Limitations of SRTM, Logan graphical method, and equilibrium analysis for measuring transient dopamine release with [¹¹C]raclopride PET

Abstract

Conventional PET methods to estimate [¹¹C]raclopride binding potential (BP _ND) assume that endogenous dopamine concentration does not change during the scan time. However, this assumption is purposely violated in studies using pharmacological or behavioral stimuli to invoke acute dopamine release. When the assumption of steady-state dopamine is violated, conventional analysis methods may produce biased or even unusable estimates of BP _ND. To illustrate this problem, we examined the effect of scan duration on ΔBP _ND estimated by three common analysis methods (simplified reference tissue model, Logan graphical reference method, and equilibrium analysis) applied to simulated and experimental single-scan activation studies. The activation – dopamine release – in both the simulated and experimental studies was brief. Simulations showed ΔBP _ND to be highly dependent on the window of data used to determine BP _ND in the activation state. A similar pattern was seen in the data from human smoking studies. No such pattern of ΔBP _ND dependence on the window of data used was apparent in simulations where dopamine was held constant. The dependence of ΔBP _ND on the duration of data analyzed illustrates the inability of conventional methods to reliably quantify short-lived increases in endogenous dopamine.

Introduction

Traditional analysis of dynamic [¹¹C]raclopride positron emission tomography (PET) studies includes estimating [¹¹C]raclopride binding potential (BP _ND) – a static parameter that represents the potential for specific binding of [¹¹C] raclopride to dopamine (DA) D2/D3 receptors in the brain. This is usually accomplished by fitting the dynamic data with compartmental or graphical (linearized) models, such as the simplified reference tissue model (SRTM) [1] or the Logan graphical method [2,3]. There are no time-varying parameters in any of the conventional models. Thus, a basic assumption of these models is that endogenous dopamine (DA) concentration is at steady-state and does not change during the course of the scan.

However, experiments are often conducted for which the assumption of steady-state DA concentration is purposely violated in order to measure changes in synaptic DA due to a pharmacological or behavioral challenge. In these studies, BP _ND is measured at rest (no challenge) and after a challenge. An increase in endogenous DA in the challenge condition competes with the radiotracer for binding at the receptor and results in lower BP _ND values relative to the rest condition [4]. In this “competition model”, decreases in BP _ND are used as an index of DA release following a wide variety of pharmacological stimuli, including amphetamine [5-7] and nicotine [8-15].

A decrease in BP _ND has been shown to be a robust and reliable index of amphetamine-induced DA release. Amphetamine has been shown to produce large increases in DA concentration [16-18] that peak over 600% above baseline [17]. It has also been shown to provoke long-lasting displacement of [¹¹C]raclopride (potentially due, in part, to receptor internalization [4,19]) and greater than 20% decrease in BP _ND [5]. Conventional analysis methods, such as SRTM, Logan graphical method (“Logan plot”), and equilibrium methods, have been able to reproducibly estimate sustained decreases in BP _ND for varying doses of amphetamine administered under a variety of experimental conditions in both humans and animals.

In contrast, it is unclear whether nicotine-induced DA release can be detected by decreases in [¹¹C]raclopride BP _ND. Based on a study of human subjects smoking 1 cigarette during a break in a scan with bolus-plus-constant-infusion (B/I) of [¹¹C]raclopride, Brody et al. reported 30% decrease in BP _ND after smoking in the left ventral caudate [13]. In later studies with larger cohorts and a more advanced scanner, but the same protocol, Brody et al. reported only 8% decrease in [¹¹C]raclopride BP _ND [9-12]. Scott et al. reported a similar decrease in BP _ND (~10%) between regular and denicotinized cigarettes smoked while in the scanner [15]. However, only 1% decrease was reported by Montgomery et al. in [¹¹C]raclopride BP _ND in response to 2mg nicotine nasal spray administered during scanning [20], and a study by Barrett et al. requiring subjects to smoke up to 6 cigarettes during the scan measured highly variable changes in [¹¹C]raclopride BP _ND (range of +57% and -67% change in BP _ND) in the ventral striatum and caudate [8].

