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2 Acta of Bioengineering and Biomechanics

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

Piszczatowski Sz.

Acta of Bioengineering and Biomechanics

2012

Vol. 14, no. 1

93-106

Development of the skeleton is a complex mechanobiological process. Shape and size of the majority of bone elements are the result of endochondral growth and ossification occurring during childhood and adolescent period. The influence of mechanical loading acting in the skeletal system on bone development is known since the 19th century, but understanding of such phenomenon seems to be still insufficient. Traditionally accepted Hueter-Volkmann law claims that increased pressure acting on a growth plate retards bone growth and, conversely, reduced pressure or even tension accelerates it. Stokes's approach is directly based on this theory. Carter's model seems to be slightly more complex because takes into account three-dimensional stress state. The subject of the research was to evaluate the mechanobiological condition of endochondral bone growth occurring within the growth cartilage where different geometrical structures (8 models) of the growth plate and various loading conditions (5 variants) were considered. Simulations were made using the finite element method and both Stokes's and Carter's models were used to estimate mechanical stimulation of bone growth. Results indicate non-uniformity of the growth conditions occurring within the growth cartilage when its layer is located between two bone blocks. Non-axial loadings result in dissymmetry of mechanical stimulation of bone growth. In general, its minimum is located in the regions of the cartilage to which maximal loadings were directed. Carter's approach is, however, more sensitive to interrelation between growth plate geometrical structure and loading direction, compared to Stokes's model. Obtained results indicate the necessity of realistic modelling of the growing bone geometrical structure, including the elaboration of custom-made models. Further research is necessary to elaborate the new formula describing mechanical influences on bone growth, taking into account the cyclic loading of a constant direction. In this way it will be possible to overcome the still existing problems with the explanation of numerous clinical phenomena.

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

Piszczatowski S.

Acta of Bioengineering and Biomechanics

2011

Vol. 13, no. 3

3-14

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.