Photon propagation and detection in SPECT: Theory, experimental validation, and applications

An analytical theory of photon propagation and detection for SPECT is presented. The theory accurately accounts for most of the physical processes involved with photon propagation and detection in SPECT. In particular, it accounts for photon propagation, nonuniform attenuation (including photoelectric absorption and all orders of Compton and Rayleigh scattering combinations and possibilities), the three dimensional depth-dependent collimator resolution, and the intrinsic energy-dependent detection probability function of the Anger camera (both the intrinsic energy-dependent detection efficiency and the intrinsic energy resolution of a NaI(Tl) scintillation crystal). The theory allows integral expressions for each scattering order of the photon detection kernel to be formulated separately. The photon detection kernel is central to iterative reconstruction algorithms like the Maximum Likelihood Expectation Maximization (MLEM) algorithms.; Numerical integration code is developed in order to calculate the lowest three orders of the kernel for general nonuniform imaging situations. The results calculated from the numerical code are compared with those obtained from experiment. The code is shown to provide an accurate tool for modeling nonuniform experimental imaging situations for both point and extended source distributions, provided a narrow energy window and a lower energy photon source, like {dollar}sp{lcub}rm 99m{rcub}{dollar}Tc and {dollar}sp{lcub}123{rcub}{dollar}I, are used.; The connectivity problem of the kernel is quantitatively investigated, within the context of source voxel-projection pixel connectivity. It is demonstrated that the main factor determining the extent of the kernel connectivity is photon scattering, with 3D depth-dependent collimator hole resolution being of secondary but still significant importance. Understanding the connectivity of the kernel is necessary for both practical and efficient implementation of it in iterative reconstruction algorithms.; Finally, using the results of the kernel connectivity investigation, the kernel expressions obtained are used to compute a reconstruction kernel for a simple, but real, imaging situation. The calculated kernel is employed in an MLEM-type algorithm and the source distribution is reconstructed from experimentally acquired projection data. The reconstructed distributions obtained from the MLEM algorithm show improved resolution within the transaxial slices as well as between the slices over the same obtained from the traditional filtered backprojection method of reconstruction.