Analytical Modeling of a Slit Collimator and Optimization for Small Animal Imaging Applications

Abstract

Purpose: The collimator design and optimization are essential in small animal molecular imaging for preclinical studies. In this study, a mathematical model was derived and used to optimize the slit collimator for small animal imaging applications.

Materials and Methods: The geometric efficiency was formulated as a source-to-detector distance for a certain amount of the collimator resolution ( ). The first-order derivative of the derived formula gives the optimized parameters. The detector performance was modeled in terms of intrinsic resolution . Furthermore, the edge penetration effect was considered using the validated model.

Results: Optimum source-to-detector distance  was found as . For an ideal detector, optimal , geometric efficiency  and slit aperture width  were found as ,  and , respectively. Where  and  are the source-to-collimator distance and detector length, respectively. For the fixed resolution of 1.0 mm, the sensitivity for different source-to-collimator distances of 50.0, 100.0, and 150.0 mm was calculated as , , and , respectively. In addition, for a sub-millimeter resolution of 0.5 mm at 15.0, 30.0, and 50.0 mm, the geometric efficiency was calculated as, , , and . For a typical source-to-collimator distance (15.0 mm), the optimal geometric efficiencies are , , , , and   for the resolutions of 0.25, 0.50, 1.0, 1.5, and 2.0 mm, respectively.

Conclusion: Based on the analytic model predictions, the performance characteristics of the slit collimator in terms of geometric efficiency and resolution were extracted. The importance of the proposed model lies both in its speed and ease of application.