Respiratory Motion Correction in 4D PET/CT: Comparison of Implementation Methodologies for Incorporation of Elastic Transformations in the Reconstruction System Matrix

Respiratory motion in emission tomography leads to reduced image quality. Proposed correction methodology has been concentrating on the use of respiratory synchronised acquisitions leading to gated frames. Such frames however are of low signal to noise ratio as a result of containing reduced statistics. Therefore a method accounting for respiratory motion effects without affecting the statistical quality of the reconstructed images is necessary. In this work we describe the implementation of an elastic transformation within a list-mode based reconstruction for the correction of respiratory motion over the thorax. The developed algorithm was evaluated using datasets of the NCAT phantom generated at different points throughout the respiratory cycle. List mode data based PET simulated frames were subsequently produced by combining the NCAT datasets with a Monte Carlo simulation. Transformation parameters accounting for respiratory motion were estimated according to an elastic registration of the NCAT dynamic CT images and were subsequently applied during the image reconstruction of the original emission list mode data. The One-pass list mode EM (OPL-EM) algorithm was modified to integrate the elastic transformation in the sensitivity matrix. Three different implementations have been investigated (no interpolation, trilinear interpolation, b-spline functions incorporation). The corrected images were compared with uncorrected respiratory motion average images. Results demonstrate that the use of elastic transformations in the reconstruction system matrix lead to uniform improvement across the lung field for different lesion sizes. The use of a trilinear interpolation or the incorporation of the b-spline functions lead to times of execution equivalent to standard image reconstruction. However, trilinear interpolation leads to artefacts in areas such as the diaphragm where the largest elastic deformations are occurring.