The application of spatial methods to epidemic estimation and prediction problems is a vibrant and active area of research. In many cases, however, well thought out and laboratory supported models for epidemic patterns may be easy to specify but extremely difficult to fit efficiently. While this problem exists in many scientific disciplines, epidemic modeling is particularly prone to this challenge due to the rate at which the problem scope grows as a function of the size of the spatial and temporal domains involved. An additional barrier to widespread use of spatiotemporal epidemic models is the lack of user friendly software packages capable of fitting them. In particular, compartmental epidemic models are easy to understand, but in most cases difficult to fit. This class of epidemic models describes a set of states, or compartments, which captures the disease progression in a population. This dissertation attempts to expand the problem scope to which spatio-temporal compartmental epidemic models are applicable both computationally and practically. In particular, a general family of spatially heterogeneous SEIRS models is developed alongside a software library with the dual goals of high computational performance and ease of use in fitting models in this class. We emphasize the task of model specification, and develop a framework describing the components of epidemic behavior. In addition, we establish methods to estimate and interpret reproductive numbers, which are of fundamental importance to the study of infectious disease. Finally, we demonstrate the application of these techniques both under simulation, and in the context of a diverse set of real diseases, including Ebola Virus Disease, Smallpox, Methicillin-resistant Staphylococcus aureus, and Influenza.

Recentes estudos sugerem a existência de sinapses elétricas mediadas por junções gap entre fotorreceptores na retina de vertebrados. Neste trabalho, descrevemos um modelo computacional dos circuitos primário e secundário mediados pelos bastonetes da retina de vertebrados. O modelo é composto pelas seguintes populações de células: bastonetes, cones, células bipolares dos bastonetes, células bipolares dos cones, células amácrinas do tipo AII e células ganglionares. As células do modelo estão acopladas entre si por sinapses químicas e elétricas segundo padrões realísticos de convergência e divergência. As sinapses elétricas ocorrem entre os bastonetes, entre os bastonetes e os cones, entre as células amácrinas AII e entre as células bipolares dos cones e a células amácrinas AII. O modelo assume que um estímulo luminoso de baixa intensidade, simulando condições escotópicas, atinge todos os bastonetes da camada receptora, porém menos da metade deles é excitada. A resposta dos bastonetes excitados é controlada por uma fotocorrente cuja amplitude pode ser alterada para simular estímulos de diferentes intensidades dentro da faixa escotópica. O modelo é utilizado para investigar os efeitos dos diferentes graus de acoplamento elétrico entre as células receptoras e entre as células amácrinas AII, além do efeito de diferentes valores de condutância do canal Ih ativado pela hiperpolarização nos bastonetes, sobre a faixa dinâmica da retina. Os resultados das simulações mostram que, para valores realísticos da condutância do canal Ih, a faixa dinâmica medida na camada receptora é maximizada para o índice de conectividade crítico para que haja percolação de ligação. No entanto, quando a faixa dinâmica é medida para as células bipolares ou ganglionares o valor máximo é obtido para um índice de conectividade subcrítico. Este resultado é conseqüência da alta convergência de sinapses químicas entre os bastonetes e células bipolares. / Recent studies suggest the existence of electrical synapses (gap junctions) connecting photoreceptors in the vertebrate retina. In this work we describe a computer model of the primary and secondary rod pathways in the vertebrate retina. The model is composed of the following cell populations: rods, cones, rod bipolar cells, cone bipolar cells, AII amacrine cells and ganglion cells. Cells of the model are connected via chemical as well as electrical synapses according to realistic convergence and divergence factors. There are electrical synapses between rods, rods and cones, AII amacrine cells, and cone bipolar cells and AII amacrine cells. The model assumes that low intensity stimuli simulating scotopic conditions reach all rods in the receptor array but less than half of them are excited. The excited rods response is controlled by a photocurrent waveform whose amplitude can be manipulated to simulate stimuli of different intensities within the scotopic range. The model is used to investigate the effects of different degrees of coupling among photoreceptors and among AII amacrine cells, as well as values of rod hyperpolarization activated current Ih on the dynamic range of the retina. Results show that for realistic values of Ih conductance the dynamic range of the rod array is maximized at the critical connectivity degree for bond percolation. However, the dynamic range of the rod bipolar and ganglion cells is maximized for a photoreceptor connectivity degree below the critical value. The latter result is a consequence of the high convergence of chemical synapses from rods to rod bipolar cells.

