A Simplistic Approach to Bone Healing Simulation

Abstract

A simple computational approach to simulation of healing in long bone fractures is presented. In particular, an algorithm that could simulate the formation, maturation, and resorption of fracture callus is developed and validated. The simplicity of the approach lies in the fact that the algorithm uses only the applied load and a single constraint parameter for the entire simulation. The work hypothesizes bone healing as a comprehensive energy minimization process where mechanical stimulation is proposed as the primary precursor for the beginning of different stages (i.e., callus formation, mineralization, and resorption). As such, the hypothesis is derived from the second law of thermodynamics which states that the energy of a closed system should be minimum at equilibrium. Alternatively, each stage of healing bone healing may be termed a state of homeostasis. The validation is done through a multi-material, time-based simulation of bone healing in a damaged tibia. The simulation uses a cross-section-based finite element model and an advanced version of an already validated structural optimization algorithm. The optimization objective is to minimize overall strain energy for the entire process, subject to a polar first moment of mass constraint. The simulation results show different stages of healing, where the algorithm generates a callus geometry similar to those observed experimentally. Eventually, a geometry similar to that in an intact cross-section is achieved by resorption of the callus from the unwanted sites.