Critical care is provided to patients who require intensive monitoring and often the support of failing organs. Cardiovascular and circulatory diseases and dysfunctions are extremely common in this group of patients. However, cardiac disease states are highly patient-specific and every patient has a unique expression of the disease or underlying dysfunction. Clinical staff must consider many combinations of different disease scenarios based on frequently conflicting or confusing measured data on a patient’s condition. Successful diagnosis and treatment therefore often rely on the experience and intuition of clinical staff, increasing the likelihood for clinical errors. A cardiovascular (CVS) computerized model that uniquely represents the patient and underlying dysfunction or disease is developed. The CVS model is extended to account for the known physiologic mechanisms during spontaneous breathing and mechanical ventilation, thus increasing the model’s accuracy of representing a critically ill patient in the intensive care unit (ICU). The extended CVS model is validated by correctly simulating several well known circulatory mechanisms and interactions. An integral-based system parameter identification method is refined and extended to account for much smaller subsets of available input data, as usually seen in critical care units. For example, instead of requiring the continuous ventricle pressure and volume waveforms, only the end-systolic (ESV) and end-diastolic (EDV) volume values are needed, which can be even further reduced to only using the global end-diastolic volume (GEDV) and estimating the ventricle volumes. These changes make the CVS model and its application to monitoring more pplicable to a clinical environment. The CVS model and integral-based parameter identification approach are validated on data from porcine experiments of pulmonary embolism (PE), positive end-expiratory pressure (PEEP) titrations at different volemic levels, and 2 different studies of induced endotoxic (septic) shock. They are also validated on 3 adrenaline dosing data sets obtained from published studies in humans. Overall, these studies are used to show how the model and realistic clinical measurements may be used to provide a clear clinical picture in real-time. A wide range of clinically measured hemodynamics were successfully captured over time. The integral-based method identified all model parameters, typically with less than 10% error versus clinically measured pressure and volume signals. Moreover, patient-specific parameter relationships were formulated allowing the forward prediction of the patient’s response towards clinical interventions, such as administering a fluid bolus or changing the dose of an inotrope. Hence, the model and methods are able to provide diagnostic information and therapeutic decision support. In particular, tracking the model parameter changes over time can assist clinical staff in finding the right diagnosis, for example an increase in pulmonary vascular resistance indicates a developing constriction in the pulmonary artery caused by an embolus. Furthermore, using the predictive ability of the model and developed methods, different treatment choices and their effect on the patient can be simulated. Thus, the best individual treatment for each patient can be developed and chosen, and unnecessary or even harmful interventions avoided. This research thus increases confidence in the clinical applicability and validity of this overall diagnostic monitoring and therapy guidance approach. It accomplishes this goal using a novel physiological model of the heart and circulation. The integral-based parameter identification methods take dense, numerical data from diverse measurements and aggregate them into a clearer physiological picture of CVS status. Hence, the broader accomplishment of this thesis is the transformation, using computation and models, of diverse and often confusing measured data into a patient-specific physiological picture - a new model-based therapeutic.

La modelación numérica del flujo de agua subterránea y del transporte de masa se está convirtiendo en un criterio de referencia en la actualidad para la evaluación de recursos hídricos y la protección del medio ambiente. Para que las predicciones de los modelos sean fiables, estos deben de estar lo más próximo a la realidad que sea posible. Esta proximidad se adquiere con los métodos inversos, que persiguen la integración de los parámetros medidos y de los estados del sistema observados en la caracterización del acuífero. Se han propuesto varios métodos para resolver el problema inverso en las últimas décadas que se discuten en la tesis. El punto principal de esta tesis es proponer dos métodos inversos estocásticos para la estimación de los parámetros del modelo, cuando estos no se puede describir con una distribución gausiana, por ejemplo, las conductividades hidráulicas mediante la integración de observaciones del estado del sistema, que, en general, tendrán una relación no lineal con los parámetros, por ejemplo, las alturas piezométricas. El primer método es el filtro de Kalman de conjuntos con transformación normal (NS-EnKF) construido sobre la base del filtro de Kalman de conjuntos estándar (EnKF). El EnKF es muy utilizado como una técnica de asimilación de datos en tiempo real debido a sus ventajas, como son la eficiencia y la capacidad de cómputo para evaluar la incertidumbre del modelo. Sin embargo, se sabe que este filtro sólo trabaja de manera óptima cuándo los parámetros del modelo y las variables de estado siguen distribuciones multigausianas. Para ampliar la aplicación del EnKF a vectores de estado no gausianos, tales como los de los acuíferos en formaciones fluvio-deltaicas, el NSEnKF propone aplicar una transformación gausiana univariada. El vector de estado aumentado formado por los parámetros del modelo y las variables de estado se transforman en variables con una distribución marginal gausiana. / Zhou ., H. (2011). Stochastic Inverse Methods to Identify non-Gaussian Model Parameters in Heterogeneous Aquifers [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/12267 / Palancia

