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Patlak Reference Plot

Contents

Introduction

Tracers undergoing irreversible trapping can be analyzed with the Patlak Reference Model. The Patlak plot [1] can be used as a reference model provided there is also some tissue where the tracer is not irreversibly bound. This is frequently applied in the analysis of [18F]-FDG studies, where a 2-tissue compartment model is used, with k 4 = 0

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However, the Patlak Reference Model is also applicable to other compartment model situations, as long as there is one tissue compartment with irreversible trapping and a suitable reference tissue. Among other hypothesis, it is assumed that the distribution volume is the same for the tissue of interest (tissue including irreversible trapping) and the reference tissue: K 1 / k 2 = K 1 ' / k 2 ' .

The operational equation for the model is:

C tissue ( t ) C ref ( t ) = K 0 t C ref ( u ) u C ref ( t ) + V ( 1 )

Where C tissue ( t ) is the TAC for the region including irreversible trapping and C ref ( t ) is the TAC for the reference region.

In this approach, the measured PET activity C tissue ( t ) is divided by the activity in the reference tissue. This value is plotted against the quotient at the other side of the equation: the integral of the TAC at the reference region divided by the activity in this same region. The latter acts as a sort of "normalized time". If the system has an irreversible compartment, this relation becomes linear after some time t* after injection, which allows estimating the slope and the intercept with a linear fit. The interpretation of these parameters depends on the particular configuration of the system.

When the compartment model in the figure is followed, the slope is:

slope = K = k 2 k 3 k 2 + k 3 ( 2 )

The intercept is also a function of the transfer constants of the system, but it is not usually taken into account for the analyses.

Input parameters

Output parameters and goodness of fit

- Goodness of fit:

To show the goodness of fit at the preprocessing step, two parameters are given, together with the estimated parameters:

NSME = || C t - C t estimate || 2 || C t - mean ( C t ) || 2

It measures the quality of the fit for the TACs. Values vary between - (bad fit) to 1 (perfect fit).

Main references

[1] Patlak, C. S., Blasberg, R. G., & Fenstermacher, J. D. (1983). Graphical Evaluation of Blood-to-Brain Transfer Constants from Multiple-Time Uptake Data. Journal of Cerebral Blood Flow and Metabolism, 3(1), 1–7.

[2] Patlak, C. S., & Blasberg, R. G. (1985). Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. Generalizations. Journal of Cerebral Blood Flow and Metabolism, 5(4), 584–590.

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