Statistical considerations in the kinetic analysis of PET-FDG brain tumour studies

Dynamic positron emission tomography (PET) imaging can be used to track the distribution of injected radio-labelled molecules over time in vivo. This is a powerful technique, which provides researchers and clinicians the opportunity to study the status of healthy and pathological tissue by examining how it processes substances of interest. Widely used tracers include 18F-uorodeoxyglucose, an analog of glucose, which is used as the radiotracer in over ninety percent of PET scans. This radiotracer provides a way of quantifying the distribution of glucose utilisation in vivo. The interpretation of PET time-course data is complicated because the measured signal is a combination of vascular delivery and tissue retention effects. If the arterial time-course is known, the tissue time-course can typically be expressed in terms of a linear convolution between the arterial time-course and the tissue residue function. As the residue represents the amount of tracer remaining in the tissue, this can be thought of as a survival function; these functions been examined in great detail by the statistics community. Kinetic analysis of PET data is concerned with estimation of the residue and associated functionals such as ow, ux and volume of distribution. This thesis presents a Markov chain formulation of blood tissue exchange and explores how this relates to established compartmental forms. A nonparametric approach to the estimation of the residue is examined and the improvement in this model relative to compartmental model is evaluated using simulations and cross-validation techniques. The reference distribution of the test statistics, generated in comparing the models, is also studied. We explore these models further with simulated studies and an FDG-PET dataset from subjects with gliomas, which has previously been analysed with compartmental modelling. We also consider the performance of a recently proposed mixture modelling technique in this study.

Use of Remote Sensing for Collection of Data Elements for Linear Referencing Systems, 2002

This report evaluates the use of remotely sensed images in implementing the Iowa DOT LRS that is currently in the stages of system architecture. The Iowa Department of Transportation is investing a significant amount of time and resources into creation of a linear referencing system (LRS). A significant portion of the effort in implementing the system will be creation of a datum, which includes geographically locating anchor points and then measuring anchor section distances between those anchor points. Currently, system architecture and evaluation of different data collection methods to establish the LRS datum is being performed for the DOT by an outside consulting team.

Dynamics of an axisymmetric electromagnetic 'crucible' melting

Different industrial induction melting processes involve free surface and melt-solid interface of the liquid metal subject to dynamic change during the technological operation. Simulation of the liquid metal dynamics requires to solve the non-linear, coupled hydrodynamic-electromagnetic-heat transfer problem accounting for the time development of the liquid metal free boundary with a suitable turbulent viscosity model. The present paper describes a numerical solution method applicable for various axisymmetric induction melting processes, such as, crucible with free top surface, levitation, semi-levitation, cold crucible and similar melting techniques. The presented results in the cases of semi-levitation and crucible with free top surface meltings demonstrate oscillating transient behaviour of the free metal surface indicating the presence of gravity-inertial-electromagnetic waves which are coupled to the internal fluid flow generated by both the rotational and potential parts of the electromagnetic force.

DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE MULTIPHASE FLOW WITH PHASE CHANGE

