Modeling the scatter response function in inhomogeneous scattering media for SPECT

We have previously developed a method for accurately and rapidly modeling the scatter response function in uniform media. In this work we studied the extension of this method to nonuniform attenuators. Our approach was to use the water-equivalent source depth, i.e. the integral of the attenuation coefficient through the nonuniform object from the source to the surface divided by the attenuation coefficient of water. We have investigated the accuracy of this approximation using Monte Carlo simulation methods. Line sources were placed at the same water equivalent depth in slabs composed of water, bone, and lung. We observed that, for perfect collimation, the scatter response functions (SRFs) obtained for these slabs are comparable at depths less than 10 cm. For larger source depths, the SRFs from the water and bone phantoms are equivalent, while the SRFs from lung phantoms are somewhat narrower. To separate the effects of the density and elemental composition, we simulated SRFs for bone- and lung-equivalent materials having the same elemental composition as water, but densities that result in the same attenuation coefficients as bone and lung, respectively. For the lung-equivalent material, the SRFs were essentially equivalent to those from lung; for the bone-equivalent material, the SRFs were closer to those from water. We have also placed voids of various sizes in slab phantoms while keeping the same water-equivalent source depth. For these simple geometries the effective depth was adequate for predicting the SRF. Finally, we have simulated the SRF for a line source in a realistic thorax phantom using several methods based on water-equivalent distances. The results indicate that one of the methods gives fair agreement with direct MC simulations in terms of predicting the magnitude and shape of the SRF.