This work explores application of a novel resolution modeling technique that incorporates the spatial-variant, medium-dependent nature of positron range. We have hypothesized that given the varied positron ranges in different mediums such as lung, blood and bone, incorporation of such differences could lead to further improved image qualities and clinical and quantitative tasks. In fact, we have quantified the relationship between the distribution of positrons annihilated in a certain medium and the amount by which 511keV photons are attenuated in that medium. Subsequently, we have shown that is possible to utilize mu-map images generated from transmission or CT imaging to arrive at so-called C-maps and a-maps that describe how positrons are annihilated in the field-of-view. Using Monte-Carlo simulation of Rb-82 myocardial perfusion imaging, we showed that while the extension from space-invariant to space-variant modeling of Rb-82 positron range showed certain improvements in myocardial defect contrast, when taking the relation between the lung and the myocardium into account, very significant qualitative and quantitative improvements were obtained.