Phase change problems arise in many practical applications such as air-conditioning and refrigeration, thermal energy storage systems and thermal management of electronic devices. The physical phenomenon in such applications are complex and are often difficult to be studied in detail with the help of only experimental techniques. The efforts to improve computational techniques for analyzing two-phase flow problems with phase change are therefore gaining momentum. The development of numerical methods for multiphase flow has been motivated generally by the need to account more accurately for (a) large topological changes such as phase breakup and merging, (b) sharp representation of the interface and its discontinuous properties and (c) accurate and mass conserving motion of the interface. In addition to these considerations, numerical simulation of multiphase flow with phase change introduces additional challenges related to discontinuities in the velocity and the temperature fields. Moreover, the velocity field is no longer divergence free. For phase change problems, the focus of developmental efforts has thus been on numerically attaining a proper conservation of energy across the interface in addition to the accurate treatment of fluxes of mass and momentum conservation as well as the associated interface advection. Among the initial efforts related to the simulation of bubble growth in film boiling applications the work in \cite{Welch1995} was based on the interface tracking method using a moving unstructured mesh. That study considered moderate interfacial deformations. A similar problem was subsequently studied using moving, boundary fitted grids \cite{Son1997}, again for regimes of relatively small topological changes. A hybrid interface tracking method with a moving interface grid overlapping a static Eulerian grid was developed \cite{Juric1998} for the computation of a range of phase change problems including, three-dimensional film boiling \cite{esmaeeli2004computations}, multimode two-dimensional pool boiling \cite{Esmaeeli2004} and film boiling on horizontal cylinders \cite{Esmaeeli2004a}. The handling of interface merging and pinch off however remains a challenge with methods that explicitly track the interface. As large topological changes are crucial for phase change problems, attention has turned in recent years to front capturing methods utilizing implicit interfaces that are more effective in treating complex interface deformations. The VOF (Volume of Fluid) method was adopted in \cite{Welch2000} to simulate the one-dimensional Stefan problem and the two-dimensional film boiling problem. The approach employed a specific model for mass transfer across the interface involving a mass source term within cells containing the interface. This VOF based approach was further coupled with the level set method in \cite{Son1998}, employing a smeared-out Heaviside function to avoid the numerical instability related to the source term. The coupled level set, volume of fluid method and the diffused interface approach was used for film boiling with water and R134a at the near critical pressure condition \cite{Tomar2005}. The effect of superheat and saturation pressure on the frequency of bubble formation were analyzed with this approach. The work in \cite{Gibou2007} used the ghost fluid and the level set methods for phase change simulations. A similar approach was adopted in \cite{Son2008} to study various boiling problems including three-dimensional film boiling on a horizontal cylinder, nucleate boiling in microcavity \cite{lee2010numerical} and flow boiling in a finned microchannel \cite{lee2012direct}. The work in \cite{tanguy2007level} also used the ghost fluid method and proposed an improved algorithm based on enforcing continuity and divergence-free condition for the extended velocity field. The work in \cite{sato2013sharp} employed a multiphase model based on volume fraction with interface sharpening scheme and derived a phase change model based on local interface area and mass flux. Among the front capturing methods, sharp interface methods have been found to be particularly effective both for implementing sharp jumps and for resolving the interfacial velocity field. However, sharp velocity jumps render the solution susceptible to erroneous oscillations in pressure and also lead to spurious interface velocities. To implement phase change, the work in \cite{Hardt2008} employed point mass source terms derived from a physical basis for the evaporating mass flux. To avoid numerical instability, the authors smeared the mass source by solving a pseudo time-step diffusion equation. This measure however led to mass conservation issues due to non-symmetric integration over the distributed mass source region. The problem of spurious pressure oscillations related to point mass sources was also investigated by \cite{Schlottke2008}. Although their method is based on the VOF, the large pressure peaks associated with sharp mass source was observed to be similar to that for the interface tracking method. Such spurious fluctuation in pressure are essentially undesirable because the effect is globally transmitted in incompressible flow. Hence, the pressure field formation due to phase change need to be implemented with greater accuracy than is reported in current literature. The accuracy of interface advection in the presence of interfacial mass flux (mass flux conservation) has been discussed in \cite{tanguy2007level,tanguy2014benchmarks}. The authors found that the method of extending one phase velocity to entire domain suggested by Nguyen et al. in \cite{nguyen2001boundary} suffers from a lack of mass flux conservation when the density difference is high. To improve the solution, the authors impose a divergence-free condition for the extended velocity field by solving a constant coefficient Poisson equation. The approach has shown good results with enclosed bubble or droplet but is not general for more complex flow and requires additional solution of the linear system of equations. In current thesis, an improved approach that addresses both the numerical oscillation of pressure and the spurious interface velocity field is presented by featuring (i) continuous velocity and density fields within a thin interfacial region and (ii) temporal velocity correction steps to avoid unphysical pressure source term. Also I propose a general (iii) mass flux projection correction for improved mass flux conservation. The pressure and the temperature gradient jump condition are treated sharply. A series of one-dimensional and two-dimensional problems are solved to verify the performance of the new algorithm. Two-dimensional and cylindrical film boiling problems are also demonstrated and show good qualitative agreement with the experimental observations and heat transfer correlations. Finally, a study on Taylor bubble flow with heat transfer and phase change in a small vertical tube in axisymmetric coordinates is carried out using the new multiphase, phase change method.

