Three dimensional stereolithography models of cancellous bone structures from muCT data: testing and validation of finite element results.

Stereolithography (STL) models of complex cancellous bone structures have been produced from three-dimensional micro-computed tomography data sets of human cancellous bone histological samples from four skeletal sites. The STL models have been mechanically tested and the derived stiffness compared with that predicted by finite element analysis. The results show a strong correlation (R2 = 0.941) between the predicted and calculated stiffnesses of the structures and show promise for the use of STL as an additional technique to complement the use of finite element models, for the assessment of the mechanical properties of complex cancellous bone structures.

Stereo visualization of 3D trabecular bone structures produced by bone remodelling simulation.

Adult human bone is constantly being renewed by a process known as remodelling. For cancellous bone this renewal process occurs at the interface between bone and marrow where bone is depleted by osteoclasts and rebuilt by osteoblasts. This remodelling process allows bone to repair itself. Software simulators for bone remodelling provide insight into the bone remodelling process; they allow investigation into bone form and structural properties, and they also allow the emulation of bone diseases and possible treatments for these diseases over long periods of time. BONESIM is a software that simulates bone remodelling in terms of Basic Multi-cellular Units (BMUs). 3D visualization of trabecular bone and its attributes is an essential tool in understanding this remodelling process for cancellous bone. It enables the bone researcher to quickly understand the dynamic behaviour of remodelling, the resulting geometry of the bone structure and it allows alternative remodelling scenarios to be compared. This paper presents the volume visualization technique that has been developed to provide this visualization tool.

Smoothing of pixelated finite element models of cancellous bone structures and the effect on the predicted structural properties of the bone.

Many areas of biomedical engineering involve the modelling of biological systems, often using data from medical scanning techniques such as computed microtomography (microCT), and the prediction of the mechanical properties of these systems via finite element models. These models, and also those produced from remodelling simulations on idealized bone structures, are inherently highly pixelated and therefore have a high degree of surface roughness. The purpose of this paper is to demonstrate that this surface roughness need not necessarily have an influence on the predicted properties of the object under examination. To demonstrate this, two-dimensional idealized models of cancellous bone structures were used that were initially depleted and then rebuilt stochastically. A hysteresis effect was observed such that a significant amount of rebuilding beyond the original density was required to regain the initial intact stiffness. To ensure that this effect was not an artefact of the high degree of surface roughness of the rebuilt structures, a two-stage smoothing procedure was applied to assess if this had any effect on the stiffness of the structures. The superpixelation of the structures appeared to have a more profound effect than the smoothing procedures, although the smoothed structures still had stiffness and density values similar to those of the original structures, with a hysteresis effect still evident. This proves that the pixelization of the structures does not have a significant effect on the predicted mechanical properties of the structures. This work has important implications for other models that exhibit a high degree of surface roughness.

Stochastically simulated assessment of anabolic treatment following varying degrees of cancellous bone resorption.

The aim of this study was to investigate the recovery in cancellous bone stiffness resulting from anabolic treatment following varying degrees of resorption, using a stochastic simulation applied to a simplistic structure consisting of five vertical and five horizontal trabeculae. The structure was initially resorbed, and "bone" elements were stochastically removed until nominal resorptions of 10%, 15%, 20%, 25%, and 30% were achieved. A stochastic simulation of anabolic treatment was then applied where bone elements were added, continuing until the original stiffness had been regained, for example, simulating treatment of a patient with an anabolic agent after a period of postmenopausal resorption. The resorption and anabolic simulations were repeated three times for each of the nominal resorptions. The stiffness of the bone structure decreased linearly with resorption, with a slope of approximately -2 and an R(2) of 97.0%; hence, the stiffness fell at approximately twice the rate of the reduction in density. When the various structures regained their original density, the resultant stiffness also had a linear relationship with the original resorption, with a slope of -1 and a lower R(2) of 86.1%. This implies that the reduction in stiffness, when original density was regained, fell proportionately with the degree of initial resorption and, therefore, after a resorption of 30%, when original density was regained, the stiffness of the resultant structure was approximately 30% less than that of the original structure. The density required for the original stiffness to be regained increased linearly with the degree of initial resorption, with a slope of approximately 0.5 and an R(2) of 65.2%, lower than that observed for the previous relationships. This indicates a greater spread of data and suggests greater variability in the formation phase beyond the point of regained original density. Because irreversible connectivity reduction is widely considered to be one of the earliest manifestations of estrogen loss, these findings, although obtained on a simulation of a simplistic cancellous bone structure, support the concept of early intervention to prevent potentially irreversible deterioration of trabecular architecture after menopause.

Finite Element Analysis of Simulations of Cancellous Bone Resorption.

A stochastic simulation of the resorption of cancellous bone has been developed and integrated with a finite element model to predict the resultant change in structural properties of bone as bone density decreases. The resorption represents the net imbalance of osteoclast and osteoblast activity that occurs in osteoporosis. A simple lattice structure of trabecular bone is considered, with an examination of the lattice geometry and discretization indicating that just five trabeculae need to be modelled. The results from the analysis show how the mechanical properties of the cancellous bone degrade with osteoporosis and demonstrate how the method can be used to predict the relationships between stiffness and density or porosity.