# Phase diagrams of bone remodeling using a 3D stochastic cellular automaton

## TL;DR

This paper introduces a 3D model to simulate bone remodeling using game theory, helping understand how bone changes under different conditions.

## Contribution

A novel 3D stochastic cellular automaton model for bone remodeling dynamics using evolutionary game theory.

## Key findings

- A phase diagram was derived to show how bone remodeling processes respond to parameter changes.
- Modeling small neighborhoods is crucial for understanding local bone microenvironment controls.
- The model can guide experiments and explore external impacts on bone remodeling.

## Abstract

We propose a 3D stochastic cellular automaton model, governed by evolutionary game theory, to simulate bone remodeling dynamics. The model includes four voxel states: Formation, Quiescence, Resorption, and Environment. We simulate the Resorption and Formation processes on separate time scales to explore the parameter space and derive a phase diagram that illustrates the sensitivity of these processes to parameter changes. Combining these results, we simulate a full bone remodeling cycle. Furthermore, we show the importance of modeling small neighborhoods for studying local bone microenvironment controls. This model can guide experimental design and, in combination with other models, it could assist to further explore external impacts on bone remodeling. Consequently, this model contributes to an improved understanding of complex dynamics in bone remodeling dynamics and exploring alterations due to disease or drug treatment.