Modeling and simulation of positron range effects for high resolution PET imaging

Employing a diffusion approximation for monoenergetic positrons and well-known theoretical and empirical relations we model positron range distributions and show them to be in close agreement with Monte Carlo simulation results produced using EGSnrc. We calculate the range-blurring effect on system resolution for 21 positron emitters of biomedical interest. The line-spread function for a tomograph with intrinsic spatial resolution of 1.5 mm FWHM is blurred to 1.7 mm FWHM for the low end-point energy emitters F-18 or Cu-64 and to about 4.3 mm FWHM for the high end-point energy emitters Rb-82 and I-120. Annihilation distributions exhibit a biphasic nature-very sharply peaked with long-range, low-intensity tails. The sharp peaks preserve high spatial frequencies while the tails, responsible for the predominant blurring effects, asymptotically approach exponential terms. By suitable manipulation of the model equations we derive the exponential constant-an apparent mass absorption coefficient-and find it to be in close agreement with a classical estimate. This long-range character introduces a blur component that can be removed during iterative reconstruction. Our model, while not entirely explicit, is conveniently formulated for application in linear algorithms such as Fourier transformation and re-projection during iterative reconstruction. The model thus facilitates range-blurring corrections, which are essential for high-resolution PET, particularly with high-energy emitters.