A consistent and 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 CP(t) and the Logan plot with reference tissue input CREF(t) are described by Eqs. (1) and (2) below for t ≥ t⁎, respectively,where CP(t) is the tracer concentration in plasma from arterial blood sampling, CREF(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, DVT is the tracer total distribution volume in tissue, and DVR is the DVT ratio of the target to the reference tissues. For the Logan plot with reference tissue input described by Eq. (2), C(t) / CREF(t) is a constant for t ≥ t⁎.
In contrast to classical compartmental modeling techniques, DVT 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 DVT 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 DVT 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.
Section snippets
Materials and methods
Theory of graphical analysis using a new plot.
Sufficient condition for graphical analysis using the new plot
The metabolite-corrected plasma input function was well-fitted by an exponential function for t ≥ 25 min. The R-square of linear regression of time t (independent regression variable) versus the natural logarithm of CP(t) (dependent regression variable) was R2 = 0.983 ± 0.011 with the slop of − 0.012 ± 0.002 (n = 55).
The plot of time t versus mean ± SD of C(t) / CP(t) in Fig. 1 shows that C(t) / CP(t) attained a constant for t ≥ t⁎, where t⁎ = 25 min for the cerebellum, and t⁎ = 42.5 min for the caudate and the
Sufficient condition for the new and Logan plots
For the reversible tracer kinetics described by Eq. (4), a sufficient condition for the new graphical analysis is that there is a t⁎ such that tracer concentration in all compartments attains equilibrium relative to the tracer concentration in plasma, i.e., Ci(t) = RiCP(t), i = 1, 2,…m, for t ≥ t⁎ (see Theory section). By similar derivation, the condition is also sufficient for classical graphical analysis of the Logan plot described by Eq. (1). Note that the sufficient condition of steady state (dA / d
Acknowledgments
We thank the cyclotron, PET, and MRI imaging staff of the Johns Hopkins Medical Institutions. This work was supported in part by NIH grants DA00412, MH078175, AA12839, AA012837, and AA10158. Thanks to Mary McCaul and Gary Wand for the kind use some of PET data.
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