An identification procedure of multi-input Wiener models for the distortion analysis of nonlinear circuits

In this contribution, a system identification procedure of a two-input Wiener model suitable for the analysis of the disturbance behavior of integrated nonlinear circuits is presented. The identified block model is comprised of two linear dynamic and one static nonlinear block, which are determined using an parameterized approach. In order to characterize the linear blocks, an correlation analysis using a white noise input in combination with a model reduction scheme is adopted. After having characterized the linear blocks, from the output spectrum under single tone excitation at each input a linear set of equations will be set up, whose solution gives the coefficients of the nonlinear block. By this data based black box approach, the distortion behavior of a nonlinear circuit under the influence of an interfering signal at an arbitrary input port can be determined. Such an interfering signal can be, for example, an electromagnetic interference signal which conductively couples into the port of consideration. © 2011 Author(s).

Finite time extinction for nonlinear fractional evolution equations and related properties

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Finite time extinction for nonlinear fractional evolution equations and related properties.

The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time. Some concrete examples of quasi-linear partial differential operators are proposed. Our results can also be applied in the framework of suitable nonlinear Volterra integro-differential equations.

Lysossomal membrane stability of the brown mussel Perna perna (Linnaeus) (Mollusca, Bivalvia) exposed to the anionic surfactant Linear Alkylbenzene Sulphonate (LAS).

The effects of the Linear Alkylbenzene Sulphonate (LAS) were evaluated on the mussel Perna perna (Linnaeus, 1758), using a cellular level biomarker. The Neutral Red Retention Time (NRRT) assay was used to estimate effects at cellular levels. Significant effects were observed for the NRRT assay, even in low concentrations. The effects at cellular level were progressive, suggesting that the organisms are not capable to recover of such increasing effects. Additionally, the results show that the levels of LAS observed for Brazilian coastal waters may chronically affect the biota.

Physiological responses of the brown mussel Perna perna (Mollusca, Bivalvia) exposed to the anionic surfactant linear alkylbenzene sulphonate (LAS).

The effects of the Linear Alkylbenzene Sulphonate (LAS) were evaluated on the mussel Perna perna, using physiological and genotoxic biomarkers. The Micronuclei (MN) assay was used to estimate effects at nuclear level, whereas the physiological effects were evaluated by measuring the oxygen consumption and ammonia excretion rates. Significant effects were observed for the MN assay and the ammonia excretion rate, even in low concentrations. The oxygen consumption was not affected in the tested concentrations. For MN and ammonia excretion, the animals exposed to intermediate concentrations were not affected, but responded to the higher concentrations, indicating the existence of compensatory mechanisms at physiological level. However, parallel to this study other authors indicate the presence of progressive effects at the cellular level, suggesting that the organisms are not capable to recover of such increasing effects. Additionally, the results show that the levels of LAS observed for Brazilian coastal waters may chronically affect the biota.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

Development of numerical tools for the simulation, design and optimization of a Helicon Plasma Thruster

This work thesis focuses on the Helicon Plasma Thruster (HPT) as a candidate for generating thrust for small satellites and CubeSats. Two main topics are addressed: the development of a Global Model (GM) and a 3D self-consistent numerical tool. The GM is suitable for preliminary analysis of HPTs with noble gases such as argon, neon, krypton, and xenon, and alternative propellants such as air and iodine. A lumping methodology is developed to reduce the computational cost when modelling the excited species in the plasma chemistry. A 3D self-consistent numerical tool is also developed that can treat discharges with a generic 3D geometry and model the actual plasma-antenna coupling. The tool consists of two main modules, an EM module and a FLUID module, which run iteratively until a steady state solution is converged. A third module is available for solving the plume with a simplified semi-analytical approach, a PIC code, or directly by integration of the fluid equations. Results obtained from both the numerical tools are benchmarked against experimental measures of HPTs or Helicon reactors, obtaining very good qualitative agreement with the experimental trend for what concerns the GM, and an excellent agreement of the physical trends predicted against the measured data for the 3D numerical strategy.

