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BACKGROUND: Several studies have demonstrated the association between the time to hypertension event and multiple baseline measurements for adults, yet other survival cardiovascular disease (CVD) outcomes such as high cholesterol and heart attack have been somewhat less considered. The Fels Longitudinal Study (FLS) provides us an opportunity to connect adult blood pressure (BP) at certain ages to the time to first CVD outcomes. The availability of long-term serial BP measurements from FLS also potentially allows us to evaluate if the trend of the measured BP biomarkers over time predicts survival outcomes in adulthood through statistical modeling. METHODS: When the reference standard is right-censored time-to-event (survival) outcome, the C index or concordance C, is commonly used as a summary measure of discrimination between a survival outcome that is possibly right censored and a predictive-score variable, say, a measured biomarker or a composite-score output from a statistical model that combines multiple biomarkers. When we have subjects longitudinally followed up, it is of primary interest to assess if some baseline measurements predict the time-to-event outcome. Specifically, in this study, systolic blood pressure, diastolic blood pressure, as well as their variation over time, are considered predictive biomarkers, and we assess their predictive ability for certain time-to-event outcomes in terms of the C index. RESULTS: There are a few summary C index differences that are statistically significant in predicting and discriminating certain CVD metric at certain age stage, though some of these differences are altered in the presence of medicine treatment and lifestyle characteristics. The variation of systolic BP measures over time has a significantly different predicting ability comparing with systolic BP measures at certain given time point, for predicting certain survival outcome such as high cholesterol level. CONCLUSIONS: Adult systolic and diastolic BP measurements may have significantly different ability in predicting time to first CVD events. The fluctuation of BP measurements over time may have better association than BP measurement at a single baseline time point, with the time to first CVD events.

Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process. First, we create a model of hematopoiesis, the processes of creating new blood cells. We analyze stem cell collection regimens and statistically sample parameter space in order to create a model accounts for the dynamics of multiple patients. Next, we modify an existing model of the wound healing response by introducing a variable for two inflammatory cell types. We analyze the timing of the inflammatory response and introduce the presence of systemic estrogen in the model, as there is evidence that the presence of estrogen leads to a more efficient wound healing response. Last, we mathematically model the gas exchange process in the lungs and body in order to lay the foundation for a model of the inflammatory response in the lung under conditions of mechanical ventilation. We introduce normal and ventilation breathing waveforms and a third state of hemoglobin in a closed loop partial differential equations model. We account for gas exchange in the lung and body compartments in addition to introducing a third discretized well-mixing compartment between the two. We use ordinary and partial differential equations to model these systems over one or more independent variables, as well as classical analysis techniques and computational methods to analyze systems. Statistical sampling is also used to investigate parameter values in order for the mathematical models developed to account for patient-to-patient variability. This alters the traditional mathematical model, which yields a single set of parameter values that represent one instance of the physiology, into a mathematical model that accounts for many different instances of physiology.}

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that considers identifiability of parameters, has been included in this work. Furthermore, to estimate parameters more efficiently and accurately, the standard error (SE- )optimal design method is employed, which calculates optimal observation times for clinical data to be collected. Finally, by combining different parameter subset selection methods and an optimal design problem, different cases for both finding optimal time points and intervals have been investigated.

Blood coagulation is a series of biochemical reactions that take place to form a blood clot. Abnormalities in coagulation, such as under-clotting or over- clotting, can lead to significant blood loss, cardiac arrest, damage to vital organs, or even death. Thus, understanding quantitatively how blood coagulation works is important in informing clinical decisions about treating deficiencies and disorders. Quantifying blood coagulation is possible through mathematical modeling. This review presents different mathematical models that have been developed in the past 30 years to describe the biochemistry, biophysics, and clinical applications of blood coagulation research. This review includes the strengths and limitations of models, as well as suggestions for future work.

