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Analyzing bone regeneration using topological optimization
Análisis del regeneramiento óseo bajo el esquema de optimización topológica
DOI:
https://doi.org/10.15446/ing.investig.v25n1.14617Keywords:
bony regeneration, topological optimisation, mathematical theory (en)dominio, optimización topológica, regeneramiento óseo, teoría matermática (es)
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The present article’s object is to present the mathematical foundations of topological optimization aimed at carrying out a study of bone regeneration. Bone structure can be economically adapted to different mechanical demands responding to topological optimization models (having “minimum” mass and “high” resistance). Such analysis is essential for formulating physical therapy in patients needing partial or total strengthening of a particular bone’s tissue structure. A mathematical model is formulated, as are the methods for resolving it.
El objetivo fundamental del presente artículo es presentar la fundamentación matemática de la optimización topológica para llevar a cabo el estudio del regeneramiento óseo. La estructura ósea posee la capacidad de adaptarse de forma económica (con un “mínimo” de masa y “alta” resistencia) a diversas solicitaciones mecánicas, lo cual responde a modelos de optimización topológica. Dichos esquemas de análisis son esenciales para la formulación de la terapia física en pacientes que necesiten fortalecer parcial o totalmente la estructura del tejido de algún hueso en particular. Inicialmente se formula el modelo matemático y sus métodos de solución.
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Copyright (c) 2005 Diego Alexander Garzón Alvarado, Máximo Alejandro Roa Garzón, Carlos Alberto Duque Daza
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