We simulate the thermodynamics and kinetics of the drift/diffusion of oxygen vacancy defects in rutile TiO2, using the density-functional based tight-binding (DFTB) method. Both static and dynamic simulations have been performed. Results indicate that DFTB is well suited to examine the dynamic behavior of oxygen vacancies in TiO2. Detailed analysis shows, that strong model size dependence in relative diffusion barrier heights between different diffusion processes requires great care in defect diffusion simulations in TiO2. Thermodynamic results on the influence of an external electric field show that, due to the large dielectric constant, the coulomb driving force on oxygen vacancy diffusion is very small. Dynamic simulation of the influence of electric fields on the diffusion requires the use of advanced molecular dynamics acceleration schemes.