An efficient sensitivity calculation of tilted apertures for preclinical multi-pinhole spect

Sensitivity performance is one of the key issues in multi-pinhole collimator design for small animal pinhole Single photon emission computed tomography (SPECT). Currently, there are two approaches in predicting sensitivity performance: analytical formula and Monte Carlo (MC) simulation. Analytical formula offers fast computation, while MC simulation provides better modeling of various physical effects and generates more accurate sensitivity prediction. Tilted pinhole apertures become popular in modern system design, because they can avoid projection overlapping and increase field-of-view (FOV) compared to traditional multiple pinholes. However, conventional analytical formula for sensitivity prediction cannot be directly applied to tilted apertures. In this research, we present a modified analytical formula to predict the sensitivity performance by considering tilted and translated pinhole apertures in a multi-pinhole collimation design. The modification is based on a construction of a virtual object plane which is parallel to the aperture plane in the tilted pinhole. Since the new formula is derived in the vector domain, it can be readily integrated to computer-aided-design software to greatly simplify the collimator design optimization. The results show that the modified formula generates sensitivity prediction similar to that from the MC simulation for a multi-pinhole system with tilted pinholes. When larger tilted pinholes are used to increase FOV, the formula can also accurately generate sensitivity prediction with a slightly reduced peak value. For a tilted pinhole aperture up to 40°, the simulation results indicate that the conventional analytical formula may overestimate as much as 25% sensitivity.