A first order system model of fracture healing

A first order system model is proposed for simulating the influence of stress stimulation on fracture strength during fracture healing. To validate the model, the diaphyses of bilateral tibiae in 70 New Zealand rabbits were osteotomized and fixed with rigid plates and stress-relaxation plates, respectively. Stress shielding rate and ultimate bending strength of the healing bone were measured at 2 to 48 weeks postoperatively. Ratios of stress stimulation and fracture strength of the healing bone to those of intact bone were taken as the system input and output. The assumed first order system model can approximate the experimental data on fracture strength from the input of stress stimulation over time, both for the rigid plate group and the stress-relaxation plate group, with different system parameters of time constant and gain. The fitting curve indicates that the effect of mechanical stimulus occurs mainly in late stages of healing. First order system can model the stress adaptation process of fracture healing. This approach presents a simple bio-mathematical model of the relationship between stress stimulation and fracture strength, and has the potential to optimize planning of functional exercises and conduct parametric studies.