Estimating neurotransmitter kinetics with ntPET: A simulation study of temporal precision and effects of biased data

Abstract

We recently introduced neurotransmitter PET (ntPET), an analysis technique that estimates the kinetics of stimulus-induced neurotransmitter (NT) release. Here, we evaluate two formulations of ntPET. The arterial (ART) approach measures the tracer input function (TIF) directly. The reference (REF) approach derives the TIF from reference region data. Arterial sampling is considered the gold standard in PET modeling but reference region approaches are preferred for reduced cost and complexity. If simulated PET data with unbiased TIFs were analyzed using ART or REF, temporal precision was better than 3 min provided NT concentration peaked less than 30 min into the scanning session. The consequences of biased TIFs or stimulus-induced changes in tracer delivery were also evaluated. ART TIFs were biased by the presence of uncorrected radiometabolites in the plasma whereas REF TIFs were biased by specific binding in the reference region. Simulated changes in tracer delivery emulated ethanol-induced blood flow alterations observed previously with PET. ART performance deteriorated significantly if metabolites amounted to 50% of plasma radioactivity by 60 min. The accuracy and precision of REF were preserved even if the reference region contained 40% of the receptor density of the target region. Both methods were insensitive to blood flow alterations (proportional changes in K₁ and k₂). Our results suggest that PET data contain information – heretofore not extracted – about the timing of NT release. The REF formulation of ntPET proved to be robust to many plausible model violations and under most circumstances is an appropriate alternative to ART.

Introduction

Researchers have used PET and SPECT to detect acute changes in endogenous neurotransmitter (NT) concentration by its displacement of receptor ligand tracers. PET and SPECT studies have detected NT release in response to pharmacological challenges, including amphetamine (e.g., Dewey et al., 1993, Innis et al., 1992, Laruelle et al., 1995, Mach et al., 1997), cocaine (Mach et al., 1997, Volkow et al., 1999), methylphenidate (Mach et al., 1997, Spencer et al., 2006, Volkow et al., 1999, Volkow et al., 1994) and other drugs, as well as behavioral challenges such as videogaming (Koepp et al., 1998), gambling and monetary reward (Pappata et al., 2002, Zald et al., 2004), and other tasks. In conventional PET analyses, NT release is detected by change in binding potential (BP: e.g., Logan et al., 1996, Logan et al., 1990), an index of the time-averaged decrease in receptor availability from baseline to activation condition. Novel methods to detect changes in NT concentration have been proposed (Alpert et al., 2003, Aston et al., 2000, Friston et al., 1997, Pappata et al., 2002, Zhou et al., 2006), but these techniques, like change in BP, provide limited or no information about the timing of NT release. To recover potentially important variations in the timing of neurotransmitter fluctuations, we have developed neurotransmitter PET (ntPET), a modeling and parameter estimation method which characterizes the temporal profile of NT release by combining PET data from rest (constant NT) and activation (time-varying NT) conditions and fitting them simultaneously (Morris et al., 2005).

PET and SPECT studies have revealed the in vivo spatial distribution of various neuroreceptors and transporters and their possible implications in pathological states such as schizophrenia (Buchsbaum et al., 2006, Talvik et al., 2003), alcoholism (Heinz et al., 1998, Szabo et al., 2004), and epilepsy (Fedi et al., 2006, Picard et al., 2006). However, the time course of neurotransmitter release in response to specific stimuli has not been measured in humans and may encode pertinent information about brain function. It has been hypothesized that the speed of dopamine release elicited by a drug may be a strong indicator of the drug’s addictive liability and potential for abuse (Spencer et al., 2006, Volkow et al., 1995, Volkow et al., 1999, Volkow and Swanson, 2003). Boileau et al. (2007) speculated that amphetamine- and placebo-induced dopamine responses may follow distinct time courses, but noted that PET was not capable of distinguishing such differences. An imaging-based method for measuring the temporal profile of NT release, with sufficient resolution and accuracy, would constitute a new tool for addressing such speculations and for evaluating drug action more broadly.

Dynamic PET data reflecting the uptake and retention of receptor tracers has been modeled successfully with the two-tissue compartment model (Mintun et al., 1984). In applying the two compartment model to the data, one assumes a constant concentration of any competitor, such as an endogenous NT. More complicated models (Endres et al., 1997, Morris et al., 1995) have been introduced to accommodate time-varying concentrations of endogenous species. With these models, one can predict the effect of a transient increase in NT level on the dynamic PET data. These models necessarily require more parameters than the Mintun model.

