PET/CT quantification of lung tissue is limited by several difficulties: the lung density and local volume changes during respiration, the anatomical mismatch between PET and CT and the relative contributions of tissue, air and blood to the PET signal (the tissue fraction effect). Air fraction correction (AFC) has been shown to improve PET image quantification in the lungs. Methods to correct for the movement and anatomical mismatch involve respiratory gating and image registration techniques. While conventional registration methods only account for spatial mismatch, the Jacobian determinant of the deformable registration transformation field can be used to estimate local volume changes and could therefore potentially be used to correct (i.e. Jacobian Correction, JC) the PET signal for changes in concentration due to local volume changes. This work aims to investigate the relationship between variations in the lung due to respiration, specifically density, tracer concentration and local volume changes. In particular, we study the effect of AFC and JC on PET quantitation after registration of respiratory gated PET/CT patient data. Six patients suffering from lung cancer with solitary pulmonary nodules underwent [Formula: see text]F-FDG PET/cine-CT. The PET data were gated into six respiratory gates using displacement gating based on a real-time position management (RPM) signal and reconstructed with matched gated CT. The PET tracer concentration and tissue density were extracted from registered gated PET and CT images before and after corrections (AFC or JC) and compared to the values from the reference images. Before correction, we observed a linear correlation between the PET tracer concentration values and density. Across all gates and patients, the maximum relative change in PET tracer concentration before (after) AFC was found to be 16.2% (4.1%) and the maximum relative change in tissue density and PET tracer concentration before (after) JC was found to be 17.1% (5.5%) and 16.2% (6.8%) respectively. Overall our results show that both AFC or JC largely explain the observed changes in PET tracer activity over the respiratory cycle. We also speculate that a second order effect is related to change in fluid content but this needs further investigation. Consequently, either AFC or JC is recommended when combining lung PET images from different gates to reduce noise.