Point spread function modeling for pinhole SPECT imaging which accounts for aperture size and orientation.

360 Objectives: In SPECT, accurate modeling of the system response is crucial for image reconstruction to improve image quality, quantification, and reduce artifacts. Our objective is to develop an analytical modeling of point spread function (PSF) adaptable to pinhole characteristics. Given the large field-of-view (FOV) in clinical systems, model parameters for only sparse locations across the FOV can be stored. We develop an efficient interpolation procedure using these stored model parameters to construct PSFs for the unmeasured locations. In this work, we evaluate our approach through GATE simulations of a multi-pinhole (MPH) SPECT system for brain imaging. Methods: In our previous work, we developed an approach to model PSF by adding higher order polynomial terms to the standard Gaussian function. However, our approach worked best for pinholes with apertures on the order of the intrinsic spatial resolution, or smaller. As the pinhole aperture increased, the PSF developed a flat region near the center deviating from the Gaussian shaped responses. Our new method of modeling starts by calculating the full-width at half-maximum (FWHM) of the measured PSF in the direction aligned with and perpendicular to the direction of the pinhole orientation. An asymmetric pillbox function slopped according to the variation in sensitivity across the aperture and having widths equal to the FWHMs is then constructed. This pillbox is convolved with a Gaussian function representing the intrinsic resolution of the system. To model the projected PSF from the oblique pinholes, we model the Depth of Interaction (DOI) effect by an exponential function and convolve it with the smoothed pillbox function. The initial PSF model constructed with all the above methods then undergoes iterative optimization of its 10 parameters. These parameters are then stored as a function of 3D position in front of the aperture. The stored parameters are interpolated between to form PSFs for locations not measured. We use the Normalized Root Mean Square Error (NRMSE) between the estimated and measured PSF to quantify the fidelity with which we model measured PSFs. Results: The NRMSE between the measured and the estimated PSFs for the direct (parallel detector and aperture surface) pinhole with aperture radius of 5mm, was 29% using standard Gaussian with 6 parameters and 20% using Gaussian function with 15 parameters. For the most oblique pinhole, the NRMSE was 27% using 6 parameters and 25% using 15 parameters. Our novel approach substantially reduced the error to 6.3% and 3.7% for the oblique and direct pinholes, respectively. Conclusions: Although the standard Gaussian approach works well for smaller pinholes, it fails as pinhole apertures become larger. The adaptive PSF modeling approach improved the accuracy of the fit by 77% when compared to the standard Gaussian function with 6 parameters and by 75% when compared to the additional Gaussian function with 15 parameters, for the most oblique pinhole of radius 5 mm. We found that our PSF modeling approach is more general and could be adapted to model pinholes with variable aperture characteristics. Our approach could also model the intrinsic resolution and depth of interaction of any crystal detector through the iterative process. Research Support: National Institute of Biomedical Imaging and Bioengineering (NIBIB), National Institutes of Health, Grant No R01 EB022092 and R01 EB022521.