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Graphical analysis methods are widely used in positron emission tomographyquantification because of their simplicity and model independence. But theymay, particularly for reversible kinetics, lead to bias in the estimatedparameters. The source of the bias is commonly attributed to noise in the data.Assuming a two-tissue compartmental model, we investigate the bias thatoriginates from model error. This bias is an intrinsic property of thesimplified linear models used for limited scan durations, and it is exaggeratedby random noise and numerical quadrature error. Conditions are derived underwhich Logan's graphical method either over- or under-estimates the distributionvolume in the noise-free case. The bias caused by model error is quantifiedanalytically. The presented analysis shows that the bias of graphical methodsis inversely proportional to the dissociation rate. Furthermore, visualexamination of the linearity of the Logan plot is not sufficient forguaranteeing that equilibrium has been reached. A new model which retains theelegant properties of graphical analysis methods is presented, along with anumerical algorithm for its solution. We perform simulations with the fibrillaramyloid-beta radioligand [11C] benzothiazole-aniline using published data fromthe University of Pittsburgh and Rotterdam groups. The results show that theproposed method significantly reduces the bias due to model error. Moreover,the results for data acquired over a 70 minutes scan duration are at least asgood as those obtained using existing methods for data acquired over a 90minutes scan duration.

Model Error Correction for Linear Methods of Reversible Radioligand Binding Measurements in PET Studies