Comparison of a semi-analytic variance reduction technique to classical Monte Carlo variance reduction techniques for high aspect ratio pencil beam collimators for emission tomography applications

A semi-analytic variance reduction technique developed for collimated gamma emission tomography problems was compared to classic Monte Carlo variance reduction techniques within the Monte Carlo N Particle Transport (MCNP) code. In the semi-analytic technique, a computationally efficient, non-analog, monodirectional source biased Monte Carlo simulation is first performed. Analytical expressions or empirical values are then used to correct for solid angle and field-of-view effects introduced by the non-analog source definition. This variance reduction technique was compared with deterministic transport sphere (DXTRAN) and geometry splitting variance reduction schemes to determine the accuracy and computational savings of each technique relative to an analog pulse height tally (F8 tally) at 1, 3, 5, and 10 mm collimator aperture radii. For radii 0.5 mm and 0.3 mm a DXTRAN sphere was used in place of an analog F8 tally, due to large particle history demands, to analyze the accuracy of the semi-analytic variance reduction technique. The computational savings and accuracy were evaluated for six to seven photopeaks depending on the method used. The monodirectional source biasing technique overestimated the count rates by approximately 9%–19% when the radius is less than 3 mm, but the technique overestimated by a factor of 2 to 7, when the radius is greater than or equal to 3 mm. The monodirectionally source biased technique offered computational saving factors on the order of 10⁸-10¹³ over 1-10 mm collimator radii studied. DXTRAN and geometry splitting methods yielded higher accuracy, but computational savings range from approximately 0.13 to 2.2 and 0.07 to 2.9, respectively indicating marginal improvement at best.