Stochastic simulations of remodeling applied to a two-dimensional trabecular bone structure

Abstract

In this investigation the stochastic dynamics of trabecular bone remodeling (which is a key concept in a range of remodeling models) is verified. For this purpose, two-dimensional binary images of horizontal histological sections of lumbar vertebral bone (L-3) were collected from young and old subjects. Then the stochastic algorithm of remodeling was applied to the images of young trabecular bone. The resulting images of “simulated” old structures and those of “real” old structures were analyzed to evaluate the following architectural parameters: bone volume/trabecular volume; mean area of marrow cavities; mean trabeculae length; marrow space star volume; Euler number density; trabecular thickness; trabecular number; trabecular separation; mean two-point distance along the skeleton of trabecular structure; probability of disconnection; the ratio of marrow space star volume to geometrical volume and dimensionless ratio of mean area of marrow cavities; and mean trabecular length squared (form factor). Using the parametric t-test, the groups of simulated and real old bone images were compared. It is found that the p value of the t-test is never less than 0.20. For eight parameters the p value is >0.45. It is concluded that, as long as the horizontal sections of lumbar vertebrae are considered (sections perpendicular to the direction of the main spine load), the stochastic algorithm of bone remodeling will properly reproduce the architectural properties of trabecular bone.