Quantification with the Partial Saturation Approach (PSA) in longitudinal studies

PET is a functional imaging technique which enables the evaluation of physiological function through the estimation of biological parameters. Pre-clinical PET imaging is very useful for investigating  the evolution towards pathology and response to therapy in animal models through the use of longitudinal studies.
 
Traditionally, a dynamic series is acquired after radiotracer injection, and the information about the spatio-temporal distribution (4D) of the radiotracer in the organ of interest is collected (PET acquisition). In parallel, the radiotracer concentration delivered to the organ is measured and an input function to the system is derived.

Several methods have been derived to estimate biological parameters such as metabolism/incorporation rate or receptor density/affinity. Most them rely on the concept of compartmental analysis (Watabe, Ikoma et al. 2006) which need an arterially sampled input function.

We have been using multiple injection protocols coupled with non-linear compartmental analysis in the rodent (Mauger, Saba et al. 2005) (Gregoire 2007) to fully identify all the model parameters and thus biological values such as receptor density and apparent affinity for the radioligand. These complex procedures cannot be used in longitudinal studies because they require blood sampling for an arterially sampled input function and long-time anaesthesia (up to 3 hours). 

Single injection protocols without blood sampling are preferred, but the minimum amount of information required to accurately estimate these parameters is often not met when data are collected from one individual in one condition. Because we are imaging rodents, the population and disease stages can be controlled and thus modelled.

To conduct longitudinal studies, it is necessary to use methods that don’t require blood sampling but will still give stable and accurate parameter estimates. Following are methods that are being optimised for longitudinal imaging:

Partial Saturation Approach

The Partial Saturation Approach (PSA) enables the quantification of receptor binding parameters (receptor density, B'max and radioligand affinity 1/KD) and assessment of changes in these parameters over a range of disease states and pharmacologically induced changes. The radiotracer [11C]Raclopride is often used for the in vivo quantification of Dopamine D2 receptor binding. The PSA was used to assess the B'max and appKd of Dopamine D2 receptors in a single injection protocol [1] and has been successfully adapted for a range of receptor occupancy levels in healthy animals.

The PSA uses the general equilibrium equation

(B/F = (B'max-B)/KdVr – dB/dT * (1/koff*F))

where B = bound ligand
F = free ligand
koff = receptor dissociation constant

which includes a residual term as an indicator of the dynamic equilibrium state. For the dynamic equilibrium assumption to be met, the residual term should be within a certain small value [2].

This method was validated for a range of disease states and pharmacologically induced changes by a series of partial saturation experiments with a noise level equivalent to that of the PET (100 noise simulations per experiment). Conditions were simulated over a range of receptor occupancies for three B'max levels and three Kd levels to mimic the expected levels in the experiments by Fischer et al [3].

The parameters appBmax and appKd were estimated for each simulated experiment using the equilibrium relation for

1. a time window driven by constraining the residual term and
2. a static time window of 10 – 50 mins.

The accuracy of the estimates from both time windows are shown in Fig. 1. below.

Figure 1. Accuracy of estimates for a static and DET-guided time window.

The study demonstrated that the PSA with a guided time window produces accurate and stable estimates where large variations of appBmax and appKd are expected due to pharmacological or disease-induced changes for [11C]Raclopride in the rodent.

The details of an example biological study using the PET SORTEO simulation software to create the parametric map of B’max (see Fig. 2) can be found here.

 Figure 2. Parametric map of B'max

This work was presented at the 9th International Symposium on Functional Neuroreceptor Mapping of the Living Brain, Aug 9-11, 2012, in Baltimore.

Wimberley, C.¹; Fischer, K.²; Pichler, B.²; Gregoire, M-C.³
1 Brain and Mind Research Institute, University of Sydney, Australia;

2 Department of Preclinical Imaging and Radiopharmacy, Eberhard Karls University, Tuebingen, Germany;

3 Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC 2232 NSW, Australia
Validation of the partial saturation approach for in vivo quantification of striatal dopamine D2 receptors with [11C]raclopride. (Oral presentation)

References:
[1] Delforge, et al; J Nucl Med, 37(1), 5-11 (1996).
[2] Wimberley et al; World Molecular Imaging Congress 2011, San Diego.
[3] Fischer, K., Wimberley, C., Magg, J., Nguyen, H. P., Gregoire, M-C., Pichler, B.
In vivo quanification of striatal dopamine D2 receptor expression and [11C]raclopride affinity using a single injection protocol. The 9th International Symposium on Functional Neuroreceptor Mapping of the Living Brain, Aug 9-11, 2012, Baltimore, USA