Respiratory motion models have potential application for estimating and correcting the effects of motion in a wide range of applications, for example in PET-MR imaging. Given that motion cycles caused by breathing are only approximately repeatable, an important quality of such models is their ability to capture and estimate the intra- and inter-cycle variability of the motion. In this paper we propose and describe a technique for free-form nonrigid respiratory motion correction in the thorax. Our model is based on a principal component analysis of the motion states encountered during different breathing patterns, and is formed from motion estimates made from dynamic 3-D MRI data. We apply our model using a data-driven technique based on a 2-D MRI image navigator. Unlike most previously reported work in the literature, our approach is able to capture both intra- and inter-cycle motion variability. In addition, the 2-D image navigator can be used to estimate how applicable the current motion model is, and hence report when more imaging data is required to update the model. We also use the motion model to decide on the best positioning for the image navigator. We validate our approach using MRI data acquired from 10 volunteers and demonstrate improvements of up to 40.5% over other reported motion modelling approaches, which corresponds to 61% of the overall respiratory motion present. Finally we demonstrate one potential application of our technique: MRI-based motion correction of real-time PET data for simultaneous PET-MRI acquisition.
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