Thesis MODELACIÓN Y SIMULACIÓN COMPUTACIONAL PARA LA EVALUACIÓN NO-INVASIVA DE PROPIEDADES MECÁNICAS EN TEJIDOS BLANDOS MEDIANTE ELASTOGRAFÍA
Date
2020-08
Authors
LEÓN HERRERA, CLAUDIA VALENTINA
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Abstract
Dentro de la amplia variedad de métodos de diagnósticos médicos, es importante destacar aquellos que sean más precisos y menos invasivos para las personas que requieran someterse a estos. La Elastografía es una alternativa a lo anterior, trabajando con parámetros de rigidez, los cuales derivan de las deformaciones que sufre el tejido ante vibraciones controladas. El caso de estudio busca involucrarse en estos temas de diagnóstico no invasivo para promover su implementación, dando a conocer su utilidad y que pueda inspirar a desarrollar mejores alternativas, puesto que la problemática actual es que, para poder detectar cuerpos anómalos en un tejido sano, muchas veces los métodos de diagnósticos clínicos implican una alta inversión y pueden resultar complejos e invasivos. Por medio del método de elementos finitos, se lleva a cabo una simulación computacional de vibraciones sobre un tejido viscoelástico lineal e isotrópico a partir de un modelo de elasticidad lineal mixto, bajo la implementación de los modelos reológicos de Voigt y Zener. Con esto, es posible recuperar valores de los desplazamientos nodales, los cuales son traducidos a parámetros de rigidez por medio de algunos algoritmos de inversión directa correspondientes al método Helmholtz, HMDI, y los nuevos métodos no publicados FV y FV-H, cuyo objetivo es determinarlos módulos de corte para cada punto del tejido estudiado, a partir de una matriz de desplazamientos. Esto permite comprobar si los métodos implementados arrojan resultados acordes a los empleados en la simulación. Los valores de módulo de corte obtenidos son graficados en función de las frecuencias utilizadas y fueron calculados los errores asociados a las magnitudes de módulo de corte y la tendencia de las curvas. Con ello, se determinó que los métodos siguen un comportamiento más acorde a las curvas asociadas al modelo Voigt. Además de esto, se observó que el método con mejores resultados en cuanto a la magnitud de los módulos de corte es el método de Helmholtz puesto que es el que más se acerca a los valores de la curva real. Y, por último, el método que obtuvo un mejor desempeño con respecto a la forma de la curva real fue el método FV-H, determinado a partir del bajo valor de error diferencial que este método obtuvo con respecto a los demás.
The wide variety of medical diagnostic methods, it is important to highlight those that are more accurate and less invasive for people who need to undergo these medical diagnostic methods. Elastography is an alternative to this, working with stiffness parameters, derived from deformations in the tissue under controlled vibrations. The case of study seeks to get involved in these non-invasive diagnostic issues to promote their implementation, making known their usefulness and that may inspire the development of better alternatives, since the current problem is that, in order to detect abnormal bodies in healthy tissue, Clinical diagnostic methods often involve a high investment and can be complex and invasive. Using the finite element method, a computational simulation of vibrations is carried out on a linear and isotropic viscoelastic tissue from a linear elasticity model using a mixed formulation, under the implementation of the Voigt and Zener rheological models. With this, it is possible to recover values of the nodal displacements, which are translated into stiffness parameters by means of some direct inversion algorithms corresponding to the Helmholtz method, HMDI, and the new unpublished methods FV and FV-H, whose objective is determine the shear modulusfor each point of the tissue studied, from a matrix of displacements. That allows to verify if the implemented methods results are according to those used in the simulation. The shear modulus values obtained are plotted as a function of the frequencies used and the errors associated with the shear modulus magnitudes and the trend of the curves were calculated. With this, it was determined that the methods follow a behavior more in line with the curves associated with the Voigt model. In addition to this, it is realized that the method with the best results in terms of the magnitude of the shear modulusis the Helmholtz method, since it is the one that is closest to the values of the real curve. And, finally, the method that obtained the best performance with respect to the shape of the real curve was the FV-H method, determined from the low differential error value that this method obtained with respect to the others.
The wide variety of medical diagnostic methods, it is important to highlight those that are more accurate and less invasive for people who need to undergo these medical diagnostic methods. Elastography is an alternative to this, working with stiffness parameters, derived from deformations in the tissue under controlled vibrations. The case of study seeks to get involved in these non-invasive diagnostic issues to promote their implementation, making known their usefulness and that may inspire the development of better alternatives, since the current problem is that, in order to detect abnormal bodies in healthy tissue, Clinical diagnostic methods often involve a high investment and can be complex and invasive. Using the finite element method, a computational simulation of vibrations is carried out on a linear and isotropic viscoelastic tissue from a linear elasticity model using a mixed formulation, under the implementation of the Voigt and Zener rheological models. With this, it is possible to recover values of the nodal displacements, which are translated into stiffness parameters by means of some direct inversion algorithms corresponding to the Helmholtz method, HMDI, and the new unpublished methods FV and FV-H, whose objective is determine the shear modulusfor each point of the tissue studied, from a matrix of displacements. That allows to verify if the implemented methods results are according to those used in the simulation. The shear modulus values obtained are plotted as a function of the frequencies used and the errors associated with the shear modulus magnitudes and the trend of the curves were calculated. With this, it was determined that the methods follow a behavior more in line with the curves associated with the Voigt model. In addition to this, it is realized that the method with the best results in terms of the magnitude of the shear modulusis the Helmholtz method, since it is the one that is closest to the values of the real curve. And, finally, the method that obtained the best performance with respect to the shape of the real curve was the FV-H method, determined from the low differential error value that this method obtained with respect to the others.
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Keywords
DIAGNOSTICO MEDICO , METODO DE ELEMENTO FINITO , SIMULACION CON COMPUTADORES