Diffusion in Bone Tissue

Abstract: In order to prevent or modify the processes of bone degeneration the modeling and remodeling of bone tissue must be better understood. In this thesis it is assumed that the primary condition leading to bone growth is a change of the chemical environment caused by transport of matter resulting from stress driven diffusion. The change in the chemical environment may consist of changes in the concentration of different substances stimulating, for example, bone building osteoblast recruitment or suppression of bone resorbing osteoclast activity. Since bone growth takes place at the outer bone surface, the hypothesis is that substances promoting bone growth are transported from the medullary cavity to the outer surface, the periosteum, of the long skeletal bone by stress driven diffusion. Inspired by an experiment performed by Lanyon and Rubin (1984) a numerical model is developed which can be solved using a regular structural finite element solver. It is found that bone growth to a higher extent takes place where high concentration of matter arises rather than where the mechanical stress is high. It is also seen that bone growth is dependent on load frequency. The model uses normalized input data, but in order to make full use of the results the actual diffusion coefficient of interest must be known, and hence an approach is developed for determining diffusion coefficients in bone tissue. By means of conductivity measurements together with an analytical solution, which is fitted to the experimental data using a Kalman filter, diffusion coefficients can be extracted.