Elastic properties of a porous titanium-bone tissue composite

The porous titanium implants were introduced into the condyles of tibias and femurs of sheep. New bone tissue fills the pore, and the porous titanium-new bone tissue composite is formed. The duration of composite formation was 4, 8, 24 and 52 weeks. The formed composites were extracted from the bone and subjected to a compression test. The Young's modulus was calculated using the measured stress-strain curve. The time dependence of the Young's modulus of the composite was obtained. After 4 weeks the new bone tissue that filled the pores does not affect the elastic properties of implants. After 24 and 52 weeks the Young's modulus increases by 21-34% and 62-136%, respectively. The numerical calculations of the elasticity of porous titanium-new bone tissue composite were conducted using a simple polydisperse model that is based on the consideration of heterogeneous structure as a continuous medium with spherical inclusions of different sizes. The kinetics of the change in the elasticity of the new bone tissue is presented via the intermediate characteristics, namely the relative ultimate tensile strength or proportion of mature bone tissue in the bone tissue. The calculated and experimentally measured values of the Young's modulus of the composite are in good agreement after 8 weeks of composite formation. The properties of the porous titanium-new bone tissue composites can only be predicted when data on the properties of new bone tissue are available after 8 weeks of contact between the implant and the native bone.