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 three different methods based on this approximation using Monte Carlo (MC) 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. To determine whether attenuation coefficients alone are sufficient to estimate the SRF or whether one must know the elemental composition, we simulated SRFs for sources in bone and lungs as well as bone- and lung-equivalent materials. The bone- and lung-equivalent materials have the same attenuation coefficient as bone and lung, respectively, but the same elemental composition as water. 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 two of the methods based on the effective depth were 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 geometric and water-equivalent distances. The results indicate that one of the methods gives reasonably good agreement with direct MC simulations in terms of predicting the magnitude and shape of the SRFs and projection data for a complex distribution simulating the heart. This method was not the same as the one that gave good agreement in the case of the simpler phantoms.