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Simultaneous positron-emission tomography (PET)-magnetic resonance (MR) imaging is a hybrid technique in oncological hepatic imaging combining soft-tissue and functional contrast of dynamic contrast enhanced MR (DCE-MR) with metabolic information from PET. In this context, respiratory motion represents a major challenge by introducing blurring, artifacts and misregistration in the liver. In this work, we propose a free-breathing 3D non-rigid respiratory motion correction framework for simultaneously acquired DCE-MR and PET data, which makes use of higher spatial resolution MR data to derive motion information used directly during image reconstruction to minimize image blurring and motion artifacts. The main aim was to increase contrast of hepatic metastases to improve their detection and characterization. DCE-MR data were acquired at 3T through a golden radial phase encoding scheme, enabling derivation of motion fields. These were used in the motion compensated image reconstruction of DCE-MR time-series (48 time-points, 6 s temporal resolution, 1.5 mm isotropic spatial resolution) and 3D PET activity map, which was subsequently interpolated to the DCE-MR resolution. The extended Tofts model was fitted to DCE-MR data, obtaining functional parametric maps related to perfusion such as the endothelial permeability (). Fifty-seven hepatic metastases were identified and analyzed. Quantitative evaluations of motion correction in PET images demonstrated average percentage increases of 16% ± 5% (mean ± SD) in Contrast (C), 18% ± 6% in SUVmean and 14% ± 2% in SUVmax, while DCE-MR and scored contrast-to-noise-ratio increases of 64% ± 3% and 90% ± 6%, respectively. Motion-corrected data visually showed improved image contrast of hepatic metastases and effectively reduced blurring and motion artefacts. Scatter plots of SUVmean versus suggested that the proposed framework improved differentiation of measurements. The presented motion correction framework for simultaneously acquired PET-DCE-MR data provides accurately aligned images with increased contrast of hepatic lesions allowing for improved detection and characterization. [ABSTRACT FROM AUTHOR]