A stochastic-mechanical model of longitudinal long bone growth.

A typical mammalian long bone will increase in length during the growth phase of the individual. This increase in length does not occur uniformly throughout the bone, since bone tissue is incapable of internal expansion after formation. The growth occurs at two, disc-shaped, regions near either end of the long bone. These regions are called growth plates. These plates are located between the osseous shaft (diaphysis) and osseous tip (epiphysis) whose bone tissues are discontinuous. The present study develops a stochastic-mechanical model for such a bone growth and demonstrates the capability of the model to reproduce the observed overall behavior of longitudinal long bone growth based on realistic information of cellular mitosis, growth and ossification. A numerical analysis was performed on the model under the assumption that the number of cells in the proliferation zone remains constant throughout the growth period. The growth curves thus obtained compare favorably with those growth curves proposed elsewhere essentially on the basis of phenomenological observation. The present model can demonstrate the effects of such parameters as the proliferation rate, initial age distribution and compressive stress on the growth. More importantly, the stochastic-mechanical model so developed permits one to incorporate further experimental evidence and statistical observation at the cellular level into the analysis to improve the solutions.