Evaluation of a maximum likelihood approach to improve spatial resolution in TOF-PET

Candidate level (15 HP)

Area: mathematical statistics in medical imaging

We are evaluating a TOF-PET (time of flight positron emission tomography) system based on silicon detectors. Initial evidence suggests that such a system could largely overcome the parallax problem encountered in other system set-ups, and also yield a time resolution (which translates to better spatial resolution) that is a factor or 4 better than existing systems.

The use of silicon as a detector material for the high energy photons (511 keV) introduces a different challenge; Compton scattering. If a photon scatters in the detector it might be detected in a neighboring pixel within the 100-200 ps time resolution. Multiple scattering might also occur, where n>2 events might be registered from one primary gamma ray within a shorter time period than the system is able to resolve. Apparently there is no way to know in which pixel the first event occurred (this is the only pixel carrying valuable spatial information that can determine on which straight line through the object the annihilation occurred).

The scatter angle and the deposited energy are however related due to conservation of momentum and energy. Furthermore, the silicon detector has the capability to measure the deposited energy in certain discrete steps. Finally, the scatter angle follows a known probability distribution (the Klein-Nishina formula). Using these three fundaments it should be possible to construct a maximum likelihood algorithm that take n (n=2, 3, 4,…) pixel locations x, y, z (known with millimeter accuracy) and n deposited energies E (with 10-20% accuracy) as input and returns the most likely location x, y, z for the first interaction.

Time allowing, or if the work is extended to a master’s level work (30 HP) it should also be evaluated how this affects the spatial resolution of the system.