Garijo Millán, Noelia
Pérez Ansón, María Ángeles (dir.) ; García Aznar, José Manuel (dir.)
Universidad de Zaragoza,
2016
Resumen: La remodelación ósea es el mecanismo que regula la relación entre la morfología del hueso y sus cargas mecánicas externas. Se basa en el hecho de que el hueso se adapta a las condiciones mecánicas a las que está expuesto. Varios factores mecánicos y bioquímicos pueden regular la respuesta final de la remodelación ósea. De hecho, se considera que la remodelación ósea pretende alcanzar varios objetivos mecánicos: reparar el daño para reducir el riesgo de fractura y optimizar la rigidez y resistencia con el mínimo peso. Durante las últimas décadas, se han propuesto un gran número de leyes matemáticas implementadas numéricamente, pero la mayoría de ellas presentan diferentes problemas como la estabilidad, la convergencia o la dependencia de las condiciones iniciales. Por tanto, el objetivo principal de esta tesis es estudiar los modelos de remodelación ósea, mostrando sus retos, su problemática y su aplicación en el ámbito clínico. En primer lugar, se han revisado dos teorías clásicas de la remodelación ósea (conocidas como modelo de Stanford y modelo de Doblaré y García). En ambos casos, se propone un aspecto novedoso planteando que el estímulo homeostático de referencia no es constante, sino que depende localmente de la historia de carga que cada punto local está soportando. Como consecuencia directa de esta hipótesis, se demuestra que las inestabilidades numéricas que normalmente presentan estos algoritmos, pueden quedar resueltas, mejorando claramente los resultados finales. Esta metodología se aplicó a un modelo de elementos finitos 2D/3D mejorando la convergencia de la solución y asegurando su estabilidad numérica a largo plazo. Por otra parte, en un intento de dilucidar las características de adaptación mecánica del hueso en diferentes escalas, se plantea una relación a nivel órgano y a nivel de tejido que depende de un cambio en el estímulo homeostático de referencia acorde con la densidad aparente, mientras que se considera que la densidad de energía de deformación a nivel de tejido permanece invariante. Esta hipótesis mejora la unicidad de la solución y la hace independiente de las condiciones iniciales, ayudando también a su estabilidad numérica. Además, en esta tesis se aborda el modelado de paciente específico que es un tema que está adquiriendo cada vez más importancia. Una de las principales dificultades en la creación de modelos de paciente específico, es la determinación de las cargas que el hueso está realmente soportando. Los datos relativos a pacientes específicos, como la geometría ósea y la distribución de la densidad ósea, puede ser utilizados para determinar estas cargas. Por lo tanto, se ha estudiado la estimación de la cargas con tres diferentes técnicas matemáticas: regresión lineal, redes neuronales artificiales y máquinas de soporte vector. Estas técnicas se han aplicado a un ejemplo teórico para obtener las cargas a través de la densidad aparente que se predice con los modelos de remodelación ósea. Para concluir, la metodología desarrollada que combina modelos de remodelación ósea con redes neuronales se ha aplicado a la predicción de las cargas de cinco tibias de pacientes. Para ello, se han determinado la geometría y la distribución de la densidad a partir de un TAC y se han introducido los valores de densidad en el modelo previamente desarrollado, obteniendo así, las cargas específicas de las tibias de los pacientes. Con el fin de validar la capacidad de esta novedosa técnica, se han comparado las cargas obtenidas de la técnica propuesta con las cargas obtenidas en un análisis de marcha de dichos pacientes. Los errores obtenidos en las predicciones han sido menores de un 6 %. Por lo tanto, se puede concluir que la metodología aquí propuesta, permite determinar de forma aproximada las cargas que un hueso específico soporta.