We believe that the between-study and within-study variability in nicotine-induced decrease in BP _ND reported in the literature may be due to violations of the assumption that endogenous DA concentration remains at steady-state during the challenge condition. Unlike amphetamine, which is a direct releaser of DA, nicotine only indirectly causes transient increases in DA concentration and transient displacement of [¹¹C]raclopride. Microdialysis studies have shown that nicotine, in doses comparable to what a human would self-administer by smoking, produces a brief 125% increase in DA which returns to baseline within 30 min [21]. Nicotine challenges in PET studies may also cause transient decreases in [¹¹C]raclopride signal which return to baseline levels just as quickly. Because of amphetamine’s long-lasting effects on DA release and tracer displacement, [¹¹C]raclopride reaches a new equilibrium state after challenge and BP _ND can be estimated by conventional models without appreciably violating the assumption that endogenous DA concentration is not changing during the scan. For nicotine challenges, DA concentration and tracer binding are continuously changing and [¹¹C]raclopride does not reach a new equilibrium state. In this scenario, specific binding of [¹¹C]raclopride will not be constant during the challenge scan and any attempt to estimate BP _ND with conventional methods will produce an estimate which is a weighted-average of the specific tracer binding as it changes over the course of the challenge scan [22]. This could result in a reduced measure of nicotine-induced decrease in BP _ND, which, coupled with a small effect size and inter-subject variability, could easily obscure detection of a significant decrease in BP _ND due to DA release from nicotine.

To investigate if inappropriate application of conventional modeling approaches could obscure detection of nicotine-induced DA release, we examined the effect of scan duration on decrease in BP _ND estimated by SRTM, Logan plot, and equilibrium analysis. We applied these analyses to simulated single-scan activation studies and human smoking studies. An observed dependence of ΔBP _ND on the duration of data analyzed suggests that conventional methods are not well-suited to reliable quantification of short-lived increases in endogenous DA.

Materials and methods

Simulations

Noiseless and noisy striatal [¹¹C]raclopride time activity curves (TACs) with varying amounts of DA release were simulated using an enhanced tracer kinetic model (Figure 1) [23]. This model includes state variables for free and bound dopamine and it includes rate constants for the tracer as well as binding and dissociation of DA to and from the receptor. TACs based on a B/I of tracer were simulated for a scan duration of 120 min consisting of 1-min frames.

Figure 1.

The enhanced tracer kinetic model accounts for variations in tracer concentration as well as endogenous dopamine (DA) [23,40]. Free (F ^DA) and bound (B ^DA) endogenous DA are represented by the compartments at top, where k _on ^DA and k _off ^DA are the association and dissociation rate constants for DA at the receptor. The standard two-tissue compartment model at bottom includes compartments for the tracer free in tissue (F) and specifically bound (B) to the receptor of interest. Rate constants describe the movement of tracer between plasma (C _p) and tissue (K ₁, k ₂) and binding to the receptor (k _on and k _off). The competition between the tracer and endogenous DA for a limited number of receptor sites is represented by the dotted-line box around B ^DA and B compartments.

For all simulations, striatal parameters were set as K ₁ = 0.0918 mL/min/g, k ₂ = 0.4484 min^-1, k _on= 0.0282 mL/(pmol · min), k _off = 0.1363 min^-1, B _max = 44 pmol/mL, and F _v = 0.04 mL/mL [24]. DA binding parameters (association and dissociation rate) were set as k _on ^DA = 0.25 mL/(pmol · min) and k _off ^DA = 25 min^-1 [23]. A noiseless cerebellum TAC was also simulated using the same model by setting k _on and k _off to 0. All simulations were implemented in MATLAB (R2006a, MathWorks, Inc., Natick, MA) using modeling functions provided by a library of COMKAT [25].

