Image-Based Multiscale Modeling of Porous Bone Materials

Mathematical and computational frameworks for multiscale modeling of bone materials are presented. Asymptotic-based homogenization is first introduced to correlate the microscopic solid-fluid phase composition and properties to the macroscopic generalized Darcy's law and balance laws, where the homogenized macroscopic continuity and equilibrium equations reassemble the governing equations in Biot's theory. To construct microscopic models directly from medical images, we introduced the active contour model based on the variational level set formulation for interface identification and boundary segmentation. Inspired by the point discretization of microstructures, we introduce the strong form collocation method with reproducing kernel approximation to solve the level set equation. A gradient-reproducing kernel collocation method is introduced to solve characteristic functions in the microstructures using image pixels as the discretization points. Finally, application to multiscale modeling of a trabecular bone is demonstrated. This edition first published 2013