Recentes estudos sugerem a existência de sinapses elétricas mediadas por junções gap entre fotorreceptores na retina de vertebrados. Neste trabalho, descrevemos um modelo computacional dos circuitos primário e secundário mediados pelos bastonetes da retina de vertebrados. O modelo é composto pelas seguintes populações de células: bastonetes, cones, células bipolares dos bastonetes, células bipolares dos cones, células amácrinas do tipo AII e células ganglionares. As células do modelo estão acopladas entre si por sinapses químicas e elétricas segundo padrões realísticos de convergência e divergência. As sinapses elétricas ocorrem entre os bastonetes, entre os bastonetes e os cones, entre as células amácrinas AII e entre as células bipolares dos cones e a células amácrinas AII. O modelo assume que um estímulo luminoso de baixa intensidade, simulando condições escotópicas, atinge todos os bastonetes da camada receptora, porém menos da metade deles é excitada. A resposta dos bastonetes excitados é controlada por uma fotocorrente cuja amplitude pode ser alterada para simular estímulos de diferentes intensidades dentro da faixa escotópica. O modelo é utilizado para investigar os efeitos dos diferentes graus de acoplamento elétrico entre as células receptoras e entre as células amácrinas AII, além do efeito de diferentes valores de condutância do canal Ih ativado pela hiperpolarização nos bastonetes, sobre a faixa dinâmica da retina. Os resultados das simulações mostram que, para valores realísticos da condutância do canal Ih, a faixa dinâmica medida na camada receptora é maximizada para o índice de conectividade crítico para que haja percolação de ligação. No entanto, quando a faixa dinâmica é medida para as células bipolares ou ganglionares o valor máximo é obtido para um índice de conectividade subcrítico. Este resultado é conseqüência da alta convergência de sinapses químicas entre os bastonetes e células bipolares. / Recent studies suggest the existence of electrical synapses (gap junctions) connecting photoreceptors in the vertebrate retina. In this work we describe a computer model of the primary and secondary rod pathways in the vertebrate retina. The model is composed of the following cell populations: rods, cones, rod bipolar cells, cone bipolar cells, AII amacrine cells and ganglion cells. Cells of the model are connected via chemical as well as electrical synapses according to realistic convergence and divergence factors. There are electrical synapses between rods, rods and cones, AII amacrine cells, and cone bipolar cells and AII amacrine cells. The model assumes that low intensity stimuli simulating scotopic conditions reach all rods in the receptor array but less than half of them are excited. The excited rods response is controlled by a photocurrent waveform whose amplitude can be manipulated to simulate stimuli of different intensities within the scotopic range. The model is used to investigate the effects of different degrees of coupling among photoreceptors and among AII amacrine cells, as well as values of rod hyperpolarization activated current Ih on the dynamic range of the retina. Results show that for realistic values of Ih conductance the dynamic range of the rod array is maximized at the critical connectivity degree for bond percolation. However, the dynamic range of the rod bipolar and ganglion cells is maximized for a photoreceptor connectivity degree below the critical value. The latter result is a consequence of the high convergence of chemical synapses from rods to rod bipolar cells.

