Approximation of hexagonal holes by square holes in Monte Carlo simulation of gamma-camera collimation

For Monte Carlo simulations, fast calculation of the distance traveled by a photon in the septal material of parallel-hole collimators can be facilitated by using a square-hole design. Square holes can provide the same geometric efficiency, resolution and lead content (g/cm²) as a comparable hexagonal-hole collimator by appropriate scaling of the hexagonal-hole septal width and hole size. Our objective was to study the validity of using square holes to estimate the hexagonal-hole collimator response. The geometric, penetration and collimator scatter components were compared for low-energy (LE) and medium-energy (ME) designs, using square- and hexagonal-holes and a 320 keV point source in air. The resolution (FWHM) was virtually identical for both hole shapes. The amount of penetration, and to a lesser extent collimator scatter, depended upon hole shape and pattern. However, for a 20% photopeak image, the difference in the total square-hole estimate relative to the hexagonal-hole was 10% and 3% for the LE and ME collimators, respectively. For an extended source and ME collimators, the relative difference was 3% for Cr-51 and 0.8% for Ga-67. When the two-dimensional penetration artifact is not critical and a small error in the amount of penetration is acceptable (e.g., when using energy-appropriate collimators), square-holes can be substituted for hexagonal-holes to decrease by 36% to 50% the time required for simulation.