An isotope dilution model for partitioning phenylalanine uptake by the liver of lactating dairy cows

An isotope dilution model for partitioning phenylalanine uptake by the liver of the lactating dairy cow was constructed and solved in the steady state. If assumptions are made, model solution permits calculation of the rate of phenylalanine uptake from portal vein and hepatic arterial blood supply, phenylalanine release into the hepatic vein, phenylalanine oxidation and synthesis, and degradation of hepatic constitutive and export proteins. The model requires the measurement of plasma fow rate through the liver in combination with phenylalanine concentrations and plateau isotopic enrichments in arterial, portal and hepatic plasma during a constant infusion of [1-13C]phenylalanine tracer. The model can be applied to other amino acids with similar metabolic fates and will provide a means for assessing the impact of hepatic metabolism on amino acid availability to peripheral tissues. This is of particular importance for the dairy cow when considering the requirements for milk protein synthesis and the negative environmental impact of excessive nitrogen excretion.

A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of lactating dairy cows

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of the lactating dairy cow is constructed and solved in the steady state. The model contains four intracellular and four extracellular pools and conservation of mass principles are applied to generate the fundamental equations describing the behaviour of the system. The experimental measurements required for model solution are milk secretion and plasma flow rate across the gland in combination with phenylalanine and tyrosine concentrations and plateau isotopic enrichments in arterial and venous plasma and free and protein bound milk during a constant infusion of [1-(13)C]phenylalanine and [2,3,5,6-(2)H]tyrosine tracer. If assumptions are made, model solution enables determination of steady state flows for phenylalanine and tyrosine inflow to the gland, outflow from it and bypass, and flows representing the synthesis and degradation of constitutive protein and hydroxylation. The model is effective in providing information about the fates of phenylalanine and tyrosine in the mammary gland and could be used as part of a more complex system describing amino acid metabolism in the whole ruminant.

Bradykinin B(1) receptor antagonist R954 inhibits eosinophil activation/proliferation/migration and increases TGF-beta and VEGF in a murine model of asthma

In the present study the effects of bradykinin receptor antagonists were investigated in a murine model of asthma using BALB/c mice immunized with ovalbumin/alum and challenged twice with aerosolized ovalbumin. Twenty four hours later eosinophil proliferation in the bone marrow, activation (lipid bodies formation), migration to lung parenchyma and airways and the contents of the pro-angiogenic and pro-fibrotic cytokines TGF-beta and VEGF were determined. The antagonists of the constitutive B(2) (HOE 140) and inducible B(1) (R954) receptors were administered intraperitoneally 30 min before each challenge. In sensitized mice, the antigen challenge induced eosinophil proliferation in the bone marrow, their migration into the lungs and increased the number of lipid bodies in these cells. These events were reduced by treatment of the mice with the B(1) receptor antagonist. The B(2) antagonist increased the number of eosinophils and lipid bodies in the airways without affecting eosinophil counts in the other compartments. After challenge the airway levels of VEGF and TGF-beta significantly increased and the B(1) receptor antagonist caused a further increase. By immunohistochemistry techniques TGF-beta was found to be expressed in the muscular layer of small blood vessels and VEGF in bronchial epithelial cells. The B(1) receptors were expressed in the endothelial cells. These results showed that in a murine model of asthma the B(1) receptor antagonist has an inhibitory effect on eosinophils in selected compartments and increases the production of cytokines involved in tissue repair. It remains to be determined whether this effects of the B(1) antagonist would modify the progression of the allergic inflammation towards resolution or rather towards fibrosis. (C) 2009 Elsevier Ltd. All rights reserved.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien-Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the FIT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is reported. (C) 2010 Elsevier B.V. All rights reserved.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

A Reynolds stress model for turbulent flows of viscoelastic fluids

A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic - Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.

