excess, lactate concentrations), liver (transaminases, bilirubin) and renal (creatinine and blood urea nitrogen plasma levels, urinary output, creatinine clearance) dysfunctions were attenuated by the V2R-antagonist when compared with AVP and placebo. The onset of septic shock was associated with an increase in AVP plasma levels as compared to baseline in all groups. Whereas AVP plasma levels remained constant in the placebo group, infusion of AVP increased AVP plasma levels up to 149 ± 21 pg/mL. Notably, treatment with the selective V2R-antagonist led to a significant decrease of AVP plasma levels as compared to shock time (P < 0.001) and to both other groups (P < 0.05 vs. placebo; P < 0.001 vs. AVP). Immunohistochemical analyses of lung tissue revealed higher hemeoxygenase-1 (vs. placebo) and lower 3-nitrotyrosine concentrations (vs. AVP) in the V2R-antagonist group. In addition, the selective V2R-antagonist slightly prolonged survival (14 ± 1 hour) when compared to AVP (11 ± 1 hour, P = 0.007) and placebo (11 ± 1 hour, P = 0.025). CONCLUSIONS : Selective V2R-antagonism may represent an innovative therapeutic approach to attenuate multiple organ dysfunction in early septic shock.

Assessing the efficiency of a pharmacokinetic-based algorithm for target-controlled infusion of ketamine in ponies

The objective of this study was to assess a pharmacokinetic algorithm to predict ketamine plasma concentration and drive a target-controlled infusion (TCI) in ponies. Firstly, the algorithm was used to simulate the course of ketamine enantiomers plasma concentrations after the administration of an intravenous bolus in six ponies based on individual pharmacokinetic parameters obtained from a previous experiment. Using the same pharmacokinetic parameters, a TCI of S-ketamine was then performed over 120 min to maintain a concentration of 1 microg/mL in plasma. The actual plasma concentrations of S-ketamine were measured from arterial samples using capillary electrophoresis. The performance of the simulation for the administration of a single bolus was very good. During the TCI, the S-ketamine plasma concentrations were maintained within the limit of acceptance (wobble and divergence <20%) at a median of 79% (IQR, 71-90) of the peak concentration reached after the initial bolus. However, in three ponies the steady concentrations were significantly higher than targeted. It is hypothesized that an inaccurate estimation of the volume of the central compartment is partly responsible for that difference. The algorithm allowed good predictions for the single bolus administration and an appropriate maintenance of constant plasma concentrations.

Lung fluid movements in hypoxia

Pulmonary edema is a problem of major clinical importance resulting from a persistent imbalance between forces that drive water into the airspace of the lung and the biological mechanisms for its removal. Here, we will first review the fundamental mechanisms implicated in the regulation of lung fluid homeostasis, namely, the Starling forces and the respiratory transepithelial sodium transport. Second, we will discuss the contribution of hypoxia to the perturbation of this fine balance and the role of such perturbations in the development of high-altitude pulmonary edema, a disease characterized by a very high morbidity and mortality. Finally, we will review possible interventions aimed to maintain/restore lung fluid homeostasis and their importance for the prevention/treatment of pulmonary edema.

Petrous bone pneumatization is a risk factor for cerebrospinal fluid fistula following vestibular schwannoma surgery

For the prevention of postoperative CSF fistula a better understanding of origins and risk factors is necessary.