Resumen (otro idioma): Bone remodeling is the mechanism that regulates the relationship between bone morphology and its external mechanical loads. It is based on the fact that bone adapts itself to the mechanical conditions to which it is exposed. Several mechanical and biochemical factors may regulate the final bone remodeling response. In fact, bone remodeling is hypothesized to achieve several mechanical objectives: repair damage to reduce the risk of fracture and optimize stiffness and strength with minimum weight. During recent decades, a great number of numerically implemented mathematical laws have been proposed, but most of them present different problems as stability, convergence or dependence of the initial conditions. Thus, the main scope of this Thesis is to study bone remodeling models, showing their challenges, their problematic and their applicability in the clinical setting. Firstly, we revisit two classical bone remodeling theories (Stanford model and Doblaré and García model). In both of them, the reference homeostatic stimulus is hypothesized that is not constant, but it is locally dependent on the loading history that each local point is effectively supporting. As a direct consequence of this assumption, we demonstrate that the numerical instabilities that all these algorithms normally present can be solved, clearly improving the final results. For this reason, we applied this methodology to 2D/3D finite element models. This contribution improves the convergence of the solution, leading to its numerical stability in the long-term. In an attempt to elucidate the features of bone adaptation at the di erent scales, we hypothesize that the relationship between the organ level and tissue level depends on the reference homeostatic stimulus changes according to the density and the tissue effective energy remains unchanged. This assumption improves the uniqueness of the solution, independently of the initial conditions selected and clearly helps in its numerical stability. In addition, patient-specific modeling is becoming increasingly important. One of the most challenging diffculties in creating patient-specific models is the determination of the specific load that the bone is really supporting. Real information related to specific patients, such as bone geometry and bone density distribution, can be used to determine patient loads. Therefore, we studied three different mathematical techniques: linear regression, artificial neural networks (ANN) and support vector machines (SVM). These techniques have been applied to a theoretical femur to obtain the load through the density that came from many bone remodeling simulations. Finally, the application of this novel methodology has been applied for the loading prediction of five real tibias. We are able to determine the subject-specific forces from CT data, from which we obtain bone geometry and density distribuviition of the five tibias. Then, the density values at certain bone regions have been introduced in the methodology developed that combines bone remodeling models and artificial neuronal networks (ANN) for obtaining the predicted subject-specific loads. Finally, in order to validate this novel technique for tibia loading predictions, we compare predicted loads with the loads obtained from the patientspecific musculoskeletal model. The errors between both loads were lower tan 6%. Therefore, the methodology proposed has been validated
Resumen (otro idioma): Bone remodeling is the mechanism that regulates the relationship between bone morphology and its external mechanical loads. It is based on the fact that bone adapts itself to the mechanical conditions to which it is exposed. Several mechanical and biochemical factors may regulate the final bone remodeling response. In fact, bone remodeling is hypothesized to achieve several mechanical objectives: repair damage to reduce the risk of fracture and optimize stiffness and strength with minimum weight. During recent decades, a great number of numerically implemented mathematical laws have been proposed, but most of them present different problems as stability, convergence or dependence of the initial conditions. Thus, the main scope of this Thesis is to study bone remodeling models, showing their challenges, their problematic and their applicability in the clinical setting. Firstly, we revisit two classical bone remodeling theories (Stanford model and Doblaré and García model). In both of them, the reference homeostatic stimulus is hypothesized that is not constant, but it is locally dependent on the loading history that each local point is effectively supporting. As a direct consequence of this assumption, we demonstrate that the numerical instabilities that all these algorithms normally present can be solved, clearly improving the final results. For this reason, we applied this methodology to 2D/3D finite element models. This contribution improves the convergence of the solution, leading to its numerical stability in the long-term. In an attempt to elucidate the features of bone adaptation at the di erent scales, we hypothesize that the relationship between the organ level and tissue level depends on the reference homeostatic stimulus changes according to the density and the tissue effective energy remains unchanged. This assumption improves the uniqueness of the solution, independently of the initial conditions selected and clearly helps in its numerical stability. In addition, patient-specific modeling is becoming increasingly important. One of the most challenging diffculties in creating patient-specific models is the determination of the specific load that the bone is really supporting. Real information related to specific patients, such as bone geometry and bone density distribution, can be used to determine patient loads. Therefore, we studied three different mathematical techniques: linear regression, artificial neural networks (ANN) and support vector machines (SVM). These techniques have been applied to a theoretical femur to obtain the load through the density that came from many bone remodeling simulations. Finally, the application of this novel methodology has been applied for the loading prediction of five real tibias. We are able to determine the subject-specific forces from CT data, from which we obtain bone geometry and density distribuviition of the five tibias. Then, the density values at certain bone regions have been introduced in the methodology developed that combines bone remodeling models and artificial neuronal networks (ANN) for obtaining the predicted subject-specific loads. Finally, in order to validate this novel technique for tibia loading predictions, we compare predicted loads with the loads obtained from the patientspecific musculoskeletal model. The errors between both loads were lower tan 6%. Therefore, the methodology proposed has been validated
Pal. clave: mecánica de medios continuos ; biomecánica ; mecánica ; continuum mechanics ; biomechanics ; mechanics
Área de conocimiento: Mecánica de medios continuos y teoría de estructuras
Departamento: Ingeniería Mecánica
Nota: Presentado: 18 02 2016
Nota: Tesis-Univ. Zaragoza, Ingeniería Mecánica, 2016
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Registro creado el 2016-04-18, última modificación el 2019-02-19