Dopamine release

Free DA (F ^DA) was modeled as a gamma variate plus a constant baseline with the start of DA release, t _d, set at 40 min post tracer injection (Equation 1):

Baseline DA level (DA ^basal) was set to 100 pmol/mL [26]. Free DA curves with a fixed peak height but increasing area-under-the-curve (AUC) were created by varying α, β, and γ, parameters which specify the shape and magnitude of a gamma variate. Five different DA signals were created: [α, β, γ] = [2, 2, 800], [2, 1, 200], [2, 0.5, 50], [2, 0.25, 12.5], [2, 0.15, 4.5] (Figure 2). All DA signals were designed to represent plausible cases of transient DA release (defined as returning to baseline during the course of the simulated scan). Total DA released was measured as the area under F ^DA(t) - DA ^basal from t _d to the end of the scan (e.g., 40 min to 120 min post injection) and ranged from 190-2665 (pmol·min)/mL. Noiseless and noisy Rest TACs with no DA perturbation were simulated by setting γ to 0.

Figure 2.

Dopamine (DA) signals with increasing area-under-the-curve (AUC) but same peak height (A) were used to simulate noiseless (B) and noisy (C) striatal time activity curves (TACs). All DA signals produced visually noticeable decreases in the noiseless simulated TACs. These decreases were less visually apparent for transient DA signals in the noisy simulated data (for ease of visualization, only one noisy curve is shown here). In (A), DA signals increase in width as β decreases.

Noise

Monte-Carlo simulations were used to produce 100 noisy PET TACs for each DA signal. Additive Gaussian noise proportional to the imaged PET activity was added to the noiseless, simulated curves [27,28] (Equation 2):

where ROI(t) is the noiseless, decay-corrected TAC, G(0,1) is a pseudo-random number from a Gaussian distribution with 0 mean and standard deviation of 1, and SD(t) is the standard deviation of the noise (Equation 3):

In this noise model, c is the proportionality constant which determines the noise level, λ is the decay constant for C-11, and Δt is the simulated frame length. The term e ^-λt applies decay to the decay-corrected ROI(t) while the term e^λt decay-corrects the standard deviation. The constant c was set to 0.002 to produce a noise level similar to that seen in regional-level TACs extracted from the ventral striatum in [¹¹C] raclopride studies completed on the High Resolution Research Tomograph (HRRT; Siemens/CTI, Knoxville, TN, USA).

Human experiments

Subjects

Healthy smokers (n = 4, 2M/2F) were recruited as subjects for a study investigating the effect of cigarette smoking and the temporal pattern of DA release. Subjects were screened to determine medical history and personal and familial psychiatric and smoking history. They were excluded from the study if they met criteria for any Structured Clinical Interview for DSM-IV Axis 1 Disorders except Nicotine Dependence. Severity of nicotine dependence was assessed by the Fagerström Test for Nicotine Dependence (FTND). Only subjects with an FTND score > 3 were included in this study. Smoking status was confirmed by breath CO levels > 12 ppm and urine cotinine levels > 150ng/mL at intake. Smokers smoked 15 ± 6 cig/day for 13 ± 15 yr. Written informed consent was obtained from all subjects before the study but only after complete explanation of the study procedures. All study procedures were approved by the Yale University Human Investigations Committee (HIC).

Experimental design

Prior to PET imaging, each subject received a 3T structural MRI using a 3D fast spoiled grass (FSPGR) MR pulse acquisition sequence with an IR prep of 300 ms (TE = 3.3 ms, flip angle = 17 degrees; slice thickness = 1.2 mm). Subjects received up to two [¹¹C]raclopride scans (rest and smoking) on separate days. Only the data from the smoking scan were used in these analyses. [¹¹C]raclopride was synthesized as reported previously [29]. Coincident with a B/I of [¹¹C]raclopride (685 ± 55 MBq, mean ± standard deviation), list-mode data were acquired for 120 min on the HRRT. A transmission scan was conducted immediately prior to the dynamic scan for attenuation correction. The Vicra optical tracking system (Vicra, NDI Systems, Waterloo, Canada) was used to measure and record subject head movement during each scan. The Vicra records subject head motion in quarternions at a rate of 20Hz from a rigid tool with reflective spheres attached to each subject’s head via a swim cap.

