A Skyrme-like model with an exact BPS bound

We propose a new Skyrme-like model with fields taking values on the sphere S3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire three- dimensional space R3. We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S3, using toroidal like coordinates.

Numerical Model for the Dynamic Analysis of Pile Foundations

Programa de doctorado: Sistemas Inteligentes y Aplicaciones Numéricas en Ingeniería Instituto Universitario (SIANI)

Dynamic structure-soil-structure interaction between nearby piled buildings under seismic excitation by BEM-FEM model

[EN]The dynamic throug-soil interaction between nearby pile supported structures in a viscoelastic half-space, under incident S and Rayleigh waves, is numerically studied. To this end, a three-dimensional viscoelastic BEM-FEM formulation for the dynamic analysis of piles and pile groups in the frequency domain is used, where soil is modelled by BEM and piles are simulated by one-dimensional finite elements as Bernouilli beams.

A BEM-FEM model for the dynamic analysis of building structures founded on elastic or poroelastic soils.

[EN]This work presents a time-harmonic boundary elementfinite element three-dimensional model for the dynamic analysis of building structures founded on elastic or porelastic soils. The building foundation and soil domains are modelled as homogeneous, isotropic, elastic or poroelastic media using boundary elements.

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.

Statistical analysis of the error associated with the simplification of the stratigraphy in geotechnical models

The uncertainties in the determination of the stratigraphic profile of natural soils is one of the main problems in geotechnics, in particular for landslide characterization and modeling. The study deals with a new approach in geotechnical modeling which relays on a stochastic generation of different soil layers distributions, following a boolean logic – the method has been thus called BoSG (Boolean Stochastic Generation). In this way, it is possible to randomize the presence of a specific material interdigitated in a uniform matrix. In the building of a geotechnical model it is generally common to discard some stratigraphic data in order to simplify the model itself, assuming that the significance of the results of the modeling procedure would not be affected. With the proposed technique it is possible to quantify the error associated with this simplification. Moreover, it could be used to determine the most significant zones where eventual further investigations and surveys would be more effective to build the geotechnical model of the slope. The commercial software FLAC was used for the 2D and 3D geotechnical model. The distribution of the materials was randomized through a specifically coded MatLab program that automatically generates text files, each of them representing a specific soil configuration. Besides, a routine was designed to automate the computation of FLAC with the different data files in order to maximize the sample number. The methodology is applied with reference to a simplified slope in 2D, a simplified slope in 3D and an actual landslide, namely the Mortisa mudslide (Cortina d’Ampezzo, BL, Italy). However, it could be extended to numerous different cases, especially for hydrogeological analysis and landslide stability assessment, in different geological and geomorphological contexts.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.

Single fluoroscopic image based 2D/3D reconstruction of a scaled, patient-specific vertebral model

Purpose Accurate three-dimensional (3D) models of lumbar vertebrae can enable image-based 3D kinematic analysis. The common approach to derive 3D models is by direct segmentation of CT or MRI datasets. However, these have the disadvantages that they are expensive, timeconsuming and/or induce high-radiation doses to the patient. In this study, we present a technique to automatically reconstruct a scaled 3D lumbar vertebral model from a single two-dimensional (2D) lateral fluoroscopic image. Methods Our technique is based on a hybrid 2D/3D deformable registration strategy combining a landmark-to-ray registration with a statistical shape model-based 2D/3D reconstruction scheme. Fig. 1 shows different stages of the reconstruction process. Four cadaveric lumbar spine segments (total twelve lumbar vertebrae) were used to validate the technique. To evaluate the reconstruction accuracy, the surface models reconstructed from the lateral fluoroscopic images were compared to the associated ground truth data derived from a 3D CT-scan reconstruction technique. For each case, a surface-based matching was first used to recover the scale and the rigid transformation between the reconstructed surface model Results Our technique could successfully reconstruct 3D surface models of all twelve vertebrae. After recovering the scale and the rigid transformation between the reconstructed surface models and the ground truth models, the average error of the 2D/3D surface model reconstruction over the twelve lumbar vertebrae was found to be 1.0 mm. The errors of reconstructing surface models of all twelve vertebrae are shown in Fig. 2. It was found that the mean errors of the reconstructed surface models in comparison to their associated ground truths after iterative scaled rigid registrations ranged from 0.7 mm to 1.3 mm and the rootmean squared (RMS) errors ranged from 1.0 mm to 1.7 mm. The average mean reconstruction error was found to be 1.0 mm. Conclusion An accurate, scaled 3D reconstruction of the lumbar vertebra can be obtained from a single lateral fluoroscopic image using a statistical shape model based 2D/3D reconstruction technique. Future work will focus on applying the reconstructed model for 3D kinematic analysis of lumbar vertebrae, an extension of our previously-reported imagebased kinematic analysis. The developed method also has potential applications in surgical planning and navigation.