Il est rapporté que la biodisponibilité orale de l’amoxicilline chez le porc est environ trois fois moindre que chez l’homme. Pour élucider les raisons de cette différence, la pharmacocinétique artérielle, veineuse porte et urinaire de cet antibiotique a été caractérisée à des doses intragastriques de 4 à 30 mg/kg et différents modèles compartimentaux physiologiques ont été conçus pour l’analyse des données. La biodisponibilité orale de l’amoxicilline est maximale à 4 mg/kg, avec une valeur moyenne de 52%. Les différences porto-systémiques de concentrations plasmatiques d’amoxicilline et la clairance urinaire ont permis de démontrer une augmentation de la clairance hépatique jusqu’à la dose de 30 mg/kg. Un modèle compartimental comprenant deux voies parallèles d’absorption (de type Michaelis- Menten d’accessibilité limitée dans le temps et d’ordre 1), deux compartiments de distribution (central et périphérique) deux voies d’élimination (excrétions urinaire et biliaire) est celui qui prédit le mieux les données observées. Ces résultats mettent en évidence le rôle prépondérant du transporteur saturable PepT1 dans l’absorption orale de l’amoxicilline administrée à faible dose, ainsi que l’importance croissante de l’absorption passive lors d’administration à forte dose. / It was reported that the oral bioavailability of amoxicillin in swine is about three times lower than in human beings. To elucidate the reasons for this difference, arterial, portal venous and urinary pharmacokinetics was documented at intragastric dose amounts ranging between 4 and 30 mg/kg, and several physiologic compartmental models were developed for data analysis. The maximum oral bioavailability of amoxicillin was recorded at 4mg/kg with a mean value of 52%. The portal-systemic plasma concentration differences of amoxicillin and its urinary clearance revealed an increase in hepatic clearance up to the 30 mg/kg dose. A compartmental model with two parallel absorption route (time-constrained Michaelis- Menten and first-order processes), two distribution compartments (central and peripheral) two elimination pathways (urinary and biliary excretions) best fitted the experimental data. These results highlight the paramount role of the PepT1 carriermediated, saturable absorption at low oral amoxicillin doses, as well as the increasing role of passive absorption at high doses.

Les études non destructives des processus physiologiques dans les produits agronomiques exigent des résolutions spatiales et temporelles de plus en plus élevées. L'imagerie par résonance magnétique nucléaire (RMN) est une technique totalement non-invasive qui permet d'accéder à plusieurs types de variables (architecture des tissus, variabilités spatiales de la composition, flux entrants et internes au cours de la croissance du fruit) plus difficilement quantifiables avec des méthodes destructives classiques. Un des enjeux majeur également réside dans la faculté de localiser spatialement ces transformations physiologiques et morphologiques dans les produits agronomiques. Les travaux de recherches réalisés dans le cadre de cette thèse ont pour objectif principal, la mise en œuvre d'une méthodologie de calcul et d'analyse quantitative en imagerie RMN appliquée à l'agronomie. L'implémentation, l'optimisation et la validation de la séquence FLASH combinée avec des agents de contraste efficaces en terme de relaxivité et bio-compatibles a permis d'une part, la cartographie des paramètres de relaxation et d'autre part, la quantification du transport de l'eau in vivo d'un système agronomique modèle au cours de sa croissance. Les nanoparticules de l'agent de contraste Gd3+[Fe(CN)6]3-/Mannitol ont été utilisées comme des marqueurs afin de localiser les flux hydriques dans le fruit. Le choix de la séquence d'imagerie FLASH a été motivé par la nécessite d'atteindre des résolutions temporelles suffisante pour suivre la dynamique des changements physiologiques liés au transport de l'eau dans ce type de matériau. La validation de la méthode de calcul du T1 menée sur le fantôme a révélé un bon accord par rapport aux T1 mesurés par relaxométrie. Nous avons également mis au point une procédure d'évaluation du rapport signal sur bruit et des incertitudes commises dans chaque voxel des images paramétriques M0 et T1. L'évaluation de ces incertitudes est un élément fondamental de cette analyse quantitative, afin d'assurer des interprétations fiables des images RMN. La segmentation des images nous a permis de localiser précisément les tissus où règne une forte activité cellulaire. Enfin, la modélisation compartimentale mis en oeuvre nous a permis de quantifier les paramètres cinétiques liés au transport de l'eau dans le fruit.Mots-clés: Imagerie RMN quantitative, paramètres intrinsèques, segmentation, modélisation compartimentale, agents de contraste, tissus végétaux / Non destructive studies of physiological processes in agronomic products require increasingly higher spatial and temporal resolutions. Nuclear Magnetic Resonance (NMR) imaging is a completely non-invasive technique providing access to several types of variables (tissue architecture, spatial variability of the composition, external and internal flow during fruit growth) more difficult