Cette thèse a pour objectif la mise en place d'une stratégie mathématique pour l'étude du processus physique de l'agrégation des protéines. L'étude de ce processus largement inconnu est particulièrement importante puisqu'il a été identifiée comme un élément clé d'une vaste gamme de maladies incurables, appelées maladies amyloïdes. Les maladies à prions appartiennent à cette classe et sont causées par l'agrégation d'une configuration mal pliée de la protéine prion. Notre travail contribue à la recherche sur les maladies à prions, en se concentrant sur deux types d'agrégats : les oligomères et les fibres.Les oligomères suspectés d'être les agrégats les plus toxiques sont étudiés dans la première partie de cette thèse. Nous fondons notre travail sur l'analyse de deux types de données expérimentales. D'une part, nous considérons les données de dispersion statique de la lumière (SLS), qui peuvent être interprétées biologiquement comme la mesure de la taille moyenne des oligomères et mathématiquement comme le deuxième moment de la concentration des agrégats. D'autre part, nous considérons les données de distribution de taille d'oligomère collectées à plusieurs instants en utilisant la Chromatographie d'Exclusion de Taille (SEC). Notre étude conduit à la conclusion importante selon laquelle au moins deux types différents d'oligomères sont présents. De plus, nous proposons une description de l'interaction entre ces oligomères en proposant pour la première fois un modèle à deux espèces. Notre modèle est composé d'un ensemble d'ODE avec les taux cinétiques comme paramètres. La description qualitative fournie par ce modèle a été couplée à l'information contenue dans les données expérimentales de SLS dans le cadre de l'assimilation de données. Au moyen de la méthode du filtre de Kalman étendue, nous résolvons un problème inverse non linéaire, estimant ainsi les coefficients cinétiques associés aux données expérimentales. Pour valider ce modèle, nous avons comparé notre estimation aux données expérimentales de SEC, en observant un très bon accord entre les deux. Notre caractérisation des espèces d'oligomères peut conduire à de nouvelles stratégies pour concevoir un premier traitement ciblé pour les maladies à prions.La méthodologie appliquée à l'étude des oligomères peut être considérée comme une première étape dans l'analyse des fibres. En raison des propriétés physiques de ces agrégats, des expériences moins nombreuses et moins précises peuvent être effectuées, et une approche mathématique peut donc apporter une contribution précieuse à leur étude. Notre contribution est de proposer une stratégie générale pour estimer l'état initial d'un système de fibres. Inspiré par la théorie de Lifshitz-Slyozov, nous décrivons ce système par une équation de transport couplée à une équation intégrale. L'estimation est faite en utilisant quelques observations empiriques sur le système. Nous considérons le cas général d'observation d'un moment d'ordre $n$. Il est en effet possible de mesurer le moment d'ordre $1$ par fluorescence de thioflavine T ou le moment d'ordre $2$ par SLS. Nous proposons une solution théorique et numérique du problème d'estimation de la condition initiale dans le cas linéaire d'un système de dépolymérisation. En particulier, pour des taux de dépolymérisation constants, nous proposons une stratégie de régularisation par noyau, qui fournit une première caractérisation de l'estimation. Dans le cas de taux de dépolymérisation variables, nous proposons la méthode d'assimilation variationnelle 4d-Var et la méthode d'assimilation de données séquentielle du filtrage de Kalman. Ces deux méthodes sont plus générales et peuvent être facilement adaptée pour traiter différents problèmes. Ce problème inverse est particulièrement intéressant puisqu'il peut également être appliqué dans d'autres domaines tels que le cycle cellulaire ou la formation de poussière. / The aim of this PhD thesis is to set up a mathematical strategy to investigate the physical process of protein aggregation. The study of this largely unknown process is particularly important since it has been identified as a key feature of a wide class of incurable diseases, called amyloid diseases. Prion diseases belong to this class and are caused by the aggregation of a misfolded configuration of the prion protein. Our work contributes to the research on prion diseases, by focusing on two kinds of aggregates: oligomers and fibrils. Oligomers, which are suspected of being the most toxic aggregates, are studied in the first part of this thesis. We base our work on the analysis of two types of experimental data. On the one hand, we consider Static Light Scattering (SLS) data, which can be interpreted biologically as the measurement of the average oligomer size and mathematically as the second moment of aggregate concentration. On the other hand, we consider oligomer size distribution data collected at several instants by using Size Exclusion Chromatography (SEC). Our study leads to the important conclusion that at least two different types of oligomers are present. Moreover, we provide a description of the interaction between these oligomers by proposing, for the first time, a two-species model. Our model is composed of a set of ODEs with the kinetic rates as parameters. The qualitative description provided by this model has been coupled to the information contained in the noisy experimental SLS data in a data assimilation framework. By means of the extended Kalman filter method, we solve a non-linear inverse problem, thereby estimating the kinetic coefficients associated to the experimental data. To validate this model we have compared our estimation to the experimental SEC data, observing a very good agreement between the two. Our oligomer species characterisation may lead to new strategies to design a first targeted treatment for prion diseases. The methodology applied to the study of oligomers can be seen as a first step in the analysis of fibrils. Due to the physical properties of these aggregates, fewer and less precise experiments can be performed and so a mathematical approach can provide a valuable contribution to their study. Our contribution is to propose a general strategy to estimate the initial condition of a fibril system. Inspired by the Lifshitz-Slyozov theory, we describe this system by a transport equation coupled with an integral equation. The estimation is performed making use of some empirical observations on the system. We consider the general case of observing a moment of order $n$. It is indeed possible to measure the first moment by Thioflavine T fluorescence or the second moment by SLS. We provide a theoretical and numerical solution of the initial condition estimation problem in the linear case of a depolymerising system. In particular, for constant depolymerisation rates, we propose a kernel regularisation strategy, that provides a first characterisation of the estimation. In the variable depolymerisation rates, we outline the variational data assimilation method $4$d-Var.This method is more general and can be easily adapted to treat different problems. This inverse problem is particularly interesting since it can also be applied in other fields such as the cell cycle or dust formation.