Laser scanning microscopy combined with image restoration to analyse a 3D model of the human epithelial airway barrier

A laser scanning microscope collects information from a thin, focal plane and ignores out of focus information. During the past few years it has become the standard imaging method to characterise cellular morphology and structures in static as well as in living samples. Laser scanning microscopy combined with digital image restoration is an excellent tool for analysing the cellular cytoarchitecture, expression of specific proteins and interactions of various cell types, thus defining valid criteria for the optimisation of cell culture models. We have used this tool to establish and evaluate a three dimensional model of the human epithelial airway wall.

Surfactant protein D modulates allergen particle uptake and inflammatory response in a human epithelial airway model

Background Allergen-containing subpollen particles (SPP) are released from whole plant pollen upon contact with water or even high humidity. Because of their size SPP can preferentially reach the lower airways where they come into contact with surfactant protein (SP)-D. The aim of the present study was to investigate the influence of SP-D in a complex three-dimensional human epithelial airway model, which simulates the most important barrier functions of the epithelial airway. The uptake of SPP as well as the secretion of pro-inflammatory cytokines was investigated. Methods SPP were isolated from timothy grass and subsequently fluorescently labeled. A human epithelial airway model was built by using human Type II-pneumocyte like cells (A549 cells), human monocyte derived macrophages as well as human monocyte derived dendritic cells. The epithelial cell model was incubated with SPP in the presence and absence of surfactant protein D. Particle uptake was evaluated by confocal microscopy and advanced computer-controlled analysis. Finally, human primary CD4+ T-Cells were added to the epithelial airway model and soluble mediators were measured by enzyme linked immunosorbent assay or bead array. Results SPP were taken up by epithelial cells, macrophages, and dendritic cells. This uptake coincided with secretion of pro-inflammatory cytokines and chemokines. SP-D modulated the uptake of SPP in a cell type specific way (e.g. increased number of macrophages and epithelial cells, which participated in allergen particle uptake) and led to a decreased secretion of pro-inflammatory cytokines. Conclusion These results display a possible mechanism of how SP-D can modulate the inflammatory response to inhaled allergen.

Clinical and biochemical description of a novel CYP21A2 gene mutation 962_963insA using a new 3D model for the P450c21 protein

OBJECTIVE: A severely virilized 46, XX newborn girl was referred to our center for evaluation and treatment of congenital adrenal hyperplasia (CAH) because of highly elevated 17alpha-hydroxyprogesterone levels at newborn screening; biochemical tests confirmed the diagnosis of salt-wasting CAH. Genetic analysis revealed that the girl was compound heterozygote for a previously reported Q318X mutation in exon 8 and a novel insertion of an adenine between nucleotides 962 and 963 in exon 4 of the CYP21A2 gene. This 962_963insA mutation created a frameshift leading to a stop codon at amino acid 161 of the P450c21 protein. AIM AND METHODS: To better understand structure-function relationships of mutant P450c21 proteins, we performed multiple sequence alignments of P450c21 with three mammalian P450s (P450 2C8, 2C9 and 2B4) with known structures as well as with human P450c17. Comparative molecular modeling of human P450c21 was then performed by MODELLER using the X-ray crystal structure of rabbit P450 2B4 as a template. RESULTS: The new three dimensional model of human P450c21 and the sequence alignment were found to be helpful in predicting the role of various amino acids in P450c21, especially those involved in heme binding and interaction with P450 oxidoreductase, the obligate electron donor. CONCLUSION: Our model will help in analyzing the genotype-phenotype relationship of P450c21 mutations which have not been tested for their functional activity in an in vitro assay.

Monte Carlo source model for photon beam radiotherapy: photon source characteristics

A major barrier to widespread clinical implementation of Monte Carlo dose calculation is the difficulty in characterizing the radiation source within a generalized source model. This work aims to develop a generalized three-component source model (target, primary collimator, flattening filter) for 6- and 18-MV photon beams that match full phase-space data (PSD). Subsource by subsource comparison of dose distributions, using either source PSD or the source model as input, allows accurate source characterization and has the potential to ease the commissioning procedure, since it is possible to obtain information about which subsource needs to be tuned. This source model is unique in that, compared to previous source models, it retains additional correlations among PS variables, which improves accuracy at nonstandard source-to-surface distances (SSDs). In our study, three-dimensional (3D) dose calculations were performed for SSDs ranging from 50 to 200 cm and for field sizes from 1 x 1 to 30 x 30 cm2 as well as a 10 x 10 cm2 field 5 cm off axis in each direction. The 3D dose distributions, using either full PSD or the source model as input, were compared in terms of dose-difference and distance-to-agreement. With this model, over 99% of the voxels agreed within +/-1% or 1 mm for the target, within 2% or 2 mm for the primary collimator, and within +/-2.5% or 2 mm for the flattening filter in all cases studied. For the dose distributions, 99% of the dose voxels agreed within 1% or 1 mm when the combined source model-including a charged particle source and the full PSD as input-was used. The accurate and general characterization of each photon source and knowledge of the subsource dose distributions should facilitate source model commissioning procedures by allowing scaling the histogram distributions representing the subsources to be tuned.

