Efficient simulation of SPECT down-scatter including photon interactions with crystal and lead

A major image degrading factor in simultaneous Dual Isotope (DI) SPECT or simultaneous Emission-Transmission (ECT-TCT) imaging, is the detection of photons emitted by the higher energy isotope in the energy window used for imaging the lower energy isotope. In Tc-99m/Tl-201 DI-SPECT typically tens of percents of the total detected down-scatter is caused by lead x rays. In Tc-99m/Gd-153 ECT-TCT, a comparable fraction of the down-scatter originates from Tc-99m photons which only partly deposit their energy in the detector crystal (i.e., due to crystal interactions). Efficient simulation methods which model down-scatter can be used to optimize DI-SPECT or ECT-TCT imaging acquisition or reconstruction protocols. In this paper we adapt a previously proposed efficient down-scatter simulation method, to include the interactions of photons with the detector crystal and collimator lead. To this end, point spread function tables including crystal and lead interactions are precalculated. Subsequently, photons are traced through the patient body until their last scatter position, and the precalculated responses are used to project the photons onto the detector plane, while photon attenuation in the patient is taken into account. The approach is evaluated by comparing simulated Tc-99m down-scatter projections with measured projections. Incorporation of photon interaction with crystal and lead leads to significantly improved accuracy of the shape of down-scatter responses, while differences in total counts between simulated and measured projections typically decrease from tens of percents to a couple of percents. Calculating 60 down-scatter projections of an extended distribution on a 64 x 64 x 64 grid takes about three minutes on a PC with two 1.2 GHz processors. We conclude that accurate and efficient simulation of down-scatter is now possible including the major effects of the nonuniform mass density of the patient as well as photon interactions with the crystal and collimator lead.