Correction for Collimator-Detector Response in SPECT Using Point Spread Function Template
Compensating for the collimator-detector response (CDR) in SPECT is important for accurate quantification. The CDR consists of both a geometric response and a septal penetration and collimator scatter response. The geometric response can be modeled analytically and is often used for modeling the whole CDR if the geometric response dominates. However, for radionuclides that emit medium or high-energy photons such as I-131, the septal penetration and collimator scatter response is significant and its modeling in the CDR correction is important for accurate quantification. There are two main methods for modeling the depth-dependent CDR so as to include both the geometric response and the septal penetration and collimator scatter response. One is to fit a Gaussian plus exponential function that is rotationally invariant to the measured point source response at several source-detector distances. However, a rotationally-invariant exponential function cannot represent the star-shaped septal penetration tails in detail. Another is to perform Monte-Carlo (MC) simulations to generate the depth-dependent point spread functions (PSFs) for all necessary distances. However, MC simulations, which require careful modeling of the SPECT detector components, can be challenging and accurate results may not be available for all of the different SPECT scanners in clinics. In this paper, we propose an alternative approach to CDR modeling. We use a Gaussian function plus a 2-D B-spline PSF template and fit the model to measurements of an I-131 point source at several distances. The proposed PSF-template-based approach is nearly non-parametric, captures the characteristics of the septal penetration tails, and minimizes the difference between the fitted and measured CDR at the distances of interest. The new model is applied to I-131 SPECT reconstructions of experimental phantom measurements, a patient study, and a MC patient simulation study employing the XCAT phantom. The proposed model yields up to a 16.5 and 10.8% higher recovery coefficient compared to the results with the conventional Gaussian model and the Gaussian plus exponential model, respectively.