Smoking challenge

During the smoking scan, 3 of 4 subjects were asked to smoke 2 consecutive cigarettes, beginning 45 min after the initial bolus of [¹¹C]raclopride. One female subject was asked to smoke two cigarettes ~30 min apart. The first cigarette was at 53 min; the second was cigarette at 87 min after time-of-injection (TOI).

All subjects were allowed to smoke their own brand of cigarette. Immediately prior to the start of smoking, a study investigator informed the subject that they were about to start smoking. The investigator handed the subject a cigarette, which the investigator lit with a long-reach lighter once the subject had placed the cigarette in his/her mouth. Subjects were instructed to smoke at their typical pace while remaining as still as possible. A small basin was provided at the subject’s chest as an ashtray. An investigator monitored the smoking session, and when subjects finished smoking each cigarette, they dropped it into the basin which the study investigator removed immediately to extinguish the cigarette. Each subject was asked if he/she felt they could smoke a second cigarette (either immediately following the first cigarette or 30 min later). All subjects accepted and smoked a second cigarette. A freestanding air exhaust and filtration system (Movex Inc, Northampton, PA) that had been previously approved by the Yale Environmental Health and Safety Office was used to capture and filter second-hand smoke.

Data processing

Dynamic scan data were reconstructed iteratively with all corrections, including motion using the information collected by the Vicra, by the MOLAR algorithm [30] with the following frame timing: 40 x 3 min. Frame-by-frame motion correction was also performed by registering each frame to an early summed (0 – 9 min) image using a six-parameter mutual information algorithm (FLIRT, FSL 3.2, Analysis Group, FMRIB, Oxford, UK). A summed (0 – 9 min) motion-corrected image was then registered to each subject’s MR, which was warped to an AAL MR template. Anatomically-based striatal regions of interest (ROIs) were defined on the template in the left and right dorsal caudate, left and right dorsal putamen, and left and right ventral striatum [31] (based on Martinez et al. and Mawlawi et al. [6,32]). TACs were extracted from these regions as well as from an AAL-defined cerebellum (reference region).

Estimating BP_ND

BP _ND was estimated for each simulated TAC and all experimental data via SRTM [1], the Logan graphical method using a reference tissue as input (“Logan plot”) [2], and equilibrium analysis (EQ) [33,34]. We chose these methods because they have been used previously to estimate [¹¹C]raclopride BP _ND in studies seeking to measure smoking- or nicotine-induced DA release. The main outcome measure considered in these studies, ΔBP _ND, was calculated as the percent difference between BP _ND ^Baseline and BP _ND ^Activation (Equation 4):

Because we focused on a single-scan study design, BP _ND ^Baseline was estimated by fitting 0-35 min of data (simulated or experimental) with SRTM and Logan plot (0 min represents time of injection). Previous studies have indicated that cues for reward may contribute to DA release [35]. Subjects in human experiments were aware that they would be smoking 45 min after the start of the scan, and study investigators entered the scanning suite up to 5 min before the start of the smoking session. To ensure that the potential cue of study investigators entering the scanning suite did not induce DA release (i.e., expectation prior to smoking) which could bias the BP _ND ^Baseline value, only 35 min of data were used to calculate BP _ND ^Baseline. For EQ, BP _ND ^Baseline was taken as the average BP _ND from 30-40 min. To test the effect of activation scan duration on ΔBP _ND, BP _ND ^Activation was estimated from increasingly wider data windows by fitting 0 - m minutes of simulated and experimental data with SRTM and Logan plot, where m = [40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 115, 120]. For EQ, BP _ND ^Activation was taken as the average BP _ND from 40 - n minutes, where n was [45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120].

