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Source anisotropy is a very important factor in the brachytherapy quality assurance of high-dose rate (HDR) 192Ir afterloading stepping sources. If anisotropy is not taken into account then doses received by a brachytherapy patient in certain directions can be in error by a clinically significant amount. Experimental measurements of anisotropy are very labour intensive. We have shown that within acceptable limits of accuracy, Monte Carlo integration (MCI) of a modified Sievert integral (3D generalization) can provide the necessary data within a much shorter time scale than can experiments. Hence MCI can be used for routine quality assurance schedules whenever a new design of HDR or PDR 192Ir is used for brachytherapy afterloading. Our MCI calculation results are compared with published experimental data and Monte Carlo simulation data for microSelectron and VariSource 192Ir sources. We have shown not only that MCI offers advantages over alternative numerical integration methods, but also that treating filtration coefficients as radial distance-dependent functions improves Sievert integral accuracy at low energies. This paper also provides anisotropy data for three new 192Ir sources, one for the microSelectron-HDR and two for the microSelectron-PDR, for which data are currently not available. The information we have obtained in this study can be incorporated into clinical practice.