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.

Averaging k2' from Separate Regional Fits

In response to a request from a PMOD user Dr. Ichise recommended the following approach for calculating k_{2}':

- k
_{2}' is the tissue clearance rate from the reference region, e.g., cerebellum. This reference tissue is always a region (ROI), not a voxel for both ROI based PKIN or PXMOD parametric imaging. If you define a reference region, there should be only one correct k_{2}' value for that particular subject (scan). - Logan in her original formulation of her reference tissue model suggested to determine k
_{2}' by using arterial data for a group of subjects and use this mean k_{2}'. - However, we showed that this k
_{2}' can be estimated for each individual without arterial data using MRTM or SRTM (three parameter estimation, one of the three parameters is k_{2}'). - I prefer to use k
_{2}' estimated this way for each subject for the subsequent MRTM2 or SRTM2. This would be more accurate than the mean k_{2}' estimated for a group of subjects as above. - Now the accuracy of k
_{2}' estimation depends on the following (see [52]): A) noise in the PET data, B) the magnitude of k_{2}' and C) the ratio of k_{2}'/k_{2}or k_{2}/k_{2}' determined by MRTM or SRTM. - The bias and variability of k
_{2}' estimation by MRTM is less as k_{2}' is larger and k_{2}'/k_{2}or k_{2}/k_{2}' ratio is further away from unity. This ratio for fallypride using cerebellum and striatum should be greater than 3, I think. In that case, k_{2}' estimation from cerebellum and striatum (use ROIs) should be minimum (see figs in the paper). - Even using the ROIs, k
_{2}' estimation is affected by noise and hence it is good to run MRTM a few times choosing ROIs with high BP_{ND}areas (say right striatum and left striatum) k_{2}'/k_{2}ratio is further away from 1) and average the k_{2}' values. This averaging is within the subject and totally different from population average. - Please use the k
_{2}' determined as above for estimation of BP_{ND}for the cortical regions. The k_{2}' estimated with cerebellum and cortical regions is not accurate because k_{2}'/k_{2}is closer to unity. - One advantage of MRTM over SRTM: To use SRTM, both cerebellum and target must be 1 tissue (1T) kinetics (use of the SRTM for 2T will bias BP
_{ND}). However, MRTM is good for tracers with 2T kinetics such as Fallypride. The only thing here is that you have to give a t* value.

Estimating k2' using a Fit with Regional Coupling

Alternatively, the a-priori knowledge that k_{2}' should always have the same value can be exploited using coupled fitting in PKIN with SRTM2 as follows:

- Select the SRTM2 model for all regions and fit it with k
_{2}' enabled.

This will result in regionally different k_{2}' values which should be quite similar across the high-binding regions. - Configure a coupled fit with k
_{2}' as the common parameter and only include the relevant regions for coupling.

Start the coupled fit which returns a common k_{2}'. This value can be used for pixel-wise fitting or the regional fitting of all TACs - For the regional fitting fix k
_{2}' in one of the coupled regions

propagate the model to all regions, and then fit all regional TACs. - The same k
_{2}' value can also be used for pixel-wise fitting with the PXMOD tool.