In this work we have developed three ordinary differential equation models of biological systems: body mass change in response to exercise, immune system response to a general inflammatory stimulus, and the immune system response in atherosclerosis. The purpose of developing such computational tools is to test hypotheses about the underlying biological processes that drive system outcomes as well as possible real medical interventions. Therefore, we focus our analysis on understanding key interactions between model parameters and outcomes to deepen our understanding of these complex processes as a means to developing effective treatments in obesity, sarcopenia, and inflammatory diseases. We develop a model of the dynamics of muscle hypertrophy in response to resistance exercise and have shown that the parameters controlling response vary between male and female group means in an elderly population. We further explore this individual variability by fitting to data from a clinical obesity study. We then apply logistic regression and classification tree methods to the analysis of between- and within-group differences in underlying physiology that lead to different long-term body composition outcomes following a diet or exercise program. Finally, we explore dieting strategies using optimal control methods. Next, we extend an existing model of inflammation to include different macrophage phenotypes. Complications with this phenotype switch can result in the accumulation of too many of either type and lead to chronic wounds or disease. With this model we are able to reproduce the expected timing of sequential influx of immune cells and mediators in a general inflammatory setting. We then calibrate this base model for the sequential response of immune cells with peritoneal cavity data from mice. Next, we develop a model for plaque formation in atherosclerosis by adapting the current inflammation model to capture the progression of macrophages to inflammatory foam cells in response to cholesterol consumption. The purpose of this work is ultimately to explore points of intervention that can lead to homeostasis.

Les immunoessais en phase solide sont utilisés pour le diagnostic in vitro afin de détecter ou de quantifier une molécule dans un échantillon biologique. Ils s'appuient sur l'interaction spécifique entre un antigène et un anticorps. Habituellement, des anticorps spécifiques aux antigènes à détecter sont immobilisés sur une surface solide pour capturer les antigènes d'intérêt et les séparer du reste de l'échantillon.Lors du développement d'un immunoessai, la sensibilité, la spécificité et le temps d’analyse sont optimisés par le choix - classiquement empirique - de ligands, de supports solides, de débits,… Une meilleure compréhension et prédiction des interactions moléculaires complexes se produisant au cours d’un immunoessai seraient utiles pour : identifier les paramètres critiques des immunoessais, simplifier et accélérer le processus d’identification des meilleures conditions opératoires et améliorer les immunoessais existants.L'instrument VIDAS®, commercialisé par bioMérieux, est l'un des systèmes d’immunoessais les plus utilisés dans les laboratoires cliniques. Dans ce travail de thèse, deux outils expérimentaux basés sur la chromatographie inverse sont construits et testés. Un modèle prédictif de la cinétique d'interaction anticorps/antigène est développé. Les outils expérimentaux, fonctionnant dans des conditions très proches du VIDAS®, sont utilisés pour valider le modèle et estimer ses paramètres caractérisant les interactions anticorps/antigène à partir de courbes expérimentales. Dans l’avenir et à partir des résultats, un des outils expérimentaux associé au modèle pourra être utilisé par bioMérieux pour concevoir des systèmes d’immunoessais / Solid-phase immunoassays are used for in vitro diagnostic to detect the presence or measure the concentration of a molecule of interest in a biological sample. They rely on the specific interaction between an antigen and an antibody. Usually, antibodies specific to the antigens to be detected are immobilized on a solid surface to capture the antigens of interest and separate them from the rest of the sample components. During solid-phase immunoassay development, sensitivity, specificity and time-to-result need to be optimized through the choice of dedicated ligands, solid supports, flow rates,… Classically, these choices are made empirically. A better understanding and prediction of the complex molecular interactions that occur in the different steps of a diagnostic immunoassay is likely to be useful to: identify the critical parameters of immunoassays, simplify and speed-up the process of identification of the best immunoassay conditions and improve the immunoassays currently available. The VIDAS® instrument, commercialized by bioMérieux is one of the most widely used immunoassay system in clinical laboratories worldwide. In this PhD work, two experimental tools based on inverse chromatography are built and tested. A predictive model of antibody/antigen interaction kinetics in immunoassays is developed. The experimental tools which mimic VIDAS® process conditions are used to validate the predictive model and to estimate model parameters characterizing antibody/antigen interaction kinetics from experimental curves. In the future, based on the results, one of the experimental tools associated with the model could be used by bioMérieux to design immunoassay systems