This dissertation addresses the modeling, identification, and control of an automated planing vessel. To provide motion models for trajectory generation and to enable model-based control design for trajectory tracking, several experimentally identified models are compared over a wide range of speed and planing conditions for the Virginia Tech Ribcraft Unmanned Surface Vehicle. The modeling and identification objective is to determine a model which is sufficiently rich to enable effective model-based control design and trajectory optimization, sufficiently simple to allow parameter identification, and sufficiently general to describe a variety of hull forms and actuator configurations. Beginning with a 6 degree of freedom nonlinear dynamic model, several linear steering and speed models are obtained as well as a thruster model. The Ribcraft USV tracks trajectories generated with the selected maneuvering models by using a back- stepping trajectory controller. A PD cascade trajectory control law is also developed and the performance of the two controllers is compared using aggressive trajectories. The backstepping control law compares favorably to the PD cascade controller. The backstepping control law is then further modified to account for nonlinear sternward dynamics and for a constant or slowly varying fluid flow. / Ph. D.

No description available.

<p> A novel mathematical model has been developed for biofilms and bioflocs. The model is based on the use of the effectiveness factor and the effect of cell density is included. The key assumption in the model is that cell density decreases in proportion to the substrate concentration within the biofilm or biofloc, reflecting lower rates of cellular metabolism. The equations given by the model were solved numerically for three types of reaction kinetics: Monod, Andrews (substrate inhibition), and multiple-Monod (twolimiting substrates), as well as for two geometries: a slab, as a representation of a biofilm and a sphere, as a representation of a biofloc. The simulations indicate that a decrease of the cell density in the biofilm and biofloc results in a decline of the effectiveness factor. Furthermore, the analytical solutions and approximate analytical versions of the effectiveness factor for the biofilm in two cell growth models: Monod and Andrews, have been derived. The effectiveness factors derived analytically are in agreement with those calculated numerically, and the approximate analytical versions are valid for the Thiele modulus greater than five. This new model was tested using operational data available in the literature, by including the effectiveness factor as a part of the design equations for an upflow anaerobic sludge blanket (UASB) reactor. </p> <p> For any biologically mediated transformation, it is critical to uniquely identify the parameters associated with microbial growth models. In this study, it is proved that the parameters of the integrated Andrews model are identifiable if the experimental data does not contain any random noise based on a criterion proposed by Beck and Arnold [1977]. When noise is present, the parameters may or may not be identifiable, depending on noise levels. A new approach has been developed based on the calculation of dimensionless sensitivity coefficients. Plotting these coefficients provides straightforward visualization of parameter identification. This method was used for quantitative evaluation of the noise level that can be associated with measurements, while still allowing parameter identification. It was demonstrated that an indirect cause of the parameter nonidentification of the integrated Andrews model is the linearization of the Andrews model at a low or high substrate concentration. Robinson [1985] obtained a similar result with the Monod model. </p> / Thesis / Master of Science (MSc)

The solutions for a class of Neutral Functional Di erential Equations (NFDE) with weakly singular kernels are studied. Using singular expansion techniques, a representation of the solution of the NFDE is obtained by studing an associated Volterra Integral Equation. We study the Collocation Method as a projection method for the approximation of solutions for Volterra Integral Equations. Particulary, the possibility of achieving higher order ap- proximations is discussed. Special attention is given to the choice of the projection space and its relation to the smoothness of the approximated solution. Finally, we study the identification problem for a parameter appearing in the weakly singular operator of the NFDE. / Ph. D.

