Respiratory Motion Estimation from Slowly Rotating X-Ray Projections: Theory and Simulation

Abstract

Accurate determination of activity within a volume of interest is needed during radiopharmaceutical therapies. Single-photon emission computed tomography(SPECT) is employed but requires a method to convert counts to activity. We use a phantom-based conversion; that is, we image an elliptical cylinder containing a sphere that has a known amount of 131-I activity inside. The regularized space alternating generalized expectation (SAGE) algorithm employing a strip-integral detector-response model was employed for reconstruction in previous patient evaluations. With that algorithm and a high-energy collimator, the estimates for sphere activity varied with changes in: 1) the level of uniform background activity in the cylinder; 2) the image resolution due to different values of the radius of rotation R; and 3) the volume of the sphere. When one used those to convert reconstructed counts within a patient tumor into an activity estimate, the resultant value may have been in error because of patient-phantom mismatch. As a potential remedy, in this paper, we use an ordered subsets expectation maximization (OSEM) algorithm with a 3-D depth-dependent detector-response model and an ultra-high-energy collimator. Results after 100 OSEM iterations and using a maximum counts registration show the estimates for sphere activity: 1) have a dependence on the level of background activity with a slope whose absolute magnitude is typically only 0.37 times that with SAGE; 2) are independent of R; and 3) are independent of sphere volume down to and including a sphere volume of 20 cm3. We conclude that using a global-average conversion factor to relate counts to activity and no volume-based correction might be reasonable with OSEM. For a test of that conclusion, target activity is estimated for an anthropomorphic phantom containing a 100 cm3 spherical tumor centrally located inferior to the lungs. With OSEM-based quantification, using: 1) a global-average conversion factor and 2) no volume-based correction, mean bias in the simulated-tumor activity estimate over 20 realizations is -7.37% (relative standard deviation =5.93%). With SAGE-based quantification using: 1) the conversion factor corresponding to the experimental estimate of ba- ckground and 2) volume-based correction, the mean bias is -10.7% (relative standard deviation =2.37%). The mean bias is smaller in a statistically significant way and relative standard deviation is not more than a factor of 2.5 bigger with OSEM compared to SAGE. In addition, with OSEM, a patient image apparently shows more highly resolved features, and the activity estimates for two tumors are increased by an average of 10%, relative to results with SAGE. compared to SAGE. In addition, with OSEM, a patient image apparently shows more highly resolved features, and the activity estimates for two tumors are increased by an average of 10%, relative to results with SAGE.compared to SAGE. In addition, with OSEM, a patient image apparently shows more highly resolved features, and the activity estimates for two tumors are increased by an average of 10%, relative to results with SAGE.compared to SAGE. In addition, with OSEM, a patient image apparently shows more highly resolved features, and the activity estimates for two tumors are increased by an average of 10%, relative to results with SAGE.