Logan Reference Plot with fixed k 2 '



The Logan Reference Tissue method is used to estimate the distribution volume ratio ( DVR ) for PET studies with reversible radioligands. BP is then derived from DVR as BP = DVR - 1 .

The method does not depend on a specific model structure of the reference tissue. Assuming the presence of reference region TAC C T ' ( t ) with an average tissue-to-plasma clearance k 2 ' , the target tissue TAC C T ( t ) is transformed and plotted as a function of the transformed reference TAC, which acts as a sort of "normalized time".

The operational equation for the method is:

0 t C T ( τ ) τ C T ( t ) = DVR 0 t C T ' ( τ ) τ + C T ' ( t ) / k 2 ' C T ( t ) + b

This resembles a linear equation, where DVR is the slope and b is an error term which decreases over time. This dependence also becomes negligible after some time t*. Then, if only the values obtained after t* are taken into account, a linear regression allows estimating DVR and b .

As mentioned, k 2 ' represents the average tissue to plasma efflux. It has to be specified as an input for the model. A representative value for the population based on previous studies can be entered, or, alternatively, k 2 ' can be estimated for each subject by applying, for instance, the SRTM method, before starting the Logan analysis.

Input parameters

Output parameters and goodness of fit

- Goodness of fit:

To show the goodness of fit at the preprocessing step, two parameters are given, together with the estimated parameters:

NSME = || C t - C t estimate || 2 || C t - mean ( C t ) || 2

It measures the quality of the fit for the TACs. Values vary between - (bad fit) to 1 (perfect fit).

Main references

[1] Logan J, Fowler JS, Volkow ND, Wang GJ, Ding YS, Alexoff DL (1996) Distribution volume ratios without blood sampling from graphical analysis of PET data. Journal of Cerebral Blood Flow and Metabolism, 16(5):834-840.