An approach for time‐dependent bone modeling and remodeling—application: A preliminary remodeling simulation

Abstract

In a companion paper, we presented a time-dependent theory for bone modeling and remodeling in response to a daily loading history. This paper represents a preliminary attempt to use the theory to determine the distribution of bone density within the adult proximal femur under an assumed normal loading history. Subsequent functional adaptation of the internal structure due to changes in the loading history are then determined. Throughout this preliminary study, the external geometry of the proximal femur is considered to be fixed, i.e., changes in the external shape are neither stimulated nor allowed. Linear and trilinear (dead-zone nonlinearity) rate remodeling laws were compared. Computer emulations using two-dimensional finite element models were successful in creating a normal-appearing distribution of bone tissue when remodeling was initiated from a solid structure of homogeneous bone density. Subsequent reduction in the loading history caused regional bone atrophy. Reinstatement of the normal loading history caused a generalized increase in bone mass but resulted in a slightly different bone distribution than was calculated for a constant loading history. These results demonstrate the utility of the remodeling theory and are consistent with the hypothesis that similar stress-related phenomena are responsible for both normal morphogenesis and functional adaptation in response to changes in the bone loading.

Material growth in thermoelastic continua: Theory, algorithmics, and simulation

“…Qualitatively, the simulation matches expected bone morphology and representative literature results for two-dimensional models [3,29]. Along the primary loading path from the femoral head, a high stress trajectory forms and a corresponding strut of high density bone grows.…”

“…This relative measure represents a translational shift of the growth density distribution data with respect to the arbitrarily selected initial homogeneous state. It permits the results obtained here, in which the model shifts the stress-attractor state such as to correspond with an equilibrated system for an initially unloaded configuration, to be directly compared with literature results in which the stress-attractor state corresponds with an unequilibrated system for an initially unloaded configuration [3,29]. The translation shift normalizes the arbitrariness of the stress-attractor and homogeneous density initial configurations between the models.…”

“…This rule is motivated by the stress state attractor stimulus model for bones of Beaupré, Orr, and Carter [4,3]. The stress state stimulus model assumes bone mass accretion occurs when the magnitude of a characteristic stress measure exceeds a stimulus stress value and mass resorption occurs when the stress measure is less than the stimulus.…”

Bone morphology allows estimation of loading history in a murine model of bone adaptation

“…If this indeed is an important factor, better results would be expected for bone in older subjects that might be more adapted to their loading history. But also in fully grown bone, other factors of biological nature like calcium homeostasis or sex hormones could be physiologically more important than a bone structure perfectly adapted to its loading regime (Beaupre et al 1990;Frost 1987;Harada and Rodan 2003;Manolagas 2000;Robling et al 2006).…”

Patches of Finite Elements for Singularly-Perturbed Diffusion Reaction Equations with Discontinuous Coefficients

“…Wagner and Weiner [7] modelled bone considering a composed material defined by its microstructure. Several authors [8,9] proposed experimental correlations that define the mechanical properties assuming isotropic behaviour as a function of the apparent density. However, bone is a porous and anisotropic material.…”