title: Temporal stability of node-based internal bone adaptation simulations.
abstract: Jacobs et al. (1995, J. Biomechanics 28, 449-459) introduced a new implementation of the remodeling theory developed by Beaupre et al. (1990, J. Orthop. Res. 8, 651-661) that eliminates certain spurious spatial instabilities of previous implementations. Due to the highly nonlinear, coupled nature of multi-dimensional adaptation simulations, direct stability analyses of this method are not practical. In this manuscript, a linearized stability analysis was used to derive an expression for the critical time step for the stability of a simple model problem. In addition to accurately predicting the temporal response of the single degree-of-freedom problem, the analysis provided a conservative estimate of the critical time step for a more realistic, multiple degree-of-freedom adaptation simulation.
authors.affiliation: RR&D Center, Veterans Affairs Medical Center, Palo Alto, CA 94304-1200, USA.
authors.forename: M E
authors.initials: ME
authors.lastname: Levenston
mesh_terms: D000222:Adaptation, Physiological; D016723:Bone Remodeling; D001842:Bone and Bones / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D013997:Time Factors