Improving contrast between gray and white matter of Logan graphical analysis’ parametric images in positron emission tomography through least-squares cubic regression and principal component analysis

Abstract

Logan graphical analysis (LGA) is a method for in vivo quantification of tracer kinetics in positron emission tomography (PET). The shortcoming of LGA is the presence of a negative bias in the estimated parameters for noisy data. Various approaches have been proposed to address this issue. We recently applied an alternative regression method called least-squares cubic (LSC), which considers the errors in both the predictor and response variables to estimate the LGA slope. LSC reduced the bias in non-displaceable binding potential estimates while causing slight increases in the variance. In this study, we combined LSC with a principal component analysis (PCA) denoising technique to counteract the effects of variance on parametric image quality, which was assessed in terms of the contrast between gray and white matter. Tissue time–activity curves were denoised through PCA, prior to estimating the regression parameters using LSC. We refer to this approach as LSC–PCA. LSC–PCA was assessed against OLS–PCA (PCA with ordinary least-squares (OLS)), LSC, and conventional OLS-based LGA. Comparisons were made for simulated 11 C-carfentanil and 11C Pittsburgh compound B (11C-PiB) data, and clinical 11 C-PiB PET images. PCA-based methods were compared over a range of principal components, varied by the percentage variance they account for in the data. The results showed reduced variances in distribution volume ratio estimates in the simulations for LSC–PCA compared to LSC, and lower bias compared to OLS–PCA and OLS. Contrasts were not significantly improved in clinical data, but they showed a significant improvement in simulation data —indicating a potential advantage of LSC–PCA over OLS–PCA. The effects of bias reintroduction when many principal components are used were also observed in OLS–PCA clinical images. We therefore encourage the use of LSC–PCA. LSC–PCA can allow the use of many principal components with minimal risk of bias, thereby strengthening the interpretation of PET parametric images.