Analytic 3D Scatter Correction in Pet Using the Klein-Nishna Equation

Abstract

In order to perform quantitative 3D positron tomography, it is essential that an accurate means of correcting for the effects of Compton scattered photons be developed. The two main approaches to compensate for scattered radiation rely on energy considerations or on filtering operations. Energy based scatter correction methods exploit the reduced energy of scattered photons to differentiate them from unscattered photons. Filtered scatter correction methods require the measurement of scatter point spread functions to be used for convolution with the acquired emission data set. Neither approach has demonstrated sufficient accuracy to be applied in a clinical environment. In this thesis, I have developed the theoretical framework for generating the scatter point spread functions for the general case of any source position within any nonuniform attenuation object. This calculation is based on a first principles approach using the Klein-Nishina differential cross section for Compton scattering to describe the angular distribution of scatter annihilation photons. The attenuation correction factors from transmission scans are included within the theory as inputs describing the distribution of matter in the object being imaged. The theory has been tested by comparison with experimental scatter profiles of point sources which are either centered, or off-center in water-filled cylinders. Monte Carlo simulations have been used to identify the detector energy threshold where the single scatter assumption employed by the theory is most satisfied. The validity of a mean scatter position assumption, used in the development of the theory, is tested using analytic calculations of a non-uniform attenuation phantom. The physical effects most responsible for determining the shape of the scatter profiles, as well as the assumptions employed by several common scatter correction methods, are revealed using the analytic scatter correction theory.