To estimate more than the four parameters of the standard model from PET data, some investigators have tried to increase the information content of the data by experimental manipulation of the system. Along these lines, multiple injections of tracer at different specific activities have been administered during a single scan session (Christian et al., 2004, Delforge et al., 1989, Delforge et al., 1990, Huang et al., 1989, Millet et al., 2000, Morris et al., 1996a, Morris et al., 1996b, Muzic et al., 1996). Multiple injection approaches facilitate observation of the system at multiple operating points; model fitting of all the data simultaneously leads to improved identifiability of parameters. Our implementation of ntPET can be seen as an extension of the multiple injection concept to a two-scan protocol in which we manipulate the neurotransmitter concentration through pharmacological or cognitive stimulation rather than the concentration of unlabeled tracer. The system is observed in the rest state during one scan and in activation during the other. Data from both scan conditions are analyzed simultaneously. The parameters that describe the uptake and retention of tracer (Θ_TR) and the parameters that describe the profile of NT release in the activation condition (Θ_NT) are estimated concurrently.

In previous PET data analyses, the use of penalty functions has been demonstrated to improve the precision of estimated parameters at the expense of increased bias (Bertoldo et al., 2004, O’Sullivan and Saha, 1999, Zhou et al., 2001, Zhou et al., 2002). Under certain conditions, constrained optimization can yield parameter estimates which minimize the objective function but fit the data poorly (Muzic and Christian, 2006). The ntPET approach, however, uses penalty terms based on prior experimental information in order to promote robust performance.

All compartmental models are driven by one or more input functions. There are two common methods for obtaining the tracer input function (TIF) for PET modeling. One is to obtain arterial blood samples, which can be processed to measure the tracer concentration in arterial plasma. The other is to formulate the TIF in terms of PET data acquired in a reference region that has negligible receptor density (Blomqvist et al., 1990, Cunningham et al., 1991). Arterial sampling is believed to yield an accurate measurement of the TIF and is considered the gold standard in PET modeling, but surgical cannulation of an artery and processing of blood samples can be quite burdensome. Reference region approaches simplify the protocol and reduce costs, although they introduce additional model assumptions. We have developed two variants of ntPET: one which measures the TIF from arterial blood samples (the ART method) and another which derives the TIF from reference region data (the REF method).

All models make assumptions, either explicitly or implicitly. PET models implicitly assume that the TIF is accurately measured. Incorrectly measured input functions may increase the bias and/or variance of estimated parameters. Activation paradigms are known to change regional cerebral blood flow to the brain regions that respond to the stimulus – indeed, this is the underlying principle in functional neuroimaging based on the blood oxygenation level-dependent (BOLD) effect (Kwong et al., 1991, Ogawa et al., 1990). However, changes in blood flow might confound models which assume that flow to the region of interest is constant during the scan. More generally, models with constant coefficients assume that the physiological parameters are constant throughout the study. Many model assumptions are not completely satisfied in practice, so we sought to quantify the impact of likely violations on the estimation of NT profiles.

In this paper, we examine the consequences of model violations on the precision and accuracy of the NT profiles estimated by ntPET from realistic simulated PET data. In particular, we studied the effect of biased TIFs and activation-induced changes in blood flow. The ART and REF variants of ntPET derive their respective TIFs from different measurements, so the relevant model violations that we investigated were necessarily different. To test the robustness of the ART method, we supplied it with arterial plasma curves that were not corrected for the presence of labeled polar metabolites. To test the REF method, we provided it with PET data from non-ideal reference regions that contained receptors. To test the effects of activation-induced changes in tracer delivery, we analyzed simulations of NT release accompanied by blood flow changes and also simulations of flow changes alone. The precise nature of activation-induced alteration of tracer delivery and its impact on blood flow parameters (i.e., K₁ and k₂) remains unclear (Alpert et al., 2003, Logan et al., 1994, Pappata et al., 2002), so multiple scenarios were examined. Based on our results, we offer recommendations on the practical application of the ART and REF formulations of ntPET, including the conditions under which the REF method could serve as an acceptable substitute for the more demanding, but perhaps more accurate, ART method.