A strategy to account for noise in the X-variable to reduce underestimation in Logan graphical analysis for quantifying receptor density in positron emission tomography

BACKGROUND: The Logan graphical analysis (LGA) algorithm is widely used to quantify receptor density for parametric imaging in positron emission tomography (PET). Estimating receptor density, in terms of the non-displaceable binding potential (BP(ND)), from the LGA using the ordinary least-squares (OLS) method has been found to be negatively biased owing to noise in PET data. This is because OLS does not consider errors in the X-variable (predictor variable). Existing bias reduction methods can either only reduce the bias slightly or reduce the bias accompanied by increased variation in the estimates. In this study, we addressed the bias reduction problem by applying a different regression method. METHODS: We employed least-squares cubic (LSC) linear regression, which accounts for errors in both variables as well as the correlation of these errors. Noise-free PET data were simulated, for (11)C-carfentanil kinetics, with known BP(ND) values. Statistical noise was added to these data and the BP(ND)s were re-estimated from the noisy data by three methods, conventional LGA, multilinear reference tissue model 2 (MRTM2), and LSC-based LGA; the results were compared. The three methods were also compared in terms of beta amyloid (A β) quantification of (11)C-Pittsburgh compound B brain PET data for two patients with Alzheimer’s disease and differing A β depositions. RESULTS: Amongst the three methods, for both synthetic and actual data, LSC was the least biased, followed by MRTM2, and then the conventional LGA, which was the most biased. Variations in the LSC estimates were smaller than those in the MRTM2 estimates. LSC also required a shorter computational time than MRTM2. CONCLUSIONS: The results suggest that LSC provides a better trade-off between the bias and variability than the other two methods. In particular, LSC performed better than MRTM2 in all aspects; bias, variability, and computational time. This makes LSC a promising method for BP(ND) parametric imaging in PET studies.