Simplified reference tissue model (SRTM)

SRTM [1] assumes that tracer activity in both the ROI and reference region can be described by a 1-tissue compartment model. The three model parameters, R₁, k₂’, and k_2a, were estimated by fitting SRTM to TACs using the following operational equation (Equation 5):

where C_T(t) is the activity of the tracer in the tissue, C _Ref(t) is the activity of the tracer in the reference region, R ₁ = K ₁/K ₁’, the ratio of K ₁ in the target tissue to K ₁’ in the reference tissue, k ₂’ is the efflux rate from the reference region, and k _2a is the apparent efflux rate of tracer from the target region. The cerebellum was used as the reference region and cerebellar TACs were presmoothed by fitting to a sum of exponentials. Parameters were estimated using unweighted least squares. Nonlinear parameter estimation was performed using a Marquardt-Levenberg algorithm [36] and custom software for IDL (8.0 ITT Visual Information Solutions, Boulder, CO). BP _ND was calculated as (Equation 6):

Logan graphical method using a reference tissue as input

The Logan graphical method using a reference tissue as input relies on the integration of tracer kinetic equations to yield a simple, linear equation whose slope equals the distribution volume ratio (DVR) of the tracer [2] (Equation 7):

The Logan graphical technique proposes that after some time t*, int’ is constant and the plot of ∫ ₀ ^tC_T(u)du/C_T(t) vs. ∫₀^tC_Ref(u)du/C_T(t) becomes linear with slope DVR. In all Logan graphical method analyses, t* was fixed at 15 min and the cerebellum was used as the reference region. BP _ND was then calculated as DVR-1.

Equilibrium analysis (EQ)

When tracer concentration is at equilibrium, BP _ND is the ratio of the difference between target tissue concentration C_T,EQ to reference tissue concentration C_Ref,EQ, relative to the reference tissue concentration (Equation 8). BP _ND is calculated as an average over multiple time frames:

where the superscript bar indicates average over some range of time frames. Equilibrium was achieved by 30 min in both simulated and experimental data.

Results

Simulations

Effect of dopamine signal on simulated time activity curves

Inclusion of a time-varying DA signal (Figure 2A) produced decreases in the simulated TACs dependent on the magnitude of the DA signal input (Figure 2B). Degree of deflection in TAC values following onset of DA release was significantly correlated (R²=0.96, p<0.005) with total DA concentration. Consistent with the transient nature of the DA inputs, activity level in many of the noiseless simulated TACs returned to baseline during the course of the scan (Figure 2B). In noisy simulations (Figure 2C), this effect was not easily visible with the naked eye.

Effect of transient dopamine signal on SRTM fitting

Fits of SRTM to simulated TACs containing DA release were poor (Figure 3A). Fits to simulated TACs containing DA release had greater residual sum of squares than fits to rest TACs for activation scan window durations of 40 min or greater (the time of DA release start in simulations). After initiation of DA release, the shape of each fit became dependent on the duration of data used (Figure 3A). As the data window was widened to include more of the transient dip in the TAC, the fitted curves were pulled down relative to the simulated data. Fitted curves went back up again as the data window was widened even more to include later data points unaffected by the transient DA release. The same effect was seen when fitting SRTM to experimental data, though a deflection in experimental TACs at time of smoking was not easily visible (Figure 3B).

Figure 3.

Example of SRTM fits of varying data window length to representative simulated (A) and experimental (B) data which contains dopamine DA release. DA release in the simulated curve is represented by a gamma variate function (Equation 1) with [α, β, γ]=[2, 0.5, 50]. Solid lines are fits. The inset in A is a close-up of the boxed section of the graph. To aid visualization in the inset, the last time point included in the fit to the data for each data window is indicated by a vertical line. The shape of each fit (and thus the BP _ND) is dependent on the amount of data used. Logan plots of the full 120-min simulated (C) and experimental (D) curves in A and B. In the simulated data, the slope of the Logan plot during DA release is changing (indicated by arrow), but the slopes before and after DA release are the same. This same effect is not visible in the Logan plot of experimental data.

