A model for the change of cancellous bone volume and structure over time

Modelling the Effects of Growth and Remodelling on the Density and Structure of Cancellous Bone

A two-stage model is proposed for investigating remodelling characteristics in bone over time and distance to the growth plate. The first stage comprises a partial differential equation (PDE) for bone density as a function of time and distance from the growth plate. This stage clarifies the contributions to changes in bone density due to remodelling and growth processes and tracks the rate at which new bone emanates from the growth plate. The second stage consists of simulating the remodelling process to determine remodelling characteristics. Implementing the second stage requires the rate at which bone moves away from the growth plate computed during the first stage. The second stage is also needed to confirm that remodelling characteristics predicted by the first stage may be explained by a realistic model for remodelling and to compute activation frequency. The model is demonstrated on microCT scans of tibia of juvenile female rats in three experimental groups: sham-operated control, oestrogen deprived, and oestrogen deprived followed by treatment. Model predictions for changes in bone density and remodelling characteristics agree with the literature. In addition, the model provides new insight into the role of treatment on the density of new bone emanating from the growth plate and provides quantitative descriptions of changes in remodelling characteristics beyond what has been possible to ascertain by experimentation alone.

The relationship between porosity and specific surface in human cortical bone is subject specific

A characteristic relationship for bone between bone volume fraction (BV/TV) and specific surface (BS/TV) has previously been proposed based on 2D histological measurements. This relationship has been suggested to be bone intrinsic, i.e., to not depend on bone type, bone site and health state. In these studies, only limited data comes from cortical bone. The aim of this paper was to investigate the relationship between BV/TV and BS/TV in human cortical bone using high-resolution micro-CT imaging and the correlations with subject-specific biometric data such as height, weight, age and sex. Images from femoral cortical bone samples of the Melbourne Femur Collection were obtained using synchrotron radiation micro-CT (SPring8, Japan). Sixteen bone samples from thirteen individuals were analysed in order to find bone volume fraction values ranging from 0.20 to 1. Finally, morphological models of the tissue microstructure were developed to help explain the relationship between BV/TV and BS/TV. Our experimental findings indicate that the BV/TV vs BS/TV relationship is subject specific rather than intrinsic. Sex and pore density were statistically correlated with the individual curves. However no correlation was found with body height, weight or age. Experimental cortical data points deviate from interpolating curves previously proposed in the literature. However, these curves are largely based on data points from trabecular bone samples. This finding challenges the universality of the curve: highly porous cortical bone is significantly different to trabecular bone of the same porosity. Finally, our morphological models suggest that changes in BV/TV within the same sample can be explained by an increase in pore area rather than in pore density. This is consistent with the proposed mechanisms of age-related endocortical bone loss. In addition, these morphological models highlight that the relationship between BV/TV and BS/TV is not linear at high BV/TV as suggested in the literature but is closer to a square root function.