A Mathematical Model Based Study on Dynamic Changes of Chondrogenesis and Osteogenesis During Condylar Neck Fracture Healing / 华中科技大学学报(医学版)

ABSTRACT

Objective To explore the healing pattern of condylar neck fractures by using mathematical models to simulate the dynamic changes of osteogenesis and chondrogenesis in the process of rat condylar neck fracture healing.Methods A math-ematical model was constructed to simulate the healing process of rat condylar neck fractures.The values of various parameters(mb,mc,cb and cc)generated by the model at different time points within 28 days were statistically analyzed.Subsequently,den-sity maps and growth curves of bone,cartilage,osteoblasts,and chondrocytes were fitted and the osteogenesis mode was de-duced.Results The bone area ratio simulated by the mathematical model was similar to that measured in rat fracture experi-ments(P＞0.05).The simulated density maps showed that osteogenesis was concentrated around the periosteum from day 3 to day 7 after fracture,and then concentrated in the cartilage region and gradually replaced cartilage from day 7 to day 21.The bone growth curve and cartilage growth curve were positively correlated from day 5 to day 8 and from day 21 to day 28.However,the curves were negatively correlated from day 8 to day 14 after fracture.The growth curves of osteoblasts and chondrocytes both showed an increasing trend before decreasing,with chondrocyte density peaking at day 6 and osteoblast density peaking at day 13.Conclusion The mathematical model can effectively simulate the healing process of rat condylar neck fractures and display the dynamic changes of osteogenesis and chondrogenesis during the whole process.This provides a new idea for studying healing methods of condylar neck fractures.