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

BPnd (Wu SRTM2 Ref) - Deprecated: 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 PXMOD implementation BPnd (Wu SRTM2 Ref) differs from that described in [1] in the following points

An unweighted fitting is employed.
Instead of performing a pixel-wise SRTM calculation and averaging k₂' in non-reference pixels, k₂' is calculated by applying SRTM to an averaged TAC from a VOI covering non-reference pixels.

Acquisition and Data Requirements

Image Data	A dynamic PET data set with an neuroreceptor 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 region (such as cerebellum or frontal cortex for D2 receptors).

Model Preprocessing

Two regional TACs (TAC1 and TAC2) are needed for Model Preprocessing.

PXMOD SRTM2 Preprocessing

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.
k2'	k₂ of the reference tissue. It can be fixed at a specified value, or fitted. If it is checked, k2' is fitted using the SRTM method implemented in PKIN. This value will be used in pixel-wise SRTM2.
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 fit during Model Preprocessing is shown in the Result panel for inspection.

PXMOD Gunn Pre-Processing Result

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