Analytical modeling and implementation of detector response for fully 3D computer simulation and image reconstruction of an MRI compatible PET insert with a dual-layer offset crystal design

In this study we present an efficient algorithm for accurate analytical modeling of detector response for fully 3D computer simulation and statistical image reconstruction of a proposed MRI compatible PET insert system that uses a dual-layer offset crystal design. The general analytical response functions for coincident detector pairs are derived first. For calculating the point spread function (PSF) of coincident pairs of individual dual-layer offset crystals, we developed an efficient 3D ray-tracing algorithm. The determination of which detector blocks are intersected by a gamma ray is made by calculating the intersection of the ray with virtual cylinders with radii just inside the inner surface and just outside the outer-edge of each detector ring. For efficient ray-tracing computation, the detector block and ray to be traced are then rotated so that the crystals are aligned along the x-axis, facilitating calculation of ray/crystal boundary intersection points. For effective data organization, an indexed histogram-mode method is also presented in this work. To validate the methods, we performed a series of analytical computer simulations based on our system design. The measured spatial resolution of the analytical PSFs in both radial and tangential directions are computed. The illustration of sinograms with different layer designs shows that our dual-layer offset crystal design can provide better sampling density than a single-layer system. The image reconstruction results from the analytical simulation exhibit promising performance of reconstructed spatial resolution, reaching nearly sub-millimeter resolution. In conclusion, we have developed an efficient algorithm for analytical calculation of the detector response for our proposed PET insert with dual-layer offset crystal arrays. This can provide an effective and efficient method for both computer simulation and quantitative image reconstruction, and will aid in the design and optimization of our PET insert s- stem.