Revisiting the Logan plot to account for non-negligible blood volume in brain tissue

Reference tissue-based quantification of brain PET data does not typically include correction for signal originating from blood vessels, which is known to result in biased outcome measures. The bias extent depends on the amount of radioactivity in the blood vessels. In this study, we seek to revisit the well-established Logan plot and derive alternative formulations that provide estimation of distribution volume ratios (DVRs) that are corrected for the signal originating from the vasculature.

New expressions for the Logan plot based on arterial input function and reference tissue were derived, which included explicit terms for whole blood radioactivity. The new methods were evaluated using PET data acquired using [¹¹C]raclopride and [¹⁸F]MNI-659. The two-tissue compartment model (2TCM), with which signal originating from blood can be explicitly modeled, was used as a gold standard. DVR values obtained for [¹¹C]raclopride using the either blood-based or reference tissue-based Logan plot were systematically underestimated compared to 2TCM, and for [¹⁸F]MNI-659, a proportionality bias was observed, i.e., the bias varied across regions. The biases disappeared when optimal blood-signal correction was used for respective tracer, although for the case of [¹⁸F]MNI-659 a small but systematic overestimation of DVR was still observed.

The new method appears to remove the bias introduced due to absence of correction for blood volume in regular graphical analysis and can be considered in clinical studies. Further studies are however required to derive a generic mapping between plasma and whole-blood radioactivity levels.