title: Phase-field boundary conditions for the voxel finite cell method: Surface-free stress analysis of CT-based bone structures.
abstract: The voxel finite cell method uses unfitted finite element meshes and voxel quadrature rules to seamlessly transfer computed tomography data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field-based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then used to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, ie, the interface width of the phase field, the voxel spacing, and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body.
authors.affiliation: Department of Civil, Environmental, and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455, USA.
authors.forename: Lam
authors.initials: L
authors.lastname: Nguyen
authors.affiliation: Department of Civil, Environmental, and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455, USA.
authors.forename: Stein
authors.initials: S
authors.lastname: Stoter
authors.affiliation: Department of Neuroradiology, Klinikum rechts der Isar, Technische Universität München, Munich, Germany.
authors.forename: Thomas
authors.initials: T
authors.lastname: Baum
authors.affiliation: Department of Neuroradiology, Klinikum rechts der Isar, Technische Universität München, Munich, Germany.
authors.forename: Jan
authors.identifier: 0000-0002-7557-0003
authors.initials: J
authors.lastname: Kirschke
authors.affiliation: School of Engineering, University of Glasgow, Glasgow, UK.
authors.forename: Martin
authors.initials: M
authors.lastname: Ruess
authors.affiliation: Department of Mechanical Engineering, Ben-Gurion-University of the Negev, Beer Sheva, Israel.
authors.forename: Zohar
authors.initials: Z
authors.lastname: Yosibash
authors.affiliation: Department of Civil, Environmental, and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455, USA.
authors.forename: Dominik
authors.identifier: 0000-0002-9068-6311
authors.initials: D
authors.lastname: Schillinger
mesh_terms: D001842:Bone and Bones / Q000000981:diagnostic imaging*; D005269:Femur / Q000502:physiology*; D020342:Finite Element Analysis; D006801:Humans; D013314:Stress, Mechanical; D014057:Tomography, X-Ray Computed
keywords: diffuse boundary methods; femur; patient-specific simulation; phase-fields; vertebra; voxel finite cell method