Simultaneous reconstruction of attenuation and activity in ToF PET/MRI with additional transmission data

Abstract

I. AIM To reconstruct quantitative PET images, an accurate cor-rection method for the attenuation of 511 keV photons in material is needed. In clinical practice, most PET scanners are combined with a CT scanner for acquiring anatomical information. This allows straightforward deduction of an atten-uation map from the CT Hounsfield units. Recently, research is being performed to combine PET with MRI instead of CT. The conversion from an MRI image to an attenuation map for PET attenuation correction is not longer straightforward. Although several studies have shown the feasibility of MRI-based attenuation correction, certain limitations remain[1], for instance due to the low MRI signal of bone. An alternative of MRI-based attenuation correction is the simultaneous reconstruction of emission and attenuation from PET emission data only. The MLAA algorithm[2] proves that this approach is feasible, but it has its constraints. It produces, for instance, less accurate attenuation values in regions with limited PET tracer uptake[3]. A possible solution for this limitation consists of adding transmission data from an external positron source positioned within the Field Of View (FOV). It has been shown that the use of an annulus shaped source for this purpose can improve the reconstructed attenuation and emission images in a phan-tom study[4]. The combination of the MLAA algorithm and additional transmission data is called the MLAA + algorithm. In this study we apply the MLAA and MLAA + methods on patient data containing a sequential Time-of-Flight (ToF) PET/MRI scan and a separate CT scan. The ToF PET/MRI scan is performed once with an annulus shaped transmission source in the FOV and once without any transmission source. Simultaneous reconstruction of attenuation and activity is performed for both scans. After co-registration, the CT scan is used as an attenuation correction map in reconstruction with the well-established MLEM algorithm. The results of the MLAA and MLAA + methods are compared visually and quantitatively with the CT-based reconstruction, as the latter can be considered the gold standard. II. METHODS AND MATERIALS A. MLAA algorithm The MLAA algorithm consists of an interleaved reconstruc-tion of emission λ and attenuation µ. One iteration k therefore holds two sequential steps. First the activity distribution is estimated, keeping the attenuation values in a voxel j constant. Secondly a new estimate of the attenuation is calculated, using the emission values calculated in the first part of the iteration. The MLAA algorithm for reconstructing 3D listmode emission data (EX) in subset (i) is the following: λ