Orientadores: Rodney Carlos Bassanezi, Adilson Jose Vieira Brandão / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-15T01:52:00Z (GMT). No. of bitstreams: 1 Cecconello_MoiseisdosSantos_D.pdf: 62393038 bytes, checksum: b7f0d1f9138d8e787749532bf661d026 (MD5) Previous issue date: 2010 / Resumo: Neste trabalho desenvolvemos ferramentas de análise qualitativa para sistemas dinâmicos definidos sobre o espaço formado pelos conjuntos fuzzy com a níveis compactos e não vazios. São propostas condições para existência de pontos de equilíbrio para o fluxo fuzzy cuja função de pertinência é sobrejetiva, generalizando alguns resultados já conhecidos. Os fluxos fuzzy considerados aqui são determinados pela extensão de Zadeh aplicada em soluções de equações diferenciais autônomas. São obtidos também condições para a existência de pontos e órbitas periódicas para o fluxo fuzzy. Em particular, demonstramos um teorema tipo Poincaré-Bendixson para tais fluxos gerados por equações autônomas bidimensionais. A análise qualitativa desenvolvida é aplicada em sistemas dinâmicos fuzzy provenientes de modelos significativos da Biomatemática. / Abstract: In this work we develop some tools for qualitative analysis of dynamical systems defined on the metric space of fuzzy sets with compact and nonempty a cuts. Conditions are offered for the existence of equilibrium points for the flow whose fuzzy membership function is surjective, generalizing some results already known. Fuzzy flows considered here are determined by Zadeh's extension applied in solutions of autonomous differential equations. We also obtained conditions for the existence of periodic points and periodic orbits for the fuzzy flow. In particular, we demonstrate a theorem like Poincaré-Bendixson for such flows generated by two-dimensional autonomous equations. The qualitative analysis results are applied to fuzzy dynamic systems from meaningful models of Biomathematics. / Doutorado / Biomatematica / Doutor em Matemática Aplicada

Orientador: João Frederico da Costa Azevedo Meyer / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T17:19:29Z (GMT). No. of bitstreams: 1 Krindges_Andre_D.pdf: 12331441 bytes, checksum: ca3fa7d1c704c02f04ba59043413e0f7 (MD5) Previous issue date: 2011 / Resumo: Um dos problemas enfrentados pelo grupo de Ecologia Matemática do IMECC da UNICAMP é o de trabalhar com difusão de uma pluma poluente com 3 variáveis espaciais, além da temporal. Esta tese não só aborda esta questão, propondo, inclusive um algoritmo computacional para esta situação, mas fá-lo resolvendo aproximadamente a Equação de Navier-Stokes num domínio irregular. A primeira parte consiste na formulação do modelo matemático para o estudo de um sistema que inclui o campo de velocidades e o comportamento evolutivo de um material poluente. Na segunda parte, é feita a formulação variacional, são constituídas aproximações via o método de Galerkin para Elementos Finitos no espaço e Crank-Nicolson no tempo para a equação de difusão-advecção, e o método da projeção para a equação de Navier-Stokes. Em seguida, faz-se a descrição do algoritmo, indicando dificuldades operacionais do ponto de vista de computação científica e apontando soluções. O domínio utilizado para o estudo de caso é o da represa do rio Manso, que, discretizada em três dimensões, foi tratado com o software livre GMSH. Finalmente, um código numérico em plataforma MATLAB foi executado e resultados são apresentados no texto. O programa e diversas considerações técnicas essenciais fazem parte dos anexos / Abstract: One of the challenges faced by the Mathematical Ecology group at the Mathematics Institute at Campinas State University is that of working with the diffusion of a pollutant plume in three spatial variables, besides time. This work not only addresses this issue by proposing an approximation strategy as well as a computer algorithm for this situation, but it also includes a three-dimensional numerical approximation for the Navier-Stokes equation in an irregular domain. The first part consists in formulating the mathematical model for the study of a system that includes the velocity field and the evolutionary behavior of a polluting material. The second part begins with the variational formulation of the Navier-Stiokes system, and approximations are undertaken via the Galerkin method for finite elements in space and Crank-Nicolson in time for both the advection-diffusion equation and the method of projection for the Navier-Stokes equations. The algorithm is described, indicating operational difficulties in terms of scientific computing as well as the way in which these aforementioned difficulties are solved. The domain used for the case study is the Manso River reservoir, which, discretized in three dimensions, was treated with the free software GMSH. Finally, a numeric code in MATLAB environment was completed and results are presented in the text. The program and various essential technical considerations are part of the annexes / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Dans cette thèse, j’aborde le problème important de l’estimation de la structure des réseaux complexes, à l’aide de la classe des modèles stochastiques dits réseaux Bayésiens. Les réseaux Bayésiens permettent de représenter l’ensemble des relations d’indépendance conditionnelle. L’apprentissage statistique de la structure de ces réseaux complexes par les réseaux Bayésiens peut révéler la structure causale sous-jacente. Il peut également servir pour la prédiction de quantités qui sont difficiles, coûteuses, ou non éthiques comme par exemple le calcul de la probabilité de survenance d’un cancer à partir de l’observation de quantités annexes, plus faciles à obtenir. Les contributions de ma thèse consistent en : (A) un logiciel développé en langage C pour l’apprentissage de la structure des réseaux bayésiens; (B) l’introduction d’un nouveau "jumping kernel" dans l’algorithme de "Metropolis-Hasting" pour un échantillonnage rapide de réseaux; (C) l’extension de la notion de réseaux Bayésiens aux structures incluant des boucles et (D) un logiciel spécifique pour l’apprentissage des structures cycliques. Notre principal objectif est l’apprentissage statistique de la structure de réseaux complexes représentée par un graphe et par conséquent notre objet d’intérêt est cette structure graphique. Un graphe est constitué de nœuds et d’arcs. Tous les paramètres apparaissant dans le modèle mathématique et différents de ceux qui caractérisent la structure graphique sont considérés comme des paramètres de nuisance. / In this thesis, I address the important problem of the determination of the structure of complex networks, with the widely used class of Bayesian network models as a concrete vehicle of my ideas. The structure of a Bayesian network represents a set of conditional independence relations that hold in the domain. Learning the structure of the Bayesian network model that represents a domain can reveal insights into its underlying causal structure. Moreover, it can also be used for prediction of quantities that are difficult, expensive, or unethical to measure such as the probability of cancer based on other quantities that are easier to obtain. The contributions of this thesis include (A) a software developed in C language for structure learning of Bayesian networks; (B) introduction a new jumping kernel in the Metropolis-Hasting algorithm for faster sampling of networks (C) extending the notion of Bayesian networks to structures involving loops and (D) a software developed specifically to learn cyclic structures. Our primary objective is structure learning and thus the graph structure is our parameter of interest. We intend not to perform estimation of the parameters involved in the mathematical models.

