A two-dimensional model for stress driven diffusion in bone tissue

Determination of spatially dependent diffusion parameters in bovine bone using Kalman filter

Although many studies have been made for homogenous constant diffusion, bone is an inhomogeneous material. It has been suggested that bone porosity decreases from the inner boundaries to the outer boundaries of the long bones. The diffusivity of substances in the bone matrix is believed to increase as the bone porosity increases. In this study, an experimental set up is used where bovine bone samples, saturated with potassium chloride (KCl), were put into distilled water and the conductivity of the water was followed. Chloride ions in the bone samples escaped out in the water through diffusion and the increase of the conductivity was measured. A one-dimensional, spatially dependent mathematical model describing the diffusion process is used. The diffusion parameters in the model are determined using a Kalman filter technique. The parameters for spatially dependent at endosteal and periosteal surfaces are found to be (12.8 ± 4.7) × 10(-11) and (5 ± 3.5) × 10(-11)m(2)/s respectively. The mathematical model function using the obtained diffusion parameters fits very well with the experimental data with mean square error varies from 0.06 × 10(-6) to 0.183 × 10(-6) (μS/m)(2).