Mechanical Remodeling of Bone Structure Considering Residual Stress

Abstract

Mechanical remodeling of bone is a kind of adaptation and is performed to regulate the stress and/or strain in the tissue in response to the changing mechanical environment due to tissue growth and atrophy. We propose a phenomenological model of mechanical remodeling of bone structure considering residual stress. The lattice continuum model is used to represent the bone structure, such as the trabecular structure of cancellous bones. The basic idea in the previous report, which concerns mechanical remodeling that takes into account the residual stress, is extended to the continuum with the internal tissue structure. A remodeling rate equation of the tissue structure is expressed so as to result in an equistress state at the remodeling equilibrium as an optimality of the bone structure in the steady state. A case study of a long bone under bending moment reveals basic features of the proposed model of the stress regulation process. Remodeling simulation for the vertebral body under repetitive bending with compression demonstrates apparent density and residual stress distributions that coincide with the experimental observations.