<p>Regardless of their origin or pathology, many, if not all, diseases have long been regarded as complex. Yet, despite the progression in the understanding of complexity and the development of systems biology, the majority of biomedical research has been derived from qualitative principles. In comparison to the ethical, temporal and logistical limitations of human experimentation, <em>in vivo</em> animal models have served to provide a more advantageous means to elucidate the underlying disease mechanisms. However, given the additional limitations presented by such models, <em>in silico </em>models have emerged as an effective complement, and, in some cases, a replacement for <em>in vivo</em> experimentation. The <em>in silico </em>models presented in this thesis were developed using mathematical and computational methods to investigate the evolution of two complex, diverse diseases from a systems biology perspective: allergic asthma and cancer.</p> <p>We generated two novel <em>in silico</em> models of allergic asthma aimed at clarifying some dynamic aspects of allergic responses. Experimentally, we utilized an <em>in vivo</em> murine model of chronic exposure to the most pervasive aeroallergen worldwide, house dust mite (HDM), for up to 20 weeks, equivalent to at least 20 human years. Using a range of HDM concentrations, experimental data were collected to study local and systemic effects. The first model applied empirical mathematical techniques to establish equations for airway inflammation and HDM-specific immunoglobulins using an iterative approach of experimentation and validation. Using the equations generated, we showed that the model was able to accurately predict and simulate data. The model also demonstrated the non-linear relationship between HDM exposure and both airway inflammation and allergic sensitization and identified system thresholds.</p> <p>The second model used mechanistic mathematical techniques to investigate the trafficking of eosinophils as they migrated from bone marrow to the blood and, ultimately, to the lungs. Making use of a limited data set, the model determined the effect of individual processes on the system. We identified eosinophil production, survival and death as having the greatest impacts, while migration played a relatively minor role. Furthermore, the model was used to simulate knockout models and the use of antibodies <em>in silico</em>.</p> <p>In the context of cancer growth and metastasis, we developed a theoretical model demonstrating the spatio-temporal development of a tumour in two-dimensions. The model was encoded to create a computer graphic simulation program, which simulated the effects of various parameters on the size and shape of a tumour. Through simulations, we demonstrated the importance of the diffusion process in cancer growth and metastasis.</p> <p>Ultimately, we believe the greatest benefit of each <em>in silico</em> model is the ability to provide an understanding of each respective disease recognized as dynamic and formally complex, but predominantly studied in reductionist, static or un-integrated approaches.</p> / Doctor of Philosophy (Medical Science)

