High resolution imaging with positron emitters: modeling range blurring effects

Employing a diffusion approximation for monoenergetic positrons and well-known theoretical and empirical relations, we have modeled positron range and calculated 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 Rh-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. Using an approximation to the model suitable for low spatial frequencies, we can calculate 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 could be easily removed during iterative reconstruction. Our model thus enables range-blurring corrections, which are essential for high-resolution PET, particularly with high-energy emitters