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

## TL;DR

This paper introduces a two-stage model to study how bone density and structure change over time and distance from the growth plate in juvenile rats.

## Contribution

The novel contribution is a two-stage modeling approach that links bone growth and remodelling to predict density and remodelling characteristics.

## Key findings

- The model accurately predicts bone density changes consistent with experimental data.
- Treatment effects on new bone density from the growth plate are quantitatively described.
- The model provides insights into remodelling characteristics beyond experimental observations.

## Abstract

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 online version contains supplementary material available at 10.1007/s11538-024-01267-3.