Derivation and development of a mathematical model for long bone growth

The objective of this work is to derive and develop a mathematical model that can be used to better understand long bone growth, specifically in the tibia. A cell balance was performed on the three regions of the growth plate, in order to determine the variables (number of proliferating cells and cell division rate of the proliferating cells) that influence the tibia growth rate as well as their relationship to the growth rate. Once this relationship was established, previously collected data were used to understand how the tibia growth rate and number of proliferating cells changes with time. These equations were then inserted into the model in order to determine how the cell division rate changes with time. Using these three equations, this model can be applied to determine how limb asymmetry occurs along with how various factors, including vitamins and hormones, can affect the tibia bone growth rate.