Optimizing the number of equivalent iterations of 3D OSEM in SPECT reconstruction of I-131 focal activities

To externally estimate the radiation dose to a tumor during therapy with I-131 radiopharmaceuticals, and its distribution, one must accurately estimate activity, and its distribution, by means of SPECT imaging. Our objective is to characterize the quantification of the total activity in focal targets and in their uniform background, and of the activity distribution within the targets, after 3D Ordered Subsets Expectation Maximization (OSEM) reconstruction with attenuation and scatter correction and no post smoothing, in the good-counting-statistics case. A cylindrical phantom containing seven spheres simulating tumors, ranging in volume from 209 to 4.2 cm3, and filled with an I-131 water solution containing background, was imaged. A Siemens Symbia SPECT/CT scanner was used to acquire 128×128 projection images, employing 60 angles over 360°. With dynamic SPECT, 10 sequential acquisitions of 15 min duration each were obtained and each was reconstructed with particular values of the number of subsets and the number of iterations. Let the product of the number of subsets times the number of iterations equal the equivalent number of iterations, EI. The counts-to-activity conversion factor was derived from the average ratio of total count divided by true activity for the largest sphere at the largest value of EI. Then, for the activity of each sphere at each of the values of EI, we evaluated (1) the fractional variance (variance in estimate over true activity), (2) the fractional bias (average estimate bias over true activity) and (3) the fractional error (the root mean square error (RMSE) in the estimate divided by the true activity). The fractional bias and fractional variance were smaller for the larger spheres compared to the smaller (the fractional bias decreased faster with an increase in the fractional variance for them as well). The RMSE was dominated by the bias. The fractional error decreased as EI increased for all sphere sizes. The minimum average value was 25.8% and occurred for EI=480 although that image had texture and was noisy. The average fractional error was already approaching that value by EI=80 at 30.7%, and that image was less noisy. For the water background surrounding the spheres, the fractional error in the activity estimate varied but little with EI; its smallest value was 13.1% at EI=480. The error in a measure of estimated sphere activity non-uniformity worsened as EI increased. (The OSEM initial guess of identical counts/voxel everywhere was perfect as far as uniformity for these uniform-activity targets.) Therefore, the EI to employ in reconstruction depends on the activity-estimation task of interest. Different dosimetric goals might best be met by employing different images generated at different values of EI.