Optimization algorithms and weighting factors for analysis of dynamic PET studies

Positron emission tomography (PET) pharmacokinetic analysis involves fitting of measured PET data to a PET pharmacokinetic model. The fitted parameters may, however, suffer from bias or be unrealistic, especially in the case of noisy data. There are many optimization algorithms, each having different characteristics. The purpose of the present study was to evaluate (1) the performance of different optimization algorithms and (2) the effects of using incorrect weighting factors during optimization in terms of both accuracy and reproducibility of fitted PET pharmacokinetic parameters. In this study, the performance of commonly used optimization algorithms (i.e. interior-reflective Newton methods) and a simulated annealing (SA) method was evaluated. This SA algorithm, known as basin hopping, was modified for the present application. In addition, optimization was performed using various weighting factors. Algorithms and effects of using incorrect weighting factors were studied using both simulated and clinical time-activity curves (TACs). Input data, taken from [15O]H2O, [11C]flumazenil and [11C](R)-PK11195 studies, were used to simulate time-activity curves at various variance levels (0-15% COV). Clinical evaluation was based on studies with the same three tracers. SA was able to produce accurate results without the need for selecting appropriate starting values for (kinetic) parameters, in contrast to the interior-reflective Newton method. The latter gave biased results unless it was modified to allow for a range of starting values for the different parameters. For patient studies, where large variability is expected, both SA and the extended Newton method provided accurate results. Simulations and clinical assessment showed similar results for the evaluation of different weighting models in that small to intermediate mismatches between data variance and weighting factors did not significantly affect the outcome of the fits. Large errors were observed only when the mismatch between weighting model and data variance was large. It is concluded that selection of specific optimization algorithms and weighting factors can have a large effect on the accuracy and precision of PET pharmacokinetic analysis. Apart from carefully selecting appropriate algorithms and variance models, further improvement in accuracy might be obtained by using noise reducing strategies, such as wavelet filtering, provided that these methods do not introduce significant bias