to quantify with conventional destructive methods. One of major challenge lies in the ability to spatially localize the physiological and morphological changes in the agricultural products. The main objective of the research work in this thesis is to carry out a methodology in order to calculate and analyze quantitative NMR imaging applied to agronomy. The implementation, optimization and validation of the FLASH imaging sequence is performed in combination with innovative biocompatible contrast agents efficient in terms of relativity which allow to map in vivo relaxation parameters and then to explore water transportation in an agronomic model : the tomato during its growth. Nanoparticles of Gd3+[Fe(CN)6]3-/Mannitol contrast agents have been used as markers to localize the water flow in the fruit. The choice of the FLASH imaging sequence is motivated by the necessity to achieve sufficient high temporal resolution for monitoring the dynamics of physiological changes related to the water transport. The validation of the T1 calculation method performed on a phantom shows a good agreement compared to T1 measured by relaxometry. A systematic procedure for the estimation of the signal to noise ratio on the parametric images is also proposed which ensures a carefull determination of the intrinsic parameters of living tissues (M0 and T1) and their uncertainties. This step in the analysis ensures reliable interpretation of NMR images and permits image segmentation in order to precisely localize the tissues where there is a high cellular activity. Finally, the time dependance and the compartmental modeling allow to quantify the kinetic parameters associated with the water transport in the fruit.Keywords: Quantitative NMR imaging, intrinsic parameters, segmentation, compartmental modeling, contrast agents, plant tissues

O presente trabalho possui como metas o estudo, simulação, identificação de parâmetros e comparação estatística de modelos compartimentais utilizados em tomografia por emissão de pósitrons (PET). Para tanto, propõe-se utilizar a metodologia de equações de sensibilidade e o método de Levenberg-Marquardt para a tarefa de estimação de parâmetros característicos das equações diferenciais descritoras dos referidos sistemas. Para comparação entre modelos, foi empregado o critério de informação de Akaike. São consideradas três estruturas compartimentais compostas, respectivamente, por dois compartimentos e duas constantes características, três compartimentos e quatro constantes características e quatro compartimentos e seis constantes características. Os dados considerados neste texto foram sintetizados preocupando-se em reunir as principais características de um exame de tomografia real, tais como tipo e nível de ruído e morfologia de função de excitação do sistema. Para tanto, foram utilizados exames de pacientes do setor de Medicina Nuclear do Instituto do Coração da Faculdade de Medicina da Universidade de São Paulo. Aplicando-se a metodologia proposta em três níveis de ruído (baixo, médio e alto), obteve-se concordância do melhor modelo em graus forte e considerável (com índices de Kappa iguais a 0.95, 0.93 e 0.63, respectivamente). Observou-se que, com elevado nível de ruído e modelos mais complexos (quatro compartimentos), a classificação se deteriora devido ao pequeno número de dados para a decisão. Foram desenvolvidos programas e uma interface gráfica que podem ser utilizadas na investigação, elaboração, simulação e identificação de parâmetros de modelos compartimentais para apoio e análise de diagnósticos clínicos e práticas científicas. / This work has as goals the study, simulation, parameter identification and statistical comparison of compartmental models used in positron emission tomography (PET). We propose to use the methodology of sensitivity equations and the method of Levenberg-Marquardt for the task of estimating the characteristic parameters of the differential equations describing such systems. For model comparison, Akaikes information criterion is applied. We have considered three compartmental structures represented, respectively, by two compartments and two characteristic constants, three compartments and four characteristic constants and four compartments and six characteristics constants. The data considered in this work were synthesized taking into account key features of a real tomography exam, such as type and level of noise and morphology of the input function of the system. To this end, we used tests of patients in the sector of Nuclear Medicine of the Heart Institute of the Faculty of Medicine, University of São Paulo. Applying the proposed methodology with three noise levels (low, medium and high), we obtained agreement of the best model with strong and considerable degrees (with Kappa indexes equal to 0.95, 0.93 and 0.63, respectively). It was observed that, with high noise level and more complex models (four compartments), the classification is deteriorated due to lack of data for the decision. Programs have been developed and a graphical interface that can be used in research, development, simulation and parameter identification of compartmental models, supporting analysis of clinical diagnostics and scientific practices.

