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Material aspects of growth plate modelling using Carter's and Stokes's approaches.

Growth plate, named also as physis, is the anatomical structure responsible for the bone growth. Apart from numerous biological and biochemical factors, biomechanics has also strong influence on its functioning. Loadings acting on the bone element during its development can change (increase or decrease) the velocity of growth. This way mechanobiological processes influence the skeletal development. Several theories try to describe the relationship between loadings acting on the physis and biological processes leading to bone growth and development. Unfortunately, some serious discrepancies exist between them. Additionally, difficulties occur during the modelling of the growth plate activity, which results from the problems in determining material parameters of the particular physis component. The aim of the study was to analyse the influence of material properties of particular parts of the physis on biomechanical conditions of the bone growth. Two concepts, based on the Carter's and Stokes's approaches, were applied to estimate the biomechanical stimulation of the bone growth occurring within the physis volume. Results of the numerical simulations show that due to inhomogeneity of the physis structure, the complex 3-D stress state occurs within the growth plate even in the case of uniform axial pressure acting on its surface. The value of the cartilage Poisson's ratio has a significant influence on the biomechanics of the growth plate activity estimated using both theories. Carter's model is additionally very sensitive to its dilatational parameter. Both methods lead to non-uniform patterns of mechanical stimulation of the bone growth within the volume of the cartilage. The differences in the stiffness between cartilaginous and bone parts of the growth plate are of fundamental importance for such phenomenon.