Effect of transient dopamine signal on Logan plot

Fits to the linear portion of the Logan plots were also dependent on the duration of data used. The fits varied with data window width and the size of the DA-induced changes in TACs. Subtle deviations from linearity, beginning at the onset of DA increase, were observed in the transformed data in Logan plot space for noiseless data (Figure 3C). However, the slopes of the transformed data before and after the time of DA release were the same. Deviations from linearity were not observed in the Logan plots of experimental data (Figure 3D).

Effect of scan duration on ΔBP_ND

ΔBP _ND varied based on the duration of data used to determine BP _ND in the activation state for both noiseless (Figure 4) and noisy (Figure 5) simulations. This effect was seen for all DA signals tested. In simulations, a distinct pattern was seen: ΔBP _ND increased as activation window duration increased, until reaching a maximum at some window width (generally 20-40 min after onset of DA release), after which ΔBP _ND decreased with even wider activation window. The activation window width for which ΔBP _ND was maximal varied by DA signal shape. Maximum ΔBP _ND was found at longer activation windows for greater total DA release (Table 1). Note: greater total DA release was associated with later DA peak in our simulations. For a given DA signal, ΔBP _ND values were highest when estimated by SRTM and lowest when estimated by the Logan graphical approach. For smaller DA responses (e.g., β=1), this resulted in negative ΔBP _ND values for some activation window widths, an effect which was exacerbated by noise (Figure 5).

Figure 4.

Effect of scan duration on ΔBP _ND estimated by SRTM (left column), Logan (middle column), and EQ (right column) for all noiseless simulated TACs. Each row represents the results from a noiseless simulated TAC containing the DA signal indicated by the β value. For all graphs, the dependent axis is ΔBP _ND and the independent axis is activation window width in min.

Figure 5.

Effect of scan duration on ΔBP _ND estimated by SRTM (left column), Logan (middle column), and EQ (right column) for all noisy simulated TACs. Points are mean values and error bars are SD of 100 noisy curves. Each row represents the results from noisy simulated TACs containing the DA signal indicated by the β value. For all graphs, the dependent axis is ΔBP _ND and the independent axis is activation window width in min.

Table 1.

Maximum ΔBP _ND values from noiseless simulation data

	Maximum ΔBP ND (%)			Activation window width for maximum ΔBP ND (min)
DA signal	SRTM	Logan	EQ	SRTM	Logan	EQ	DA peak time
β=2	3%	1%	2%	60	55	40-50	41
β=1	5%	3%	4%	60	60	40-55	42
β=0.5	8%	6%	7%	65	65	40-60	44
β=0.25	12%	10%	11%	75	75	40-75	48
β=0.15	15%	14%	14%	90	90	40-85	53

Rest data

All analyses were also performed on noiseless and noisy simulated Rest data (containing no DA release). ΔBP _ND from Rest scan data (ΔBP _ND ^Rest) did not vary noticeably by activation scan duration in any method tested (SRTM, Logan, or EQ) (Figure 6). In noisy simulations, there were biases in ΔBP _ND ^Rest; for an activation window of 120 min ΔBP _ND was 0.8% ± 6.1% for SRTM, -4.1% ± 7.0% for the Logan graphical approach, and -1.0% ± 3.7% for EQ.

Figure 6.

Effect of scan duration on ΔBP _ND estimated by SRTM (left column), Logan (middle column), and EQ (right column) for Rest data. Points are mean values and error bars are SD of 100 noisy curves. ΔBP _ND ^Rest values did not vary with activation scan window duration.

Human experiments

ΔBP _ND was observed to vary with activation scan duration in experimental data from 4 human subjects (Figure 7). A similar pattern to that seen from analysis of simulated data can be seen clearly in the left ventral striatum in the 2 male subjects and left dorsal caudate in the 2 female subjects (Figure 8). Dependence of ΔBP _ND on activation scan duration was not seen in other regions examined in these 4 subjects.

