Publication: Análisis de la influencia de la porosidad en las propiedades mecánicas del hueso trabecular
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2015-06
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2015-07-06
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Abstract
En los huesos que constituyen el esqueleto humano, se encuentran fundamentalmente dos tipos de tejidos: tejido óseo cortical, conocido como hueso cortical, y tejido óseo trabecular, conocido como hueso trabecular. Aunque ambos estén formados por los mismos tipos de células, y presenten composiciones similares, es en la estructura interna en la que se aprecian sus diferencias.
Mientas que en el hueso cortical el tejido óseo aparece de forma compacta, en el hueso trabecular este tejido se agrupa de forma irregular formando capas, denominadas trabéculas, de forma que entre ellas aparecen oquedades que confieren a esta estructura la apariencia típica de esponja.
El hueso trabecular presenta, por tanto, una densidad mucho menor que la que tiene el hueso cortical, debido a la mayor porosidad, y ésta es clave para determinar el comportamiento mecánico de este tipo de estructura. Sin embargo, esto no es algo sencillo, pues la porosidad puede ser distinta para cada hueso, y puede aumentar o disminuir como consecuencia de distintos desórdenes metabólicos.
Mediante la ejecución de un script escrito en lenguaje de programación Python, se han generado modelos aleatorios en Abaqus/CAE, herramienta informática de diseño y análisis por el Método de los Elementos Finitos, que representan volúmenes elementales representativos (RVE´s por su siglas en inglés) de la estructura del hueso trabecular. Estos RVE´s permitirán estudiar el comportamiento con la porosidad de las principales constantes elásticas de la estructura, considerándose ésta como elástica, lineal e isótropa.
Se ha estudiado un rango de porosidad que abarca desde el 0 % hasta el 55 %, en incrementos del 5 %, y se ha observado como aumentan o disminuyen los valores del Módulo de elasticidad (E), Módulo de cizalla (G) y Coeficiente de Poisson.
Mientras que el Módulo de elasticidad (E) y el Módulo de cizalla (G) disminuyen con la porosidad, desde 13 GPa (0 %) hasta 2,5 GPa (55 %) el primero, y desde 1,8 GPa (0 %) hasta 0,4 GPa (55 %) el segundo, ambos presentando una línea de tendencia polinómica de segundo grado, el Coeficiente de Poisson aumenta, desde 0,3 (0 %) hasta 0,35 (55 %), con una línea de tendencia recta.
Two main types of tissues can be found in the skeletal bones: cortical bone tissue, known as cortical bone, and trabecular bone tissue, known as trabecular bone. Although both of them are composed by the same type of cells and have similar compositions, their internal structure is different. Whereas in the cortical bone the bone tissue appears compactly arranged; in the trabecular bone the bone tissue is grouped irregularly forming layers known as trabeculae. This arrangement causes the apparition of hollows which give the structure this typical spongy appearance. The trabecular bone therefore has less density than the cortical bone, due to a larger porosity. This is the key to determine the mechanical behaviour of this type of structure. However, this is not easy because of the variation in the porosity of each bone and the increase or decrease of the porosity due to different metabolic disorders. Through the implementation of a script written in Python programming language, random models have been generated in Abaqus/CAE, a software tool of design and FEM analysis. These models represent RVEs of the trabecular bone structure, which let us study the behaviour of the main elastic constants of the structure with the porosity. We will consider an elastic, lineal and isotropic structure. A range of porosity that goes from 0 % to 55 % with increases of 5 % has been studied, and the increase or decrease of the Elastic modulus (E), Shear modulus (G) and Poisson´s ratio have been watched. Whereas the Elastic modulus and the Shear modulus decrease with the porosity, from 13 GPa (0 %) to 2.5 GPa (55 %) the first one, and from 1.8 GPa (0 %) to 0.4 GPa (55 %) the second one, both having a second degree polynomial trend line; the Poisson´s ratio increases from 0.3 (0 %) to 0.35 (55 %) with a straight trend line.
Two main types of tissues can be found in the skeletal bones: cortical bone tissue, known as cortical bone, and trabecular bone tissue, known as trabecular bone. Although both of them are composed by the same type of cells and have similar compositions, their internal structure is different. Whereas in the cortical bone the bone tissue appears compactly arranged; in the trabecular bone the bone tissue is grouped irregularly forming layers known as trabeculae. This arrangement causes the apparition of hollows which give the structure this typical spongy appearance. The trabecular bone therefore has less density than the cortical bone, due to a larger porosity. This is the key to determine the mechanical behaviour of this type of structure. However, this is not easy because of the variation in the porosity of each bone and the increase or decrease of the porosity due to different metabolic disorders. Through the implementation of a script written in Python programming language, random models have been generated in Abaqus/CAE, a software tool of design and FEM analysis. These models represent RVEs of the trabecular bone structure, which let us study the behaviour of the main elastic constants of the structure with the porosity. We will consider an elastic, lineal and isotropic structure. A range of porosity that goes from 0 % to 55 % with increases of 5 % has been studied, and the increase or decrease of the Elastic modulus (E), Shear modulus (G) and Poisson´s ratio have been watched. Whereas the Elastic modulus and the Shear modulus decrease with the porosity, from 13 GPa (0 %) to 2.5 GPa (55 %) the first one, and from 1.8 GPa (0 %) to 0.4 GPa (55 %) the second one, both having a second degree polynomial trend line; the Poisson´s ratio increases from 0.3 (0 %) to 0.35 (55 %) with a straight trend line.
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Biomecánica, Abaqus/CAE, Programación orientada a objetos, Porosidad, Hueso trabecular