Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies

The work presented in this paper evaluates the statistical characteristics of regional bias and expected error in reconstructions of real PET data of human brain fluorodeoxiglucose (FDG) studies carried out by the maximum likelihood estimator (MLE) method with a robust stopping rule, and compares them with the results of filtered backprojection (FBP) reconstructions and with the method of sieves. The task that we have investigated is that of quantifying radioisotope uptake in regions-of-interest (ROI's). We first describe a robust methodology for the use of the MLE method with clinical data which contains only one adjustable parameter: the kernel size for a Gaussian filtering operation that determines final resolution and expected regional error. Simulation results are used to establish the fundamental characteristics of the reconstructions obtained by our methodology, corresponding to the case in which the transition matrix is perfectly known. Then, data from 72 independent human brain FDG scans from four patients are used to show that the results obtained from real data are consistent with the simulation, although the quality of the data and of the transition matrix have an effect on the final outcome. The most important results are that, for equal resolution, expected pixel-by-pixel error in the MLE and sieves reconstructions are lower in the regions of low counts than in the regions of high counts, the lowest being for the MLE. In contrast, FBP reconstructions show an expected error that is high and nearly independent of the number of counts in a region. As a consequence, the determination of radioisotope uptake in ROI's of high activity has approximately the same standard deviation in MLE, sieves, and FBP reconstructions, while the standard deviation in ROI's of low uptake is substantially lower for MLE, while sieves take an intermediate value. The use of a well-constructed Monte Carlo transition matrix improves all the results with real data in a measurable way. We conclude that our proposed MLE methodology and the method of sieves have a definite advantage over FBP. There is a tradeoff between shorter computation time, a slight bias but lower standard deviation for MLE and longer computation time, a basically unbiased estimation but higher standard deviation for sieves.