PHOTON PROPAGATION AND DETECTION IN SINGLE-PHOTON EMISSION COMPUTED-TOMOGRAPHY - AN ANALYTICAL APPROACH

An analytical theory of photon propagation and detection in single-pho ton emission computed tomography (SPECT) for collimated detectors is d eveloped from first principles. The total photon detection kernel is e xpressed as a sum of terms due to the primary and the Compton scattere d photons. The primary as well as contributions due to every order of Compton scattering are calculated separately. The model accounts for t he three-dimensional depth dependence of the collimator holes as well as for nonhomogeneous attenuation. No specific assumptions about the b oundary or the homogeneity of the attenuating medium are made. The ene rgy response of the detector is also modeled by the theory. Analytical expressions are obtained for various contributions to the photon dete ction kernel, and the multidimensional integrals involved are calculat ed using standard numerical integration methods. Theoretically calcula ted projections and scatter fractions for the primary and the first th rough second scattering orders are compared with our own experimental results for a small cylindrical primary radiation source immersed at v arious positions in a uniform cylindrical phantom. Also, theoretically calculated scatter fractions for a small spherical (pointlike) source in a uniform elliptic phantom are compared with experimental and Mont e Carlo simulation results taken from the recent literature. The resul ts from the analytical method are essentially exact and are free from the inaccuracies inherent in the numerical simulation methods used to deal with the photon propagation and detection problem in SPECT so far . The method developed here is unique in the sense that it provides ac curate theoretical predictions of results averaged over an infinite nu mber of simulations or experiments. We believe that our theory enhance s an intuitive understanding of the complex image formation process in SPECT and is an important step toward solving the inverse problem, th at of reconstructing the primary radiation source distribution from th e measured gamma camera projections.