Analytical calculation of photon distributions in SPECT projections

In this paper the authors present a method for analytically calculating the distribution of photons detected in single photon emission computed tomogr aphy (SPECT) projections. The technique is applicable to sources in homogen eous and nonhomogeneous media. The photon distribution (primary, first-, an d second-order Compton scatter) is computed using a precalculated camera-de pendent look-up table in conjunction with an attenuation map of the scatter ing object and a map of the activity distribution. The speed and accuracy o f this technique is compared to that of Monte Carlo simulations. The cases considered are a point source in a homogeneous and also in a nonhomogeneous scattering medium, an extended source in a nonhomogeneous medium, and a ho mogeneous cylinder filled uniformly with activity, The method is quantitatively accurate and faithfully reproduces the spatial distribution of the unscattered and scattered photons. For comparable stat istical precision in the peak of the calculated distribution, their approac h can result in a gain in calculation time over Monte Carlo simulators. For point sources, the computation times are improved by a factor of 20-150, H owever, this gain depends on the source configuration, and calculation time s become comparable for an 800 voxel source and are five times slower for a 55 000 voxel source. The method also offers an increase in the speed of co mputation of higher order Compton scatter events over a similar analytical technique.