Logan's Reference Tissue Model based on Average k2'

The distribution volume ratio (DVR) can directly be calculated from the graphical method by using data from a reference region C'(t) with an average tissue-to-plasma clearance k₂' . Result is the linear regression equation

which contains DVR as the regression slope and an intercept int' which becomes constant after an equilibration time t*. The method does not require a 1-tissue compartment model structure of the data.

Implementation Notes

After switching to the Logan NonInvasive model in PKIN a suitable reference region must be selected. k₂' is an input parameter which must be manually edited, or estimated by using first the MRTM or SRTM model. Logan NonInvasive allows to fit a linear regression within a range starting at the parameters Start Lin. The results are the regression slope (= DVR = k₃/k₄+1) and intercept. Derived from the slope is binding potential BP=k₃/k₄.

There is also an error criterion Max Err. to fit Start Lin. For instance, if Max Err. is set to 10% and the fit box of Start Lin. is checked, the model searches the earliest sample so that the deviation between the regression and all measurements is less than 10%. Samples earlier than the Start Lin time are disregarded for regression and thus painted in gray.

Note: The k₂' resulting from the SRTM or MRTM method might be a reasonable estimate for the average clearance rate k₂'. Therefore, when switching in PKIN from the SRTM or MRTM model to Logan NonInvasive, k₂' of those methods is automatically copied to k₂', as long as Model conversion in the Configuration menu is enabled. See also.

Abstract [36]

"The distribution volume ratio (DVR), which is a linear function of receptor availability, is widely used as a model parameter in imaging studies. The DVR corresponds to the ratio of the DV of a receptor-containing region to a nonreceptor region and generally requires the measurement of an arterial input function. Here we propose a graphical method for determining the DVR that does not require blood sampling. This method uses data from a nonreceptor region with an average tissue-to-plasma efflux constant k₂ to approximate the plasma integral. Data from positron emission tomography studies with [11C]raclopride (n = 20) and [11C]d-threo-methylphenidate ([11C]dMP) (n = 8) in which plasma data were taken and used to compare results from two graphical methods, one that uses plasma data and one that does not. k₂ was 0.163 and 0.051 min-1 for [11C]raclopride and [11C]dMP, respectively. Results from both methods were very similar, and the average percentage difference between the methods was -0.11% for [11C]raclopride and 0.46% for [11C]dMP for DVR of basal ganglia (BG) to cerebellum (CB). Good agreement between the two methods was also achieved for DVR images created by both methods. This technique provides an alternative method of analysis not requiring blood sampling that gives equivalent results for the two ligands studied. It requires initial studies with blood sampling to determine the average kinetic constant and to test applicability. In some cases, it may be possible to neglect the k₂ term if the BG/CB ratio becomes reasonably constant for a sufficiently long period of time over the course of the experiment."

Watabe's Reference Tissue Model with 2 Compartments

An extension of the simplified reference model has been developed by Watabe et al. [49] for ligands which do not follow the usual assumptions of the reference tissue models. Instead of a 1-tissue compartment model, the reference tissue is described by a 2-tissue model as illustrated below.

Assuming that the non-specific distribution volume of both tissues is the same, the following operational equation for fitting the tissue TAC can be derived (see Millet et al [50], appendix C):

When the parameters k₂', k₃', and k₄' are fixed to constants determined with receptor-rich tissue, only R₁ and k₂ need to be fitted for estimating the binding potential BP.

Implementation Notes

After switching to the 2 Tissue Reference Model in PKIN a suitable reference region must be selected. For convolution with the exponentials, the reference tissue TAC is resampled on a regular grid, which can be specified by the sampl. interval parameter in PKIN.