Joint estimation of respiratory motion and PET image in 4D PET reconstruction with modeling attenuation map deformation induced by respiratory motion

Objectives The aim is to develop a joint estimation method of respiratory motion and a PET image with respiratory motion and attenuation compensation (AC) at a reference frame when a CT-based attenuation map is available only at a given respiratory phase.

Methods We developed an iterative method that alternating between two steps: (1) updating the PET image estimate by applying a 4D ML-EM PET image reconstruction method which models the current motion estimate in the system matrix, and (2) updating the motion estimate using a gradient-descent line-search optimizer to search for the optimized B-spline non-rigid transform which maximizes the likelihood function of the respiratory-gated PET sinograms given the current PET image estimate. The method is unique in two ways: (1) step 1 was started with the initial motion estimation using respiratory-gated 4D PET images obtained with uniform AC, (2) the respiratory motion was modeled in the deformation of both PET image estimate and the CT-based attenuation map in step 2. We showed that the method converges to the solutions close to the truth. Also, the method was evaluated with Monte-Carlo simulations using the 4D XCAT phantom with respiration motion. We inserted 12 lesions of 10mm diameter in the liver and lung regions of the XCAT phantom. The uptake to background ratio was 2:1 for liver and 2.5:1 for the lung lesions.

Results The average error of the respiratory motion estimation was ~3mm for the lung and liver regions, which was close to that based on respiratory-gated PET images with AC using co-registered CT-based attenuation maps. Depending on the lesion locations, the SNR of the images of the 10mm lesions was ~10% to ~70% higher than those without motion compensation.

Conclusions The proposed joint estimation method is accurate and practical for respiratory motion estimation and 4D PET image reconstruction of respiratory-gated PET sinograms with AC and respiratory compensation.

Research Support NIH grant EB 16