Simplified Reference Tissue Model 2 (SRTM2)

Wu and Carson [32] aimed at making the Simplified Reference Tissue Model (SRTM) more robust for pixel-wise applications and called it Simplified Reference Tissue Model 2 (SRTM2). They noted that with SRTM k₂' is calculated with each pixel TAC, although the same reference TAC is used for all pixels. Therefore they implemented a two-step approach:

1. Calculate k₂' using SRTM in all pixels except for pixels without specific binding.
2. Fix k₂' : Average k₂' in all brain pixels outside the reference region. Use this fixed value for the pixel-wise SRTM calculations, reducing the number of fitted parameters from 3 to 2.

The operational equation of the SRTM was re-written to allow for fixing of k₂'

The three parameters R1, k2a and k'2 are estimated in step 1. In step 2 k₂' is fixed, and only R1 and k2a are estimated. k2a is the apparent k2 (k2a = k2 /(1+BP)).

The binding potential can then be calculated as

SRTM2 is based on the same assumptions as SRTM:

1. The distribution volume is the same for the tissue of interest and the reference tissue: K₁/k₂=K₁'/k₂'.
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. This assumption may not be valid for all tracers. (Even in the test data, the approximation is not accurate at early time points.)

Note: As with the SRTM method, BP 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 for the SRTM2 estimates, most likely because the fixed k₂' can not compensate any more a part of the model inadequacy [32].

Implementation Notes

After switching to the Simplified Ref Tissue Model 2 in PKIN a suitable reference region must be selected. For convolution with the exponentials, the reference tissue TAC is resampled on a regular grid, which can be specified by the resampling interval parameter in PKIN.

Note that k₂', the transfer of tracer from the reference tissue back to the plasma, can also be fitted. After removing the fit check of k₂', it remains fix at the entered value. This allows to study the bias when fixing k₂'.

Abstract [32]

"The Simplified Reference Tissue Model (SRTM) produces functional images of receptor binding parameters using an input function derived from a reference region and assuming a model with one tissue compartment. Three parameters are estimated: binding potential (BP), relative delivery (R₁), and the reference region clearance constant k₂'. Since k'₂ should not vary across brain pixels, the authors developed a two-step method (SRTM₂) using a global value of k₂'. Whole-brain simulations were performed using human input functions and rate constants for [18F]FCWAY, [11C]flumazenil, and [11C]raclopride, and parameter SD and bias were determined for SRTM and SRTM₂. The global mean of k₂' was slightly biased (2% to 6%), but the median was unbiased (<1%) and was used as the global value. Binding potential noise reductions with SRTM2 were 4% to 14%, 20% to 53%, and 10% to 30% for [18F]FCWAY, [11C]flumazenil, and [11C]raclopride, respectively, with larger reductions for shorter scans. R1 noise reduction was larger than that of BP. Simulations were also performed to assess bias when the reference and/or tissue regions followed a two-tissue compartment model. Owing to the constrained k₂', SRTM₂ showed somewhat larger biases due to violations of the one- compartment model assumption. These studies demonstrate that SRTM₂ should be a useful method to improve the quality of neuroreceptor functional images."