The effect of gamma ray penetration on angle-dependent sensitivity for pinhole collimation in nuclear medicine

The sensitivity of a pinhole collimator for gamma ray imaging in nuclear medicine is dependent on the angle of incidence of the gamma rays. The effect of penetration near the pinhole aperture on angle-dependent sensitivity was investigated using experimental measurements and numerical modeling. Projection data measurements were acquired with Tc-99m and I-131 point sources using tungsten pinhole inserts with 1.0 to 4.0 mm diameter apertures. Curves of the form sinx theta, where theta is the angle of the incident ray with the surface of the detector crystal, were fit to sensitivity measurements from the projection data. Experimentally measured x values were between 3.3 and 4.1 for Tc-99m and between 5.1 and 7.2 for I-131. Penetration near the pinhole aperture was modeled using (1) an expression for effective pinhole diameter that is a generalization of Anger's formula for normally incident photons and (2) a photon transport simulation code. Experimentally measured sensitivity exponents x from new and previously reported experimental observations were modeled within 15% by the numerical simulations. For modeling using the generalized expression for effective diameter the average error was 1.4% and the standard deviation was 7.7%. For the photon transport simulation code the average error was 1.5% and the standard deviation also was 7.7%. The effect of pinhole aperture design parameters on angle-dependent sensitivity for high resolution pinhole apertures was modeled using a photon transport simulation code. The sensitivity exponents x were greater for 364 keV photons than for 140 keV photons and were greater for small aperture diameters, small acceptance angles, and large aperture channel heights. These results provide theoretical justification for incorporating sinx theta sensitivity corrections, with x greater than the value of 3 for an impenetrable pinhole, in filtered back projection and iterative reconstruction algorithms for single photon emission computed tomography (SPECT) pinhole imaging. Simulated I-131 SPECT studies for uniformly active cylinders showed that activity concentrations were underestimated toward the outside of the cylinders when a sin3 theta rather than the correct sinx theta sensitivity correction was applied in image reconstruction.