Figure 7.

Binding potential (BP _ND) images from a male subject who smoked two cigarettes at 45 min after time of injection. A. BP _ND estimated by SRTM from 120 min of data. B. BP _ND estimated by SRTM from 70 min of data. Both images show the same coronal slice through the striatum, and images are on the same intensity scale. Throughout the striatum, BP _ND values estimated from only 70 min of smoking scan data are lower than those estimated from the full 120 min of data. In ΔBP _ND calculations, this will result in greater ΔBP _ND for 70 min of smoking scan data than 120 min of smoking scan data.

Figure 8.

Effect of scan duration on ΔBP _ND estimated by SRTM (left column), Logan (middle column), and EQ (right column) for experimental data. Arrows indicate times at which cigarettes were smoked. ΔBP _ND values estimated from human smoking studies were dependent on the activation scan window duration. The pattern seen in simulations was identified in the left ventral striatum (top two rows) of two male subjects (M1 and M2) and in the left dorsal caudate (bottom two rows) of two female subjects (F1 and F2). Note: Unlike subjects M1, M2, and F1, who smoked 2 cigarettes at 45 min after time of injection (TOI), subject F2 smoked two cigarettes ~30 min apart, at 53 min and 87 min after TOI.

Discussion

This study examined the effect of the duration of the activation scan on ΔBP _ND estimated with SRTM, Logan plot, and EQ applied to PET data containing effects of transient DA release. Through analysis of simulations, we showed that the magnitude of ΔBP _ND is dependent on the amount of activation scan data used in estimation of BP _ND ^Activation. We found a similar effect in human data from a study of smoking-induced DA release. We believe that together, these findings illustrate the limitation of applying standard analysis methods to data acquired while the endogenous DA signal was varying rapidly during the scan.

The methods used in this study assume that BP _ND is a static parameter. For a method to be fruitful and reliable, varying the length of the scan data fitted should not change the BP _ND value estimated. As we show in our analysis of simulated Rest data (Figure 6), ΔBP _ND ^Rest didn’t vary with activation scan duration. A slightly biased ΔBP _ND ^Rest was found by all methods and was greatest with the Logan plot. This suggests that more than 35 min of data may be necessary for these methods to produce unbiased BP _ND estimates. In the case of the Logan plot, a longer t* for shorter scan durations (e.g. 35 min) may reduce this bias. Noise has also been shown to introduce a negative bias in BP _ND estimated by the Logan plot [37].

Unlike simulated Rest data, ΔBP _ND varied with the activation scan duration for simulated data containing transient DA release. ΔBP _ND tended to decrease as more data after onset of DA release was included in the analysis (i.e. the data window was widened). Because the DA release in our simulations was transient and the effect of DA release on the tracer signal was brief, inclusion of data beyond the period of DA release appears to have washed out the effect of the DA release on ΔBP _ND. This suggests that at typical scan durations (90 min-120 min) used in [¹¹C]raclopride studies, ΔBP _ND measured by these common methods may have low sensitivity to transient DA release.

Endres and Carson [22] showed that when neurotransmitter release is time-varying, distribution volume (and hence binding potential) ΔBP _ND is a time-weighted average of ΔBP _ND(t) weighted by the free tracer concentration [22]. Our simulations are a demonstration of this principle. We also show that if DA release is transient and total DA release is modest, it may not be detectable via ΔBP _ND depending on the duration of activation scan data analyzed. This is due not only to the kinetics of endogenous DA but also those of the tracer. Yoder et al. [38] showed that ΔBP _ND is dependent on the relative timing and kinetics of both the tracer and the endogenous ligand. In our simulation studies, onset of DA release was 40 min after time of injection. Had DA release occurred earlier during the activation scan, ΔBP _ND would be even smaller for longer (90, 120 min) scan durations because there would be more PET data which had returned to baseline levels after DA release included in the estimation of BP _ND ^Activation. This would further decrease the likelihood of detection of transient DA release by ΔBP _ND for typical [¹¹C]raclopride scan durations of 90 or 120 min.