La modélisation dynamique des systèmes écologiques constitue une méthode incontournable pour comprendre,prédire et contrôler la dynamique des écosystèmes semi-naturels, qui fait intervenir des processuscomplexes. Le principal objectif de cette thèse est de développer un modèle permettant de simuler la dynamiqueà moyen terme de la végétation herbacée dans les prairies permanentes, en tenant compte à lafois de la productivité et de la biodiversité. Les prairies sont des réservoirs présentant une forte biodiversitévégétale, qui soutiennent de nombreux services écosystémiques. Sur le plan agricole, cette importantediversité contribue à la qualité de la production fourragère, et de plus, elle permet une plus grande résistancede la végétation face à des changements climatiques (réchauffement moyen, vagues de chaleur etde sécheresse).Pourtant, cette notion clé de biodiversité n’est que faiblement prise en considération dans la modélisationde l’écosystème prairial : elle est souvent absente ou alors présente sous une forme très simplifiée. Enréponse à ces considérations, ces travaux de thèse présentent la construction d’un modèle de successionbasé sur des processus, décrit par un système d’équations différentielles ordinaires, qui représente ladynamique de la végétation aérienne des prairies tempérées. Ce modèle intègre les principaux facteursécologiques impactant la croissance et la compétition des espèces herbacées, et peut s’ajuster à n’importequel niveau de diversité, par le choix du nombre et de l’identité des espèces initialement présentes dansl’assemblage. Ce formalisme mécaniste de modélisation nous permet alors d’analyser les relations qui lientdiversité, productivité et stabilité, en réponse à différentes conditions climatiques et différents modes degestion agricole.[...]Ces résultats soulignent alors le besoin de prendre en compte le rôle clé joué par la biodiversité dansles modèles de l’écosystème prairial, de par son impact sur le comportement des dynamiques simulées.De plus, pour rendre correctement compte des interactions au sein de la végétation, le nombre d’espècesconsidéré dans le modèle doit être suffisamment important. Enfin, nous comparons les simulations devégétation de ce modèle à des mesures issues de deux sites expérimentaux, la prairie de fauche d’Oensingen,et le pâturage de Laqueuille. Les résultats de ces comparaisons sont encourageants et soulignentla pertinence du choix et de la représentation des processus écologiques clés qui composent ce modèlemécaniste.Ce travail de thèse propose donc un modèle, en total adéquation avec les besoins actuels en terme demodélisation de l’écosystème prairial, qui permet de mieux comprendre la dynamique de la végétationherbacée et les interactions entre productivité, diversité et stabilité. / Dynamic modelling of ecological systems is an essential method to understand, predict and control thedynamics of semi-natural ecosystems, which involves complex processes. The main objective of this PhDthesis is to develop a simulation model of the medium- and long-term dynamics of the herbaceous vegetationin permanent grasslands, taking into account both biodiversity and productivity. Grasslandecosystems are often hot spots of biodiversity, which contributes to the temporal stability of their services.On an agricultural perspective, this important biodiversity contributes to the forage quality, andbesides, it induces a higher ability of the vegetation cover to resist to different climatic scenarios (globalwarming, heat and drought waves).However, this key aspect of biodiversity is only poorly included in grassland models : often absent ofmodelling or included in a very simple form. Building on those considerations, this PhD work exposes thewriting of a process-based succession model, described by a system of Ordinary Differential Equationsthat simulates the aboveground vegetation dynamics of a temperate grassland. This model implementedthe main ecological factors involved in growth and competition processes of herbaceous species, and couldbe adjust to any level of diversity, by varying the number and the identity of species in the initial plantcommunity. This formalism of mechanistic models allows us to analyse relationships that link diversity,productivity and stability, in response to different climatic conditions and agricultural management.In mathematical grassland models, plant communities may be represented by a various number of statevariables, describing biomass compartments of some dominant species or plant functional types. The sizeof the initial species pool could have consequences on the outcome of the simulated ecosystem dynamicsin terms of grassland productivity, diversity, and stability. This choice could also influence the modelsensitivity to forcing parameters. To address these issues, we developed a method, based on sensitivityanalysis tools, to compare behaviour of alternative versions of the model that only differ by the identityand number of state variables describing the green biomass, here plant species. This method shows aninnovative aspect, by performing this model sensitivity analysis by using multivariate regression trees. Weassessed and compared the sensitivity of each instance of the model to key forcing parameters for climate,soil fertility, and defoliation disturbances. We established that the sensitivity to forcing parameters ofcommunity structure and species evenness differed markedly among alternative models, according tothe diversity level. We show a progressive shift from high importance of soil fertility (fertilisation level,mineralization rate) to high importance of defoliation (mowing frequency, grazing intensity) as the sizeof the species pool increased.These results highlight the need to take into account the role of species diversity to explain the behaviourof grassland models. Besides, to properly take into account those interactions in the grassland cover, theconsidered species pool size considered in the model needs to be high enough. Finally, we compare modelsimulations of the aboveground vegetation to measures from two experimental sites, the mowing grasslandof Oensingen, and the grazing grassland of Laqueuille. Results of these comparison are promising andhighlight the relevance of the choice and the representation of the different ecological processes includedin this mechanistic model.Thus, this PhD work offers a model, perfectly fitting with current needs on grassland modelling, whichcontribute to a better understanding of the herbaceous vegetation dynamics and interactions betweenproductivity, diversity and stability.