MR-guided joint reconstruction of activity and attenuation in brain PET-MR

With the advent of time-of-flight (TOF) PET scanners, joint maximum-likelihood reconstruction of activity and attenuation (MLAA) maps has recently regained attention for the estimation of PET attenuation maps from emission data. However, the estimated attenuation and activity maps are scaled by unknown scaling factors. We recently demonstrated that in hybrid PET-MR, the scaling issue of this algorithm can be effectively addressed by imposing MR spatial constraints on the estimation of attenuation maps using a penalized MLAA (P-MLAA⁺) algorithm. With the advent of simultaneous PET-MR systems, MRI-guided PET image reconstruction has also gained attention for improving the quantitative accuracy of PET images, usually degraded by noise and partial volume effects. The aim of this study is therefore to increase the benefits of MRI information for improving the quantitative accuracy of PET images by exploiting MRI-based anatomical penalty functions to guide the reconstruction of both activity and attenuation maps during their joint estimation. We employed an anato-functional joint entropy penalty function for the reconstruction of activity and an anatomical quadratic penalty function for the reconstruction of attenuation. The resulting algorithm was referred to as P-MLAA⁺⁺ since it exploits both activity and attenuation penalty functions. The performance of the P-MLAA algorithms were compared with MLAA and the widely used activity reconstruction algorithms such as maximum likelihood expectation maximization (MLEM) and penalized MLEM (P-MLEM) both corrected for attenuation using a conventional MRI segmentation-based attenuation correction (MRAC) method. The studied methods were evaluated using simulations and clinical studies taking the PET image reconstructed using reference CT-based attenuation maps as a reference. The simulation results showed that the proposed method can notably improve the visual quality of the PET images by reducing noise while preserving structural boundaries and at the same time improving the quantitative accuracy of the PET images. Our clinical reconstruction results showed that the MLEM-MRAC, P-MLEM-MRAC, MLAA, P-MLAA⁺ and P-MLAA⁺⁺ algorithms result in, on average, quantification errors of -13.5 ± 3.1%, -13.4 ± 3.1%, -2.0 ± 6.5%, -3.0 ± 3.5% and -4.2 ± 3.6%, respectively, in different regions of the brain. In conclusion, whilst the P-MLAA⁺ algorithm showed the best overall quantification performance, the proposed P-MLAA⁺⁺ algorithm provided simultaneous partial volume and attenuation corrections with only a minor compromise of PET quantification.