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dc.rights.licenseAtribución-NoComercial 4.0 Internacional
dc.contributor.advisorRamirez Osorio, Jorge Mario
dc.contributor.authorFonnegra García, Daniel
dc.description.abstractWe design a phenomenological parsimonious model for glucose homeostasis in healthy humans. The model consists of a two-reservoir nonlinear differential system depending on a set of parameters with physiological meaning, which values are found by fitting the model to a provided data set. The available data consists of almost continuous sub-cutaneous measurements of glucose together with a list of nutritional values of the meals ingested by different users. The set of model parameters is then split into those that are meal-dependent, and those that should be constant across meals for each user separately. With this split, we propose an algorithm to predict the meal parameters by having as input the nutritional value of the meal. The results validate our model because the parameter values fall within human normal ranges according to the available literature, while at the same time, fitting the data with very low errors. A random tree regressor is proposed to predict the values of the meal-dependent parameters that best fit the model from the meal’s nutritional values logged by the users. We find that, unfortunately, the meals nutritional value data lack integrity and we could not find a model that fitted the relation between nutritional value and meal parameters.
dc.description.abstractDiseñamos un modelo fenomenológico parsimonioso para la homeostasis de la glucosa en humanos sanos. El modelo consiste en un sistema diferencial no lineal de dos depósitos que depende de un conjunto de parámetros con significado fisiológico, cuyos valores se encuentran ajustando el modelo a un conjunto de datos proporcionado. Los datos disponibles consisten en mediciones subcutáneas casi continuas de la glucosa junto con una lista de valores nutricionales de las comidas ingeridas por diferentes usuarios. El conjunto de parámetros del modelo se divide entonces en los que dependen de la comida y los que deben ser constantes en todas las comidas para cada usuario por separado. Con esta división, proponemos un algoritmo para predecir los parámetros de la comida teniendo como entrada el valor nutricional de la comida. Los resultados validan nuestro modelo porque los valores de los parámetros se encuentran dentro de los rangos normales de los humanos según la literatura disponible, mientras que al mismo tiempo, se ajustan los datos con errores muy bajos. Se propone un regresor de árbol aleatorio para predecir los valores de los parámetros dependientes de la comida que mejor se ajustan al modelo a partir de los valores nutricionales de la comida registrados por los usuarios. Encontramos que, desafortunadamente, los datos del valor nutricional de las comidas carecen de integridad y no pudimos encontrar un modelo que se ajustara a la relación entre el valor nutricional y los parámetros de la comida.
dc.rightsDerechos reservados - Universidad Nacional de Colombia
dc.subject.ddc510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
dc.titleModelamiento y asimilación de datos de la respuesta glicémica en humanos
dc.title.alternativeModeling and data assimilation of the glycemic response in humans
dc.rights.spaAcceso abierto
dc.publisher.programMedellín - Ciencias - Maestría en Ciencias - Matemática Aplicada
dc.contributor.corporatenameUniversidad Nacional de Colombia - Sede Medellín
dc.publisher.departmentEscuela de matemáticas
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellín
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dc.subject.proposalmodelamiento matematico
dc.subject.proposalmathematical modeling

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