A data driven method for estimation of B_avail and appK_D using a single injection protocol with [¹¹C]raclopride in the mouse

Highlights

• We explore and validate a data driven method for the estimation of B_avail and appK_D.

• Extends the partial saturation approach, a simple, single injection PET protocol.

• The PSA doesn't require blood sampling so is ideal for longitudinal imaging studies.

• We extended and validated the PSA for a range of experimental conditions.

• Will be useful for the longitudinal study of neurodegenerative disease in mice

Abstract

Purpose

The partial saturation approach (PSA) is a simple, single injection experimental protocol that will estimate both B_avail and appK_D without the use of blood sampling. This makes it ideal for use in longitudinal studies of neurodegenerative diseases in the rodent. The aim of this study was to increase the range and applicability of the PSA by developing a data driven strategy for determining reliable regional estimates of receptor density (B_avail) and in vivo affinity (1/appK_D), and validate the strategy using a simulation model.

Methods

The data driven method uses a time window guided by the dynamic equilibrium state of the system as opposed to using a static time window. To test the method, simulations of partial saturation experiments were generated and validated against experimental data. The experimental conditions simulated included a range of receptor occupancy levels and three different B_avail and appK_D values to mimic diseases states. Also the effect of using a reference region and typical PET noise on the stability and accuracy of the estimates was investigated.

Results

The investigations showed that the parameter estimates in a simulated healthy mouse, using the data driven method were within 10 ± 30% of the simulated input for the range of occupancy levels simulated. Throughout all experimental conditions simulated, the accuracy and robustness of the estimates using the data driven method were much improved upon the typical method of using a static time window, especially at low receptor occupancy levels. Introducing a reference region caused a bias of approximately 10% over the range of occupancy levels.

Conclusions

Based on extensive simulated experimental conditions, it was shown the data driven method provides accurate and precise estimates of B_avail and appK_D for a broader range of conditions compared to the original method.

Introduction

Positron emission tomography (PET) is an important technique for studying neuroreceptor systems in vivo in preclinical and clinical research. For example, [¹¹C]raclopride is a PET radioligand which is used extensively to study dopamine D2 receptor expression. The aim of such studies is to obtain reliable regional estimates of characteristic binding parameters, such as the available receptor density B_avail and in vivo affinity appK_D, as defined in Innis et al. (2007), and to detect changes in these parameters from a baseline condition as an indicator of altered dopaminergic function, including disease states, such as Parkinson's disease (Antonini et al., 1997) or schizophrenia (Seeman and Kapur, 2000) or after pharmacological intervention.

Several methods have been derived to estimate B_avail and appK_D in vivo and most of them rely on the concept of compartmental analysis (Watabe et al., 2006) and multiple injection experiments, requiring an arterially sampled input function. Multiple injection protocols coupled with non-linear compartmental analysis have been used to fully identify all the model parameters and to derive the biological values B_avail and appK_D for the radioligand (Delforge et al., 1993, Morris et al., 1996).

The parameters B_max and K_D can be calculated in vitro using a Scatchard approach which is a linearisation of the binding data collected during a saturation binding experiment. A Scatchard like plot can also be employed on in vivo data in which bound and free values of the radioligand are taken from multiple experiments or multiple injections with different levels of injected mass. The parameters calculated with this in vivo Scatchard approach are the B_avail, the receptors available in vivo to bind to [¹¹C]raclopride and appK_D the apparent affinity of [¹¹C]raclopride for the D2 receptor (Innis et al., 2007). The interaction between the binding of endogenous dopamine and [¹¹C]raclopride to D2 receptors has not yet been elucidated, however, it was shown in Leriche et al. (2009) that there is a correlation between the in vitro measured binding parameters B_max and K_D, and the in vivo receptor density and affinity as estimated using the Scatchard approach from Delforge et al. (1993). This indicates that at a baseline level, the B_avail estimated remains unaffected by endogenous ligand, whereas the appK_D is affected.

