Model Configuration and Assumptions

The **Simplified Reference Tissue Model 2** (SRTM2) was derived by Wu and Carson [1] from the SRTM with the aim of improved parametric mapping. The model structure is the same

as well as the assumptions:

- The distribution volume is the same for the tissue of interest and the reference tissue: K
_{1}/k_{2}=K_{1}'/k_{2}'. - The kinetics in the receptor-rich tissue of interest is such, that it is difficult to distinguish between the specific and the free/non-specific compartment; ie. the TAC can be fitted by a 1-tissue compartment model with an uptake rate constant k
_{2a}= k_{2}/(1+BP_{ND}).

Operational Model Curve

The operational equation of the SRTM was re-written to allow for fixing of k_{2}'. This is relevant for parametric mapping because the model in each pixel TAC uses the same reference TAC and therefore should employ the same k_{2}'. Defining the ratio of tracer delivery R_{1} as K_{1}/K_{1}' and the binding potential BP_{ND} as k_{3}/k_{4}, the following operational equation can be derived for the measured TAC in a receptor-rich region:

The three unknowns R_{1}, k_{2} and k_{2a} in this equation can be fitted using nonlinear regression techniques. The binding potential can then be calculated as

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

The operational equation includes three unknowns: **R1**, **k2**, and **k2a **which can be fitted using nonlinear fitting techniques. Note that **k2'**, the transfer of tracer from the reference tissue back to the plasma, can also be fitted. This can be employed by first estimating k_{2}' with a coupled fit and adequate TACs, and then fixing it for all regional fits as described above. Furthermore, fixing of k_{2}' allows studying the bias introduced by an inadequate k_{2}'.

**Note: **As with the SRTM method, BP_{ND} estimates from SRTM2 tend to be biased if the 1-tissue compartment model assumption does not apply. The magnitude of the bias is even larger, most likely because the fixed k_{2}' can not compensate any more a part of the model inadequacy.

Reference

1. Wu Y, Carson RE: Noise reduction in the simplified reference tissue model for neuroreceptor functional imaging. J Cereb Blood Flow Metab 2002, 22(12):1440-1452. DOI