p-version of the finite-element method for highly heterogeneous simulation of human bone

A three-dimensional model of the human tibia bone subject to realistic static physiological conditions was developed using the p-version of the finite-element method. The p-version of the finite-element method in combination with the blending-function method enabled the construction of elements displaying accurate representation of the domain's boundary. This allowed the modeling of complex structures like bones using few elements and circumvented the problems of complexity and inaccuracy that are typical of current commercially available finite-element mesh generators. In these methods large p-elements are integrated with high-order functions, permitting the coupling of the mechanical properties of each integration point directly to a voxel matrix extracted from computerized tomographies. This allowed order of 1000 different properties to be assigned per element thereby rendering a highly heterogeneous bone model. The final objective of this bone model is to offers a platform for the study medical devices and bone composition and behavior in fracture processes and in pathologies as osteoporosis. The results show realistic stresses and displacements of the human tibia under static loading. The stresses are distributed along the whole bone and more pronounced towards the periphery, where there is a larger concentration of cortical bone.