$$\frac{\mathit{B}}{\mathit{F}}=\frac{{\mathit{B}}_{\mathit{max}}-\mathit{B}}{{\mathit{K}}_{\mathit{D}}}$$

The equilibrium equation that applies to this approach is shown in Eq. (1) with B = bound concentration of ligand and F = free concentration of ligand. To utilise the Scatchard plot in vivo, Farde et al. (1986) proposed a method where a series of PET experiments with varying specific activities (receptor occupancy levels) on the same individual were used in saturation experiments to determine the B_avail (available receptor density in vivo) and appK_D (Farde et al., 1986, Farde et al., 1989). Following that, a method which uses one scan with multiple injections of the tracer with different ligand concentrations was developed (Delforge et al., 1993). Multiple injection studies with no blood sampling have been done by Ikoma et al. (2010) using a slightly modified version of the Simplified Reference Tissue Model (SRTM) and a Scatchard like plot. These methods generally require blood sampling to generate an arterial input function needing arterial cannulation, multiple scans or injections, long time anaesthesia (up to 3 h) and/or sophisticated experimental procedures and are therefore not feasible for use in longitudinal mouse imaging studies.

Reference tissue methods, such as the SRTM by Lammertsma and Hume (1996) do not use an arterially sampled input function and are therefore simpler than the abovementioned methods. These methods use the kinetic from a region devoid of receptors in place of the arterially sampled input function. Commonly, the reference tissue methods are used to determine the BP_ND (Innis et al., 2007)_, which is a ratio of B_avail and appK_D, however a change in BP_ND can result from a change in B_avail and/or appK_D which can confound the interpretation of changes in the parameter.

The partial saturation approach (PSA) was originally proposed by Delforge et al., 1995, Delforge et al., 1996 to estimate the B_avail and appK_D independently in a single injection, single scan experiment without blood sampling using [¹¹C]FMZ. The method is based on setting up an “in vivo equilibrium state” after a single injection of the ligand of sufficient mass to partially saturate the target receptors. The method exploits the natural decrease in bound ligand concentration to give a range of values needed for a Scatchard analysis. It requires a dose of the ligand that is sufficiently large to occupy a significant percentage of receptor sites but not too large so as a significant decrease can be observed during the limited time of the scan (1 h at most). The desired level of receptor occupancy should be at least 50% (Delforge et al., 1996) and ideally should be 60–70%. In addition, the receptor binding kinetic parameters, the association rate constant (k_on) and the dissociation rate constant (k_off) need to be fast enough to ensure a reasonable decrease of ligand concentration over the period of the PET scan. If an apparent equilibrium state can be achieved, where the ratio between the B and the F (the concentration of non displaceable ligand) has negligible change, the equilibrium equation as shown in Eq. (1) will be valid. The method requires the use of an independent measurement of the free ligand concentration, which is estimated using the concentration of ligand in a reference region free from any target receptors.

To be able to apply the PSA confidently, the following assumptions should be validated for a range of experimental conditions, firstly, the reference region has a kinetic curve that reflects the free ligand within the target area, secondly, a time window of the scan period should be used so that a dynamic in vivo equilibrium state is set up and thirdly, the occupancy of the receptors is adequate to allow a good range of bound and free ligand concentrations over the time of the PET scan.

The longitudinal study of neurodegenerative disease in the mouse can be difficult due to long and complex experimental protocols, difficulties with cannulation, and no a priori information about the receptor system. It would be ideal to have a simple, single injection protocol, such as the PSA, that could produce stable and robust B_avail and appK_D estimates for a range of receptor occupancy levels and disease states. With that in mind the aim of this study was to increase the range and applicability of the PSA by developing a data driven strategy for determining B_avail and appK_D, and validating the strategy using a simulation model based on experimental mouse data. The strategy defines the range where robust and accurate estimates are produced for a range of healthy and diseased states with the ultimate goal being to generalise the method for use with [¹¹C]raclopride PET experiments in the mouse brain.