Application of the PTT Model to Axisymmetric Free Surface Flows

This work is concerned with numerical simulation of axisymmetric viscoelastic free surface flows using the Phan-Thien-Tanner (PTT) constitutive equation. A finite difference technique for solving the governing equations for unsteady incompressible flows written in Cylindrical coordinates on a staggered grid is described. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are applied. The numerical method is verified by comparing numerical predictions of fully developed flow in a pipe with the corresponding analytic solutions. To demonstrate that the numerical method can simulate axisymmetric free surface flows governed by the PTT model, numerical results of the flow evolution of a drop impacting on a rigid dry plate are presented. In these simulations, the rheological effects of the parameters epsilon and xi are investigated.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom-Pom model

This work presents numerical simulations of two fluid flow problems involving moving free surfaces: the impacting drop and fluid jet buckling. The viscoelastic model used in these simulations is the eXtended Pom-Pom (XPP) model. To validate the code, numerical predictions of the drop impact problem for Newtonian and Oldroyd-B fluids are presented and compared with other methods. In particular, a benchmark on numerical simulations for a XPP drop impacting on a rigid plate is performed for a wide range of the relevant parameters. Finally, to provide an additional application of free surface flows of XPP fluids, the viscous jet buckling problem is simulated and discussed. (C) 2011 Elsevier B.V. All rights reserved.

Two fluid numerical model for coastal applications

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

Biomechanical model of human cornea based on stromal microstructure

The optical characteristics of the human cornea depends on the mechanical balance between the intra-ocular pressure and intrinsic tissue stiffness. A wide range of ophthalmic surgical procedures alter corneal biomechanics to induce local or global curvature changes for the correction of visual acuity. Due to the large number of surgical interventions performed every day, a deeper understanding of corneal biomechanics is needed to improve the safety of these procedures and medical devices. The aim of this study is to propose a biomechanical model of the human cornea, based on stromal microstructure. The constitutive mechanical law includes collagen fiber distribution based on X-ray scattering analysis, collagen cross-linking, and fiber uncrimping. Our results showed that the proposed model reproduced inflation and extensiometry experimental data [Elsheikh et al., Curr. Eye Res., 2007; Elsheikh et al., Exp. Eye Res., 2008] successfully. The mechanical properties obtained for different age groups demonstrated an increase in collagen cross-linking for older specimens. In future work such a model could be used to simulate non-symmetric interventions, and provide better surgical planning.

Numerical model of the human cornea based on stromal microstructure: identification of mechanical properties for two age groups

The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

Discrete element methods for asphalt concrete : development and application of user-defined microstructural models and a viscoelastic micromechanical model

As an important Civil Engineering material, asphalt concrete (AC) is commonly used to build road surfaces, airports, and parking lots. With traditional laboratory tests and theoretical equations, it is a challenge to fully understand such a random composite material. Based on the discrete element method (DEM), this research seeks to develop and implement computer models as research approaches for improving understandings of AC microstructure-based mechanics. In this research, three categories of approaches were developed or employed to simulate microstructures of AC materials, namely the randomly-generated models, the idealized models, and image-based models. The image-based models were recommended for accurately predicting AC performance, while the other models were recommended as research tools to obtain deep insight into the AC microstructure-based mechanics. A viscoelastic micromechanical model was developed to capture viscoelastic interactions within the AC microstructure. Four types of constitutive models were built to address the four categories of interactions within an AC specimen. Each of the constitutive models consists of three parts which represent three different interaction behaviors: a stiffness model (force-displace relation), a bonding model (shear and tensile strengths), and a slip model (frictional property). Three techniques were developed to reduce the computational time for AC viscoelastic simulations. It was found that the computational time was significantly reduced to days or hours from years or months for typical three-dimensional models. Dynamic modulus and creep stiffness tests were simulated and methodologies were developed to determine the viscoelastic parameters. It was found that the DE models could successfully predict dynamic modulus, phase angles, and creep stiffness in a wide range of frequencies, temperatures, and time spans. Mineral aggregate morphology characteristics (sphericity, orientation, and angularity) were studied to investigate their impacts on AC creep stiffness. It was found that aggregate characteristics significantly impact creep stiffness. Pavement responses and pavement-vehicle interactions were investigated by simulating pavement sections under a rolling wheel. It was found that wheel acceleration, steadily moving, and deceleration significantly impact contact forces. Additionally, summary and recommendations were provided in the last chapter and part of computer programming codes wree provided in the appendixes.