Effects of boundary conditions in TOF-MLAA reconstruction for PET/MR

We describe an evaluation of effects of mis-matched boundary conditions caused by MR detection or PET emission being smaller than the attenuating medium in TOF-MLAA for PET/MR. Effects of different boundary conditions: (a) mismatched boundary between the initial μ-map estimate and the true μ-map and (b) mis-matched boundary between the emission image and the true μ-map were investigated using 2D and 3D GATE simulations. It was observed that the estimated μ-value decreases as the size of the initial μ-map decreases and vice versa. Correct μ-values were recovered when the boundary of the initial μ-map estimate matched with that of the true μ-map. These trends were observed independent of the size of the emission. When the emission was smaller than the attenuating medium, edge overshoot was observed in the estimated μ-map independent of the size of the initial μ-map. On the other hand, the edge overshoot was barely visible when the emission covered the whole attenuating medium. Furthermore, the edge overshoot was observed to be more severe in the axial direction as compared to the radial direction. The edge overshoot was not very apparent in the emission image since the overshoot in the μ-map was located mainly outside the emission. However, the intensity or magnitude of the emission image was overestimated due to the overestimated attenuation correction factors for the lines-of-response which passed through the overshoot region. Other than having the emission covered the whole attenuating medium, it was observed that constraining the wall region in the estimated μ-map can also reduce the edge overshoot and improve the accuracy of the emission image. In summary, the size of the initial μ-map in TOF-MLAA affects the estimated μ-value. Furthermore, when the boundary of the emission is smaller than that of the attenuating medium, the estimated μ-map contains edge overshoot which causes overestimated emission image.