### Watabe's Reference Tissue Model with 2 Compartments

Model Configuration and Assumptions

The **2 Tissue Reference Tissue** method proposed by of Watabe [1] has been developed 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. The second compartment C_{2}' may represent specific or non-specific binding.

Operational Model Curve

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 [2], appendix C):

When the parameters k_{2}', k_{3}', and k_{4}' are fixed to constants determined with receptor-rich tissue, only R_{1} and k_{2} need to be fitted for estimating the binding potential BP_{ND}. The equation parameters and their relation to the model are given by:

For convolution with the exponentials, the reference tissue TAC C_{T}'(t) is resampled on a regular grid, which can be specified by the **Resampling** parameter.

Parameter Fitting

After switching to the **2 Tissue Reference Model** a suitable reference region must be selected. The operational equation includes six fitting parameters: **R1**, **k2**, **k2'**, **k3'**, **k4'**. Per default, the fit boxes of **k2'**, **k3' **and **k4' **are off with the idea, that the values are determined externally. However, any of them may also be fitted. Fitting is performed using nonlinear techniques, and the main outcome is **BPnd**.

References

[1] Original abstract: Watabe, H et al. The reference tissue model: Three compartments for the reference region. Neuroimage 11: S12.

[2] Model description in Appendix C: Millet P, Graf C, Buck A, Walder B, Ibanez V: Evaluation of the reference tissue models for PET and SPECT benzodiazepine binding parameters. Neuroimage 2002, 17(2):928-942. DOI