Determination of k2' for Models Assuming a Pre-determined k2' Value

Some of the reference methods require an a priori average value of k₂', while other methods such as the MRTM or the SRTM reference methods estimate k₂' 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 k₂':

1. k₂' 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 k₂' value for that particular subject (scan).
2. Logan in her original formulation of her reference tissue model suggested to determine k₂' by using arterial data for a group of subjects and use this mean k₂'.
3. However, we showed that this k₂' can be estimated for each individual without arterial data using MRTM or SRTM (three parameter estimation, one of the three parameters is k₂').
4. I prefer to use k₂' estimated this way for each subject for the subsequent MRTM2 or SRTM2. This would be more accurate than the mean k₂' estimated for a group of subjects as above.
5. Now the accuracy of k₂' estimation depends on the following (see [52]): A) noise in the PET data, B) the magnitude of k₂' and C) the ratio of k₂'/k₂ or k₂/k₂' determined by MRTM or SRTM.
6. The bias and variability of k₂' estimation by MRTM is less as k₂' is larger and k₂'/k₂ or k₂/k₂' ratio is further away from unity. This ratio for fallypride using cerebellum and striatum should be greater than 3, I think. In that case, k₂' estimation from cerebellum and striatum (use ROIs) should be minimum (see figs in the paper).
7. Even using the ROIs, k₂' estimation is affected by noise and hence it is good to run MRTM a few times choosing ROIs with high BP_NDareas (say right striatum and left striatum) k₂'/k₂ ratio is further away from 1) and average the k₂' values. This averaging is within the subject and totally different from population average.
8. Please use the k₂' determined as above for estimation of BP_ND for the cortical regions. The k₂' estimated with cerebellum and cortical regions is not accurate because k₂'/k₂ is closer to unity.
9. 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 k₂' should always have the same value can be exploited using coupled fitting in PKIN with SRTM2 as follows:

1. Select the SRTM2 model for all regions and fit it with k₂' enabled.
   
   This will result in regionally different k₂' values which should be quite similar across the high-binding regions.
2. Configure a coupled fit with k₂' as the common parameter and only include the relevant regions for coupling.
   
   Start the coupled fit which returns a common k₂'. This value can be used for pixel-wise fitting or the regional fitting of all TACs
3. For the regional fitting fix k₂' in one of the coupled regions
   
   propagate the model to all regions, and then fit all regional TACs.
4. The same k₂' value can also be used for pixel-wise fitting with the PXMOD tool.