Mathematical models are useful for simulation, design, analysis, control, and optimization of complex systems. One important step necessary to create an effective model is designing an experiment from which the unknown model parameter can be accurately identified and then verified. The strategy which one approaches this problem is dependent on the amount of data that can be collected and the assumptions made about the behavior of the error in the statistical model. In this presentation we describe how to approach this problem using a combination of statistical and mathematical theory with reliable computation. More specifically, we present a new approach to bounded error parameter validation that approximates the membership set by solving an inverse problem rather than using the standard forward interval analysis methods. For our method we provide theoretical justification, apply this technique to several examples, and describe how it relates to designing experiments. We also address how to define infinite dimensional designs that can be used to create designs of any finite dimension. In general, finding a good design for an experiment requires a careful investigation of all available information and we provide an effective approach to dthe problem. / Ph. D.

The harmonic oscillatory tests for a fighter aircraft configuration using the Dynamic Plunge-Pitch-Roll (DyPPiR) model mount at Virginia Tech Stability Wind Tunnel are described and analyzed. The corresponding data reduction methods are developed on the basis of multirate digital signal processing techniques. Since the model is sting-mounted to the support system of DyPPiR, the Discrete Fourier Transform (DFT) is first used to identify the frequencies of the elastic modes of sting. Then the sampling rate conversion systems are built up in digital domain to resample the data at a lower rate without introducing distortions to the signals of interest. Finally linear-phase Finite Impulse Response (FIR) filters are designed by Remez exchange algorithm to extract the aerodynamic characteristics responses to the programmed motions from the resampled measurements. These data reduction procedures are also illustrated through examples. The results obtained from the harmonic oscillatory tests are then illustrated and the associated flow mechanisms are discussed. Since no significant hysteresis loops are observed for the lift and the drag coefficients for the current angle of attack range and the tested reduced frequencies, the dynamic lags of separated and vortex flow effects are small in the current oscillatory tests. However, large hysteresis loops are observed for pitch moment coefficient in the current tests. This observation suggests that at current flow conditions, pitch moment has large pitch rate and alpha-dot dependencies. Then the nondimensional maximum pitch rate q__max is introduced to characterize these harmonic oscillatory motions. It is found that at current flow conditions, all the hysteresis loops of pitch moment coefficient with same nondimensional maximum pitch rate are tangential to one another at both top and bottom of the loops, implying approximately same maximum offset of these loops from static values. Several cases are also illustrated. Based on the results obtained and those from references, a state-space model is developed to describe the unsteady aerodynamic characteristics up to the high angle of attack regime. A nondimensional coordinate is introduced as the state variable describing the flow separation or vortex burst. First-order differential equation is used to govern the dynamics of flow separation or vortex bursting through this state variable. To be valid for general configurations, Taylor series expansions in terms of the input variables are used in the determination of aerodynamic characteristics, resembling the current approach of the stability derivatives. However, these derivatives are longer constant. They are dependent on the state variable of flow separation or vortex burst. In this way, the changes in stability derivatives with the angle of attack are included dynamically. The performance of the model is then validated by the wind-tunnel measurements of an NACA 0015 airfoil, a 70 degree delta wing and, finally two F-18 aircraft configurations. The results obtained show that within the framework of the proposed model, it is possible to obtain good agreement with different unsteady wind tunnel data in high angle-of-attack regime. / Ph. D.

As simulation plays an increasingly central role in modern science and engineering research, by supplementing experiments, aiding in the prototyping of engineering systems or informing decisions on safety and reliability, the need to quantify uncertainty in model outputs due to uncertainties in the model parameters becomes critical. However, the statistical characterization of the model parameters is rarely known. In this thesis, we propose a variational approach to solve the stochastic inverse problem of obtaining a statistical description of the diffusion coefficient in an elliptic partial differential equation, based noisy measurements of the model output. We formulate the parameter identification problem as an infinite dimensional constrained optimization problem for which we establish existence of minimizers as well as first order necessary conditions. A spectral approximation of the uncertain observations (via a truncated Karhunen-Loeve expansion) allows us to estimate the infinite dimensional problem by a smooth, albeit high dimensional, deterministic optimization problem, the so-called 'finite noise' problem, in the space of functions with bounded mixed derivatives. We prove convergence of 'finite noise' minimizers to the appropriate infinite dimensional ones, and devise a gradient based, as well as a sampling based strategy for locating these numerically. Lastly, we illustrate our methods by means of numerical examples. / Ph. D.