High frequency time series data have become increasingly common. In many settings, such as the medical sciences or economics, these series may additionally display semi-reflective boundaries. These are boundaries, either physically existing, arbitrarily set, or determined based on inherent qualities of the series, which may be exceeded and yet based on probable consequences offer incentives to return to mid-range levels. In a lane control setting, Dawson, Cavanaugh, Zamba, and Rizzo (2010) have previously developed a weighted third-order autoregressive model utilizing flat, linear, and quadratic projections with a signed error term in order to depict key features of driving behavior, where the probability of a negative residual is predicted via logistic regression. In this driving application, the intercept (Λ0) of the logistic regression model describes the central tendency of a particular driver while the slope parameter (Λ1 ) can be intuitively defined as a representation of the propensity of the series to return to mid-range levels. We call this therefore the "re-centering" parameter, though this is a slight misnomer since the logistic model does not describe the position of the series, but rather the probability of a negative residual. In this framework a multi-step estimation algorithm, which we label as the Single-Pass method, was provided. In addition to investigating the statistical properties of the Single-Pass method, several other estimation techniques are investigated. These techniques include an Iterated Grid Search, which utilizes the underlying likelihood model, and four modified versions of the Single-Pass method. These Modified Single-Pass (MSP) techniques utilize respectively unconstrained least squares estimation for the vector of projection coefficients (Β), use unconstrained linear regression with a post-hoc application of the summation constraint, reduce the regression model to include only the flat and linear projections, or implement the Least Absolute Shrinkage and Selection Operator (LASSO). For each of these techniques, mean bias, confidence intervals, and coverage probabilities were calculated which indicated that of the modifications only the first two were promising alternatives. In a driving application, we therefore considered these two modified techniques along with the Single-Pass and Iterative Grid Search. It was found that though each of these methods remains biased with generally lower than ideal coverage probabilities, in a lane control setting they are each able to distinguish between two populations based on disease status. It has also been found that the re-centering parameter, estimated based on data collected in a driving simulator amongst a control population, is significantly correlated with neuropsychological outcomes as well as driving errors performed on-road. Several of these correlations were apparent regardless of the estimation technique, indicating real-world validity of the model across related assessments. Additionally, the Iterated Grid Search produces estimates that are most distinct with generally lower bias and improved coverage with the exception of the estimate of Λ1. However this method also requires potentially large time and memory commitments as compared to the other techniques considered. Thus the optimal estimation scheme is dependent upon the situation. When feasible the Iterated Grid Search appears to be the best overall method currently available. However if time or memory is a limiting factor, or if a reliable estimate of the re-centering parameter with reasonably accurate estimation of the Β vector is desired, the Modified Single-Pass technique utilizing unconstrained linear regression followed by implementation of the summation constraint is a sensible alternative.

The ability to construct accurate mathematical models of real systems is an important part of control systems design. A block oriented systems identification approach models the unknown system as interconnected linear and nonlinear blocks. The subject of this thesis is a particular configuration of these blocks referred to as a Wiener model. The Wiener model studied here is a cascade of a one input linear block followed by a nonlinear block which then provides one output. We assume that the signal between the linear and nonlinear block is always unknown, only the Wiener model input and output can be sampled. This thesis investigates identification of the linear transfer function in a Wiener model. The question examined throughout the thesis is: given some small amount of a priori information on the nonlinear part, what can we determine about the linear part? Examples of minimal a priori information are knowledge of only one point on the nonlinear transfer characteristic, or simply that the transfer characteristic is monotonic over a certain range. Nonlinear blocks with and without memory are discussed. Several algorithms for identifying the linear transfer function of a block oriented Wiener system are presented and analyzed in detail. Linear blocks identified have both finite and infinite impulse response (i.e. FIR and IIR). Each algorithm has a carefully defined set of minimal a priori information on the nonlinearity. Also, each approach has a minimally restrictive set of assumptions on the input excitation. The universal applicability of each algorithm is established by providing rigorous proofs of identifiability and in some cases convergence. Extensive simulation testing of each algorithm has been performed. Simulation techniques and results are discussed in detail.

For surface-water resource management studies, it is important to quantify all of the mechanisms that contribute to water quantity and influence water quality. In this regard, various methods have been used to ground-water fluxes in lake systems. These have included physical measurements (e.g., seepage meters), flow-net analyses, water budgets, chemical tracers, ground-water flow models, and statistical analyses. The method developed for this study for calculating ground-water inflow uses a simplified, 1-layer (surficial aquifer) ground-water flow model. The test area was on a set of lakes known as the Winter Haven Chain of Lakes in Polk County, Florida. The technique combines the use of a numerical model (MODFLOW) with an inverse prediction technique (PEST) to determine net surficial recharge rates. Within the model, the lakes were represented as constant-head boundaries. A general, surficial ground water no-flow boundary was delineated around the entire lake system based on the topographic boundaries. The model used annual average lake elevations to create a constant-head boundary for each lake for each year. Annual average elevations of surficial well heads were used as target well data. Model results generally support previous studies in the region, concluding that the lake chain receives significant inflow from the surficial aquifer and leaks to the Floridan aquifer. As a consequence, ground-water quality constituency was found to be of critical importance. One of the most important observations from this study is the need for accurate ground-water concentrations for ridge lake water quality management. The initial measured values used in this study were highly variable, uncertain, and likely underestimated the effect that ground water has on nutrient loading to the Winter Haven Chain of Lakes.

