Modeling all orders of scatter in nuclear medicine

The fundamental information in nuclear medicine is the distribution of gamma-ray photons as a function of position, direction and energy. Functionals of this distribution (i.e. output from the imaging system) are measured experimentally by some photon-collection process. We call the collection of these functionals the image. The distribution of photons is described by the integro-differential Boltzmann equation. The differential part describes the generation, propagation and attenuation of photons. The integral part describes the scattering of photons as an integral over direction and energy. The Boltzmann equation is difficult to solve because of the scatter integral and the size of the problem when discretized. Many techniques deal with the scatter integral by discretely considering successive orders of scattering. Our method models all orders simultaneously using spherical harmonics to efficiently describe the directional dependence. Our method also partitions the problem to take advantage of the fact that a scattering event results in an energy loss. Then, within a parallel computing paradigm, we assume that the source and the attenuation map of the medium are known and we solve for the distribution. This distribution can then be used in any imaging system model to approximate experimental images