Principle of Reference Models

The measurement and analysis of the blood samples for kinetic modeling is an invasive and demanding procedure. Therefore, methods have been developed to obviate the need for invasive blood sampling. The solutions found replace the arterial input curve by an indirect input curve, namely the time activity curve of some reference tissue. Therefore they are called *reference methods*. Reference methods are not able to provide a full kinetic analysis. However, assuming certain relations between the kinetics of the tissue of interest and the reference tissue, they can provide valuable measures of interest.

Model Structure

Most of the reference methods are dedicated to reversibly binding neuroreceptor tracers. A reference tissue must be found which is devoid of receptors, and then it is assumed that the distribution volume of the non-displaceable compartment (free tracer in tissue and non-specific binding) is the same among the tissues. Under these assumptions a measure of the receptor concentration called *binding potential* (BP) can be calculated from the two time-activity curves.

The reference methods differ in their mathematical approaches, and they show substantial differences with regard to noise sensitivity and processing speed. They are described in the following sections. The compartment models are based upon the following configuration:

In the model equations C'(t) represents the TAC from the reference region (k_{3}=0 in the 2-tissue compartment model), and C(t) the TAC from a receptor-rich region (k_{3}>0).

PXMOD Implementations

The measurements required for the receptor reference methods are a dynamic PET or SPECT acquisition without the need for external blood sampling. The operator must delineate a reference region devoid of receptors (e.g. frontal cortex for D2 receptors). For the model preprocessing step he also must delineate a receptor-rich region (e.g. basal ganglia for D2 receptors). The model then applies the reference model to the TACs from both regions and presents the results to the user for inspection. If the result is not satisfactory, the user may change some of the parameters and try the fit again. At the end of preprocessing some parameters such as the regression start time t* or k_{2}' have been determined which will be used for the pixel-wise fits. The pixel-wise calculations result in BP maps. To avoid meaningless values which mix up the display it is recommended to restrict the accepted BP values to a reasonable range.

Models with Fixed k2'

Some of the reference methods require an a priori average value of k_{2}', while other methods such as the MRTM or the SRTM reference methods estimate k_{2}' together with the other parameters in each individual pixel. There are three ways of obtaining a value of k_{2}'

- Calculation of k2' with several regional TACs in the PKIN kinetic tool (recommended): In this case regional TACs are derived from the dynamic PET study and loaded into PKIN. One of the TACs should represent appropriate reference tissue (without receptors), while the others should be derived from tissue with high specific binding. The latter TACs are then fitted with one of the reference models which yield k
_{2}' (MRTM, SRTM), and the resulting k_{2}' values are averaged. An alternative is the use of SRTM2 and coupled fitting, with k_{2}' being estimated as a common parameter. More detail on these approaches is available in the PKIN Users Guide. After k_{2}' has been calculated it has to be entered in the model preprocessing pane and the fit flag removed. - Calculation of k
_{2}' with a single regional TAC in PXMOD during preprocessing: This approach has the advantage of simplicity, but it is not possible to get an average value from different tissues. A work-around would be to define a representative VOI which encompasses several tissue types, but it is not exactly equivalent to the first method. - The SRTM2 model has been revised and also allows to derive k2' from the value distribution of an initial run of SRTM. A representative k2' can then be obtained as the median of the k2' values in a part of the brain (avoiding the reference tissue), and restricted to physiological values. Note that this k2' value available and could be manually entered in the other reference tissue models.