A novel application is presented for a fault-tolerant adaptive model predictive control system for small-scale helicopters. The use of a joint Extended Kalman Filter, (EKF), for the estimation of the states and parameters of the UAV, provided the advantage of implementation simplicity and accuracy. A linear model of a small-scale helicopter was utilized for testing the proposed control system. The results, obtained through the simulation of different fault scenarios, demonstrated that the proposed scheme was able to handle different types of actuator and system faults effectively. The types of faults considered were represented in the parameters of the mathematical representation of the helicopter. Benefits provided by the proposed fault-tolerant adaptive model predictive control systems include: The use of the joint Kalman filter provided a straightforward approach to detect and handle different types of actuator and system faults, which were represented as changes of the system and input matrices. The built-in adaptability provided for the handling of slow time-varying faults, which are difficult to detect using the standard residual approach. The successful inclusion of fault tolerance yielded a significant increase in the reliability of the UAV under study. A byproduct of this research is an original comparison between the EKF and the Unscented Kalman Filter, (UKF). This comparison attempted to settle the conflicting claims found in the research literature concerning the performance improvements provided by the UKF. The results of the comparison indicated that the performance of the filters depends on the approximation used for the nonlinear model of the system. Noise sensitivity was found to be higher for the UKF, than the EKF. An advantage of the UKF appears to be a slightly faster convergence.

<p>An intrinsic mathematical model for simulation of fixed bed chromatography was demonstrated and compared to more simplified models. The former model was shown to describe variations in the physical, kinetic, and operating parameters better than the latter ones. This resulted in a more reliable prediction of the chromatography process as well as a better understanding of the underlying mechanisms responsible for the separation. A procedure based on frontal liquid chromatography and a detailed mathematical model was developed to determine effective diffusion coefficients of proteins in chromatographic gels. The procedure was applied to lysozyme, bovine serum albumin, and immunoglobulin γ in Sepharose™ CL-4B. The effective diffusion coefficients were comparable to those determined by other methods.</p><p>Molecularly imprinted polymers (MIPs) are traditionally prepared as irregular particles by grinding monoliths. In this thesis, a suspension polymerization providing spherical MIP beads is presented. Droplets of pre-polymerization solution were formed in mineral oil with no need of stabilizers by vigorous stirring. The droplets were transformed into solid spherical beads by free-radical polymerization. The method is fast and the performance of the beads comparable to that of irregular particles. Optimizing a MIP formulation requires a large number of experiments since the possible combinations of the components are huge. To facilitate the optimization, chemometrics was applied. The amounts of monomer, cross-linker, and porogen were chosen as the factors in the model. Multivariate data analysis indicated the influence of the factors on the binding and an optimized MIP composition was identified. The combined use of the suspension polymerization method to produce spherical beads with the application of chemometrics was shown in this thesis to drastically reduce the number of experiments and the time needed to design and optimize a new MIP.</p>

<p>In several projects within ABB there is a need of state and parameter estimation for nonlinear dynamic systems. One example is a project investigating optimisation of gas turbine operation. In a gas turbine there are several parameters and states which are not measured, but are crucial for the performance. Such parameters are polytropic efficiencies in compressor and turbine stages, cooling mass flows, friction coefficients and temperatures. Different methods are being tested to solve this problem of system identification or parameter estimation. This thesis describes the implementation of such a method and compares it with previously implemented identification methods. The comparison is carried out in the context of parameter estimation in gas turbine models, a dynamic load model used in power systems as well as models of other dynamic systems. Both simulated and real plant measurements are used in the study.</p>

<p>This masters thesis concerns a modeling project performed at Volvo Technology in Gothenburg, Sweden. The main purpose of the project has been to develop a physical model of the climate in construction vehicles that later on can be used in the development of an electronic climate controller. The focus of the work has been on one type of wheel loader and one type of excavator. The temperature inside the compartment has been set equal to the notion climate. </p><p>With physical theories about air flow and heat transfer in respect, relations between the components in the climate unit and the compartment has been calculated. Parameters that has had unknown values has been estimated. The relations have then been implemented in the modeling tool Simulink. </p><p>The validation of the model has been carried out by comparison between measured data and modeled values by calculation of Root Mean Square and correlation. Varying the estimated parameters and identifying the change in the output signal, i.e the temperature of the compartment, have performed a sensitivity analysis. </p><p>The result of the validation has shown that the factor with the greatest influence on the temperature in the vehicle is the airflow through the climate unit and the outlets. Minor changes of airflow have resulted in major changes in temperature. The validation principally shows that the model gives a good estimation of the temperature in the compartment. The static values of the model differs from the values of the measured data but is regarded being as within an acceptable margin of error. The weakness of the model is mainly its predictions of the dynamics, which does not correlate satisfyingly with the data.</p>

In recent years many researchers have investigated the use of Markov random fields (MRFs) for computer vision. The computational complexity of the implementation has been a drawback of MRFs. In this paper we derive deterministic approximations to MRFs models. All the theoretical results are obtained in the framework of the mean field theory from statistical mechanics. Because we use MRFs models the mean field equations lead to parallel and iterative algorithms. One of the considered models for image reconstruction is shown to give in a natural way the graduate non-convexity algorithm proposed by Blake and Zisserman.