Development of the premature infant nose throat-model (PrINT-Model): an upper airway replica of a premature neonate for the study of aerosol delivery

Clinical efficacy of aerosol therapy in premature newborns depends on the efficiency of delivery of aerosolized drug to the bronchial tree. To study the influence of various anatomical, physical, and physiological factors on aerosol delivery in preterm newborns, it is crucial to have appropriate in vitro models, which are currently not available. We therefore constructed the premature infant nose throat-model (PrINT-Model), an upper airway model corresponding to a premature infant of 32-wk gestational age by three-dimensional (3D) reconstruction of a three-planar magnetic resonance imaging scan and subsequent 3D-printing. Validation was realized by visual comparison and comparison of total airway volume. To study the feasibility of measuring aerosol deposition, budesonide was aerosolized through the cast and lung dose was expressed as percentage of nominal dose. The airway volumes of the initial magnetic resonance imaging and validation computed tomography scan showed a relative deviation of 0.94%. Lung dose at low flow (1 L/min) was 61.84% and 9.00% at high flow (10 L/min), p < 0.0001. 3D-reconstruction provided an anatomically accurate surrogate of the upper airways of a 32-wk-old premature infant, making the model suitable for future in vitro testing.

Reynolds-stress turbulence model in the KIVA code for engine simulation

A Reynolds-Stress Turbulence Model has been incorporated with success into the KIVA code, a computational fluid dynamics hydrocode for three-dimensional simulation of fluid flow in engines. The newly implemented Reynolds-stress turbulence model greatly improves the robustness of KIVA, which in its original version has only eddy-viscosity turbulence models. Validation of the Reynolds-stress turbulence model is accomplished by conducting pipe-flow and channel-flow simulations, and comparing the computed results with experimental and direct numerical simulation data. Flows in engines of various geometry and operating conditions are calculated using the model, to study the complex flow fields as well as confirm the model’s validity. Results show that the Reynolds-stress turbulence model is able to resolve flow details such as swirl and recirculation bubbles. The model is proven to be an appropriate choice for engine simulations, with consistency and robustness, while requiring relatively low computational effort.

Experimental model to evaluate in vivo and in vitro cartilage MR imaging by means of histological analyses

OBJECTIVES: Implementation of an experimental model to compare cartilage MR imaging by means of histological analyses. MATERIAL AND METHODS: MRI was obtained from 4 patients expecting total knee replacement at 1.5 and/or 3T prior surgery. The timeframe between pre-op MRI and knee replacement was within two days. Resected cartilage-bone samples were tagged with Ethi((R))-pins to reproduce the histological cutting course. Pre-operative scanning at 1.5T included following parameters for fast low angle shot (FLASH: TR/TE/FA=33ms/6ms/30 degrees , BW=110kHz, 120mmx120mm FOV, 256x256 matrix, 0.65mm slice-thickness) and double echo steady state (DESS: TR/TE/FA=23.7ms/6.9ms/40 degrees , BW=130kHz, 120x120mm FOV, 256x256 matrix, 0.65mm slice-thickness). At 3T, scan parameters were: FLASH (TR/TE/FA=12.2ms/5.1ms/10 degrees , BW=130kHz, 170x170mm FOV, 320x320, 0.5mm slice-thickness) and DESS (TR/TE/FA=15.6ms/4.5ms/25 degrees , BW=200kHz, 135mmx150mm FOV, 288x320matrix, 0.5mm slice-thickness). Imaging of the specimens was done the same day at 1.5T. MRI (Noyes) and histological (Mankin) score scales were correlated using the paired t-test. Sensitivity and specificity for the detection of different grades of cartilage degeneration were assessed. Inter-reader and intra-reader reliability was determined using Kappa analysis. RESULTS: Low correlation (sensitivity, specificity) was found for both sequences in normal to mild Mankin grades. Only moderate to severe changes were diagnosed with higher significance and specificity. The use of higher field-strengths was advantageous for both protocols with sensitivity values ranging from 13.6% to 93.3% (FLASH) and 20.5% to 96.2% (DESS). Kappa values ranged from 0.488 to 0.944. CONCLUSIONS: Correlating MR images with continuous histological slices was feasible by using three-dimensional imaging, multi-planar-reformat and marker pins. The capability of diagnosing early cartilage changes with high accuracy could not be proven for both FLASH and DESS.