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 tomography (SPECT) projections. The technique is applicable to sources in homogeneous and nonhomogeneous media. The photon distribution (primary, first-, and second-order Compton scatter) is computed using a precalculated camera-dependent look-up table in conjunction with an attenuation map of the scattering object and a map of the activity distribution. The speed and accuracy of 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 homogeneous cylinder filled uniformly with activity. The method is quantitatively accurate and faithfully reproduces the spatial distribution of the unscattered and scattered photons. For comparable statistical precision in the peak of the calculated distribution, their approach 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. However, this gain depends on the source configuration, and calculation times become comparable for an 800 voxel source and are five times slower for a 55000 voxel source. The method also offers an increase in the speed of computation of higher order Compton scatter events over a similar analytical technique