以影像為基礎之多尺度模擬多孔骨頭材料

Abstract

在本研究中，將發展一數學與數值分析架構以模擬多尺度多孔隙材料並將之應用於 骨頭材料之行為研究。首先，以漸進均勻化分析連結具固液體相位材料之微觀組成 特性與宏觀廣義達西定律及相關平衡方程。為了建立由醫學影像所得之微觀模型， 引入邊界識別分離法，例如無邊緣活動圍道結合水平集函數，以識別分離出不同相 位。由於影像係由離散之畫素點所組成，本研究將引入強形式配置法，結合再生核 近似法求解水平集函數與微觀尺度問題(microscopic cell problems)。最後，所提出 之方法將應用於骨頭中之鬆質骨並模擬預測其材料力學性質。

The mathematical and computational frameworks for multi scale modeling of porous materials will be developed and applied in bone material modeling in this work. The asymptotic based homogenization will be introduced to correlate the microscopic solid-fluid phase composition and properties to the macroscopic generalized Darcy’s law and balance laws. To construct microscopic models directly from medical images, the active contour model based on variational level set formulation for interface identification and boundary segmentation will be introduced. Inspired by the pixel point discretization of microstructures, the strong form collocation method with reproducing kernel approximation will be introduced to solve the level set equation and microscopic cell problems. Finally, the application of the proposed framework to multiscale modeling of a trabecular bone will be investigated.