Monte Carlo methods have been established along the time as the gold standard for computer simulations in the medical physics community. Depending on the problem and user's needs, deterministic radiation transport simulations may provide a more detailed and faster solution. In this work we investigate the possibility of using deterministic radiation transport simulations as a viable and more convenient tool for real clinical applications. Therefore, the discrete ordinates PENTRAN code is used to calculate average organ doses in voxelized human phantoms and the results are compared with state-of-the-art MCNP5 Monte Carlo simulations in the diagnostic energy range (50-140 keV). Generally, good agreement for the average organ scalar fluxes, less than 6% difference, is obtained provided adequate quadrature order, mesh size and energy group structure is used in the deterministic calculations. The energy group structure, particularly for the diagnostic energy range, has a major impact on the deterministic solution for the average organ doses since the interaction and mass energy absorption coefficients are highly energy dependent in the diagnostic range. Though an optimization of the group structure is possible, it is problem (namely x-ray source spectrum) and organ dependent, which impose serious limitations of the deterministic solution for practical application in diagnostic medical physics.