Our simulations suggest that the discrepancy in ΔBP _ND between findings in two separate smoking studies by Brody et al. [11,13] may be due solely to differences in the amount of data used to estimate BP _ND ^Activation. In the studies by Brody et al., subjects were scanned for 50 min, taken off the camera for 10 min with the tracer infusion still running and allowed to smoke 1 cigarette outside, then returned to the camera and scanned for an additional 30 min. EQ was used to estimate BP _ND. In an early study [13], BP _ND ^Activation was estimated from the average of 10 min of data collected after each subject smoked a cigarette (60-70 min post-injection), and a 30% decrease in BP _ND due to smoking was reported in the left ventral caudate. In later studies [9-12], 30 min of data (60-90 min post-injection) were used to estimate BP _ND ^Activation, and only an 8% decrease in BP _ND was found in the left ventral caudate. Brody et al. did not offer a persuasive argument to explain this large discrepancy between studies. However, the drop in effect size with increased activation scan window is consistent with our simulation findings which show that for β=1, an activation scan window of 40-60 min gives ΔBP _ND = 4% but an activation scan window of 40-80 min gives ΔBP _ND = 2% (Figure 4). The actual ΔBP _ND from the Brody et al studies depends on how big the DA effect was and its temporal kinetics, as well as other factors such as how the regions were drawn, but our simulations predict that there would be a discrepancy in ΔBP _ND reported using 20 min vs. 40 min of activation scan data precisely in the direction of the observed discrepancy in the Brody et al. studies.

The dependence of ΔBP _ND on activation scan duration demonstrated by simulations was also observed in analysis of our human data. This pattern seen in simulations was seen only in the left ventral striatum of the two male subjects studies and only in the left dorsal caudate of the two female subjects. Based on our simulations, this suggests the presence of transient DA release in these regions. The regional difference in DA release in males and females seen here may suggest a gender-effect in DA response to smoking, one which we are currently pursuing.

The interpretation of these results is limited to the framework in which these studies were completed. We tested SRTM, the Logan graphical method, and EQ on B/I data from a single-scan activation study design. While application of EQ to this study design is common, SRTM and the Logan graphical method are typically applied to data from dual-scan (aka “paired-bolus”) activation studies. Nonetheless, we believe that application of the methods as done here demonstrates a general danger of applying conventional analysis methods to [¹¹C]raclopride data which contain transient DA release. When the data violate the assumption that DA concentration is at steady-state, BP _ND is no longer a static parameter and the measured ΔBP _ND becomes a time-weighted average of the instantaneous ΔBP _ND(t). Practically speaking, this may increase inter-subject variability in ΔBP _ND since the kinetics of DA release may vary across subjects. This variability will, in turn, reduce effect size.

This would seem to suggest that shorter scan durations may improve the detection of transient DA release via ΔBP _ND. However, because ΔBP _ND depends on the timing and kinetics of DA relative to that of the tracer, interpretation of ΔBP _ND as an index of the amount of DA released is not straightforward. Instead of optimizing conventional methods to detect a significant ΔBP _ND, it may be better to estimate DA release using advanced models, which take into account the time-variation in DA signal. The linear extension of the simplified reference region model (LSRRM) [39] and the neurotransmitter PET (ntPET) suite of methods [40-43] both allow endogenous neurotransmitter to vary during the course of the scan. These methods may be better suited for estimating transient DA release, such as smoking-induced DA release, from [¹¹C]raclopride PET data.

Conclusions

The dependence of ΔBP _ND, as estimated by SRTM, Logan plot, and EQ method, on the duration of activation data analyzed illustrates the inability of conventional methods based on time-invariant parameters to reliably quantify short-lived increases in endogenous DA. Ultimately, more complicated models which take into account time-variation in DA are needed to properly measure the effect of stimulus-induced DA release when the DA response is brief.

Conflict of interest statement

The authors have no conflicts of interest to declare.