A stochastic-mechanical model for the growth of longitudinal as well as transverse direction of a mammalian long bone is proposed.
In the longitudinal direction, a stochastic birth process is applied to represent the growth behavior of the cells within the growth plate. The birth rate of the cell is affected by a mechanical model representing a bone-periosteum system. The average number of cells within the growth plate and those that are lost from the growth plate can be calculated at any time instant. This average number is distributed with respect to cell age. The size of the cell is also a function of its age. Combining these two factors, the length of the bone can be found as a function of time. The length of the growth plate and the average number of cells in the growth plate are also found as functions of time. As for the transverse direction of the growth, a stochastic model based on a continuously parametered Markov chain process with a specially assigned intensity function is used. Both volume-distributed growth and surfacedistributed growth are considered in the model. Numerical examples are carried out in both directions.
The results are compared with some observed data and good agreement is found.