O presente trabalho possui como metas o estudo, simulação, identificação de parâmetros e comparação estatística de modelos compartimentais utilizados em tomografia por emissão de pósitrons (PET). Para tanto, propõe-se utilizar a metodologia de equações de sensibilidade e o método de Levenberg-Marquardt para a tarefa de estimação de parâmetros característicos das equações diferenciais descritoras dos referidos sistemas. Para comparação entre modelos, foi empregado o critério de informação de Akaike. São consideradas três estruturas compartimentais compostas, respectivamente, por dois compartimentos e duas constantes características, três compartimentos e quatro constantes características e quatro compartimentos e seis constantes características. Os dados considerados neste texto foram sintetizados preocupando-se em reunir as principais características de um exame de tomografia real, tais como tipo e nível de ruído e morfologia de função de excitação do sistema. Para tanto, foram utilizados exames de pacientes do setor de Medicina Nuclear do Instituto do Coração da Faculdade de Medicina da Universidade de São Paulo. Aplicando-se a metodologia proposta em três níveis de ruído (baixo, médio e alto), obteve-se concordância do melhor modelo em graus forte e considerável (com índices de Kappa iguais a 0.95, 0.93 e 0.63, respectivamente). Observou-se que, com elevado nível de ruído e modelos mais complexos (quatro compartimentos), a classificação se deteriora devido ao pequeno número de dados para a decisão. Foram desenvolvidos programas e uma interface gráfica que podem ser utilizadas na investigação, elaboração, simulação e identificação de parâmetros de modelos compartimentais para apoio e análise de diagnósticos clínicos e práticas científicas. / This work has as goals the study, simulation, parameter identification and statistical comparison of compartmental models used in positron emission tomography (PET). We propose to use the methodology of sensitivity equations and the method of Levenberg-Marquardt for the task of estimating the characteristic parameters of the differential equations describing such systems. For model comparison, Akaikes information criterion is applied. We have considered three compartmental structures represented, respectively, by two compartments and two characteristic constants, three compartments and four characteristic constants and four compartments and six characteristics constants. The data considered in this work were synthesized taking into account key features of a real tomography exam, such as type and level of noise and morphology of the input function of the system. To this end, we used tests of patients in the sector of Nuclear Medicine of the Heart Institute of the Faculty of Medicine, University of São Paulo. Applying the proposed methodology with three noise levels (low, medium and high), we obtained agreement of the best model with strong and considerable degrees (with Kappa indexes equal to 0.95, 0.93 and 0.63, respectively). It was observed that, with high noise level and more complex models (four compartments), the classification is deteriorated due to lack of data for the decision. Programs have been developed and a graphical interface that can be used in research, development, simulation and parameter identification of compartmental models, supporting analysis of clinical diagnostics and scientific practices.

