BPnd (Wu SRTM2 Ref): Simplified Reference Tissue Model with fixed k2'

Wu and Carson [1] aimed at making the SRTM basis function approach even more robust 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:

Calculate k₂' using SRTM in all pixels.
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'. This is relevant for parametric mapping because the model in each pixel TAC uses the same reference TAC and therefore should employ the same k₂'. Defining the ratio of tracer delivery R₁ as K₁/K₁' and the binding potential BP_ND as k₃/k₄, the following operational equation can be derived for the measured TAC in a receptor-rich region:

Equation SRTM2

The three unknowns R₁, k₂ and k_2a in this equation can be fitted using nonlinear regression techniques. The binding potential can then be calculated as

Equation SRTM2 BP

The current PXMOD implementation BPnd (Wu SRTM2 Ref) allows estimating k₂' as the median of all k₂' values calculated by SRTM in a defined VOI. IN contrast to [1] and unweighted fitting is employed. Note that there is a deprecated version of the model which used the k₂' obtained from regional fitting.

Acquisition and Data Requirements

Image Data	A dynamic PET data set imaging a receptor tracer which behaves kinetically similar to a 1-tissue compartment model.
TAC 1	TAC from a receptor-rich region (such as basal ganglia for D2 receptors).
TAC 2	TAC from a receptor-devoid reference region (such as cerebellum or frontal cortex for D2 receptors).
VOI	VOI definition of the brain excluding the reference tissue which can (optionally) be used for getting an estimate of k₂'. Recommendation is to use the relevant brain regions outside the reference tissue.

Model Preprocessing

Two regional TACs (TAC1 and TAC2) as well as a VOI are needed for Model Preprocessing.

In the lower part the following parameters are configured:

k2a min	Minimal value of k_2a (slowest decay of exponential).
k2a max	Maximal value of k_2a (fastest decay of exponential).
# Basis	Number of basis functions between k2a min and k2a max. Note that increments are taken at logarithmic steps. This number is directly proportional to processing time.
Resampling	Specifies the interval of curve resampling which is required for performing the operation of exponential convolution. Resampling should be equal or smaller than the shortest frame duration.
Threshold	Discrimination threshold for background masking. Will not have an effect if a mask image has been defined.
k2'	k₂ of the reference tissue. It can be specified in four different ways: Fixed at a specified value: uncheck box and enter value Fitted using TAC1 and TAC2: The SRTM method implemented in PKIN is called to fit TAC1 with reference TAC2 and the resulting k2' is used. Median k₂' in VOI within R₁ range: SRTM is applied to all pixels in the specified VOI. Restriction of the R₁ values within a range is used as a filter for removing noise. The median of all k₂' values with R1 in the range is finally used. Median k₂' in VOI within BP range: As above, but using a physiologic range of BP for filtering. The median of all k₂' values with BPnd in the range is finally used. Note that checking of the ranges is not required for the procedure, only for changing the restriction range.
BPnd	Estimated binding potential (= k₃/k₄ according to the underlying model).
R1	Ratio of tracer delivery in each pixel relative to the reference tissue (R1=K₁/K₁').
k2	Estimated rate constant k₂.
k2a	k_2a value which provides the best least squares fit in each voxel.

The result of the regional fit during Model Preprocessing is shown in the Results panel for inspection.

Note the lower text section which lists the k₂' results of all three procedures as well as the k₂' configured for the pixelwise analysis.

The model features an additional panel SRTM Fitting Results which allows inspecting the SRTM parametric maps with in the VOI. The parameter can be switched in the upper right. Due to outlier results it may be required to manually enter a physiologic value as the upper image threshold as illustrated below.

Model Configuration

PXMOD SRTM2 Parameter

BPnd	Estimated binding potential (BPnd= k₃/k₄ according to the underlying model).
k2	Estimated efflux rate constant k₂ .
R1	Ratio of tracer delivery in each pixel relative to the reference tissue (R₁=K₁/K₁'). Therefore the map often has a similar appearance to a perfusion image.
k2a	k_2a value which provides the best least squares fit.

Note: The k2a parametric map should be checked in the initial setup of a processing protocol. The estimated k2a values should not be truncated by too narrow k2a min and k2a max values.

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