Accurate 3D Positron Range Correction Method for Heterogeneous Material Densities in PET

Abstract

Objective: The positron range is a fundamental, detector-independent physical limitation to special resolution in positron emission tomography (PET) as it causes a significant blurring of the reconstructed PET images. A major challenge for positron range correction methods is to provide accurate range kernels that inherently incorporate the generally inhomogeneous stopping power, especially at tissue boundaries. In this work, we propose a novel approach to generate accurate three-dimensional (3-D) blurring kernels both in homogenous and heterogeneous media to improve PET spatial resolution. Approach: In the proposed approach, positron energy deposition was approximately tracked along straight paths, depending on the positron stopping power of the underlying material. The positron stopping power was derived from the attenuation coefficient of 511keV gamma photons according to the available PET attenuation maps. Thus, the history of energy deposition is taken into account within the range of kernels. Special emphasis was placed on facilitating the very fast computation of the positron annihilation probability in each voxel. Results: Positron path distributions of 18F in low-density polyurethane were in high agreement with Geant4 simulation at an annihilation probability larger than 10-2~10-3 of the maximum annihilation probability. The Geant4 simulation was further validated with measured 18F depth profiles in these polyurethane phantoms. The tissue boundary of water with cortical bone and lung was correctly modeled. Residual artifacts from the numerical computations were in the range of 1%. The calculated annihilation probability in voxels shows an overall difference of less than 20% compared to the Geant4 simulation. Significance: The proposed method significantly improves spatial resolution for non-standard isotopes by providing accurate range kernels, even in the case of significant tissue inhomogeneities.