Dual respiratory and cardiac motion estimation in PET imaging: Methods design and quantitative evaluation

Purpose: The goal of this study was to develop and evaluate four post-reconstruction respiratory and cardiac (R&C) motion vector field (MVF) estimation methods for cardiac 4D PET data. Method: In Method 1, the dual R&C motions were estimated directly from the dual R&C gated images. In Method 2, respiratory motion (RM) and cardiac motion (CM) were separately estimated from the respiratory gated only and cardiac gated only images. The effects of RM on CM estimation were modeled in Method 3 by applying an image-based RM correction on the cardiac gated images before CM estimation, the effects of CM on RM estimation were neglected. Method 4 iteratively models the mutual effects of RM and CM during dual R&C motion estimations. Realistic simulation data were generated for quantitative evaluation of four methods. Almost noise-free PET projection data were generated from the 4D XCAT phantom with realistic R&C MVF using Monte Carlo simulation. Poisson noise was added to the scaled projection data to generate additional datasets of two more different noise levels. All the projection data were reconstructed using a 4D image reconstruction method to obtain dual R&C gated images. The four dual R&C MVF estimation methods were applied to the dual R&C gated images and the accuracy of motion estimation was quantitatively evaluated using the root mean square error (RMSE) of the estimated MVFs. Results: Results show that among the four estimation methods, Methods 2 performed the worst for noise-free case while Method 1 performed the worst for noisy cases in terms of quantitative accuracy of the estimated MVF. Methods 4 and 3 showed comparable results and achieved RMSE lower by up to 35% than that in Method 1 for noisy cases. Conclusion: In conclusion, we have developed and evaluated 4 different post-reconstruction R&C MVF estimation methods for use in 4D PET imaging. Comparison of the performance of four methods on simulated data indicates separate R&C estimation with modeling of RM before CM estimation (Method 3) to be the best option for accurate estimation of dual R&C motion in clinical situation.