A consistent and efficient graphical analysis method to improve the quantification of reversible tracer binding in radioligand receptor dynamic PET studies

Abstract

The widely used Logan plot in radioligand receptor dynamic PET studies produces marked noise-induced negative biases in the estimates of total distribution volume (DV_T) and binding potential (BP). To avoid the inconsistencies in the estimates from the Logan plot, a new graphical analysis method was proposed and characterized in this study. The new plot with plasma input and with reference tissue input was first derived to estimate DV_T and BP. A condition was provided to ensure that the estimate from the new plot equals DV_T or BP. It was demonstrated theoretically that 1) the statistical expectations of the estimates from the new plot with given input are independent of the noise of the target tissue concentration measured by PET; and 2) the estimates from the time activity curves of regions of interest are identical to those from the parametric images for the new plot. The theoretical results of the new plot were also confirmed by computer simulations and fifty-five human [¹¹C]raclopride dynamic PET studies. By contrast, the marked noise-induced underestimation in the DV_T and BP images and noise-induced negative bias in the estimates from the Logan plot were demonstrated by the same data sets used for the new plot. The computational time for generating DV_T or BP images in the human studies was reduced by 80% on average by the new plot in contrast to the Logan plot. In conclusion, the new plot is a consistent and computationally efficient graphical analysis method to improve the quantification of reversible tracer binding in radioligand receptor dynamic PET studies.

Introduction

Due to its simplicity, computational efficiency, and readily apparent visual representation of tracer kinetic behavior, a graphical analysis method using the Logan plot (Logan et al., 1990, Logan et al., 1996) has been widely used to characterize and quantify reversible tracer binding in radioligand receptor dynamic PET studies. The Logan plot with plasma input C_P(t) and the Logan plot with reference tissue input C_REF(t) are described by Eqs. (1) and (2) below for t ≥ t⁎, respectively,

$$\frac{\underset{0}{\overset{t}{\int }}\mathit{C}\left(s\right)ds}{\mathit{C}\left(\text{t}\right)}={\mathrm{D}\mathrm{V}}_{\text{T}}\frac{\underset{0}{\overset{t}{\int }}{\mathit{C}}_{\text{P}}\left(s\right)ds}{C\left(\text{t}\right)}+\alpha$$

$$\frac{\underset{0}{\overset{t}{\int }}\mathit{C}\left(s\right)ds}{\mathit{C}\left(t\right)}=\mathrm{D}\mathrm{V}\mathrm{R}\frac{\underset{0}{\overset{t}{\int }}{\mathit{C}}_{\text{REF}}\left(s\right)ds}{C\left(t\right)}+\beta$$

where C_P(t) is the tracer concentration in plasma from arterial blood sampling, C_REF(t) is the time activity curve (TAC) of reference tissue obtained by applying regions of interest (ROIs) of reference tissue to dynamic images, C(t) is the ROI or pixel-wise TAC of the target tissue tracer concentration measured by PET, DV_T is the tracer total distribution volume in tissue, and DVR is the DV_T ratio of the target to the reference tissues. For the Logan plot with reference tissue input described by Eq. (2), C(t) / C_REF(t) is a constant for t ≥ t⁎.

In contrast to classical compartmental modeling techniques, DV_T and DVR estimates obtained by the Logan plot for reversible tracer kinetic binding are independent of specific compartmental model configurations that may differ from tissue to tissue (Koeppe et al., 1991, Gunn et al., 2002, Turkheimer et al., 2003). However, the application of the Logan plot is limited by the noise level of target tissue tracer concentration C(t). There is noise-induced negative bias in the estimates of DV_T and binding potential (BP) (= DVR − 1) from the Logan plot, and the underestimation in the estimates from the Logan plot is dependent on both the noise level and magnitude of tissue concentration C(t) (Abi-Dargham et al., 2000, Fujimura et al., 2006, Gunn et al., 2002, Slifstein and Laruelle, 2000, Logan et al., 2001, Wallius et al., 2007). The noise-induced underestimation can result in reduced contrasts in the estimates of BP among targeted tissues, and reduced statistical power to discriminate populations of interest by a specific tissue BP (Zhou et al., 2008). Unfortunately, the C(t) measured by the PET scanning is often accompanied by high noise levels especially when employing pixel-wise tracer kinetic methods. Instead of regular linear regression for the Logan plot, a few numerical methods have been proposed to reduce the noise-induced negative bias but with higher variation in DV_T and BP estimates and higher computational cost (Buchert et al., 2003, Joshi et al., 2007, Varga and Szabo, 2002 Ogden, 2003).

In this study, we first derived an improved graphical analysis method using a new plot with plasma input and with reference tissue input for the quantification of reversible tracer kinetics. The new graphical analysis method was characterized by theoretical analysis, computer simulation, and fifty-five human [¹¹C]raclopride ([¹¹C]RAC) dynamic PET studies. Conventional graphical analysis using the Logan plot was applied to same data sets for comparison. With given input function, the effects of noise in the target tissue concentration C(t) on the estimates from the new and Logan plots were analyzed and evaluated.