In internal emitter therapy, an accurate description of the absorbed dose distribution is necessary to establish an administered dose-response relationship, as well as to avoid critical organ toxicity. Given a spatial distribution of cumulated activity, an absorbed dose distribution that accounts for the effects of attenuation and scatter can be obtained using a Monte Carlo method that simulates particle transport across the various densities and atomic numbers encountered in the human body. Patient-specific information can be obtained from CT and SPECT or PET imaging. Since the data from these imaging modalities is discrete, it is necessary to develop a technique to efficiently transport particles across discrete media. The Monte Carlo-based algorithm presented in this article produces accurate absorbed dose distributions due to patient-specific density and radionuclide activity distributions. The method was verified by creating CT and SPECT arrays for the Medical Internal Radionuclide Dose (MIRD) Committee's Standard Man phantom, and reproducing the spatially averaged specific absorbed fractions reported in MIRD Pamphlet 5. The algorithm was used to investigate the implications of replacing a mean absorbed dose with a distribution, and of neglecting atomic number and density variations for various patient geometries and energies. For example, the I-131 specific absorbed fraction for spleen to liver is the same as for liver to spleen, yet the distributions were different. Furthermore, neglecting atomic number variations across the vertebral bone led to an overestimation of I-125 absorbed dose by an order of magnitude, while no error was observed for I-131.