To explore the motion of particles in turbulence, direct numerical simulation (DNS) of the Navier-Stokes equations can be coupled to a Lagrangian particle tracking (LPT), which solves the particle equation of motion under the point force approximation. Only quite recently, this numerical tool has been extended to predict the dynamics of non-spherical particles. Nevertheless, such DNS/LPT is generally limited since the models used to evaluate the hydrodynamic force and torque are valid for low particle Reynolds numbers (creeping flow regime). In order to overcome this limit, we introduce in the present study models recently developed for the hydrodynamic force and torque which are valid outside Stokes regime. To evaluate the effects of these new models on the particle dynamics, we computed the particle-laden turbulent flow recently examined by Mortensen et al.(Phys. Fluids, 2008) with a DNS/LPT method based on theoretical modelsfor the hydrodynamic force and torque valid under creeping flow conditions. We considered the same set of prolate ellipsoidal particles. Nevertheless, in opposite to them, we kept the ellipsoidal major axislength constant, and lower than the Kolmogorov spatial scale. From a comparison with the statistical results provided by Mortensen et al.(Phys. Fluids, 2008), it will be shown that we obtained similar tendencies for the translational motion while some differences are noted for rotational motion.