Numerical Analysis and Redesign of a High Speed Linear Cascade Wind Tunnel for Aircraft Gas Turbine Engines Testing

Linear cascade testing serves a fundamental role in the research, development, and design of turbomachines as it is a simple yet very effective way to compute the performance of a generic blade geometry. These kinds of experiments are usually carried out in specialized wind tunnel facilities. This thesis deals with the numerical characterization and subsequent partial redesign of the S-1/C Continuous High Speed Wind Tunnel of the Von Karman Institute for Fluid Dynamics. The current facility is powered by a 13-stage axial compressor that is not powerful enough to balance the energy loss experienced when testing low turning airfoils. In order to address this issue a performance assessment of the wind tunnel was performed under several flow regimes via numerical simulations. After that, a redesign proposal aimed at reducing the pressure loss was investigated. This consists of a linear cascade of turning blades to be placed downstream of the test section and designed specifically for the type of linear cascade being tested. An automatic design procedure was created taking as input parameters those measured at the outlet of the cascade. The parametrization method employed Bézier curves to produce an airfoil geometry that could be imported into a CAD software so that a cascade could be designed. The proposal was simulated via CFD analysis and proved to be effective in reducing pressure losses up to 41%. The same tool developed in this thesis could be adopted to design similar apparatuses and could also be optimized and specialized for the design of turbomachines components.

A Comparative Analysis of Dynamical Models for Tidal Dissipation in Natural Satellite Ephemerides

The study of the tides of a celestial bodies can unveil important information about their interior as well as their orbital evolution. The most important tidal parameter is the Love number, which defines the deformation of the gravity field due to an external perturbing body. Tidal dissipation is very important because it drives the secular orbital evolution of the natural satellites, which is even more important in the case of the the Jupiter system, where three of the Galilean moons, Io, Europa and Ganymede, are locked in an orbital resonance where the ratio of their mean motions is 4:2:1. This is called Laplace resonance. Tidal dissipation is described by the dissipation ratio k2/Q, where Q is the quality factor and it describes the dampening of a system. The goal of this thesis is to analyze and compare the two main tidal dynamical models, Mignard's model and gravity field variation model, to understand the differences between each model with a main focus on the single-moon case with Io, which can help also understanding better the differences between the two models without over complicating the dynamical model. In this work we have verified and validated both models, we have compared them and pinpointed the main differences and features that characterize each model. Mignard's model treats the tides directly as a force, while the gravity field variation model describes the tides with a change of the spherical harmonic coefficients. Finally, we have also briefly analyzed the difference between the single-moon case and the two-moon case, and we have confirmed that the governing equations that describe the change of semi-major axis and eccentricity are not good anymore when more moons are present.

Transmission Of Intra-cellular Genetic Information: A System Proposal.

One of the great challenges of the scientific community on theories of genetic information, genetic communication and genetic coding is to determine a mathematical structure related to DNA sequences. In this paper we propose a model of an intra-cellular transmission system of genetic information similar to a model of a power and bandwidth efficient digital communication system in order to identify a mathematical structure in DNA sequences where such sequences are biologically relevant. The model of a transmission system of genetic information is concerned with the identification, reproduction and mathematical classification of the nucleotide sequence of single stranded DNA by the genetic encoder. Hence, a genetic encoder is devised where labelings and cyclic codes are established. The establishment of the algebraic structure of the corresponding codes alphabets, mappings, labelings, primitive polynomials (p(x)) and code generator polynomials (g(x)) are quite important in characterizing error-correcting codes subclasses of G-linear codes. These latter codes are useful for the identification, reproduction and mathematical classification of DNA sequences. The characterization of this model may contribute to the development of a methodology that can be applied in mutational analysis and polymorphisms, production of new drugs and genetic improvement, among other things, resulting in the reduction of time and laboratory costs.