Deep penetration radiation transport calculations have been performed to determine the dose rates at a positron emission tomography (PET) facility in China. The radiation source is a cyclotron that is used for the production of the PET isotopes, with a labyrinthine concrete wall arrangement to minimize dose to operation personnel. Since directionally biased Monte Carlo calculations did not reach an acceptably low standard error after a week of CPU time, approximate adjoint fluxes were calculated for each of four detector locations using coarse-mesh adjoint discrete ordinates calculations and were used to bias the Monte Carlo calculations. This biasing resulted in improved computational efficiency of a factor of one to three orders of magnitude. This result shows the value of even approximate adjoint flux biasing to speed up Monte Carlo calculations.