Il est rapporté que la biodisponibilité orale de l’amoxicilline chez le porc est environ trois fois moindre que chez l’homme. Pour élucider les raisons de cette différence, la pharmacocinétique artérielle, veineuse porte et urinaire de cet antibiotique a été caractérisée à des doses intragastriques de 4 à 30 mg/kg et différents modèles compartimentaux physiologiques ont été conçus pour l’analyse des données. La biodisponibilité orale de l’amoxicilline est maximale à 4 mg/kg, avec une valeur moyenne de 52%. Les différences porto-systémiques de concentrations plasmatiques d’amoxicilline et la clairance urinaire ont permis de démontrer une augmentation de la clairance hépatique jusqu’à la dose de 30 mg/kg. Un modèle compartimental comprenant deux voies parallèles d’absorption (de type Michaelis- Menten d’accessibilité limitée dans le temps et d’ordre 1), deux compartiments de distribution (central et périphérique) deux voies d’élimination (excrétions urinaire et biliaire) est celui qui prédit le mieux les données observées. Ces résultats mettent en évidence le rôle prépondérant du transporteur saturable PepT1 dans l’absorption orale de l’amoxicilline administrée à faible dose, ainsi que l’importance croissante de l’absorption passive lors d’administration à forte dose. / It was reported that the oral bioavailability of amoxicillin in swine is about three times lower than in human beings. To elucidate the reasons for this difference, arterial, portal venous and urinary pharmacokinetics was documented at intragastric dose amounts ranging between 4 and 30 mg/kg, and several physiologic compartmental models were developed for data analysis. The maximum oral bioavailability of amoxicillin was recorded at 4mg/kg with a mean value of 52%. The portal-systemic plasma concentration differences of amoxicillin and its urinary clearance revealed an increase in hepatic clearance up to the 30 mg/kg dose. A compartmental model with two parallel absorption route (time-constrained Michaelis- Menten and first-order processes), two distribution compartments (central and peripheral) two elimination pathways (urinary and biliary excretions) best fitted the experimental data. These results highlight the paramount role of the PepT1 carriermediated, saturable absorption at low oral amoxicillin doses, as well as the increasing role of passive absorption at high doses.

Infusion pumps are used in all departments of a hospital, in the emergency care unit as well as in pediatrics. The pumps administer intravenous medications for the purpose of helping patients to manage pain and are unfortunately not spared from emerging errors. Due to the complexity of the process involved in infusion pumps, errors regarding delay in administration are encountered. Especially vulnerable to errors are pediatric patients, due to the high risk of over- or under-dosing. This study aims to investigate the effects on administration delay by analysing the medical supply and system utilized for the infusion pumps. This is accomplished through implementation of Compartmental Modeling in Pharmacokinetics in combination with a self developed mathematical model for estimating the administration delay. Simulations were performed for analysing how various sizes of medical supply effected delay time. The result from the computed mathematical model indicates that increased volumes on utilized equipment will increase delay time. The combined use of a decreased flow rate and smaller equipment sizes will have the greatest affects on the delay in administration. The result obtained from the computed compartmental model can be useful for medical staff to be able to estimate the delay in administration. However, further validation is required before the utilization of the model can be applied in hospitals. / Infusionspumpar används på alla avdelningar på ett sjukhus, inom akutvården samt inom pediatrik. Pumparna administrerar olika mediciner i syfte att hjälpa patienten att hantera smärta och är tyvärr inte förskonade från att fel kan förekomma. På grund av komplexiteten i processen, involverad i infusionspumpar, uppstår fel gällande förseningar i administrering av medicin. Speciellt sårbara för dessa typer av förseninigar är pediatriska patienter, på grund av den förhöjda risker gällande över- eller underdosering. Denna studie syftar till att undersöka effekterna gällande administreringsfördröjning genom att analysera det medicinska utrustningen och systemet som används för infusionspumparna. Detta uppnås genom implementering av kompartmentmodellering i farmakokinetik i kombination med en egenutvecklad matematisk modell för att uppskatta administreringsfördröjningen. Simuleringar utfördes för att analysera effekterna av olika storlekar på medicinsk utrustning i förhållande till fördröjningen av administreringe. Resultatet från den beräknade matematiska modellen indikerar att ökade volymer gällande den medicinska utrustningen kommer att öka fördröjningstiden. Den kombinerade användningen av en minskad flödeshastighet och mindre utrustningsstorlekar kommer att ha störst inverkan på förseningen i administreringen. Resultatet som erhålls från den beräknade kompartmentmodellen kan vara användbar för sjukvårdspersonal för att kunna uppskatta förseningen i administrationen. Ytterligare validering krävs dock innan användningen av modellen kan tillämpas på sjukhus.

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